Why is it your job to teach your kid math?

Parents are being forced to hit the books and help tutor their kids through a confusing curriculum.

by Cynthia Reynolds

Have you finished your homework, mom?

Photo by Marianne Helm

When mother of two Anna Stokke began digging into the elementary school math curriculum last year, she was flabbergasted by what she found. Instead of teaching the standard methods of arithmetic, the emphasis had shifted to a wide range of alternative methods, such as using grids, blocks, or strips of paper to multiply. Stokke is a professor of math at the University of Winnipeg, but even she found the methods confusing. “It was shocking,” she recalls. “We’re talking about adding, subtracting, multiplying and dividing. It shouldn’t be so overly complicated that even parents can’t understand it. It’s absolutely ridiculous.”

Stokke began speaking out and soon parents from all over Canada were sending her similar stories of discontent: kids who couldn’t do their homework without help, parents who couldn’t make heads or tails of the assignments so they were hiring tutors, or spending hours looking up math sites on the Internet because the textbooks are so vague. She heard from teachers who felt pressured not to teach the traditional methods. Stokke and her husband, Ross—who is also a math professor at the University of Winnipeg—started up a biweekly math club for their daughter and 11 of her friends to pick up the educational slack. Out of concern for math education in general, Stokke, along with three colleagues, also co-founded the Western Initiative for Strengthening Education in Math (WISE Math), a coalition lobbying to improve K-12 math education. Parents (and teachers) from all over Canada have flooded their online petition with support. “I don’t have a problem with alternate strategies,” Stokke says. “But I fear they’re learning so many, that in the end they’re not mastering any.”

It was never supposed to be this way. Changes in the curriculum—which have rolled out cumulatively over the past decade and intensified in recent years—had sounded so promising: instead of stifling them with rote memorization and rigid methods, children are to use their own learning style to explore mathematical knowledge and conceptualize innovative solutions to complex problems, preparing them for an ever-changing tech-based economy. But the execution of this vision hasn’t been so idealistic. Instead of building a generation of math whizzes, it’s creating a Tower of Babel, where teachers can’t understand textbooks, students can’t understand teachers, and parents and children have no idea what the other is talking about. The confusion, some critics say, lays the groundwork for innumeracy that sticks with students through the grades, into post-secondary school and out into the workforce—this week business leaders reported that a growing chunk of Canadian kids simply don’t have what it takes to fill skilled positions.

To sort out the discord, some boards are hiring cadres of costly numeracy consultants to facilitate workshops for families and teachers, and developing online tools for parents to access. In many districts, families are left to grapple with the mess themselves. Either way, more parents are starting to speak out about the increasing amount of time, money and stress required to teach their kids what they should be able to master at school. “Kids spend six hours a day there—I think the schools should be able to teach math to children themselves,” says Stokke. “It’s completely wrong-headed. And the moment you say parents should play a significant role in public education, you have a two-tiered system.”

This month, in Hamilton, the Catholic school board is launching one of the more intensive initiatives to support parents—SuccessMaker, an online math program intended for the classroom, redirected for home use. Consisting of animated games and word problems, for the program to be effective it requires that parents commit 20 minutes a night, for a minimum of four nights a week, over a span of eight weeks. “We recognized that parents were having difficulty supporting their kids, so we wanted to give them this tool,” says Sandie Pizzuti, assistant superintendent of academic programs and services at the Hamilton-Wentworth Catholic District School Board. The flyer marketing the initiative uses language that goes directly to the core of parental fears: “Concerned about your child’s math scores? Does your child say he or she hates math? Finding it difficult to help with math homework? Wish you had the time or money to have your child tutored in math?” So far, 200 parents have signed up for the information session and they anticipate they’ll register about 500 parents; the ministry is covering the initial $12,500 in licensing fees.

Spending 20 minutes on math would qualify as a really great night for Jane Snider, a Saskatoon mother who asked to use a pseudonym for her daughter’s sake. When her daughter entered Grade 7, she began asking for help with homework. Snider tried to step in, but was blindsided by the methods they were supposed to employ, such as using graph paper to show how you can divide fractions and strips of paper to demonstrate ways to multiply them. “I never expected to run into problems at this grade level, and I knew I was making a mess of it,” says Snider, so she turned things over to her husband, an engineer. Accustomed to solving equations with formulas, her husband was spending up to two hours after work learning the new strategies and terminology himself, then teaching them to his daughter. There were times, says Snider, when he couldn’t understand the assignment at all. “It just became a blur of stress and frustration,” she says, adding that her daughter has lost all confidence with math and now professes to hate it. “We’ve had to spend so many nights dealing with this mess when we could be doing other things. It makes me so angry.”

Giving parents a better sense of the subject is one reason more schools are offering Math Nights. The theme of the workshops can vary, but in some cases parents are taught the same math strategies as their children. But with only an hour, one Toronto mother who attended a Math Night at her Grade 3 son’s school left confused. “But I’m glad I went—at least now I know how not to help my son,” she says, explaining that she was told that stacking two-digit numbers and carrying the one isn’t a good method for addition because kids don’t understand what it means to carry the one, that they’re really adding 10. Instead she learned alternate methods that yielded deep understanding, which the parents were told is more important than arriving at the correct answer. “But that seems wrong. Why does it matter so much for someone to always realize they’re adding 10? You get the right answer, and I do think that’s important.”

As one of the designers of the math curriculum for the western provinces, Debbie Duvall now works as a math consultant for the Elk Island public school district near Edmonton, where she gives workshops to parents. If a student can’t remember what 9 x 6 is, she says, they’re lost. But with a deeper understanding of multiplication, students realize they can multiply 10 by 6—an easier calculation—and subtract 6 to arrive at the answer. “We want to provide options for kids,” says Duvall, adding that at least one parent comes up to her after her workshops to say they wished they were taught this way. Taking into account all learners’ styles and capabilities is another big part of the approach. Back in Hamilton, numeracy consultant Kerry Dwyer-Mitchell recently divided a Grade 4 class into groups to teach multiplication through a pizza game (how many pieces are needed if 27 kids want three slices each?). Each group, she says, brainstormed a different strategy, such as repeated addition, adding partial products, or using a manipulative, like Base Ten Blocks. “Traditionally, you’d get your algorithm and you would just do it,” says Dwyer-Mitchell. “But they’re free to use whatever works best for them.”

Yet it’s that very freedom that, some say, is at the root of much of the confusion. “They’re really creative—but they don’t know what to do with it,” says Kim Langen, CEO and co-founder of the after-school math enrichment program Spirit of Math, based in Toronto. “The rigour of the procedure is being lost and the bar is getting set far too low.” While students need a minimum B+ to apply for Spirit of Math, Langen says that even these achievers can possess a worrying level of innumeracy—Grade 5 students who don’t know multiplication facts, have never encountered division, and just look at you blankly when you ask them what 23 + 7 is. In order to build students’ math facts, the first 10 minutes of the 90-minute session is dedicated to drills—then, explains Langen, because they’re not bogged down on simple calculations, they can handle the high-level conceptual work. “We had one vice-principal who saw the incredible difference drills made,” she says. “But he said, ‘I can’t do drills—the board won’t let me.”

And it’s not just students struggling, says Langen. When a parent came to her in tears because she couldn’t help her daughter who was struggling with math, Langen met with the teacher. At the meeting, the teacher sought Langen’s advice—she couldn’t get her students to understand metric conversions, in this case, converting 110 cm into metres. She showed Langen the blackboard filled with an elaborate matrix that neither adult really understood. Langen reached for a metre stick. “I told her she could use this to show there are 100 centimetres in one metre, and she just lit up.” Though she was taken aback by the encounter, Langen is quick to add that the teacher was bright, just uncomfortable with math—and this highly conceptual approach is often toxic for teachers without a solid grounding in math. “It’s so overcomplicated now. We use the old-fashioned methods. They’re fast, they work and it’s part of the reason parents come to us.” Nathalie Foy of Toronto has enrolled her Grade 5 son in the program. “I wish I didn’t have to supplement their education,” says Foy, “For one, it’s expensive. But this is a safety net—and now he knows his math facts cold.” At more than $1,800 per school year, it’s a pricey measure, but with more than 30 per cent of Canadians supplementing their children’s education, it’s one that more parents are investing in, especially as their kids move up the grades.

Christian Mihaila is a Grade 6 teacher who also works for Vancouver-based Academic Advantage, tutoring Grades 9 to 11 math. He says that a different set of problems can arise when students make the leap into high school math. From kindergarten to Grade 8, students become accustomed to using visual methods like grids and physical manipulatives like blocks to solve problems. When they hit high school, it’s suddenly more abstract, more pencil and paper, more . . . old school. But by then, the math has become too advanced for most parents to effectively help with and they either have to hire a tutor or drop their kids down to an easier stream. Or hope the school’s no-fail policy will continue to sail them through the grades and into university, where professors from coast to coast are vociferously complaining that first-year students are woefully unprepared in math. WISE Math co-founder Robert Craigen at the University of Manitoba was appalled to discover that two of his students had never learned long division, a necessary skill for his course. “Math is a universal language, but our kids aren’t learning how to speak it,” he says.

Back in Winnipeg, this domino effect is one of Anna Stokke’s biggest concerns. If they don’t know their math facts, she says, they won’t be able to do fractions, which means they won’t be able to handle algebra, which means calculus is out, which means they can’t be engineers, doctors, pharmacists, economists, programmers, or any discipline that requires math, including skilled tradeswork. But one thing they can become? Teachers, who can go through the system with minimal math training and arrive in class expected to inspire children to create and conceptualize their own mathematical knowledge—and relying on a new set of parents to fill the gap. “This is a never-ending cycle of innumeracy,” says Stokke. “And we have an obligation to speak up for the kids.”




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Why is it your job to teach your kid math?

  1. My multiplication table was drilled into my head by rote in grade three. It is the one piece of information from my school years that I use every day.

    • Quick, what’s 54 x 93?

      • 160 – 13…147…I think?

        In my day I would have multiplied 54 by 93…what’s the diff really?

        • Tables don’t do you any good unless you understand the principles at work in them. Because unless you’re some kind of savant, you simply can’t hold big enough tables in your head.

          • Tables up to 10×10 should be by rote in addition to whatever conceptual exercises are needed to show the meaning – then the algorithm for using this table to find all other multiplications is simple.  The fact that the table to 10×10 is not drilled in at all any more is a problem.  it’s all well and good to show a 3×9 piece of graph paper and count your way to 27 squares to show what multiplication represents.  But at some point you need to cut away from the graphical tools because they don’t scale and learn to just work with the numbers.

          •  The presence of manipulatives is not mutually exclusive to memorizing your multiplication tables.

          • that’s why they taught us the easiest method to calculate that type of problem, strips of paper, grids etc. are not necessary if you use the time tested methods.

          •  The problem is that the easiest method in the short run is not always the easiest method in the long run. For example, having a deep understanding that 37×41 is really (30+7)(40+1) and a visual way to make sense of this will have incredible benefits when kids are faced with (x+3)(x-5)

          • Oh, I disagree, Thwim.  Take the times tables, for instance.  Sure, I learned 1×1 to 12×12 when I was a kid.  But I’ve been a college math teacher for decades now, and it seems to me that if people know up to 9×9, that’s plenty – x10 and x11 are easy.  And since the x0, x1 and x2 are also really easy, it’s only 3×3 to 9×9 that people need to memorize.  Within that batch of 49 combinations, almost half are symmetrical – 3×5 and 5×3 are the same.  So there are only 28 that need to be memorized.  You don’t need to be a savant to memorize this many, and, once you have done so, everything else is way easier:  you can start to see the principles, because you’ve got the foundation.

          • really – quick what is 9×9?  it’s called building blocks

          • 81

            I think it’s easier for me since my first language is cantonese and I learned it in catonese.  All the numbers 1-9 have one syllable (unlike say, seven), there is more of a syllable-digit-spacing pattern that helps with memory?  Even better, even though the proper way to say 81 is eight-ten-one, I just boil it down to digits.  9 9 81, 4 7 28.

            I had a very large and very colourful multiplication table when I was younger than 8, that I like looking at, because it was colourful.

            Rote is okay, as long as you don’t screw up and have kids associate it with stress and feeling stupid.  Which was piano for me, I dreaded going because it was hot and the teacher always sounded like she was one step away from smacking me even though she didn’t.

          • 9×9 = 9×10 – 9

            You see, multiplication tables are pretty lousy building blocks if you don’t understand what’s going on behind them.

            However, if you *do* understand, then you can do things that let you figure out 54×93 = 54×100-54×7=54×100-50×7-4×7=5400-350-28=5022

          • I don’t understand what is wrong with learning the basics by rote, if it’s backed up with understanding.  In the early 80s, by Gr 1 or 2 we were learning “grouping arrays” (ie, 12 objects on the paper, with the direction to draw circles to make four groups of three)…the basic “groups of” idea behind multiplication and division.  Then by Gr 3, we were starting to learn the Times Tables up to 12 (with math drills and flash cards). 

            With those basic building blocks in place, students could then move on to long multiplication and division…

          • Nothing wrong with them at all, but the point I was making to marjory — which perhaps I wasn’t clear enough about — it’s not just the memorization which is used every day. It’s the understanding beneath it.

          • I agree with what you have addressed…

        • Oh lord I got that wrong didn’t I? Got my dunce cap right with me.

      • try using the current methods to anser that “quick”. that’s the problem with those of you that think the change has been benificial ( assuming you do) no one ever had the 54 times tables memorized. the entrenched buraeaucracy howver needs to attempt to justify their existence somehow though.

      • 4500
        150 = 4650
        93 186 372
        5022

        for me this is the first way i came up with but i’m sure there are better ones.  i can keep track of numbers this way.

        • 54×100 = 5400
          54×7 = 350 + 28 = 378
          5400 – 378 = 5022
          That’s my preferred method.

          •   54
              93
            ——
              12
             15
             36
            45
            ——
            5022

            Effortless and brief — nothing wrong with your breakup, Owen, but it masks something:  many people complain over multi-digit subtractions that require “borrowing”, like the one in your last step.  It relies heavily on memorized basics, another strong argument for drills to reinforce foundational skills in early education.

            Anyone who has attended a workshop run by the consultants promoting the “no algorithms approach” will see something like the following example:

            512 – 497

            In the OLD method, you’d line them up and start on the right.  Can’t take 7 from 2, so you have to borrow.  Change the 1 to 0 and the 2 to 12.  7 from 12 is 5 (IF You remember this).  Now you have to subtract 9 from 0 .  Borrow again … anyone lost yet?  And we’re only halfway done!

            Then the consultant will say “Here’s how WE teach your children how to do this — it’s called a strategy”.  Observe that 497 is 3 less than 500 subtracting 500 from 512 is easy: that’s 12.  Then we correct by adding the 3 back on:  the answer is 15.

            And the triumphal pitch line:  ”Which method do you wish YOU were taught?  Which way do you think your children should be taught?”

            There are several problems with the conclusion this example is supposed to be forcing.   I’ll mention three.

            First, It is a STRATEGY, not an algorithm.  It works in a teensy minority of problems.  Yes, there are other strategies taught, but none of them are general. Altogether the collection of strategies only works in a minority of small “toy” problems.  They are not well suited to, say, multiplying two randomly chosen 4 digit numbers (especially if one or both include a decimal point) or to adding five randomly selected 3 digit numbers.  The standard algorithms work EVERY TIME.  Further, they don’t work only on toy or small problems.  With only a larger investment of effort, one can solve larger problems.  The “strategies” fundamentally break down when numbers are too big, for example, to draw a rectangle diagram for them.  Such as … numbers in real world problems.  The strategies tend to be used for numbers up to 2 or at most 3 digits, and even then not all cases fit them “comfortably”.  This is why, throughout the curriculum framework documents, you will repeatedly read phrases like “…for larger numbers students should use a calculator”.

            Second, it is claimed that, while the traditional methods do not teach understanding, strategies are all about understanding.  But it should be obvious that, when one learns a hodge-podge of processes and you’re left to sort out which one to use on your own, there is no overriding understanding whatsoever, no systematic framework into which one fits the general picture.  Knowledge and understanding come by having tools that allow us to organize information in our world into a “big picture”.  That is what the standard algorithms do.  In order for students to “understand” arithmetic they must be exposed to methods that, IN PRINCIPLE, work in all cases.  If a child has this there is no harm in using calculators to preserve effort in large problems.  But without it, turning to calculators is a crutch that reinforces lack of understanding.

            Finally, there is nothing “new” about this or similar strategies.  I have gone through the same example with groups of adults having no advanced education.  Halfway through the deliberate muddling of digit-work, I ask if someone already has the answer.  Someone does.  Then I ask for a show of hands and — by golly — practically the entire room does!  I ask how they got it, and — lo and behold — they all used “the strategy”.  

            So then I ask “At what grade level were you taught this strategy?”  They weren’t.  They weren’t taught the strategy, you see, because it was unnecessary for anyone to teach it to them.  When students are exposed to enough variation in early arithmetic, they develop obvious mental shortcuts in places where they recognize problems with a certain characteristic.  Familiarity breeds fluidity.  And this is a typical trick that people develop.  

            Trouble is, along with eliminating standard algorithms, the current approach de-emphasizes drill-work and repetitive exercises, the very place where students develop such strategies ON THEIR OWN.  It is said that drill- work destroys understanding.  You’ll often hear the pejorative phrase “drill and kill” in this context.  But nothing could be further from the truth.  Familiarity through repeated exposure and variation is absolutely essential for understanding.  Insight is like oil — you have to drill for it. In reality, there is no need whatsoever to TEACH these tricks (“strategies”) because if students are given proper levels of exposure they develop them themselves.  PLUS they go home with a method that works EVERY TIME in their back pocket, and understand processes that apply in EVERY CASE.

          • That’s how I would figure it out (the multiplication problem)…it’s so much quicker!

            I agree with all you’ve said. I’ve witnessed my 12 yr old son use “strategies” to answer 3-digit addition and subtraction in seconds. Pretty impressive, but did he understand how to do it the “long way” too? (Turns out he did…so I’m comfortable letting him continue to use his “strategies” when he can).

          • Well said!

          • This is the smartest comment I’ve seen on this entire thread.  Thank you for writing it.  

          • And you can use your fingers and toes to add up six, five and two!

            mb

          • I’m with you Robert & I’m curious about your age. I’m 65 & was taught by rote – tedious at the time but well worth it from my current perspective. I was good at arithmatic – still am… but never any good at math. Algebra might as well have been Greek but I di eventually pass & Geometry was a breeze by comparison. I took math till the end of gr. 11 and passed it, with limited understanding but some invaluable tools used with ease to this day. I can use those times tables efficiently – I even teach them; it’s like having a calculator in your head. And basic arithmatic skills will get you through most day to day calculations – anything more complicated – use a calculator. Beyond that hire someone else to do it. I write for other people & get paid for it so I’m quite willing to pay someone to do complicated math for me  - at least I undestand the basic principles of it. Thank you Miss Rosenberg & Mrs Bain and all the other grade school teachers who drilled it into us… and to my dad who taught me how to add long columns of figures – by ‘bunching’ later called something else; 7+3 = 10, 6+4= 10, 5+5 = 10 etc… a tool I still use.
            I my day they taught grammar much the same way – quite useful in my long & checkered career. Just listen to people today – on the street, on the radio, on TV, in the ads & it’s plain that method got tossed aobut the same time as the times tables! People today don’t even understand prepositions! never mind verb tenses. ‘To’ cannot be swicthed for ‘of” or ‘on’ or ‘under’…

            jnh

          • How is this different than students’ attitude towards math, and their success (or lack thereof) from years past? When I was in high school, most of the students who were good at math were the students who would have been good regardless of the teacher and their style. The mistake is attributing success in math then to the use of rote and algorithms. The students who “owned the math” then were going to own it no matter what strategy was used

            Let’s keep some semblance of perspective here, the amount of students who hate math now is no higher than the amount of students who hated math when I was in school. Students weren’t lining up to take calculus then, so why are we making it sound like those were the “glory days” of math and we have to do whatever it takes to get back there?

            Multiple strategies to responding to a particular problem in math is supposed to increase students’ flexibility, NOT replace efficient algorithms. I’m disappointed that people believe that we don’t need to understand why we “carry the 1″. It is that very attitude that created the general dislike towards math in the last generation or two. Ironically, those generations are todays teachers who generally lack a passion and/or understanding for math. 

            I believe efficiency and understanding in math should go hand-in-hand. I’m disappointed that ignorance still persists in this area. It seems to be all about people trying to take credit for “saving the day”. We need to stop trying to save the day and save our students’ education; all of them, not just the students who “get it”, but also those who don’t. 

            To think algorithms will solve all our students’ woes is ignorant, and to think multiple strategies will with no acknowledgement of efficiency is equally ignorant. Let’s please try to find a balance so that ALL students can begin to enjoy math the way we all want them to

      •  Hey, that’s not one anyone’s memorized from a table.  What’s your point?

        • That’s exactly my point.

          •  But if you’ve memorized the tables, you’d have the basic single-digit multiplication available to solve the algorithm fairly simply.

      • What’s 11×72 – and if you can’t write down the answer without thinking you have a problem.

      • I would go 50 x 90 = 4500, then 50 x 3 = 150, then 90 x 4 = 360, then add 12. Answer is 5022.

        This is why we show kids different methods.

    • But do you understand why the multiplication table is why it is?  I think that the blatent memorization that the article promotes is wrong – understanding is the key to knowledge, and that is what today’s curriculum is rightly endorsing.  Math does not exist in a vaccuum.  As a undergrad student at the prestigious school with an above A average, as well as A+ in my math courses, I can tell you that understanding the math has brought me success.

  2. This article is misleading, and it’s unfortunate that it frames public school teachers as simpletons who have no idea what it is they are doing or why they are doing it.  I did some “digging” of my own through the Ontario mathematics curriculum document, and I found expectations such as, “evaluate expressions that involve integers,including expressions that contain brackets and exponents, using order of operations” (pg 112), and “measure the circumference, radius, and diameter of circular objects, using concrete materials (Sample Problem: Use string to measure the circumferences of different circular objects” (pg 113).  These expectations don’t seem particularly mystifying to me.   How is it that parents ‘from all over Canada’ are so confused?  Do you have any data to support your claims, or is your evidence just anecdotal?

    • Paintchips- don’t confuse the curriculum, which demonstrates the desired learning outcomes, with instructional methods, which this article is about.

      I’m a math teacher, and I very rarely use the instructional methods taught to me in university. They are ineffective for the vast majority of students. Granted, I teach in junior high, so I can’t speak to higher or lower levels, but I use drills and rote learning for a slim majority of my practice time.

      For instance, when the area of a rectangle is to be determined, a student could draw the object on graph paper and count the squares, or use Base 10 blocks to build the object and count the squares, but that is very time-consuming (and, I expect, a little demeaning) and does not reflect the reality of the tasks expected of students in high school, university, or the real world.  My students are expected to know the formula, how that formula works, and execute the equation.

    • You’ll probably count this as anecdotal, but while I was good at math in school, use basic math daily and can often add subtract multiply or divide in my head as fast as I can do it using a calculator, I have often been baffled by my daughter’s elementary and middle-school math. The methods they are expected to follow are overly complicated and take way longer than the way we were taught.

      • Sure, and I completely understand the necessity for competency with basic math skills.  Especially as children progress to high school, something as simple as having a solid grasp of multiplication facts can become the difference between passing or failing grade 9 math.  Higher concepts become unattainable without a solid foundation.  Moreover, a student’s success in grade 9 math is often an indicator of how successful their overall high school career will be. 

        I teach grade 8, and mathematics is of course a daily focus.  Both myself and the other intermediate teachers in my school are dedicated to making sure that our students are prepared for high school, and our focus is on building foundational competencies.  Maybe I’m not in touch with what is going on in the rest of the country, but this article does not ring true to my own experiences as an educator. 

        • Glad to hear it is not true of your experience. My own experience lies somewhere between yours and what is expressed in the article. My ex is a teacher; I have a teaching degree and taught for thre years. So I know how edicts from above can run counter to common sense and good teaching practices. (My degree is in English and I well remember the “whole language” nonsense wherein kids were expected to learn language skills by osmosis and any teacher caught giving instruction in spelling or grammar would face the wrath of the system.)

      • There’s an assumption that if it takes a “long time” that it’s a bad thing. When, in a “real life” job were you timed on how fast you could get an answer to a mathematical equation? I do understand that there are deadlines to meet and timelines to meet goals in “real life” jobs. 

        A university Math professor would have learned through the wrote process and they clearly had an interest in Math and thus would have been successful in learning the rote process and would now say that if I don’t understand it then it’s not right for children. Just as an english professor who learned how to spell phonetically may say that if they don’t understand the whole word process would say that it is not right for  children.

        What I’ve seen in my classroom is that more students are understanding math and using or coming up with strategies that make them successful. Some of them even use the rote process. Now I have students who would not be successful with the rote process who are successful even though their parents don’t understand the strategy they’ve learned. 

        Yes, I know that 9×9 is 81….but I also know at least 3 other strategies in which to solve this….some take longer than others, some are concrete (strips of paper or grids) some abstract…..but they all get to 81….then again…I’m just an inexperienced simpleton when it comes to math because I’m a teacher. 

        •  I don’t think anyone is saying that teachers are inexperienced simpletons.

          The issue as I see it (as a parent of school-aged children) is that in SOME districts (across the country, it would appear) teachers’ hands are tied when it comes to how they deliver the curriculum.  Some teachers are told they MUST teach and evaluate ALL students on EVERY strategy, when it might be more effective to teach all the strategies and let each student use what they are comfortable with.

        • Every time I wait for a teenager to give me a looney instead of 95 cents change I can hear the clock ticking in my head as I watch them stair blankly at the change I hand over. Yes there are real life times where math has to be done on a timer and patterns don’t appear to be helping the youth I deal with daily. Just because you teach it and you like it doesn’t mean it’s working.

      • Look at factoring a quadratic function and you will understand why it is important to know how to factor small integers in your head.

    • It is all over Canada.   I live in NB and students are having problems with the “new math strategies” here including my daughter in grade 3.  Not all teachers understand it and not all teachers can teach it.  My daughter understands math if we get her to do it the old way.

      • I agree Jim, my daughter (also in gr 3) was having difficulty understanding multi-digit addition and subtraction.  I showed her the carry/borrow 1 system, and it was a success, she got it – and can do the equations without difficulty.

  3. …and tomorrow is Pi day

    • Excellent link, Emily! 

    • My kids use the Khan Academy. It’s brilliantly done. Straightforward, friendly, and (this is the best part) never impatient. Kids can & do pause, rewind and repeat until the concepts are clear. Then they do exercises until proficient. Probably the best practical application of the internet I’ve seen yet.

      I am a student there too. When my high school kids ask for help with trigonometry, I go to Khan Academy to brush up on my Soh Cah Toa.

      • Thanks for letting me know….I’ve never heard from anybody that actually uses it!

        I’m so tickled that we’ve got a new way of teaching kids so that they understand a concept and feel confident with it!

    • The problem on this site is that my daughter has been told that she is not allowed to stack numbers and borrow.  Is this the case with others?

    • I checked out the Khan Academy and it is good, but it doesn’t show the new “strategies” that my daughter is being shown in grade 3.  When we helped her using the “old” way, she picked it up quickly, but when she took the work back to school, she was told to show her work using the new strategy and that she is not allowed to stack the number and borrow or carry numbers.  She is only allowed to use the one method that her current teacher is using.  To be blunt, this is bullshit.  Other teachers are using other “new strategies”, whatever the Hell they are.  There is no standard across the system at all. No wonder children are so confused and having problems.

      • Oh I agree that  it’s BS….it was when my dad showed me how to do something too, and the teacher wouldn’t accept it because it wasn’t the ‘approved’ method of the time.

        Noop, there is no ‘standard’.  There never was. And I agree, we are confusing our kids …it’s a dumb way to run a school system. The whole thing needs an overhaul

  4. This article is mis-leading. Just because the curriculum allows for multiple styles of instruction does not mean that a teacher is required to use all of them in the classroom. All parents should be spending time with their children at night to help them review their homework but that doesn’t mean the parents must adhere to the teacher’s style of instruction. I am a grade 2 and 6 math teacher in Mississauga and have a very high success and engagement rate with my students. I will be the first to say that many of the instruction styles the curriculum provides us are confusing at best but they do work for specific students who are having a hard time grasping concepts the “mainstream” way. It is the responsibility of an effective teacher to not use many of the styles provided in the curriculum and teach using a style that most of the students can understand. This article makes it sound as if math teachers are just throwing concepts at their students without support or instruction. This article reads as if all students are missing the concepts when in fact their students examples could be those students who are not grasping concepts through a variety of teaching styles and learning methods. The example of Robert Craigen’s two students not learning long-division may not be the fault of their teachers, in fact I am fairly certain that their educational sphere did everything in their ability to teacher them long-division through many different ways however some people for whatever reason cannot grasp mathematics and that is not the fault of their educators. 

    •  You are right – it is not the fault of the teachers that kids aren’t learning long division.  It’s the fault of the WNCP math curriculum that Manitoba has adopted.  Long division has been completed eliminated in the curriculum and in many divisions teachers are explicitly told not to teach it.  Over the next few years, as more and more students enter universities having learned under the new curriculum, the majority of students will not have been taught long division.

      • Why should they have to learn long division when calculators can do it for them?  The curriculum should change to reflect advancements in technology.  Math should teach people to think…not to memorize.

        • Because the exercise of doing long divisions by hand builds in a feel for what the result should be allowing you to catch when your calculator does something funky, and a backup method when the calculator’s not handy.  A blind trust in technology is not a step forward.

          • I learned long division in the 3rd/4th grade. In the 9th/10th grade we learned how to divide algebraic expressions from one another in a very similar way to divide we were taught in elementary with regular numbers.

          • Things can be more complicated than that. While I do not know how computers do these operations in binary (I am only a math major, not a CS major), I do know that computers use calculus to do trig. For example, if you want sin (pi / 3), it would need to use repeated differentiation to approximate an answer 0.8660……so you do not expect people to do trig for a weird value like tan (3pi/10) or something. Sometimes, you have to trust technology.

        • Hi, I’m the Rob Craigen mentioned in the piece, and someone alerted me to these comments.  I’d like to thank Mr. B and SPW for providing what we like to call in the profession a “teachable moment”.

          First, Mr. B, I blame neither the students nor their teachers for the lack of long division.  To expand on the teensy factoid that appeared in this article from the 45 minute interview I gave, the reason I asked the question in the first place is that, as a university representative on our province’s Math Curriculum steering committee, I was watching for this very thing because, as mrmath says above, long division is completely excised from the current revision of the WNCP curriculum that affects all of the Western Provinces.  In fact, all four standard algorithms of elementary arithmetic are GONE.  The  curriculum has been implemented grade by grade and this was the first year we expected the “early implementers” to graduate students taught with the “no algorithms” approach.  From here, if nothing changes, the number of such students will increase until the ONLY public school graduates knowing long division will be those whose teachers serve them contraband or whose parents school them in the dark art at home.

          Second, SPW, your comment reveals an ignorance of the whole point of learning math.  Why learn anything you can pay someone to do or obtain a device to do for you?  Taking your statement to the extreme, we could raise a pampered but severely ignorant generation of adult infants, completely dependent and completely incompetent.

          But that is not really what’s wrong with the comment. It’s merely why it is silly.

          What’s wrong is the fantasy that understanding can be had in the absence of competence and skill.  The problem is that the developers of the current curriculum have bought into precisely that fantasy.  Cognitive developmental psychologists tell us what every parent knows:  understanding and skill form a mutual scaffolding — you cannot have one without the other.  Want to teach understanding?  Then it is ESSENTIAL that you provide a framework of skills along with it.  

          The four standard algorithms are critical skills upon which hang some of the most important elements of understanding in the framework of the mathematical education students need to advance.  This is an inappropriate place to attempt a full development, so I’ll just assert what most educators know:  the modern concept of number, which lies at the heart of mathematical UNDERSTANDING, turns on a key fact learned in the traditional curriculum before grade 8:  that rational numbers have repeating decimals whereas irrational numbers do not.

          The ancients would have been astonished that children could understand this, for they found the presence of irrational numbers deeply puzzling, even disturbing.  The development of a theoretical tool that assists understanding to this level is one of the great accomplishments of western society.

          What is that tool?  Ask yourself, SPW — I’m sure you are familiar with the above fact — how do you know that rational numbers have repeating decimals?

          It so happened that, in the calculus class where I did that little survey, this factoid came up in our lesson and I asked my students who were able to provide a simple proof with just two words:  ”Long Division”.  Except, of course, for the two who had never been taught this essential tool.

          Calculators are wonderful things.  But they will never replace the essential insights gained from learning the four standard algorithms.  If you care about teaching understanding in math, you ought to care about those algorithms.

          • Wrong.  Go read the current curriculum.  You have not seen one single child that had graduated from that curiculum, as it is not yet offered in grade 12 (next year will be year 1)

            To make it simple, so you can understand, not one University Student is a product of the math program currently in use.  Not one.  The students you see are products of the LAST program, and if you were truly involved in THAT debacle, then this article should be about your irresponsibility.

            The logical conclusion here is that if you would lie about one thing, then you would lie about everything. 

            As for long division, it is indeed in the new curriculum. 

            Go fish.

          • Lorne, Lorne.  You didn’t read my comment very carefully.First, I HAVE read the curriculum.  I have sat on the Manitoba Provincial Committee, whose job it is to implement the curriculum, since 2005.Second, I was quite clear that the whole point of identifying those students in my class who had not seen long division was to detect the presence of students from schools that were EARLY IMPLEMENTERS of the new WNCP curriculum.  Navigate, if you will, to the Manitoba Ministry of Education website, where you will find a timeline for changing to the new curriculum, and verify the following:System-wide implementation is to be complete by 2013.  Early-implementing schools were to produce their first high-school graduates in the Spring of 2011.  Thus, a FEW such students are now in university; soon to be a LOT.You say that long division is in the new curriculum — are you talking about the WNCP curriculum, used across Western Canada, as I am?  Well, Lorne, that is news to me.  I invite you to publicly shame me on this point.  Here’s how:  Go to the official website for the curriculum, wncp.caNavigate to the current framework documents (which describe every learning outcome in the curriculum).  Handily, these are pdf files that you can text-search at your convenience.Search for “long division”.I look forward to you reporting back to us what you find.  I predict that you’ll find exactly one place where long division is mentioned:  In the Grade 12 Precalculus stream, where teachers are told that students can understand the remainder theorem in terms of long division of polynomials (an interesting prospect, given that long division of numbers does not appear in the learning outcomes or achievement indicators for ANY grade level).Happy hunting!

          • Wow, you are one rude knowitall.

          • Wow!  Looks like I touched a nerve with that calculator comment.  As it turns out I am  high school math teacher with 30 years of experience.  Just playing devil’s advocate here to stir things up.

        • Yes, let’s just teach them to use calculators and computers, they will never have a need to think on their own.  WTF are you smoking?  A huge part of learning is memorizing.  Do you think Doctors know everything, and when faced with a problem, they just automatically figure it out?  No, they learned and memorized.  They know what medication is good for what disease, because the remember their education and training.  If you can’t remember or memorize, you can’t learn.

    • It seems that there is a disproportionately large number of “people for whatever reason cannot grasp mathematics” and although you may not think that is the fault their educators, I tend to disagree.  I believe the people who teach mathematis don’t have enough tricks in their bag…they don’t know enough about math to teach it in enough different ways to overcome people who don’t grasp the subject easily.  I had trouble as a child with mathematics.  Later, I had a teacher who had her PhD in mathematics and I soared.  I believe math teachers should have a degree in mathematics and then a post degree in education so that they can assit the many people who don’t grasp the subject readily.  Afterall, it isn’t really those that grasp it easily that need the teacher the most, is it?

    • Wrong.  My daughter was told to only use the method that her teacher showed her, not to stack numbers or use the borrow or carry methods.  This is why it’s so frustrating.

    • Sounds like you are a teacher the way you are defending them.  There are some good teachers, but there are also some bad teachers, lazy teachers, etc…  I have dealt with several of them and our education system in NB is suffering very badly.  Our government keeps making cuts to the system and it is hurting the students.

  5. One thing about the new math is for students to be able to figure our their own algorithms when figuring out things like adding two 2-digit numbers, subtracting, dividing, or adding fractions.  If you want to figure out what it means to design your own algorithm, here is a problem:

    It takes 3 hours 52 minutes and 47 seconds to to go from Toronto to Sudbury.  It takes another 2 hours 14 minutes and 38 seconds to go from Sudbury to Sault Ste. Marie.  How long does it take to go from Toronto to Sault Ste. Marie? ( Don’t worry about gas breaks.)  Clue: you are not using units of 10′s or 100′s.

    Part of the problem with the new math is that students are not taught particular algorithms by the teacher unless that teacher chooses to demonstrate a particular way.  There are good points in having students work to create their own algorithms.  They can hopefully understand the meanings of the values in their responses.  For example 35 + 65 does not equal 910.  Through estimation, the students should be able to figure out that their responses should be anywhere between 90 and 110.  Then, they should be able to solve the problem by either adding the one’s first or do some other method like adding 30 + 60, then 5 + 5.  The answer will be 100.

    One concern about teaching the new math is working with children with special needs.  They will struggle until someone helps them with an algorithm.  The Khan Academy and Jump programs help students step by step.

    Another concern has to do with different cultural groups learning math in different ways.  For example, Chinese and Korean students will learn problem solving in some rote fashion which they excel. However, the new math requires students to explain their understanding of how they solved the problem.  For example, “What’s one way to make two dollars in change?”

    Student: “40 nickels!”

    Teacher: “How did you get that answer?”

    Student: “I don’t know, I just did it in my head.”

  6. “instead of stifling them with rote memorization and rigid methods,
    children are to use their own learning style to explore mathematical
    knowledge and conceptualize innovative solutions to complex problems”

    Or in other words, we teach them complete bullshit.  Rather than spending hours every night (this is just math – parents also have to teach grammar and spelling because the schools don’t do that anymore either), it would be far less confusing for the kids to just be home-schooled in the first place.

    My wife teaches accounting, payroll and finance at a private college, and at least half of her students, high school grads all, who have chosen this field, do not know how to calculate sales tax, and do not understand that 1/2 and 0.5 and 50% are equivalent.  This is what the “new math” has wrought…… but they have good self-esteem!

  7. I’m an Engineer in Alberta and my brother who is in Grade 3 has outrageous math homework. One of his assignments was to “estimate” for multiplication. What’s 9 x 9? Use 9 x 10 and write down the answer to that instead. For a whole sheet of homework! So basically if you got the question wrong, it was right, and if you put down the actual answer, IT WAS MARKED WRONG. He now goes to tutoring for 45 minutes each week, and his marks have doubled from failing to honours. Yeah, alternative methods are great tools to use, but when you are FORCED to use these methods, even when they don’t make sense, you’re penalized for them.

    • That, I think, is the bigger concern.  The point of these tools is to give children the freedom to  figure out how to do things in a way that works for them.  If you force them to use a particular tool, however, you’re taking away the very point of using these tools in the first place.

    • If your brother had estimated 9×9 as 45 he could be employed to give “cost analysis” to the government 

  8. Why do parents (and university professors) continue to insist that the way they learned was the best?  My grade eight son has a better understanding of basic mathematical concepts and problem solving than most adults.  He doesn’t memorize facts but knows how to find answers.  

    • I agree that they have a better understanding of maths concepts, but unfortunately application of concepts and transferal of this understanding to real problems is where I find their knowledge lacking. I remember doing two main strains of maths, Pure and Applied and it is Appllied that is suffering now.
      Also I can remember sitting down with my parents doing my homework and using them as a resource when I found a concept too difficult to get my head around at school. I thought parents being involved in the home part of their child’s education was normal; I didn’t realise that this was passed off in its entirety to the state.
      Could be another case of people wanting kids but not wanting to do the work that that entails.

  9. Maybe if teachers were spending less time constantly complaining about their pay and benefits, they could spend some time being, I don’t know, capable at their jobs?

    • You are right there, and don’t forget about complaining that they don’t get a day off every time it snows, or how much it sucks to have snow on the weekend because it is a waste of a snow day.

  10. Most teachers are too lazy to teach anyone but the top 5 or 10 percent of their students. The rest are a waste of the teacher’s time. This story is nothing new,, it has been going on for years.

    Thats why the teaching methods have degenerated into gross obfusication. No one knows whats going on and the teacher can give high marks to whoever the teacher wants to put in the top 5 or 10 percent of the class.

    The unfortunate part of this story is that the top 5 or 10 percent are not necessarily the smart students, just the kids whose parents have money or a high social status in the community.

    It doesn’t take a degree and someone being paid (I won’t say earn) 50 grand a year to put a few examples on the blackboard, tell the kids to do all the odd questions from page 125 to page 130, never check the homework and call the students who fail the next test stupid.

    • Another critic who’s evidently never taught but yet knows all about lazy teachers. How bout lazy uninformed criticism?

      • “.How bout lazy uninformed criticism?”

        Yeah, I get it all the time.

  11. My daughter gets 90′s in math but the other students in her class are struggling. Even though she is a very good student, the teacher screamed at her in front of the whole class and said she was doing it wrong even though she got the right answer. I was not impressed, she had a formula as to how she got the answer and figuered it out when the teacher couldn’t.

    • Exactly the problem.  My daughter has had correct answers, but has been told she found them the wrong way, and to show her work the way the teacher showed her.  That is bullshit.

  12.  I would’ve said quite the opposite – the pace of school education is tailored to the bottom 50%.  The top 5-10% are being held back because the entire room needs to learn at the same pace.

  13. As a sixteen year old 10th grader and I could not agree more with the results I see in the class room around me and the story written. I see other students using Ipods or printout multiplication charts, exasperated teachers telling kids time and time again how to do grade 3 work. I appreciate that this was put on the front page, because really, it’s about time people realized it.

  14. This is irresponsible, one-sided and negative reporting that has, no doubt, insulted many gifted, thoughtful and effective math teachers across the country.  I am an elementary school teacher, and I have had the pleasure of teaching problem-based math to students for a number of years.  The reporter who wrote this story neglected to get a classroom teacher’s opinion which, to me, shows a lack of balance in telling the story.  Yes, it is true that parents are often frustrated when faced with something unfamiliar when asked to help with homework, but that is a problem that can arise in any subject.  Teaching rote math skills serves to strengthen one ability – memorization.  Students need to understand the meaning behind the numbers, problems and algorithms before they can apply them with accuracy and efficiency.  Problem-based math does this by encouraging students to apply what they already know, to use their own invented strategies such as manipulatives, charts, diagrams, slips of paper, and yes, even calculators, and to work with peers and teachers to understand real-world problems in order to develop a strong number sense before just having them learn and apply a formula.  When they understand the meaning behind what multiplication and division problems are actually asking them to do, and they have been able to apply this in a way that makes sense to them, then most teachers also allow and encourage students to apply this rich foundation of understanding to a formula or algorithm.  Math teaching at its best is thoughtful, nuanced and rich.  This article painted the work of today’s teachers as disorganized and groundless.  There is plenty of research backing up today’s methods. Check out Van De Walle, Trevor Brown, and David DeCoste to name a few.  I am particulary offended by the last sentence of the article that paints teachers as less-than educated professionals who can’t fill the ‘real’ jobs out there.  We have one of the most important jobs in society and this article is disrespectful to those who dedicate their lives to loving and teaching your children. 

    • What drivel.

      I have had two children go through the public school system. And I am a professor of mathematics at a “big research-intensive” university in Canada (26 years experience, research active and my teaching evaluations are in the top 5 percentile).

      In my experience, the answer to the question that forms the title of this article is clear: Because math teachers, generally speaking, in the K-12 system do not themselves understand math, are not trained in math and are afraid of math.

      And I know. More than once I would read over a marked assignment written by my son, for example, and it was clear that the teacher didn’t understand the solution presented. It has also certainly happened that the solution the teacher though was correct was in fact simply wrong. When confronted, the inevitable result would be that the teacher got defensive and angry.

      Teachers should be subjected to annual peformance review like everybody else and the bad ones fired and parent-teacher associations whould have the right to sit on these evaluation committees.

      And I will go further, having been involved in an off and on way in university administration over the years and having seen the data from across Canada, I can say with absolute certainty that the academic records of students that enter faculties of education are among the weakest at any university and the pass rates within faculties of education are striking high compared to all other faculties. Yes, students with weak academic skills enter the teaching so-called profession and that these are the people that teach our kids in K-12. It’s a joke.

      The fact remains, the reason why little johnny or suzy isn’t learning math properly in K-12 is because the teachers themselves don’t understand it.

      It’s the blind leading the blind.

    •  I am also a teacher, and I agree with this article 100%. Van de Walle is a theorist whose research always supports his own biased agenda. Too many superintendents and education directors fall easily for the twisted theories of a Van de Walle. Public education is in a crisis situation. It’s about time there was some dialogue on how to fix this very broken system.

      • Have you tried using his methods?

    • As a parent of a Grade 3 student I have seen multiplication strategies being done over a period of 2 weeks (not even every day) – an insufficient time for an 8-year-old to grasp what is asked of her to grasp. During that time she’s been bombarded with various strategies and, I am sure, confused with some. Then, at the end of that 2 week period, she is supposed to “think outside the box” and do an art project (draw groups of candy) in order to achieve Level 4 (exceeding provincial curriculum expectations). If, however, she solves the problem without the “crutches”, she is (just) meeting the provincial curriculum expectations for that grade and is discouraged to use the method that suits her best.
      I am sorry, but I do not understand! Those strategies are supposed to be the training wheels used just until you achieve the necessary skill level needed for the two-wheel ride.
      As educators aren’t we supposed to give our students the tools so that one day they will become autonomus learners? Isn’t it our job to observe and adapt to our students’ needs, even if they are above the grade level not just below?

    • Concerend, hate to tell you but you’re completely wrong here. Most grade school teachers in the public system have no background in math and really don’t understand it.
      My kid brother is quite a bit younger than me and when I came home for a weekend my parents would regularly ask me to remark his math assignments and test – without fail, the teacher’s answers would be wrong (and generally worse than his). And they’d tell me that whenever they went in for parent teacher conferences the teachers would pull out my comments and be very upset because I was daring to question their authority – my parents had a very simple answer – get it right and we won’t ask his brother to review your comments – get it wrong and he won’t stop.
      That’s why my kids have never seen the inside of a public school and never will.

    • I so agree with this statement especially about how teachers are being given no support. Thank you. There’s alot of ignorance and I wish that people are more involved or are at least aware of the development in the curriculum. They should be asking, who’s writing this stuff and why? And then ask how much is this gonna cost us. Unfortunately, the teachers are just pawn as someone said in the thread.

  15. It wouldn’t be fair to say that teachers are lazy or incompetent and that’s why the kids aren’t learning math.  Seems these days they are only allowed to teach the board approved curriculum, one that takes “into account all learners’ styles and capabilities”.  I wouldn’t necessarily call this dumbing it down but the main focus is trying to accommodate everyone, which rarely ever works.  As parents we should better understand our kids’ capabilities and help them learn accordingly. 

  16. So… new-fangled teaching methods that parents don’t understand leads to more parents doing their kid’s homework for them? Colour me unconvinced. I think the problem is that mom didn’t like getting a B in primary school math, when the real lesson for mom should be: stop doing your kid’s freakin’ homework. It’s bad for you (you have better things to do), it’s bad for your kids (they won’t learn), and it’s bad for other kids (grade inflation).

    We don’t celebrate this enough in Canada, but we have a great education system – in a large part because we teach principles well, rather than rote memorization. In the PISA we consistently score well, and there hasn’t been the decline in math scores that this article seems to presume exists. Yet in a typically Canadian fashion we like to assume that the American story of declining quality of education applies to us as well. Step aside healthcare, our education system is our real success story. 

  17. I picked up this issue solely because of the cover story, and I hadn’t bought a Maclean’s magazine in well, forever. Math education is an interesting and often polarizing topic in education, with no easy answers. I like the discussion in the comments here, and Robert Craigen thanks for expanding  upon what you said in the article.

    Also, I’d like to add that while people like SPW sound ignorant when they say things like “Calculators can do long division quicker,” ignoring any impact of the understanding of place value, rational and irrational numbers, multiplication, and division etc (as mentioned by Mr. Craigen) gained in the process of doing those long division questions, there is some truth to those seemingly ignorant claims. It’s obviously important to focus on the process and methods of multiplication and division, but we can’t forget that we have some amazing technologies that can help us out for certain types of questions.

    From what I’ve seen in classrooms, I’ve seen teachers at all levels afraid to let students use calculators for anything, and I’d say it hurts more than helps in most cases.

    I’ve written up a post about this article on my blog (http://www.macroeducation.org/response-macleans-article-why-is-it-your-job-teach-kid-math/) if anyone cares to read it. It was too much to post here, and I have to warn that it’s a bit long.

  18. Let me address some of your points. 

    While I agree that teachers should have been interviewed, the individuals who should really have been asked to provide a statement should have been the students. It’s about them after all. 


    Yes, it is true that parents are often frustrated when faced with something unfamiliar when asked to help with homework, but that is a problem that can arise in any subject. ”

    Unfortunately, math isn’t exactly a subject where there’s significant divergence in meaning. If international students can come to Canadian universities and exceed and outperform Canadian students with no Canadian educational experience then it’s fair to assume that parents should be able to do the same with their kids in primary education. The point is addition, subtraction, multiplication, division, etc, shouldn’t BE unfamiliar. If the systems used make no sense to engineers or math professors who are capable of using numbers then there is obviously a problem. ”
    Teaching rote math skills serves to strengthen one ability – memorization.   ”

    I’m sorry, but knowing that 9 x 7 is 63 is not memorization in my opinion. It’s something that should be an automatic response in the same way as knowing the difference between left and right. No adult takes their thumb and index finger and tries to figure out which hand forms the “L”. There should be no reason kids should be multiplying 7 x 10 and then subtracting to get to the right answer.  And yes, it’s wonderful that kids understand that 2 x 5 is actually 2 +2 +2 +2 + 2 (and they SHOULD know this), but if they’re REQUIRED to do that to answer the question, then there’s a significant problem. But by your account, such a system should be utilized by our children, even promoted as being superior to anything else. 

    “Problem-based math does this by encouraging students to apply what they already know, to use their own invented strategies such as manipulatives, charts, diagrams, slips of paper, and yes, even calculators, and to work with peers and teachers to understand real-world problems in order to develop a strong number sense before just having them learn and apply a formula.”

    Calculators? Really? You realize that most university calculus don’t allow any calculators. In fact, what I  remember from Canadian elementary schools is the fact that we spent half the time trying to see what swear words we could spell upsides on our calculators (A$$HOLE, HELL etc). I guess that I helped me expand my vocabulary, but it didn’t improve my math skills. 

    I don’t understand how kids are supposed to apply “their knowledge” if at this point, by almost your own admission, you haven’t taught them anything because they’ve been busy using “inventive strategies” to explore numbers on their own. 

    Not all teachers are bad. There are some great teachers out there. But the reality is, there are also some that are complete rubbish. What Anna Stokke wants to address is the fact that many teachers receive poor math training and curricula in both public schools and education faculties is cheating the kids of a real education.

  19. Today’s math curriculum ensures that there will be plenty of work for me to do for years to come…  This article makes some very good points.  Deep understanding is good, but basic understanding needs to come first.  Without an understanding of how to add fractions or do long division or carry numbers, there is no foundation for deeper understanding to be built on.  Creative teaching methods have their place, but when it comes to building a mathematical foundation, the tried and true old fashioned methods should not be discounted – including memorizing that times table.

  20. I was educated first by the British system from grades 1 to 8, and then ended up in Canada for the rest.   I’m now teaching at a university.

    While it is true that I had to do rote learning from early on, at a certain level we were required to understand the principles behind these algorithms that we are learning.  When I got to grade 9 in Canada one of the things that amazed me was that the material was mostly things that I have learned in grade 4 or 5.  I went from a B+ to A- math student to being labelled a “math genius” in my school simply because I was competent for material that I have learned much earlier.  I later found out that some of the material I already learned in grade 8 (and struggled through) would not appear  until grade 12 here.  My experience as I was going through high school is that most people have such a weak foundation and can’t remember facts that I consider basic.  When they are finally taught advanced topics, they struggle even more.  I struggled too, but I would be struggling on the new concepts that are taught to me.  My classmates would often be struggling on the foundations as well even if they may not realize it.

    I was lucky in grades 11 and 12 to have math teachers who actually had a real mathematics degree (e.g. honours degree), but this seems to be a dying breed.  At least they encouraged me to look elsewhere for more advanced topics.  If I wasn’t so bored I probably wouldn’t have learned so much more and ended up doing well in much harder topics in university.

    The “old math” worked for me, but is this “old system” really that great?  Many people got bad marks and didn’t understand anything.  And maybe it is very stressful for the kids (it was certainly for me).  That is very true.  But at least we are honest with them about their skills.

    Maybe some people would have benefited from the “new math”.  But let’s not kid ourselves here.  Many people now “understand math better” and not “struggling so much” because we evaluate them differently under the new system.  They still don’t understand any real math.  Take someone with 80% in grade 12 “old math” and someone with the same grade for “new math”, throw them a “real world” problem, and you will see the “old math” student consistently solving problems that “new math” students cannot solve but not the other way around.

    “Discovery-based” education is great for those relatively few students who actually try to discover things.  The average student can’t (or won’t) be doing more than just memorizing the discovery.  For them, it is better to memorize the rules and the boring stuff because these things are more applicable.  In the old days we have average people who don’t understand very deeply but at least can do basic tasks.  Now the average person neither understand very deeply, nor can they do these tasks.

  21. Parents should help their kids, after all they should be the one who know their kids learning style the best. I have a 20 year old daughter in university and I remember sitting with her for up to 2 hours a day from the time she was in kidergarden all the way to the 8th grade helping her with her school work. Along the way we noticed the “new math” simply did not work for her so we adapted. After she learned the basics, she never had to study for aa math exam. Has has to put in the time with your child. You have to know your child and you have to decide that your child and thier education is more important than sitting on the couch drinking a beer while watching grown men play. There are no shortcuts, you really reap what you sow and so will your kids

  22. It sounds like the cirriculum hasn’t changed much, since my son was in elementary school in Alberta.

    The math cirriculum at the time was a confusing nightmare that focused on “estimating” from Grade 1 to 3. When my son entered Grade 5, we paid for a tutor, and enrolled him in night classes (along with about a 1/3 of the class) for the latter part of Grade 6. One teacher told us our son wasn’t “wired for math”. He managed to scrape by with a C+ and was promoted to Grade 7. For the record, the rest of his marks where average – Bs and Cs. We were told by various teachers that he was an average student at best, who possibly had ADD. It was recommended that he should consider going into a general studies type program in middle school.

    Over the summer, we moved to Maryland. He was tested by the County’s school board to make sure that he was, in fact, eligible to move on to Grade 7. He failed miserably in math and English. He tested at a Grade 2 level in math and a Grade 3 level in English! Obviously, the school wasn’t going to send him all the way back to Grade 2 or 3, but he did have to repeat Grade 6. His math teacher went over all his work. She determined that the way he’d been taught was hugely confusing – made no sense. A similar cirriculum had been used in MD, but had been dumped, because it was so bad. Anyway, she stated that he would understand math by the end of the year.

    Not only did he know his math, he was offered a spot in the Johns Hopkins gifted program. He was in the 99th percentile (PSATs) by the end of the year, and excelled in all his subjects. He continued to do extraordinarly well for the rest of his school years in MD and DC.

  23. During any time of significant change there is always discomfort and criticism from the old for the new. The old often is reluctant to give the new time to prove itself and because it does not make sense from their experience it is not wanted. You have to consider that the people so in favour of the old methods were successful using those methods. Learners come in many styles and teaching only one method will not enable as many students to be successful as will teaching several different methods. Because something was good for you does not make it good for everyone. Understanding is key for any subject beyond mere memorization. As for the old method being “time tested” therefore successful that is a myth. The whole reason the curriculum changed is because ressearch showed that students were not able to

  24. be successful in high school and post secondary math because their understanding was lacking. Armed only with algorithms that applied to specific circumstances they were not flexible in their understanding of numbers and became frustrated. You wonder why the person at the till can’t make change when you give her 20.85 and the item cost is 12.85, it’s because the algorithm didn’t specify. It said to cross out the next digit, add a one and subtract. Students who understand numbers and have worked in many wways with them see the interconnections and can provide change.

    Don’t short change our children because it isn’t they way you did it. For every person who is successfull with the old way there is at least one person who was not, one person who dropped math as fast as they could because it became too complicated without understanding, one person who hated math in school and made different career and life choices because there was only the right way or the wrong way.

    • Yes! Well said- I have many friends who are worried about retraining and returning to university due to math. When I taught them some math conceptually, concretely and pictorially, they asked “why didn’t we ever learn it this way??” The assumption that the old way worked is an assumption and is very far from factual.

  25. Canada keeps following American bandwagons even though their education system is generally much, much worse than ours on any number of fronts.  Decades ago, it was New Math.  Now it is New-New Math, which is really foo-foo dust…squared.  The Math curriculum seems to want to create more pure mathematics professors, even though there are a limited number of jobs in that field.  Anything practical or needed for business, like money, is taught for a few days at most in the elementary grades.  Now those skills are considered applications and are insulted with the phrase “rote skills”.  In most provinces, there are five strands to be taught each year from Grade 1 – 8, so in Ontario, we are teaching Algebra (no kidding), Probability (yep!) with as much or more time and emphasis as Arithmetic and Finance.  Because it is in the Elementary curriculum, this is what is tested. 

  26. I have had two children go through the public school system. And I am a professor of mathematics a “big research-intensive” university in Canada. In my experience, the answer to the question that forms the title of this article is clear: Because math teachers, generally speaking, in the K-12 system do not themselves understand math, are not trained in math and are afraid of math.

  27. Last week I had an intervention at my daughter’s school regarding her multiplication test. I wanted to know what was required of her in order to get Level 4 (which she always used to get). I am an educator myself (a teacher trainer), my husband an engineer (taught math at the University) and we come from Europe where curriculum implementation is narrowed down to syllabus (used to ensure consistency between schools and that all teachers know what must be taught and what is not required) and where there is a prescribed and logical flow of the lesson material. So, I had a talk with my daughter’s Grade 3 teacher, and was completely disgusted with what I had learned. My daughter solved the multiplication problem (5 containers each containing 25 candies) using both multiplication algorithm (5×25) and addition (25+25+25+25+25). She even checked her answer by drawing 5 groups of 25 tallies.I was told that for Level 4 she should have thought “outside the box” and drawn 125 candies!? Furthermore, she should have shown as she did her addition that 5 ones and 5 ones make 10 by drowing lines and writing the numbers on the side of her addition. And that would’ve been “thinking outside the box”! I told the teacher that I want my daughter not to use the “crutches” (I’ve been teaching her to be more effective- that’s what math is all about) and I argued that her not using all those ridiculous and time consuming “strategies” IS thinking outside the box because she’s one step ahead of her classmates who wasted who knows what time drawing 125 candies! I don’t even want to mention that my daughter’s class did the multiplication only for two weeks (and not even every day) and after that went on the division for which, you’ll all agree, you need a sound understanding and knowledge of the multiplication (tables). I just want to know why education here in Canada is not as transperent as everywhere else? Why does the quality of our children’s education depend so much on one (omniscient) individual and their interpretation of the Curriculum? I want to be able to take a proactive role in my children’s education and to know what methods are being (ab)used in their classrooms.I want to know when they are being tested and what is expected of them BEFORE they take the test. I want to know that if we move to a different neighbourhood and change schools,they won’t do the same material they’ve already done just because there is no prescribed order of the material taught.
    I am disappointed and worried. As an educator, I have already seen the reprecussions of this system; as a parent I want it changed.

    •  I agree with you re: having to draw 25 candies for full marks.  I’ve come across the same issue.  Some teachers are very particular…a square with 4 circles as wheels didn’t look enough like a “car”, for example (sheesh!).  Students should NOT be graded down if they have the right answer.  Perhaps the students who “think outside the box” and complete the “pictures, numbers and words” segments should get bonus points, rather than penalizing the students who figure out the correct answer using only one.

      Not ALL teachers (in fact, very few) are as “particular” as the example I gave above, but not ALL teachers are great, either. 

      I respect teachers, and for the most part we’ve been very lucky with the quality of teaching our children have received at our Ontario public school (as an aside:  It’s a lower-middle class school in a large city…not a “rich” suburban school).  Perhaps it’s because my children are “easy” learners?  They “get” the math fairly quickly.  How much of that is their teachers, how much is curriculum, and how much is just innate, intuitive math ability? 

      Sorry for veering a bit off topic…my mind was wandering and my fingers followed. 

  28. There is a simple premise that has worked for me my entire life.  If it ain’t broke, don’t fix it.  Now that i have children and I grow increasingly frustrated to see how the “grand thinkers” at the various ministries of education believe we should be constantly changing the curriculum to address some idealogical ideal.  The very idea that we should completely change how math has been taught for years simply because they believe that a new, but entirely untested, idea is better is just wrong. Don’t get me started about how the schools decided that phonics was no longer any good – and now we have a generation of kids that can’t read properly.  We’ve had to struggle to teach our kids phonics to undo the damage caused by the schools early reading program… 

  29. As a public school student, I completely agree with this article. The curriculum teaches us an inordinate number of equations in a very short time when one method would suffice. This causes a great deal of confusion and frustration for all parties involved. The Ministry of Education needs to revise the mathematical curriculum, and soon.

  30. To every parent struggling with math who can’t afford or would rather not pay thousands of dollars, I’d recommend the JUMP math series of workbooks. At $20 a year that’s a lot cheaper. I’ve been using them with my children since my older child was in grade 5, and they’re quite different in their gifts and needs. The workbooks operate step by step building on both skills and concepts in an orderly way. The home page is: http://jumpmath1.org/ 

  31. One of the biggest problems in Ontario is that the ministry keeps changing the expectations and students in grade 3 are trying to learn concepts that we learned in grade 5 or 6. Also, there has been so much emphasis placed on literacy that math has gone by the wayside and the ministry knew this would happen. Math has been put on the back burner and the ministry and the boards knew this. They caught teachers and students in their mess.

  32. We are dealing with this in NB.  What exactly is the job of a teacher now?  They get paid pretty well and only work 39 weeks per year at the most, but they send home bag after bag of work for “parents to teach”.  WTF is up with this?  Do I not pay enough taxes to have my children taught at school?  Have the unions ruined careers such as teaching?

  33. I would like to thank today’s teachers for all the uneducated, disrespectful bullies that I have had the displeasure of working with in industry. I have worked with illiterates and innumerates in the field of industrial instrumentation. Some of these people have the smarts of people who should not have even graduated, or been given a licence. The skill level in my occupation has gone down to a disgusting low level.

    • The article does point out “no-fail” policies, which are in place in many schools across Canada. As teachers we are not allowed to fail students. Even if we give them a passing mark, we are not surprised to see students advanced to the next level the following year.

  34. I am a mathematician educated at some of the most prestigious places.  I have hard time understanding my kids math. It looks like re-engineered mathematics. I find so many inaccuracies in the manuals and the material that is handed to the kids. I wrote the Ontario  Ministry of Education. After several weeks I got a useless response from a policy person. I reported to them concrete errors in a concrete book used in 9th Grade. The same book is still used with the same errors served to the students. We are already way behind many Third Word countries. Very soon we will be irrelevant in science.

  35. I am a public school teacher in Manitoba, and I agree with much that is said in this article. I know many K-8 teachers, for example, who cannot subtract fractions with unlike denominators. These teachers are shaping our young students. The math situation is a disgrace and parents and anyone concerned better wake up very quickly.

    I know many teachers who feel the same way as me, yet we are afraid to speak up for fear of losing our jobs or being forced to teach courses we don’t want to teach. The whole public system is very rotten. Principals and superintendents know the least of what happens in the classroom, yet these well paid careerists are making the decisions that are damaging many students. Teachers are just pawns who are expected to agree with the latest fad or bite their tongue so that real debate is stymied. Parents who know the value of education should be VERY concerned.

    • Dear Silenced teacher,
      Thank you for sharing your story.  I know that you want to remain anonymous.  Would you consider setting up a fake email account and contacting one of the co-founders of WISE Math?

      • There are several issues that this post highlights: (1) elementary teachers are under prepared to teach mathematics and there are a number of contributing factors (e.g., not enough mathematics education in their teacher training program or prior), (2) school boards are not investing in hiring subject specialists to do this specialized teaching at the elementary panel, and (3) professional development is helpful but not the solution.

  36. Add to this that if the child does not get it, the child has a “problem”. I have three children being exposed to this math teaching. In each case although each has very different skill levels – they all have been accused of having problems in math because they can’t understand what is in the text book ironically called “Math makes sense”. It’s a real travesty. No need to go back to basics. There’s lots of interesting approaches; see John Mighton’s writings. My experience is that if you complain there is a circling of the wagons as the teachers and schools see it as an attack. Very frustrating.

  37. Awesome… Without math you can’t become anything useful… But you can be a teacher and teach kids to be even stupider than you are!!! Classic!

  38. I think leading kids through all the creative, hands-on, active ways of learning about how numbers work is great.  And at the same time they also need to have the basic number facts down.  Both can be worked on in parallel.

    Imagine building a house:  we make sure the foundation is strong and level; we can also be imagining how colourful and different we’re going to make the exterior walls look, or the upstairs bathroom, but without that strong, reliable foundation, we won’t be able to bring our imagined ideas to life.

  39. Part, maybe most, of the problem is that we are teaching calculus type mathematics to ver younger students when 99% or more of us will never use that in our lives.  For example, our kids spent hours on problems that required the use of the symbols, yet at the age of 52 with years of trade and commerce behind me, I have never in my life used these symbols.  Ditto for complex graphing, etc.  Beyond the deep imprinting of the 10×10 multiplication square, and the vital importance of understanding natural fractions- 1/2, 1/4/ 1/8 & the decimal equivalents- 1/2=.500, 1/4=.250, 1/16=.0625, etc. most of the math I was taught in school has been wasted.
    In trade school, we were required to learn advanced trigonometry which was vital to the trade.  Learning it in high school would have been pointless, yet, as a tradesman, I encountered many would-be apprentices who excelled at math, yet could not over the course of several months grasp the concept of 1/16 equals 6.25%, or a 1/8″ depth of cut meaning .250″ off the diameter, or even begin to grasp the meaning of the small lines on a tape measure and see the 7/8″ mark at a glance.
    Today, I am often required to calculate, in my head, the temp rise in a given container of water based on the number of BTU’s per hour applied.  In my hobby, we discuss and understand fairly esoteric mathematical equations on a regular basis.  The key is that it’s applied math.  It’s useful, and that’s the key.
    It is pointless to try and teach 12 year olds the importance of recognizing the when they will never-NEVER- likely use it, and even more pointless if we haven’t deeply embedded the understanding of the 10×10 square and the significance of natural fractions.  It’s pointless to teach calculus to teenagers, when we haven’t skilled them at sound, basic math such as how to calculate the volume of a cylinder, the area of a triangle, or the weight of a given volume of a given material.
    We’ve quit teaching hard, solid skills in reading, writing, and arithmetic, and then wonder why kids can’t read, write, or do math.

  40. There are very few teachers in the elementary panel with teaching qualifications in mathematics. Moreover, it should not be assumed that even a mathematics consultant has credentials in mathematics education. The public should be asking more questions about subject specialization and what it means to children’s learning.

    • That is because there is a growing tendency to force all elementary homeroom teachers to teach their own math, whether they are comfortable doing so or not.  Meanwhile teachers who have expertise in math are only allowed to teach math to their own class and are forced to teach English whether they like it or not.

  41. Look. The whole point of a public school is to produce semiliterate “TLDR”-s. Which is why the little lab mice will be able to recite talking points, follow instructions and remember that the only defence from bullies is whatever petty authority is given to them. Conversely, they should not be capable of forming an informed opinion on anything or standing for themselves.
    Why did you expect basic math to be an exception? I genuinely fail to understand such a specific concern.

  42. I learned my multiplication tables up to 10×10 (possibly 12×12, but I don’t remember that clearly) by rote. I do math visually, but feel that knowing the multiplication tables gave me a solid foundation for that. There’s no reason it shouldn’t continue to be used in conjunction with the frou frou strips of paper and graphs, IMO.

  43. My son is in Grade 2 in Castlegar, BC – I have been trying to find a way to understand this “NEW” MATH.  I love math & was eager & willing to help him nightly to learn to ‘love’ it as much as me.  After the 1st assignment that i didn’t understand and the “manipulatives” that he was to use to “maybe” reach a correct answer – I became frustrated and hated these assignments myself – when I complained that I wanted him taught the “proper” way to add & subtract – the teacher told me to not teach him that way because when he gets to Grade 8 he won’t understand algerbra! She also said that math use to be taught with “rules” – now there are no “rules” – it’s teaching kids to find a solution in different ways and not with pencils/paper – with charts, etc…..It’s crazy – if they can’t come up with the right answer (they might get close ) she gives them the answer after they play with “manipulatives” for 15 minutes….What the hell has happened to MATH.  There’s rules to guide us in everything in life – learning to drive a car – we teach our kids the “rules” – what has changed?   So together we fight through these ridiculous methods & my son continues to hate MATH – as do I – pls. help us in BC we are in big trouble.

    • The manipulatives are meant to be used as an introduction, so that when the procedure is introduced it will actually makes sense. The procedures are important in math, but they are not all that is important in math. The mistake the government of BC made is not changing the curriculum (the changes are based on sound brain based research and pedagogical research), but rather, that they changed it without re-training the teachers. If all educators were properly trained in teaching the new curriculum, these issues wouldn’t be arising.  I say this as a math teacher in BC, who has had a huge amount of success with the new curriculum (far more than with the old).

  44. You’re right, without a solid accurate foundation, you will never be able to build on anything. You have to put in the work to get to the fun stuff!

  45. The public (citizens of canada) needs to take back the education system from the “educators”. Not teachers in general but people who are in control of education and whose main goal is making their own life easier, with no realistic realization of the outcome of thier actions. I went to school in the 80′s and 90′s and I feel I learned substantially less than my parents who were educated in the 60′s and 70′s. Talking to my younger cousins who graduated in the last couple years it is obvious they know even less. Just look at our public knowledge of our government systems for an example!

    Our governments seem to have less and less control over the education system, either by choice or by neglect, and its time we made them step up and take back control. Educate kids so that they will be prepared for life and living and working in society. Our democracy and future freedom depends on it whether we like it or not. 

  46. what? the ‘old’ system worked so well they needed to replace it?
    Why do these people come up with this crap … and who in hell is wasting public money by paying them?

  47. Jerking the curriculum around is never good.  Incremental improvement would be best since it will take time for the teachers and parents to absorb it. 

    I can say as a post secondary teacher it is astounding how poor some students are at manipul…. uhh  rearranging equations.  I figured this was because they never worked with fractions…   uhh  rational numbers. Fractions are first mentioned in grade 6.  It’s been so long since I took math I don’t remember which grade I learned fractions in.An anecdote; I was working a problem with a student and we came to 5 x 12 and the student grabbed for their calcula…..   uhh  technology.  I was so startled I boomed “DON’T TOUCH THAT CALCULATOR! I apologized immediately, it can be scarring to be spoken to in loud tones.

    I guess all I wanted to say is balance the approach please.  There are at least 8 modes of learning and a good teacher will try to use as many of these modes as possible.

    Khan Academy is amazing, free, comprehensive, wide ranging and good.  Imagine having a tutor repeat a presentation 20 times until you get it.  I use Khan Academy in the classroom when I think he explains something better than I would.  There are teachers that routinely use Khan Academy to give their students the main instruction and class time is mainly for doing “homework” and helping students one on one.  I can’t believe a major publication hasn’t made a story of The Khan Academy.

  48. Thanks for posting about this.  I was a teacher and found that the Math Makes Sense curriculum…didn’t make sense and was very confusing to students.  I stopped using it.  I do find it useful for students to understand the concept behind the math but just as a introduction, not as something they continually need to do. 

    I have created a website to help parents access products and free info about the education system, how to teach reading to their children and other fantastic resources.  Please take a look to get some advice on teaching your children at home from a young age.

    http://www.edusavvyparents.com

  49. The very basic building blocks of knowledge, multiplication tables and periodic tables, needed to be drilled in by rote – until you have those blocks, you don’t have anything to be creative with!  Trust me kiddos, the beginning is the hardest, learning music notes, learning basic formulas, but once you have enough of it in your head to be fluent, it’s yours.

    …and I’m sick and tired of social experiments being tried out on general populations of kids.

  50. I find this terrifying.  There’s a reason why people learned rote mathematics and it WORKED – it’s because by memorizing, it, it removes cognitive burden and allows your brain to focus on other more important things – say, actually SOLVING the problem.  If you spend more time trying to figure out what 9 x 6 is, as opposed to the context of the math problem, then I guarantee you that you’ll hate math.

    These articles are inspiring me to homeschool my kids.  Fortunately, I have a pure mathematics minor.  But what about parents who don’t?  These stupid policies developed most likely by math illiterates are furthering the inequality between the educated vs. uneducated and rich/poor.

    • You are absolutely right!  It is time to return to basics in mathematics.  The curriculum should be fixed immediately.

      Currently I teach in the intermediate division. While 1/3 of my class is well ahead of the curriculum, at least half are very far behind.  I feel I need to spend time teaching concepts that should have been learned in Grade 3 or 4 (such as multiplication and division) before I can even begin to teach the intermediate level curriculum.  What a mess!

      Parents are well advised to make sure their own kids have learned how to add, subtract, multiply, and divide without the use of calculators or manipulatives before they get to Grade 7 and 8. 

  51. “It’s completely wrong-headed. And the moment you say parents should play a significant role in public education, you have a two-tiered system.”  
    Professor Stokes Have you ever visited an inner city school in this country?? We already have a two-tiered system. 

  52. Maybe the powers to be really want to dumb things down. After all, a dumb population is an easily controlled population; a population that will need to rely more and more on government. How else do you explain the great emphasis on social justice and saving the whales in schools, as compared to being expected to perform challenging math?

    Less social justice and making kids feel guilty about the environment, and more back to basics education is what is needed.

  53. Dear everyone, multiplication, simply, is not repeated addition….

  54. The problem is not that the teachers are not qualified, or good. The main problem is that there is a relentless campaign to produce stupid people. The teachers are not allowed to do their job. There is a continuous dilution of the curricula,  not only for math. The word discipline is not allowed in schools.   If you do not give the forming minds a disciplined way of thinking and behaving they will be not prepared for the real life. In real life if you don’t do the “homework” you are not being forgiven or given a second chance.  Continuously lowering the the standard was the only way to “keep” marks going up or stay the same. I think we reached a threshold when a chain reaction is imminent and the  quality of the education is in dire straits. 

      We should thank for that to our Ministry of Education a School Boards which are stuffed with incompetent people holding on their chairs and who invent useless policies just to justify their time. In fact these policies, which try to reinvent the wheel, do more damage than helping education.  

      In addition the use of technologies prevents the use of children’s brains when they need it most. Even pocket calculators should be banned. No child has any incentive to learn multiplication table when it is much easier to click a few buttons.       

  55. My daughter is in grade 5, and I love all the different strategies she’s been learning the last couple of years and how she can figure out fairly complicated problems in her head using these tools. BUT she does get stuck on basic multiplication facts, and that does require drilling. Like everything – the answer is probably somewhere in the middle – a combination of traditional math skills, along with the much better understanding of how you can manipulate numbers. 
    The key is making sure teachers are well trained with these new skills — it’s not always easy for a teacher who has been teaching older methods for many years to switch over to the new methods. They may need a lot of support.On the other hand, my other daughter graduated from high school last year, and struggled with her top level math classes from grade 10 onwards. We hired a tutor each year. That math seems far, far more complicated than the grade 12 algebra I excelled in. And I don’t believe that’s even the latest curriculum that she was learning — that’s being switched over in the next few years in our high school as kids come up through it. Not sure what the differences are. I guess I’ll find out when daughter #2 goes through it.

    • I disagree. Please read my reply to Nikki. These new methods just make things worse.  There is no wonder that your daughter has problems with basic things.  The teachers are well trained, but they are forced to use these new methods, which have produced only failures.

      The math is not more complicated then 10-20 years ago, on the contrary, Calculus was thinned out, many things have been taken out. Nobody learns integrals in high school anymore. The struggles you mention are a result of implementing these new and wonderful methods instead using the methods which produced good scholars for generations. In addition taking out the authority from teachers there are no incentives for children to learn anymore. Read the book I mentioned above, our brain learns only through coercion, which is the only way to create “new synapses” = learning

      • Good scholars for generations? I think that’s optimistic. I may have done very well in algebra, but many didn’t. Traditional methods work very well for some, but not all. 

        • I never claimed that everyone did well in the past, but there were no chronic problems with math as they are now with the toy play which takes the abstraction out of the equation. Math was more difficult than what is taught now in schools. People had more time to study as there were less distractions in the class and at home. Teachers did not have to deal with cell phones, pocket calculators, mp3 players and many other disrupting tools. We had less gadgets and more brain. Traditional methods worked because they used well known and tested learning strategies. Now there are many people at the Board level who need to justify their time and position by changing things, which did not need to be changed. Why change something that works?  I am very sorry that you are not able to see all those things.

      • Teachers are NOT forced to use these new methods. Many teachers choose to use these ‘methods’.  Rather, they choose to use a different philosophy of learning…one not focused on reductionistic behaviorism.

        What authority loss are you referring to Bogdan?  Is it the loss of authority due to everybody and their dog thinking that they know best about how to teach a specific set of students in a specific context? 

  56. The problem is not that the teachers are not qualified, or good. The main problem is that there is a relentless campaign to produce stupid people. The teachers are not allowed to do their job. There is a continuous dilution of the curricula,  not only for math. The word discipline is not allowed in schools.   If you do not give the forming minds a disciplined way of thinking and behaving they will be not prepared for the real life. In real life if you don’t do the “homework” you are not being forgiven or given a second chance.  Continuously lowering the the standard was the only way to “keep” marks going up or stay the same. I think we reached a threshold when a chain reaction is imminent and the  quality of the education is in dire straits. 

      We should thank for that to our Ministry of Education a School Boards which are stuffed with incompetent people holding on their chairs and who invent useless policies just to justify their time. In fact these policies, which try to reinvent the wheel, do more damage than helping education.
     
      In addition the use of technologies prevents the use of children’s brains when they need it most. Even pocket calculators should be banned. No child has any incentive to learn multiplication table when it is much easier to click a few buttons.

  57. I have been teaching math using manipulatives and focusing on both conceptual understanding and procedural fluency for 6 years (and taught using “traditional” methods for 5 years before that). I have also been working with teachers and teaching them how to use the manipulatives effectively in the classroom. What I have noticed is this: what is challenging for adults (including teachers and parents) is often easy for a student. Most adults have never seen math concepts taught concretely and must divert away from their procedural knowledge to understand it differently. It feels confusing, and overly complicated. When a student encounters the concrete application FIRST, it’s not so confusing or complicated- they get it and they often like it. Furthermore, they don’t forget it. Before teaching fractions concretely, students forgot how to add or subtract very quickly after “learning” them- because they only had a rote procedure. Now my students know that they need the same size pieces (common denominator) because fractions have to have equal sized parts in order to name them, so they know WHY they need a common denominator and as a result, they don’t forget it just like they don’t forget how to  add 5 + 3. The other point I’d like to add is that there is very little mention in this article about HOW the brain learns. The new curriculum is based on sound brain and pedagogical research. All change takes time and will have obstacles. We need to be educating our teachers better, and our parents. I have seen in my own classroom, and heard from countless other teachers who I’ve worked with, the power of teaching using methods that work for many different styles of learners and understanding the concepts in math. I would NEVER go back to the old method!

    • Sorry, I disagree. Because of these “new” and “innovative” methods the level of our children goes down every year.  Don’t get caught in Board propaganda! The sound brain and pedagogical research is pure BS. Have you seen those researches? Read the book “The brain that changes itself” and you may change your opinion.  

      It is well known that the brain needs repetition to build synapses.  The brain functions on the principle “use it or lose it”. By making things “easier” you just lower the bar and make them think less. By repetition fundamentals are well established and using those they can build on.  There is a certain age when people can learn fast: languages, math etc. They need to learn certain work ethic and principles at early age.

      • I have done the research; I focused my major project for my Masters around making math more meaningful in the middle school years. I have also read “The brain that changes itself” and use those principles as well. The students FIRST learn through making meaning of the math, THEN they practice the skills using procedures until fluent. They absolutely still need the practice and “drills” but they also need some understanding as well. Times tables should be memorized but first allow the student to understand what multiplication is so that can easily use other mental math strategies to estimate and solve problems.

        • I am glad that you are not focused on “thinking only”.  Thinking undoubtedly is very important, however, you can’t think without  basic knowledge. We should not put the carriage before the horse.
          I din not say that memorization is all, but in our schools there is too much emphasis on thinking and memorization is belittled. Memorization is very important. We need to train to build muscles and the same goes with the brain. 
          Another brain formation fact is discipline which is not enforced in schools. A young forming brain needs to be guided and not let “discover” everything. It may discover some wrong things too.

          I know what is taught in OISE and other educational institutions, but I believe that they have a wrong approach to education. We can see the results already.

          •  There is a difference between discipline and support.  I would argue that it is support from parents and support for students that makes the difference, not ‘discipline’.

        • The problem is that too often we never get around to the times tables being memorized or other operations being consolidated without the use of manipulatives.

          Now we are beginning to reap the rewards!

    •  When I hear about doing things based on “sound brain and pedagogical research” all I really hear is “someone wants to turn their master’s thesis into a book and sell it to every school board possible”.  I’ve been to enough workshops and been handed enough “resources” (ie dust collecting doorstops) to know.  Understanding the why is vital, I agree.  You don’t need new pedagogies and manipulatives to explain the why.  I use pictures of pizza:  if I have 1/2 and 1/4 of 2 pizza’s leftover and I want to save room by putting them in the same box in my fridge, how much pizza do I have?  (hint:to figure this out the pieces have to be the same size)  Do a few examples like this and they get it.  Want one for equivalant fractions?  Here’s a joke:  a guy walks into a pizza store and orders a whole pie.  The waiter asks “would you like it cut into 4 or 8 pieces?  Guy says “I’m not that hungry today, please cut it into 4″.  Kids get the joke and remember a very important lesson: it doesn’t matter how many slices you cut it into, the amount of pizza is the same.  I do all this on a CHALKBOARD (practically a bad word in teaching now) and they all get it.  These are grade 7 and 8′s and they all have the same reaction:  somebody finally explained this to me.

    • Well said Nikki!  I agree 100%

  58. The problems both my sons have encountered with the new math is its need for the increased reading comprehension and writing skills required to achieve any degree of success with the new math programmes.  Both boys have learning deficits in those areas and although skilled in areas requiring visual spacial amd hands on skills they are not achieving success in math because they cannot understand what is being asked and explain the solutions to problems presented.  They also were not drilled in the basic math facts to assist them in computations.  We have had to drill basic facts at home and paid a private tutoring service to help them get basic numeracy skills so they can get enough math to get high school credits to enrol in community college programmes to achieve their career choices in the construction industry.

  59. The heading below this box where I am invited to make a comment reads, “Showing 118 of 116 comments”.  I wonder where this writer learned his/her math? 

  60. Knowing the times table, by memory, is a very useful and necessary tool in studying Math. Gives you number recognition – the ability to estimate, judge if an answer is reasonable, figure out all kinds of math questions quickly and accurately without relying on a calculator - whatever method you use – even some of Thwims convoluted ones. Easier to UNDERSTAND math concepts once you’ve memorized the timestables, and learned operations by rote.
    Knowing that 1/2 x 1/3 means that you divide a figure into three equal parts, and then take half of one of them, makes a lot more sense after you’ve practiced the rote method many times, and you don’t get the kid to figure out 7/9 x 14/23 using the “visual” method!
    You talked to a lot of “experts” in this article, but few teachers.
    Thanks to the teachers that wrote comments on this article.

    • I agree.  Better to learn the basic facts and computational methods for math operations and then go back to investigate why they work with simple examples and concrete materials when needed.  That’s the way I learned (way back in the 1950′s) and I was much more able to teach the subject to my students when I became a teacher in the elementary school system way back in the 1970′s. But even I found the new methods difficult and confusing for most students I taught in my last years of teaching in the early 2000′s.  Too much material was presented and too much was expected much too early before students were really cognitively ready for the concepts presented. It was almost impossible to assign homework as most parents found the concepts even more incomprehensible than the students did in most units presented. And I found that classroom teachers having to present the material were not really consulted before the new math programme was implemented.

  61. Math tables were drilled into us by Grade 3! I don’t see what’s so wrong about using rote learning. Anatomy is memorized in the same fashion. Once you know it’s stuck with you.

  62. In BC, the new math students are in grade 11. If college students are having trouble, it was with the old curriculum.

    •  In Manitoba, the new math began in the early  90s with 2 math series called Quest 2000 and Interactions. They were terrible math programs, yet most Manitoba schools implemented them. Students who used these math programs are definitely in university as we speak, and have been for a few years, so I can understand how university students don’t have proper math skills.

      Those 2 useless math programs have recently been replaced with the equally useless Math Makes Sense, Math Focus, and Math Links programs.

      Kids need to spend time completing math computations and learning the basics….not spending an hour cutting strips of paper to confuse them even more when dividing fractions.

      •  I should also add that if anyone has ever looked through the Quest 2000 or Interactions programs, they will very quickly understand why a number of students have such poor math sense.

        I remember telling my principal that I didn’t want to use these programs in my classroom. He told me I had no choice because the division invested a pile of money buying them. I told him they were making math very confusing for my students, and other students in other grades. He didn’t care about that.

        • Quest 2000 was at least preferable to the Nelson Math programme which is the one implemented in Ontario and Alberta in the early 2000′s.  I’m not sure if it used in other provinces.  It is too heavily laden with confusing language and an emphasis on multiple solutions to problems (also confusing to kids who want to just find the answer).  Concepts are also introduced way to early for children to understand. 

    • Hi Pete.  I refer you to my earlier reply to someone who mentioned this.  Sorry, it’s not so simple.  Silenced Teacher here makes another good point — the current “reform” trend began a long time ago.  ”No algorithms” began to be vigorously sold to schools with the NCTM “Standards” report over 20 years ago, which also marked the divorce of mathematical curriculum development from the professional mathematical community — one of the root causes of the problems we’re seeing today).  But ever since the tinkering began in the 1970s serious harm has been done, and continues to be done to the teaching of mathematics.   Critics, by the way, are not simply calling for the clock to be turned back.  In recent years serious improvements have been made (at least on the policy side).  For example, in 44 states the “no algorithms” approach to elementary arithmetic has been tossed out.  For a good idea of what we’re promoting at wisemath dot org, navigate to our site, download the NMAP report and read (at minimum) the 45 recommendations there.

      •  Why should the ‘professional mathematical community’ who teaches less than 10% of the students who attend K-12 schools determine what is best for the 90% who THEY NEVER WORK WITH?

        Oh, and thank you very much for excluding professional teachers from your hierarchy.  I forgot that they weren’t professionals and are not part of the mathematical community.

        I would argue that the ‘professional teaching community’ knows more about those 90%.

        Lastly, it is not about an either or approach.  It is rather about approaching things in more than one way.

        I teach math and science in high school and teach it well, new curriculum and old.  I would suggest that you are more concerned about your own identity than the 90% of students who you will never see.

  63. I can understand these alternative systems, but believe we should start with basic memorizing of tables, followed by universal algorithms. The visual concepts should be added later to permit operations in other bases and dimensions. Don’t forget the old abacus and slide rules either. In earning my science and engineering degrees in both math and chemistry, we were not allowed calculators because only the rich kids could afford those modern gadgets. I can still beat the typical sales clerk, calculator in hand, doing the same computation in my head.

    • Same here. Basic knowledge is essential to be learned to create a strong brain. Calculators , GPSes, etc are good, but for the young mind they can slow down their development. 

  64. As a BC public school teacher, I think that the problem is due in large part to the expectation that students have been taught successfully when they do well on standardized tests. The text books are presumably written to further that purpose. I strongly suspect that the Ministry of Education in BC (where I teach) is unlikely to approve a textbook which is not in keeping with that goal. I happen to be spared this dilemma in my subject area – secondary school music – because standardized testing is very seldom required and the practicality of measuring outcomes in music teaching is very evident: the students have been successfully taught when the musical performance outcome sounds better than it did last month.
    No job requiring mathematical aptitude, however, requires students to be able to pass standardized tests (unless, I suppose, it is a job as a designer of such tests). The texts are presumably therefore designed to teach students to do something which they will never, as adults, be asked to do and which no adult who uses mathematics in his/her daily life (whether for employment, household management, or for hobby activities) ever needs to do either. It is small wonder, then, that these texts make little if any sense to those who apply mathematics in the “real world” or, for that matter, to those who teach it.

    •  Hooray!  I think this is more about people and their identities than students and their learning and understanding.

  65. Is the effectiveness of  the “new math” in these comments the “new math”, the new “new math” or the original “new math”? I remember the problems kids and their parents and teachers had with the “new math” introduced in the 1970′s. Professional educators are still squirming around, hoping the next revolution resolves the last round of introduced deficiencies. Remember, all the material introduced K-12 represents the mathematical knowledge of roughly 1760. A university degree gets you up to about 1850, with a few sparks of more recent insights.

    Start math with the basic tools, and a child’s experience with success..

  66. School math results are actually even worse than they appear.  They do not tell you how many of their A students had outside help.  When I heard that 30% of the class ahead of my daughter’s failed Gr. 9 math (both schools in a high socioeconomic area), I enrolled her in Kumon.  When she graduated high school with 100% on her calculus exam, no one put an asterisk next to the school’s average indicating “supplemented by private tutoring”.   Most elementary school teachers have been poorly taught themselves and are downright math phobic.  It’s the blind leading the blind expecting them to teach kids math.  Meanwhile, the excuse for throwing out what worked, rote learning of the basics is the same idiotic justification as with phonics and Whole Language.  The kids were not bored.  Teachers and excess administrators were bored.  Kids are excited as they gain mastery and progress to another level.  But idle administrator hands make the work of the devil.  Rote learning is the critical beginner stage and solid base for higher levels of conceptual thinking later on as Kumon progression reflects (structured by a Japanese math teacher).  BTW, all these curriculum dabblers are former teachers, every last one, so they cannot escape responsibility by shrugging their shoulders and saying “the higher ups are forcing them to give up what works and substitute whooey”.  And when have teachers ever had problems taking on authorities for what really interests them, their remuneration and hours?

    • Teachers have a lot of trouble taking on authority when it comes in the form of principals, supers, and higher ups! 
      Ambitious teachers are forced to “jump through hoops” to demonstrate to others “how great” the flavour of the day techniques are if they wish to have any hope of being promoted to VP or principal.
      Even questioning of the latest “social experiments” is highly frowned upon.  Blind acceptance is expected.  People who refuse to do this are considered “trouble-makers,” and speaking up can put their career path in jeopardy.

      Sorry to be so blunt, but this is what I have observed in the last 15 years.

  67. The new new new new math reminds me of the whole language ideas. In LA we teach mini lessons, model how to be better readers and writers. From my experience, the discovery method is not all it is cracked up to be. Pardon my old fashioned ideas.

  68. Multiplication tables up of 1 to 10, or preferably 1 to 12 (my school preferred 1-13) are just so incredibly simple. They provide the tools required for every subsequent step. I think the difficulty faced by some students and many teachers is that due to time issues, they take a class to step three before confirming that step one and two are successfuly learned.

    And for commentary on subtraction, the word “borrowing” should be stricken from the teaching vocabulary. Once you have firmly established that the numbers in each place in the decimal system are the counts for 1s, 10s, 100s etc, you should “subtract”, not “borrow” from the next bigger place and add that unit to the smaller place, then complete the subtraction. The system is identical for any base, so you don’t have to relearn anything in more advanced concepts. It is easy to use blocks, strips of paper, tiddlywinks or whatever to demonstrate the concept.

  69. How many of you have encountered a high school student working in retail, who when the total is $10.24 – you give a $20 then add, after they have punched in the numbers on the till — oh, here’s a quarter… they stare at you blankly, because they no longer know what change to give… 

  70. I completely agree with the article.  My son is currently in grade 8 and I can’t seem to understand the strategies he’s being taught in class.  I also don’t want to confuse him by teaching him ‘old’ strategies that were taught to me long time ago.  Luckily he’s able to sign onto a website for free math tutoring at night through a live chat with teachers.  The program is called HomeworkHelp.  I think this program is only available in Ontario though. 
    https://homeworkhelp.ilc.org

  71. I’m a math teacher and I can tell you that the only reason this new way of teaching math exists is because most teachers did very well in school in everything EXCEPT math.  They are the ones who changed the way math is taught thinking “if only I had been taught it this way I would have succeeded.”  All the best math teachers I’ve ever met ignore these fads and teach the way math has been taught for 1000′s of years.  Most principals, etc don’t care as long as the parents are happy and the standardized test scores are up.

    • I agree. There was a completely interesting article about the “feminization” of public school education in the Globe and Mail. Perhaps this is another side effect. I was a bit of a prodigy in math and know the method they are describing. It can be used to calculate large multi-digit products in your head, but there are a few things you need to know first. You need to know your basic multiplication table by rote. You also need to have a spatial IQ over 150.
      Trying to teach this method to children without the fundamentals is as realistic as getting a toddler to run a 100 yard dash under 10 seconds.

  72. I am not here to dismiss Strategies, but to highlight the relevance of Algorithms.

    eg 1. Algorithms play an intrinsic role in Computer Science. The vary nature of many computer programs are algorithmic in nature. Many of them rely heavily on mathematics to solve both everyday and complex problems. Try creating a small computer program using Strategies instead of an Algorithm – that would be counter-intuitive since the aim of a program is to solve problems of the general case which cannot be done with Strategies technique since they solve special cases.

    eg 1. The famous mathematician who discovered Algebra, created a step by step method for solving for x for certain equations. The word Algorithm means Step by Step. He first experimented in a similar fashion to what Educators are asking children to do as described in this article, but then why did he create an algorithm (which by the way comes from the Mathematician’s name). For whom was this meant? It was meant for us to use. And then if we are interested in learning the intricacies of the theory, we can explore this further. We are not all going to be pure theoretical mathematicians, but we certainly can apply a step by step method and later, once we develop a comfort level, we can dig deeper into what, how, why the algorithm works and when it may not work or coming up with another method altogether.

  73. The big problem is that many teachers who teach math are not comfortable with math concepts because they have not taken Math since grade 10. The grade 8 math we teach now is similar to the grade 10 I learned. There is no specific Math course required for elementary teachers to teach math. So some grade 7 and 8 students are learning Math from teachers who have only completed up to grade 10 level Math. I believe the Ministry of Education should mandate that all middle school teachers (Grade 6, 7, & 8) must have at least one university Math credit and an Intermediate Math course qualification. 

    So if you have a student in middle school, ask their Math teacher when was the last time they took a Math course.

    • Yes.  Part of the problem is that there is a growing trend of forcing all homeroom teachers to teach their own math, whether they are comfortable doing so or not. 

      Meanwhile, teachers who have expertise in math are not allowed to teach it as a rotary subject, but instead they are limited to teaching it only to their own class.

  74. I’m interested in setting up a group like WISEMath for Ontario. If you have had similar experiences to those described in the article and would like to see changes made to the Ontario curriculum to improve the standard of math education, please contact me. I can be found on Facebook or email clive.packer (at) gmail (dot) com.

  75. I agree 100% with the points addressed in this article…I’m an elementary school teacher and parent – we need to get back to the basics…the pendulum has swung too far to the left!

  76. Well, that was an unbiased article…

    Weren’t university math professors all up in arms over the last decade about how poor the math skills were in ‘this generation’ of students?  This was well before new curricula hit the classrooms.

    In fact, weren’t the new curricula designed to address that issue in the first place?  I think we have an obligation to speak up for the kids.  Maybe all of that memorization just didn’t work EITHER.  Maybe it is NOT the curriculum but rather the lack of support for schools and teachers both financially and the view/attitude towards learning and the teaching profession as a whole.

    Maybe it is the fact that we have many grade 9 and 10 students working 20 to 30 hours a week at a paid job, often on top of extracurricular activities.  Maybe it is the 7 hours of non-school based screen time the average high school kid chooses (with the help of their parents) to spend their time on.

    •  I agree with you that academics don’t seem to be very important anymore. But this new math is doing harm to those students who value education.

  77. This is a mass over generalization of the methods teachers are using to engage, empower, and educate students in math. It seems that these parents are faced with the dilemma of many of us who experienced the more traditional ways of math teaching…we were taught tricks, not why and how the math actually works. That is truly the reason that people are frustrated and are unable to assist their children. I have a mathematics degree, an elementary school math specialist, and have taught for more than ten years in Ontario and have seen huge gains in my students through these methods hat allow children to explore and engage in math in ways that make sense to them. To see the students engaged in class and having conversations about the math, as well as expressing now much more they now understand is the reward. It is empowering to children when they are stuck and can work their way through a problem because they have the ability to apply their knowledge to the situation, not just a trick someone showed them. We want these children to be confident and creative thinkers…problem solvers. Providing them with situations where they can practice this safely in the classroom, will only help them in the future. I am sorry for those who have had negative experiences with these methods, but as the article mentioned, there is pressure on teachers, and when they themselves are not confident in the subject, perhaps because of their own math experiences, then it does prove much more difficult. When done well, the math class should be based on what the students need. A balance of exploration, application, and practice gives students the foundation they need to carry them from year to year, the confidence that they need to take risks and apply what they know, as well see the practical application in what they are learning.

    •  I am a math major…not an “Elementary Math Specialist” and the new methods are destroying young students ability to do math. The so-called elementary math specialists that I frequently meet with know very little about math. They do, however, know how to make fun lessons using Smarties.

      • ̶̶l̶i̶k̶e̶   love

  78. I do not want to think that Stokke is unnecessarily picking on teachers as a profession that doesn’t require the learning of basic Maths concepts, teacher education as I know it is not devoid of general basic Mathematical curriculum. I will suggest that Stokke take a 2 years teacher education training to find out.

  79. A major part of the problem parents are having comes from having memorized the math they learned, which does not lead to an understanding that would allow creative real world problem solving.  The new curricula are aimed at making math useful, at giving students with many different learning styles the problem solving tools, and basing it on understanding not rote memorization.  One of the most important methods in understanding math concepts is to use concrete objects like base-10 blocks or strips of graph paper to convey a visual and tactile understanding of the operation, like multiplying (10-1) times 6.  Six tens minus 6 ones can be visualized as an area touched with fingers and does not need to be a rote memorized fact.  Once this method is understood for finding basic number facts, it is easily transferred to algebra like (X-1) times (X - 6).

    Previous teaching methods depended upon rote memorization of techniques that did not convey  understanding that left high school graduates unable to use the algebra to solve real world problems. 

    Teachers and parents need to diagnose the way each student learns.  Many students who have language difficulties will find problem solving by manipulating objects with their fingers works well for them, because the jumble of numbers and symbols written on paper, makes no sense.  Surely those of us educated 30+ years ago persevered to memorize the symbol manipulation techniques on paper, did not truly understand the underlying concept.  A good example is the old method of doing square root on paper and pencil.  But finding the length of a side of a square as the square root of a number which is the area of the square, conveys understanding, and using square tiles or graph paper cut into pieces.  This jumble of words can be confusing, but just put a pile of squares on the table and aske the person the make a square and tell them to give you the length of one side.  That is easy for someone who struggles with language, such as immigrants and many First Nations students that are also trying to learn English as a second language at school.

    People who found math easy have the most difficulty understanding that they learned to memorize their number facts and then years later came to understand what they were doing with the various mysterious algorithms.  ‘Memorize now to understand later’ is not preferred to ‘understand first and use technology to provide the number facts’. 

    The level of math has increased in the past few years so that students in grade 10 are doing the math the retiree writing this learned in grade 12 or first year university.  Probability and statistics were not taught in high school 30 years ago.  There is a lot more to learn in this modern world.  Many students are trying to learn concepts when they are not ready for them–with a bit more maturity the concepts will be easier, but every learner is different.  Larger class sizes reduce the time the teacher has to analyze each student’s learning style.

    • “Previous teaching methods depended upon rote memorization of techniques that did not convey  understanding that left high school graduates unable to use the algebra to solve real world problems.”

      Then why is it that my previously-homeschooled daughter, who placed into grade ten math when she started public high school, found herself tutoring ninth graders who could barely add, subtract, or multiply, and who had absolutely no understanding of fractions?  I taught her through the elementary years with  ”previous teaching methods” (and I’m an English major who squeaked through grade 13 Functions and Relations–not a mathie), and yet she was the one who ended up trying to explain numbers to those taught by the wonderful new way. Something–if you’ll pardon the expression–doesn’t add up here.

  80. You should look into JUMP Math, designed by Professor John Mighton at the Fields Math Institute at the University of Toronto. The teacher manual is free online, and the books are reasonable since it’s nonprofit. It combines both the conceptual understanding with plenty of practice on the basics. As a teacher, I have used it for years, and all my kids are confident mathematicians who do extremely well.  http://jumpmath1.org

    • Thumbs up for JUMP Math–lots of homeschoolers use it too.

  81. Thank you for publishing what a lot of elementary teachers and parents (like my wife and me) are thinking but can’t say.

  82. This is an interesting article that strikes very close to home. After one public and two  private schools we decided to home school our son. The public school curriculum in Canada has now aimed so low even a retarted child can no longer benefit from it. Fortunately we have the money and the time to be able to home school. Our son now belongs to the advance boys network and has completed 3 years math and science in one year. Next year looks even better. There is no chance he will see the inside of a public school ever again, and I do feel sorry for those that have no choice but to attend.

  83. I absolutely agree with  Anna Stokke. I came from different country couple years ago, and wanna say that my son in Grade 4 know absolutely nothing about traditional Math method. I am in shock what they learn in Grade 4 , they don’t teach kids in normal way. They teach some games and some visual strategies that for me absolutely wrong. I bought couple Math books from Amazon and teaching my son by myself which is ridiculous that I have to do it instead teachers.Math is Math , kids have to learn at least 2 way or methods to understand math, and also they need practice. In Winnipeg schools we don’t have books at all … How my kid should practice math with no books ?
    Compare to Universal level Grade 4 in Canada = Grade 2 in Worlwide. What a shame !!!

  84. I am really worry about my son’s math education here !

  85. Ohh this is a painful subject for us as well. I don’t trust this new method of teaching at all.
    Lets start from that our kids have no books at all in elementary school ??? WTH going wrong with  our educational system ? Compare to Universal level our kids way way behind in Math .

  86. This article has some good points about the ‘no-fail’ policy and a lack of basic math drills.  I think is misses some important points though.  First, while it’s true that you can’t do higher order math without basic math concepts it is also true that memorization alone isn’t enough.  The math curriculum as I see it is undergoing a similar struggle to the one faced by language duing the 1970′s.  The debate was over ‘whole language’ vs. ‘phonics’.  Eventually it was realized that BOTH were needed.  This is essentially the same thing.  We need BOTH the memorization AND the understanding.  Unfortunately, educators are being told that the ‘kill and drill’ method is out.  Why?  We teach kids to read by having them memorize the alphabet and all the sound combinations and then practice with ‘kill and drill’ until reading becomes automatic.  THEN we focus on comprehension.  Why can’t we do the same with math?  It’s rediculous to think that if you solve a problem once or twice and understand it that you will remember it the following year.  You need to practice before the skill is really developed.  Since educators are no longer allowed to do this at the base elementary level, the kids miss out and get pushed forward to the higher grades were they no longer have the skills needed to understand what they are being taught.

    Secondly, and more importantly, it misses the point that PARENTS ARE RESPONSIBLE FOR THEIR CHILDRENS WELL-BEING.  This means that we spend time with them teaching them, and yes, helping them learn.  If a person lacks the time and responsibility needed to ensure that their children get the help they need then they shouldn’t have them.  If your kid can’t count….HELP THEM.  Don’t just complain.  Make sure they do their homework and get the extra help they need.  While you’re at it……teach them to be respectful and responsible, then maybe they will pay attention in class, ask for help and do their homework on their own.  That’s what we did when I was a kid.

  87. I teach math in high school, and I cringe every time I see a grade 10 student reach for their calculator
    to find 5 x 6, something they should be able to do in their head in
    grade 3. The problem is that students are forwarded into grade 8 with too many of them not knowing their basic skills (multiplication, division, fractions, decimals, etc.) instead of being held back until they know them. Many kids learn that they get forwarded whether they do the work or not, so why should they work? This means teachers have grade 8 and 9 to try to get them up to the level they were supposed to be at entering high school, otherwise they end up in the basic math stream and can say goodbye to any plans they had of a career requiring a university degree (doctor, nurse, vet, engineer, etc.), no matter how bright they are.

  88. The problem that I see, as an elementary teacher, is that we expect kids to have a deep understanding of these concepts too soon, before they are developmentally ready. I agree with the push for understanding and critical thinking, but in my opinion it is thrust upon kids too early. I teach things to 10-year-olds that I specifically remember learning in late high school, when I was actually ready to learn them.

  89. I’m a grade 2 teacher in Ontario and I have to agree with the message of this article. I’m required to teach the new way, and i do it, but twice a week I slip in drill work. I know from observation that it increases my students’ confidence in math and the brighter ones prefer using the “old” algorithms because they are simple and quick. Luckily my principal knows what I’m doing and turns a blind eye.

  90. As a private tutor I see the disastrous effects of new-age math instruction all the time. Kids need to be drilled–yes drilled–on multiplication tables and even basic adding and subtractng facts. there is nothing wrong with rote memorization of times tables. Rote memorization i how we remember birthdays, phone numbers,a nd computer passwords.

  91. We should master “what is” before expecting “why is”. It is an unfair expectation (and generally beyond students’ developmental cognitive abilities) to expect them to come to conclusions about “why” math concepts are, before they really learn what the concept is. Frankly, most adults can’t do this either (with reason!). Let’s stop putting the horse before the cart and teach students math they can do, and use. Higher-level thinking will come to some students, once they’ve mastered the basics.

  92. I don’t agree in rote memorization. I was a kid that excelled in math and could answer anything if it was given to me as 12 + 59, but as soon as you put it in a context or showed it in a different way I was totally lost. Rote memorization is how you end up with kids that go 12 + 3 and end up with an answer of 42 and don’t understand why it’s wrong.

  93. While discovery learning is powerful the problem with allowing children to “do it however works best for them” in math is that not all methods will carry forward into the higher skill sets of math, thats just the way it is. So we need to teach children the method that will work best long term mathematically speaking. It is that simple.

  94. “But do you understand why the multiplication table is why it is?”

    This is the very root of the problem that plagues the curriculum. Do you need to know a reason for this? Does the fulfillment of your life rest in being able to answer why 3X3=9?

    Meandering drivel. Who cares. News flash: there are things you need to just learn and accept and memorize and move on.

  95. “Teachers, who can go through the system with minimal math training and
    arrive in class expected to inspire children to create and conceptualize
    their own mathematical knowledge—and relying on a new set of parents to
    fill the gap. “This is a never-ending cycle of innumeracy,” says
    Stokke. “And we have an obligation to speak up for the kids.””

    No doubt teachers who reply to this comment feel outrage and are indignant at the suggestion that we have minimal training.

    As an elementary teacher, I completely agree with the above statement. Nowhere was I “trained” to teach math. My brief year in teachers’ college was spent explaining why I had to feel a certain way about the injustice of residential schools.

    Teachers need to accept the fact that they are simply not trained to teach math. Unless you take additional professional development courses or additional qualifications in math, or unless you have a formal math background, you have no training. Period.

    There are a certain number of math facts that frankly do not need to be explained ad nauseam. There is simply not enough room or time in the curriculum to allow for children to explain how they got 5+3. In light of time constraints, asking a child to justify their thinking when they add 20+20 is a waste of time.

    Consider the gap that is produceds between the generation we are educating now and the previous generation stll teaching math, as evidenced in the article. We focus more on strategies instead of the algorithm because education policy wonks ensconced in their ivory towers churn out paper after paper exalting the need for children to express themselves through math. The problem is, 2-3 children can do this, and the rest fall by the sidelines because they are not cognitively ready yet to declare this. I find it a complete waste of time and feel that I am doing a child an injustice when I assign them a low mark, simply because they were unable to use a strategy yet the algorithm is fine.

    We are comfortable in our self-entitled nanny state in Ontario, clinging falsely to the notion that we have one of the best curriculums in the world. Meanwhile on other continents young children are still taught by rote up to a certain age and they are far outpacing our students on an international level. The world will not be made up of future jobs with a need for someone to constantly express themselves. The world will most likely to continue being a niche-driven economy and we are essentially creating a generation of children with shaky foundations who, all the while being able to “express” themselves, are bereft of any base. If you disagree, consider the silent mathematic illiteracy epidemic sweeping high schools, along with their literacy levels. High school and university students are simply incapable of writing papers suited for their grade levels.

  96. So has anybody actually used the SuccessMaker program which cost $12,500? Was it better than the terrible “Math Makes Sense” textbooks being used in schools?

  97. What I find find most disgusting about this is the blatant hypocrisy of the Duvall’s of the world.“We want to provide options for kids,”

    Ya, right. But if your kid does it any other way than the 4 strategies that we show him, we’ll mark it wrong and label him as stupid.

  98. There is alot of overgeneralizations being made here, “…they won’t be able to do fractions, which means they won’t be able to handle algebra, which means calculus is out, which means they can’t be…”
    I must admit that as a teacher, there’s alot of new exciting ways to understand a concept and there is a push in a curriculum for conceptual understanding. The content and skill that the students have to learn stay the same. They gotta know their facts and they gotta know their procedural skills. The endeavour of teaching math is for students to make connections between the pictoral (or representation by manipulatives like blocks or shapes), the graph (scatter plot, Singapore math, pie chart, etc…), the tabular (organizing ideas using some thinking map to realize patterns), and with the numeracy (math sentences, the abstract, procedural knowledge). The key is balance. In the past, the emphasis has been on the latter. This is more prevalent in the high school level (old school). I don’t disagree that parents should take advocate but they should be addressing their concerns as well to the Department of Education. They have a voice and a right to express their concerns about the curriculum or the textbook/resource being used in their school division/district and they definitely have the voice to express what content should be taught in the schools and how.

  99. By the way, people, please learn that (a+b)*(c+d)=ac+ad+bc+bd, that will be good for any multiplication now, is it not? For example, suppose you want 67 * 97, that would be (60*90+60*7+7*90+7*7=5400+420+630+49=6499). If you do not know that, you have serious problems in math.

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