Not Your Grandmother's Math

'emmett' photo (c) 2011, susanrm8 - license: http://creativecommons.org/licenses/by-sa/2.0/Every Friday my syndicated column appears in a bunch of newspapers in southeastern Ontario and Saskatchewan. And–gasp!–sometimes I actually write about stuff other than sex. Lately I’ve been preoccupied with The Good Girl’s Guide to Great Sex, but here’s this week’s column for something different. If you have children in elementary school, and you’ve tried to help them with math lately, you may be able to relate:

When I was in grade two, I distinctly remember breaking out in a cold sweat when my teacher divided us into pairs to drill our subtraction facts. I could not for the life of me remember what 13-7 was. Nevertheless, I ended that year being able to recite all my math facts backwards and forwards, because that’s how we were taught.

Maclean’s magazine ran an interesting article recently detailing how math drills are passé. Not just that, but public schools often don’t teach long division anymore, or reinforce the other algorithms we grew up with (like add up the column and carry the 1). Today they do something more visual and more complicated.

A few years ago, our family went on a trip to a Kenyan orphanage, and our local Board of education graciously donated a complete set of grade 3 textbooks to ship over. When we showed the principal of the school those textbooks, he smiled sheepishly and said, “no, thanks.” I asked him to elaborate. Uncomfortably, he finally admitted, “They don’t teach things systematically. They spend too much time teaching about calculators. And they don’t teach the proper addition and subtraction techniques.”

As I flipped through the book to see what he was talking about, I recalled a story my nephew had told me about scoring 0 on a question on a math test. The question asked, “what is 6 times 6? Explain your answer three ways.” All he wrote was 36. That wasn’t good enough, apparently.

According to our education superiors in the government ministries, we face a math crisis because children were taught the “facts” but not the reason behind them. So today they use math manipulatives, like base 10 blocks. They use different algorithms to add things up, instead of memorizing and perfecting just one. They have lattices and grids and paper strips instead of just columns of numbers.

Through these methods, we’re supposed to produce children who can think creatively, rather than children who can just recite their times tables. And the benefit of North American education over Kenyan education, supposedly, is that our children will excel in this kind of creative thinking.

I understand. But the vast majority of our students will not be software developers or engineers. They will be interior designers, who have to calculate the surface area of a room to know how much paint to order. They will be cashiers who have to make change. Or they will install flooring, and need to know how many boards to order. That’s why I would prefer we educate people to actually know what 6 x 7 is.

In Kenya, kids who had missed out on years of formal education, and who were using scratch pads with broken pencils, sitting two to a desk, could do math in grade 5 that we in Canada don’t do until grade 8. And they don’t use calculators, either.

Look, I can drive a car. I can sit in the driver’s seat, turn the key, and steer the wheel. I don’t understand why a car works, but I can get from point A to point B.

Similarly, by teaching and reinforcing the basics, at least kids could use math, and with that practice often came understanding. Now we’re trying to teach them to understand it first, but they’re not able to use it. We’re attempting to teach kids how to build an engine, but they still don’t know how to steer a car. And how well, ultimately, will someone do if they haven’t mastered the fundamentals? Perhaps it’s time to get back to basics. That’s what our grandparents did, and they knew how to make change.

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Comments

  1. Amen, Sheila! This is exactly what I have been saying for my kids’ whole lives – and why, as a homeschooler, we’re focusing in the elementary years on the basics. I do use some different techniques – particularly for my right-brained learner who has a hard time memorizing the traditional way – but the point now is memorizing the facts so that, later, they can be applied.
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    • That’s what we did, too. It’s funny, because in that article it talked about how classrooms are now using Base 10 Blocks, and fraction cubes, and all kinds of things like that, and I thought, “we used those in our homeschool, too. What’s the big deal?” But they were all excited because they were now doing this INSTEAD of the boring stuff. We did it IN ADDITION to the “boring” stuff. We didn’t replace memorizing; we just used them to enhance learning. I don’t know why people think it’s an all or nothing thing. Why can’t you still use the long division algorithm, for instance, even if you also use manipulatives? It makes no sense to me.

  2. i can’t do math. any kind of math. it makes my head hurt. :(
    molly stillman recently posted…English Muffin BreadMy Profile

  3. you’re so right!
    For the past 2 years, we have been using Classical Conversations as our homeschool curriculum. CC is based on classical education….or the trivium. The trivium says that there are 3 stages of learning in a child’s life…
    1. Grammar stage (foundational…knowledge…memorizing facts….putting a peg on the wall for later use…K-3 grade)
    2. Dialectic stage (when the child starts wanting to understand how things work…understanding…hanging information on the pegs….4-7 grades)
    3. Rhetoric stage (when the child is able to take what they’ve learned, and present it to others in conversation or oral and written presentation…application….wisdom…8-12 grades)

    understanding the different stages of learning has transformed how we educate our children.
    hope that helps someone.
    (if anyone is interested in CC, their website is: http://www.classicalconversations.com)
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    • That’s what we’ve done in our homeschool, too. The first four grades were for memorizing a ton of stuff–and they did it so well! Now they’re able to really use it. I think schools are trying to skip the Grammar step and move right to the Logic step, and you can’t do that.

      • Sorry, by your schema it would have been “dialectic” stage, not logic stage, but it’s the same thing.

  4. I totally agree! There’s no reason why they can’t be taught both–but the foundation has to come before the walls and roof.

  5. Wonderful article! This is what we’ve been telling our kids for years! We don’t let them use calculators here at home, and we will drill them, too. Wish more parents and teachers would go back to the “old” ways!

  6. I am passing your post onto my sister, who is a 6th grade math teacher who continually battles with her principal and the system because what she is supposed to teach just doesn’t produce students who can use math in their real life.

    When children don’t know the basics, they can’t keep a checkbook, can’t make wise comparisons on spending choices, and the cost of debt. They tend to make small and large choices that over time compound into problems and situations that hold them hostage. They are also at the mercy of folks who just may take advantage of them.

    Thanks for bringing attention to this problem. So many young parents are so trusting and are completely unaware of what the rest of us have been shouting from the rooftops for years.
    Kim recently posted…5 Ways to create margin in your lifeMy Profile

    • Oh, Kim, that must be so hard on your sister! I really respect teachers who WANT to teach the basics, but feel so constrained by the system. And I’ve known teachers who have been told “you can’t make kids memorize their times tables. It’s demoralizing. Just help them be able to work it out on their own later.” What do those teachers do? I would so frustrated.

  7. I commented a little on this on your wall last week, but I was/am one of those people who struggled a lot with math drills. I excelled in every subject, except math. My parents wanted to hold me back a grade. My teachers were against that because I was so great in everything else, I would have grown board repeating it ALL, which likely would have yielded the reverse of what my parents wanted (and they were right). Then my parents wanted me tested for dyslexia. Once again, my teachers explained to them that I had no other signs of anything being wrong. I was paying attention, I was trying, I was above average in everything else. Maybe I just wasn’t good at math, or maybe something hadn’t “clicked”, yet. This went on for two years. In the second half of grade 2, a teacher put piece of tape across the top of my desk that looked like a ruler. She said, “when you want to subtract, just count backwards on this ruler.” Magic. That something clicked. Nobody explained that before. They didn’t say, “you know subtracting is just counting backwards that many numbers.” No, they said, ” 11-5=6, 12-4=8″, etc. Some kids just memorized, others kids figured out the reason for it on their own, but me, I kept waiting for someone to tell me. Instead, we continued to learn by rote, the teachers continued to have me stay in at recess to finish the drills I didn’t in class and my parents continued to stand over me asking themselves out loud why I didn’t understand this as I did extra drills at home(tears streaming down my face). Of course, until that fateful day in grade 2. By that time, though, the damage was more or less done. I hated math. HATED IT. I at least knew how to subtract after that, but the mere mention of math class made my anxious for the remainder of my schooling.

    As the years went on, each time I had to master a new math skill, how fast I learned that skill depended on the teacher and whether or not s/he took the time to show us why. For example, although we did recite the multiplication tables every day, my teacher also explained that multiplying was just adding that number that many TIMES. I still wasn’t head of the class, mainly because I was convinced that I was just stupid when it came to math, but I learned and if I got stuck or forgot the answer, I knew “why”, so I could figure it out.

    Does this mean I think the schools should be focusing only on visuals and “whys”? No. I really don’t. I think it’s now overkill in the other direction. I do think that only doing drills is a poor teaching method. In fact, I think that timed drills should be at the discretion of the teacher and only used when it would be an appropriate learning tool for the majority of the class. I think in the past, we didn’t know enough about different learning styles. Now we know and we are overcompensating for past mistakes. Unfortunately(or fortunately in some cases) the curriculum is chosen and enforced by the school boards, not the people teaching it. I think teachers need to be able to be somewhat flexible and be encouraged to adapt their teaching methods each year based on their observations of the overall class learning styles. They can give individual assistance to students who really need it using the other teaching methods.

    • I said I excelled in all other subjects, but then I spelled bored as board and made a number of other mistakes. Sorry :(

    • Exactly, Rachel! It’s not an either-or thing. It should be a “both”. We used a 100-number chart to teach adding and subtracting. They just moved down to add 10, or moved backwards and forwards to add or subtract. They really got it. And we used lots of manipulatives. But I still made them memorize their facts. It makes algebra much easier later!

    • Rachel, I hear what you are saying. I have two daughters who learn very, very differently, and it was very frustrating for our daughter who was not the focused, logical, linear thinker. I do believe it is up to the teacher to show how or why to do something in more than 1 way, since we all learn differently.

      I always disliked math in school and never saw a real world purpose to it until I was out in the real world having to use the Pythagorean Theorem at my job doing drawings and having to provide exact dimensions of angled cabinet fronts. Who knew math was used in the real world? :-)
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  8. Debbie Hendricks says:

    I recently found a program that we are using to shore up math facts. It is called Xtramath.com, and seems to be working very well for my very distracted, not too good at memorizing children.

  9. I have been to stores where the employee has had to pull out a phone to addup the bills I handed her to pay. It is unacceptable, in my mind, to not be able to add/subtract whole numbers.

    • What’s really bad is if the bill is for $12.82 and you give them $13.07. That’s like cruel and unusual punishment.

      • I do that all the time! My family always is encouraging me to just give the cashier all bills rather than some change, but I do it to cut down on the change I am carrying around. Inevitably, though, the cashiers look a little puzzled. If they didn’t have the register to do the math for them, I really don’t think they’d have a clue what to do with the “odd amount” I give them.
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        • Lorrie McD. says:

          Sheila:
          I do that quite frequently. I had one incident which showed they weren’t even counting the change at the drive-thru! I told the young man that I had given him more than the total. He claimed I hadn’t. I said yes I had and you owe me 10 cents. He gave me 30 cents. I told him he game me too much. He told me “Just keep it” after I tried to give him the money back.

  10. Okay, now wait on just a minute guys. Give the cashiers a break. Not everyone does math well in their heads, just as not everyone is great at spelling out loud. Sometimes it doesn’t matter if you do drills or not. If a person’s brain isn’t wired that way, it just isn’t. Does that mean the cashier cannot add or subtract? Not necessarily. Not only that, but cashiers need to cover their behinds. They cannot be off by even a penny, and if you take 50 people going through your line up at suppertime plus 6 screaming kids running around the check-out multiplied by their frustrated parents plus other annoyed customers and a dozen price checks, well that equals a lot of room to make a mistake. How would your spelling be under those conditions? If I was a cashier, I think I would use the register, too, just to be sure.

    • not that pennies exist anymore…. :P

    • Exactly. I work at a small business, and actually have to write everything down by hand rather than ring it up, and add everything together. I group things by price, so, 2 of $6.95 is $13.90. One of $9.95 has tax of $0.80 and is $10.75. I can tell you roughly what the tax is going to be on any given purchase, just because I’ve been doing it for so long. Subtraction and percentages are involved for discounts, etc. You start to be able to figure things out without even thinking about it. I have a lot of things memorized, I don’t even have to look at the prices of a lot of things – but I double check it on the calculator anyway, and I double check the price anyway, because if I mess something up and charge a customer too much or too little, either the customer or my boss will be very unhappy.
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  11. In many subjects, teachers tend to stress the memorization of facts over the understanding of concepts. In general, I would like to see a greater trend toward conceptualization. But here’s the thing. Math subjects like addition and subtraction are foundational. Having a conceptual understanding of them IS important, but you still need to have those times tables memorized before you can move on to higher levels of math. I really enjoy math and I minored in it at college. But I still wish I had a better recall of my multiplication tables.

    • Exactly, Karen, I think that’s the point! These things are foundational (just like phonics is). Yes, the concepts are important but I don’t think you can fully understand those concepts until you get the foundations.

  12. Just to be clear, I said “how would your spelling be” but what I meant was, “how, for example, would your typing be”. I know we are talking in terms of math, but I’m trying to make a point lol.

  13. Not your grandmother’s math, indeed!!! I’M a grandmother now! And I’m struggling with my Kindergartner’s elementary learning. I’m not sure I should say this but I think I may see homeschooling in the future. We definitely need to get back to basics!!!
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  14. I don’t have kids yet, but I’ve seen a lot of parents online saying they have no idea how to help their kids with their math homework! It kind of scares me for when I have kids. I’ve always been good at math, but who knows if I’ll be able to figure out how the kids are “supposed to” do it by the time I have to worry about it!

  15. I agree that math skills are fundamental–tools that make more complex thought processes, like calculus or algebra, easier later on. I’m not the best “DRILLER” homeschool-momma, but I did buy the Flashmaster (awesome little device), which helped the kids practice those times tables repeatedly. I’m so excited to see them learning to apply those fundamentals to the trickier concepts now that they’re older.

    BTW–this applies just as much to basic grammar or reading skills. I’m saddened to see many traditional grammar tools, like diagramming, biting the dust. Diagramming helped me “see” where words fit in sentences, and verb conjugation memorization helped TREMENDOUSLY with learning foreign languages.
    Heather Day Gilbert recently posted…Faith and Family Friday–HELP ME PLEASE, MY KIDS ARE WILD!My Profile

    • Oh, I LOVED diagramming sentences when I was young! I made my kids do it, too. They weren’t as fond of it, but it really stressed the whole dangling participle problem! And phonics are so important. I’m amazed at how many teenagers can’t sound out complex words.

  16. I’m a teacher (not math, thank God), and I get why kids need to learn how to think creatively, not just how to memorize. Bloom’s taxonomy lists memorizing as the bottom level of learning, and that shouldn’t be the stopping place. Also teachers are under so much pressure with standardized testing that I’ve heard many math teachers say there just isn’t time to do times tables or drills. The calculators allow teachers to focus on the material that will be on the test, since they rarely get to cover all of it anyway and their jobs often depend on how well students do.

    In my humble opinion, the direction education needs to go is to make sure teachers are highly qualified and then let them decide how best to teach the students they have. Teaching is part science and part art. Instead, states are going to more of a scripted approach where teachers no longer have much say in the methods they use. An ideal education is a mixture of teaching styles that reaches all students one way or another, but our current education system doesn’t necessarily allow that to happen.

  17. For once, I’m not sure I agree. Yes, I agree that at first, kids need to just memorize the math facts, but the way we learned by adding the one’s place, then the 10s place, carry where necessary was “new math” in the 50s — check out Tom Leher’s song “new math” http://www.youtube.com/watch?v=8wHDn8LDks8.

    My understanding that what they are teaching now is more the way a calculator does it. Hubby could explain, but he’s not around. Honestly, I don’t know if what they are teaching now is less or more or what, but yes, I think kids should be taught to understand! We have such a tendency to say “well, I don’t understand, and I can still do it, so screw it” which is what has resulted in our dumbed down culture.

    I suspect that I’ve misunderstood something here, I’ve probably over- reacted some. Please correct me if I have!
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    • The problem as I see it, Rachael, is that they are teaching kids to understand it but not to do it. There is no one formula, for instance, for adding up a column of numbers. There are numerous different formulas, and they use a different one each week. They don’t teach the typical algorithm for long division. They don’t insist that you master your times tables.

      Without these fundamentals, you’ll never really be able to do algebra. For instance, if you have the equation x2+x-56, and you have to solve it, you have to be able to figure out what multiplies to -56 and what adds to 1 (in this case, +8 and -7). But that’s really hard if you don’t know, in the first place, what multiplies to 56. To do high level math, you just have to “know” it.

      So if all they’re teaching kids is how to conceptualize something, but they’re not actually teaching them how to “do” it consistently, they’re going to have big problems in high school, which is exactly what we’re seeing.

  18. To me, understanding is super important. I cannot learn something until I understand it. When I was a kid, if I didn’t understand something, it became a huge scary thing that I would puzzle over and stress over and inevitably give up. This included math – and horror of horrors, diagramming sentences. I was reading chapter books at the age of five, I was reading big fat classics at the age of eight, but I couldn’t diagram a sentence to save my life because it just didn’t make sense to me. Things really have to completely click in my head before I can remember and apply them. Otherwise, it’s just a big tangle that I can’t make sense out of.
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  19. Amen sister…. can’t help my 7th grader with his math anymore….we can get the right answer, but we don’t get there the “right” way!

  20. This is exactly why I love classical education, because it teaches the straight facts first and THEN teaches the theory and principles underlying the facts. And after that, it teaches the students how to adequately express the truth they have learned. Our country took a wrong turn when it started moving away from classical education back in the early twentieth century.
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  21. AMEN SISTER! I homeschool, and I have decided that my babies should learn FACTS first…. we are drilling multipication with my 2nd grader right now, we don’t move on until she knows the table we are working on both front and back!

    This has also been a hot topic among me and several others…. it is bad when a computer breaks down at a local store and the cashier stands looking at you dumbfounded because he/she has NO CLUE how to make change. When I worked in high school at a grocery store we had to count the change back from the total. I told my cashier how to make change the other day…… she looked at me like I had worked a miracle and then asked “How did you know how to do that?” SERIOUSLY…. is public education really giving our kids and education???? I could really get on my “soap box” about this!!! I don’t blame the Kenyan I would have refused the books as well!!!!

  22. My daugher is still a few years from Kindergarten, but I keep hearing articles like this and they make me nervous. I sill have a hard time with math, and am starting to seriously question if I’ll be able to help my daughter with homework when the time comes.
    I have been starting to consider homeschooling instead of public schools because I agree so much with what so many others have been saying. I do wonder if I CAN homeschool, I know it takes a lot of work (and that’s fine) but I don’t even know where to begin….

  23. Allyson Jordan says:

    I completely agree! I used to be an Early Childhood Education major in college (but have since switched to Psychology) and had to take this class called Math for Elementary Teachers. We went over the classic way of adding, subtracting, etc. as well as some of the other algorithms that are out there. Even being a sophomore in college at the time, it was so hard for me to grasp some of the algorithms that emphasized understanding why 2+2=4 rather than knowing how to actually use it because it wasn’t the classic way that I learned. I would also agree with what others (and you) have said, though, too. Not everyone learns the same way, so memorizing addition tables to learn the facts may not work as effectively as some would hope. I definitely agree that a “both” approach is the best.

  24. A recently retired education correspondent for a national newspaper in the UK explained it to me as a difference between “Concepual Maths” and “Functional Maths”. I have found it annoying when I have gone into a store and the total amount came to GBP 8.18 and I have handed the assistant a ten pound note and a twenty pence coin, and been given the twenty pence coin back, then I have had a one pound coin and eighty-two pence in change, especially when the assisitant has apologised for giving me small denomination coins because ‘we havn’t got any fifty pence pieces right now’.

    I do not know about Canada and the US, but I do know that in the UK there is concern raised at “Grade Inflation” where the results are better each year and so, where before an employer might have hired someone with “Ordinary Level Certificates” they now want “Advanced Level Certificates”, and so on until graduate level jobs now include jobs that 25 years ago went to “A” level candidates.

  25. Grace H. says:

    As someone who works in high school math, I can see both sides of the issue…

    Students MUST know their fundamentals. It is a waste of everyone’s time to pursue ‘higher’ maths if you can’t add/subtract or have a grasp of basic math concepts. Students, parents, and teachers need to be willing to put in the time reinforcing these if they are weak (outside of a high school course). Teachers need to stop passing students who don’t understand the material. Parents/students, stop pressuring teachers to ‘just pass’ a student who doesn’t get it yet grasp the material – it’s a disservice to everyone involved.

    The new Common Core standards in the US focus a lot on reasoning and application – they take a different approach than what parents may be ‘used to seeing’ in math, but the expectation is to provide students the logic to reason through a real-life situation and the math skills to execute that plan.

    Lastly, those of you who would like to review math (or some other subjects) for your own knowledge or to help your students, you may want to check out http://www.khanacademy.org/ – there are tons of well-explained examples to help grasp a concept, from arithmetic & pre-algebra all the way up to college-level materials.

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