Thursday, February 4, 2016

Math wars confusing curriculum and pedagogy

Recently, in the media there has been a lot of false statements around the WNCP curriculum, and consequently these attacks fall on the hands of teachers.  Before I continue I will explain two important words in the educational world.

Curriculum: This is simply WHAT a teacher needs to teach.  For example, a Grade 3 student needs to be able to recall and understand up to 5 x 5.

Pedagogy: Is HOW the teacher teaches.  For example, using direct instruction, peer coaching, PBL, etc.

Contrary to social media, presentations, and other means of critiquing the curriculum, the curriculum does not say:
  • How teachers need to teach the outcomes.
  • Discovery learning is a must. In fact the word discovery does not appear once in the entire document.
  • "21st Century skills development", and "experiential learning".  Neither of these phrases appear once in the entire document.
  • Students should not be memorizing their basic facts.
Keep in mind that the curriculum is the WHAT not the HOW nor even the WITH WHAT.

Recently, an event, around public education, was held in Calgary at a private, gated school. The event was designed to inform parents of "the best practices in math".  While the event was designed to encourage change at the government level, make no mistake this was a blatant attack on math teachers in Alberta, and other teachers in provinces following the same curriculum.

 Here is one of their recommendations:

Now as you can see "Teaching Strategy" does not fall under curriculum but actually pedagogy.  The irony is that I am sure all teachers, at some point, do some direct instruction.  I have had the honor of being in many math classrooms around the province and I can attest that teachers have balance.  This slide almost paints the picture that teachers are simply sitting around hoping that students will learn math through osmosis.   Also, there is no "imposing of one model of instruction".  Enter a classroom and you will see that teachers truly implement strategies which are the most beneficial based on the classroom make-up and the outcome(s) being taught.

Next we have "Some things to watch out for"

Of course some of these points make sense.  We should be wary of many phrases as their intent could be misguided. Also, in reference to the second point, no one is arguing against memorization and procedures.

For their third point, I have not met one person who suggests that students should not memorize their math facts. The difference is, however, students should memorize these facts out of application and use, not out of necessity.

This means, show students math in a context and for a purpose, and the memorization will occur.  Have students roll dice, play cards, board games, car games, etc, as most (if not all) games have some link to reasoning, logical thinking, and mental mathematics.

"Understanding is not more important than skill"- This is again in reference to the actual art of teaching in the classroom.   I have yet to meet one teacher who denies that skill is useful, but let's remember if we only focus on skill then learning can be disguised with simple memorization.

So why is there such an attack on the curriculum?

I believe because some are confusing the terms curriculum and pedagogy.   Also, because we have a generation (parents) who learned math through memorizing algorithms and are confused around why their own children are not coming home with the same algorithms. Recently, some parents are now seeing the benefit of the change.

Also there has been use of the drop in PISA scores, however there has been no actual evidence that this drop has been caused by curricular changes.

The confusion, for a child, might start when a child is learning one way at school, and then coming home to hear that the strategy is not right.  We must also realize that teachers are trained professionals around education.  These professionals implement effective instruction based on the individual needs of the students.  It is unfortunate that some want to see the art of teaching go to a procedural task of "tell students what to do, ask students to imitate the learning, repeat".

If you have a question around the math your child is learning, phone the teacher.  Social media, news, and other hands not in K-12 education, have a way of distorting the truth.  Keep in mind that teachers are trained to teach your child math in a way that is meaningful, and creating a passion towards numbers.

I remember back when I was in school and how there was an immense number of people whom hated math.  It seemed as if math was the number one hated subject in school. (No research simply guessing here).  Isn't it time this changes?  Isn't it time we cultivate passion and number sense?

Math class needed a change, and this change is healthy.  There is now balance.  Before there was a focus to teach it one way and all students were required to learn that one way.  Finally, alternative efficient strategies are not only accepted but encouraged!  We are allowing students to not only learn math, but actually like it!


  1. I keep insisting that the problem is neither curriculum, nor pedagogy, but the school system's insistence on moving students on to the next level even when they are not ready for the next step.
    We ask that teachers move on to build the next floor when the previous one is not safely completed. No wonder the building collapses at some point and people end up hating the whole idea of that building!
    In school I ended up hating poetry because I was not given the foundations for understanding it, I was only asked to memorize some poems and move on to critical analysis. The same happens in math on a larger scale.
    Does that mean that we should fail more students? NO! it means that we should assist them in achieving the desired objectives and skills before we move them on. Instead we now either label them as unsuited for math (or worse) or ignore their difficulties and ask them to do something about it, even though they don't know what to do.

  2. People like me (a retired math prof) have a great deal of trouble distinguishing between curriculum and pedagogy. I think that’s due to our not having any experience in the K-12 setting. I have opinions about the current Alberta curriculum (mostly favourable), but I try to shut up when tempted to offer advice on how to teach it. Like some of my colleagues, I’m not always entirely successful in that regard. Thanks for a useful post.

  3. In regards to your comment "Math class needed a change, and this change is healthy. There is now balance. Before it was taught one way and all students were required to learn that one way, and now alternative efficient strategies are not only accepted but encouraged! We are allowing students to not only learn math, but actually like it!"

    I completely disagree with how you stated it...SOME classes need a change and MANY classes have been doing exactly what we are saying "new" math is for a very long time. Good teachers (of which there are many) have ALWAYS allowed for exploration of different strategies to help develop a child's understanding of the math curriculum.

  4. Sorry to see that the Math Wars are breaking out again in Canada, though I suspect that like here in the US, they've never really stopped since the 1990s (or the 1960s/70s in some ways). The history of efforts to improve mathematics education in the US & Canada needs careful study going back about a century, but very few people who weigh in on these issues have done so. A good starting place is Jeremy Kilpatrick's chapter, "Mathematics Education in the United States and Canada," in Handbook on the History of Mathematics Education (2014). There is also Christopher J. Phillips' THE NEW MATH: A POLITICAL HISTORY (2014). Any book on the subject that treats "the New Math" movement that emerged after Sputnik as some monolithic entity is not to be trusted. Neither is any text or author who treats the late-20th century efforts of NCTM and similar organizations to reform math education as either a monstrous case of mad scientists gone wild or of beneficent and omniscient educators with flawless ideas and programs. The viciousness of the US Math Wars is such that it's difficult if not impossible to discuss these sorts of issues with anything close to fairness, at least if people from opposing camps are involved.

    Unfortunately, it seems from what you refer to that not much has changed. Much of the rhetoric and arguments could have been lifted from the 1990s websites for Mathematically Correct and/or NYC-HOLD, two organizations that fiercely opposed pretty much anything and everything that emerged from what I would call progressive reform efforts in the late '80s and right through to aspects of the Common Core's Principles for Mathematical Practice.

    I wish that we had made some progress in the last 25+ years on these issues, but it seems like the arguments and attack methods of traditionalists have changed very little. And the political odor that surrounds their efforts remains hard to ignore. This isn't the first time such things have erupted in Canada; it certainly won't be the last (though perhaps things are less confused by issues such as the Common Core, anti-Obama sentiment, and the like). The fight for reasonable teaching methods and content goes on because unfortunately there simply are not enough competent teachers, particularly at the K-5 level, who allow for exploration of different strategies and who are able to fearlessly guide students through the complexities surrounding elementary mathematics.

  5. 1. I have met a university professor in education that argued vehemently against memorization of times tables, even when done purposefully and without drill and kill. Simply, no one should bother to memorize those. And probably that's the message (s)he's giving her student teachers.
    2. Curriculum does specify, to a certain extent, how one is supposed to teach, via the achievement indicators. Take grade 7, outcome on solving linear equations; the outcome says solve linear equations pictorially, concretely and algebraically (quoting from memory), and the achievement indicators say the tiles method, the balance method and the algebraic method (probably other items too); I understand the goal of the achievement indicators, but many teachers don't, and they teach and test all achievement indicators, which means the curriculum is, at least in practice, and at least in some cases, telling teachers how to teach.

  6. I have heard a lot about the right methods to teach Math. It is a very tricky subject to make student happy about learning. Since it is challenging for some kids to process you have to really be engaged in the process and make Math interesting for your students. I appreciate the effort to ease the pain of teaching math for all the teachers. I guess that even coursework writers online would agree that writing is easier than doing math. This article, however, explains the methods in a way that will be useful for many people involved in the process of learning.