My wife is also a teacher, although she is of the math/science variety as opposed to my music/social studies focus. In the past couple of years there’s been quite a bit of angst where we are in Alberta about the ‘New Math’, and so I get quite a bit of information on that subject.

A quick aside for those of you that are either not aware of or just hazy on what ‘New Math’ is. The math curriculum in Alberta (and many of the curricula across Canada, as well) was revamped in the past few years to explicitly downplay ‘basic skills’ (this would be like those times-tables worksheet many of my and earlier generations did) and try to emphasize ‘discovery learning’ or ‘progressive education’ (letting student find their own *personal* approach to something like long division – also can involve teaching 5-6 different methods and letting students pick the one they favour). This wave is commonly referred to as the ‘New Math’ and is widely debated amongst education professionals and parents alike.

Okay, back on track. I’ve written before about the downwards trend in Canada’s international math scores rankings. The occasion that prompted this entry was a great article in this weekend’s Globe and Mail (I am a shameful sucker for a real print newspaper – I just love the feeling of reading a paper with a big cup of coffee). It talked in great depth about the ‘problem’ of math in Canadian education systems today, and examined both sides of the ‘New Math’ versus ‘old math’ debate.

I, of course, showed it to my wife, since she is intimately familiar with the material. She read it over, chuckled at a few lines, and tossed out a few ones that she really thought hit the mark. She only asked me one question throughout the entire reading, near the end, but it crystallized for me exactly what I felt about this debate.

The question she asked dealt with the following passage:

“Both sides like to use a music analogy to make their case. The ‘basic skills’ camp asks: Can someone become [sic] proficient musician without learning the scales and where the notes sit on the staff? The ‘progressive education’ side counters: What’s the point of drilling young musicians on scales, if they want to give up the instrument as soon as their parents will allow?”

After reading that, she turned to me with a bemused smile and asked: “You’re a musician; what do you think of that comparison?”

My reaction was instantaneous and obvious – it’s a ludicrous question. I would never ever spend all of my instructional time drilling only scales or only note names. That, as astutely noted above, leads inevitably to frustration and boredom, especially with younger, less-disciplined students.

However, neither will I ever spend all of my instructional time allowing students to ‘discover’ for themselves what the note names are. You’re not going to ‘discover’ that A440 is A440 by intuition and problem-solving, because it’s an arbitrary label. That’s something you just have to memorize. Stuff that falls into this category also might include getting students to ‘feel’ and ‘listen’ their way towards playing a familiar tune. You can do some of that, but more complex songs are out of their reach without at least some guidance on where to start (which you can’t have without basic knowledge such as note names, key signatures, etc.).

It’s worth noting that most teachers I have met and talked to feel similarly about this whole ‘New Math’ thing – there are some really good ideas in there, but it can be confusing and the de-emphasis of basic skills does not do much to ease anyone’s passage through the higher levels of math in particular.

I think that you don’t need to be all-or-nothing on this issue. There’s no sense in completely disregarding some things that we know work. We know that memorizing times-tables and such really does have effects on your ability to perform more complex calculations. However, we also know that merely having students sit in rows and recite mindless lists does nothing for their engagement or problem-solving skills.

So, as it turns out, the healthy balance is necessary. Just as I cannot produce an Alain Trudel or Wynton Marsalis without some basic scales and drill work, neither will I stifle that burgeoning mastery by forbidding them to play something that speaks to them until an arbitrary line of 12 memorized scales and reading in multiple clefs is crossed.

A final thought, again mostly from my wife: she mentioned as she finished the article that most teachers agree that you need a well-rounded math curriculum that doesn’t simply forget about basic skills. She also concluded that this is what happens when you have an education system being run by people who have no background or experience in education. Just as you don’t want a math teacher who actually has no math training (which is *whole* other can of worms, by the way; it is scary how many teachers get thrown subjects that they have no previous training in because of lack of funding), it’s mind-boggling when you look down a list of the ministries of education in Canada and realize how few of the major officials have any experience in a classroom.

Let’s stop worrying about doing things one way or another, but designing a system that allows the people in it to take all the best elements and use them effectively for the good of those that really matter – the students.

I’m in no position to talk too loudly given my own inexperience, but I would like to mention that here in America, we have the ACT I’m sure you’re aware of. My state just passed a law that, if experimentation proves fruitful (notice the law comes before the experiment), the ACT can be used as a “high school exit exam.” 10 schools are already going to be using this; students can NOT graduate without a certain ACT score.

So you have the typical Algebra I -> Geometry -> Algebra II sequence. Guess what’s now taught in each class? A hodgepodge of ACT related problems with no cohesion or linking of subjects. You had to learn about parallel lines and transversals and congruent triangles to make sense of parallelograms, which are later needed to prove ideas in right triangles. You need to do operations on like terms before you can factor equations.

This is high school level math, but the point I’m getting at applies to any level: I think rather than being concerned with test scores or whether or not a “type of math teaching” is good or bad, we need to emphasize the skill set of the teacher. Teachers should be allowed to come up with their own manner of teaching children and the textbook be relegated to “mere reference” and a set of problems homework and quizzes can be assigned from. “Math Education” should simply be a collective pool of experienced people’s ideas that we can draw from to help us go through various topics: I find myself pretty good at explaining most algebra and geometry topics, but I can’t explain mutually independent events for probability and statistics because I never had much training in that area (which you hinted at in your own post about teachers and training).

Instead, the pressure seems to be “you WILL teach THIS method and that’s all.” So I merely wish to expand your final thought: “…designing a system that allows the people in it to take all the best elements and use them effectively AT THEIR OWN DISCRETION, TO THEIR OWN ABILITIES…”

I say that entirely in the context of “every student learns differently. So, too, does every teacher teach differently AND at different efficacy levels within each topic.” Again, I may be an overall competent (or I hope!) teacher, but there are some topics I simply will not explain very well.

The pressure is always “here is THE method, use it to be good at your job”, especially when the government body doesn’t actually practice in the field. Politicians get elected on easy-to-grasp sound bytes, which of course fall flat on their faces in the classroom.