Just a brief comment today… [BTW: Is that one of the best indicators on my blog that it is not going to be a brief comment? Maybe I need to work on Matthew 5:37…]
I read the following (from an AP article by Nancy Zuckerbrod) in the St. Louis Post-Dispatch today:
“Schools could improve students’ sluggish math scores by hammering home the basics, such as addition and multiplication, and increasing the focus on fractions and some geometry, a presidential panel recommended Thursday.”
You can read the online article yourself, here.
I know it almost sounds like a no-brainer: “Kids have trouble in math if they can’t add, multiply, or do fraction stuff? Duh!” But if you’ve been in the business of educating children on mathematics, you realize that there is a whole culture in America that is focused on not properly establishing those fundamentals. After all, the (sad, persistent) argument goes, calculators can do those things now, so why teach the kids how to do them?
I don’t have enough time to go into the “why” in any detail at all, but the fact is that learning to properly do addition, multiplication, and fractions without a calculator does more than give a child skills in, well, adding, multiplying, and working with fractions. It makes necessary changes in the brain and mind that prepare it for later work. And the skills that are fundamental to doing these basics calculator-free are inherent elements in skills that will need to do later work in more advanced mathematics (like algebra, which the article mentions).
The former statement of those last two may seem like speculation on my part (which it is; I certainly have done no studies). But the later statement is undeniably true, and if you have taught algebra you probably recognize that fact. For a brief time before I needed to change careers, I did some summer work as a consultant for schools that were switching over to a “block schedule” format, in which kids go to the same classes every other day (e.g., Algebra on Monday, Wednesday, and Friday on “A” weeks, and on Tuesday and Thursday on “B” weeks). Such an arrangement always produced anxiety in the math department — anxiety which I believed from personal experience was justified. However, there were ways of surviving, and one of those techniques I taught was “piggybacking” mathematical concepts: taking maximum advantage of connections between early topics and later topics that share identical or very analogous skills — for example, adding fractions with different denominators in arithmetic and adding two rational expressions in algebra.
Most math teachers will tell you that math topics build on each other, but the extent to which the topics do so and the extent to which some skills are almost unchanged from the top of the structure to the bottom is rarely fully grasped. (And personally, relegating all the fundamentals to our increasingly-capable electronic calculators is like saying, “Hey–we have cars and Segways now: why walk?”)
The state of American mathematics education (and the brief article helps communicate how dreadful that state is) reminds me of one of my favorite verses from Scripture:
“If the foundations are destroyed, what can the righteous do?”
Frankly, it’s nice to see some “official” recognition that it is the truly the foundations that need attending to. There are some great math teachers out there struggling with all they have to build on broken foundations. Maybe this report will help.
On a side note… I am reminded of a meeting of our Spokesmen Club in Dallas, Texas, many moons ago, in which I was assigned to give an “Instruct” speech — that is, a 6-minute speech in which I teach those assembled how to do something that would be in some way profitable to them. The event was going to be a “Ladies’ Night,” so my Beautiful Wife would be attending as a guest, along with other wives and female guests. The speaking was going to take place after a nice meal in a local restaurant.
In the days leading up to the event I wanted to speak with my wife on the idea I had chosen to develop for the speech, because I appreciate her insight. Her comment below is pretty much an exact quote:
Me: Hey, sweetie! For my “Instruct” speech at the Ladies’ Night, I was thinking of explaining how to add and multiply fractions properly. What do you think?
Beautiful Wife: Well, that sounds like a great idea. But please don’t be offended if you see me sitting in the audience with a fork stuck into my leg to keep me awake.
I gave a speech on how to take better photographs.