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?”

Psalm 11:3

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.

All right, I was wrong. You should have given the fractions speech. Sorry. It could have been a interesting topic that would have been not only your forte but educational as well.

Miss you,

Nean

Wow — a comment from the missus! No, sweetie, I think you were right. And just think of all the family photo albums we improved from that speech!

Miss you, too,

Wallace

If memory serves, such studies have been done (studies have been done on just about everything), and confirm your hunch (and mine from experience) that it trains the mind for later things. (So does music, which is founded in mathematical relationships — but that’s another topic.)

A.A. Milne and his son Christopher (Robin) Milne both were in scholarship form in mathematics as children and teens; and while neither actually went that route professionally, both believed — with great merit, I submit — that “maths” laid much of the foundation for their actual careers.

Christopher Robin’s grade school teacher was puzzled by C.R.’s quirky insistence that he could do hard sums but not easy ones. (I know how he felt; I was very much the same way! I hammered algebra and analytical geometry in principle, but my simple mistakes constantly tripped me up in practice.)

Again “when he was very young”, C.R. was asked by A.A. to recite the numbers in order.

C.R.: One, two, three, four… (to however far he went before he was interrupted)

A.A.: How far can you go?

C.R.: (quizzical look) To the end!

A.A. wrote that this answer appealed to the latent mathematician in him…

If you follow the link provided with my name, you’ll see the take that the comic strip “Rose is Rose” (Monday, March 17 edition) has on this issue… 🙂