Math and Your Brain

I found this article from the New Yorker courtesy of M-MV.
Thanks!

And if evolution has equipped us with one way of representing number, embodied in the primitive number sense, culture furnishes two more: numerals and number words. These three modes of thinking about number, Dehaene believes, correspond to distinct areas of the brain. The number sense is lodged in the parietal lobe, the part of the brain that relates to space and location; numerals are dealt with by the visual areas; and number words are processed by the language areas.

Nowhere in all this elaborate brain circuitry, alas, is there the equivalent of the chip found in a five-dollar calculator. This deficiency can make learning that terrible quartet—“Ambition, Distraction, Uglification, and Derision,” as Lewis Carroll burlesqued them—a chore. It’s not so bad at first. Our number sense endows us with a crude feel for addition, so that, even before schooling, children can find simple recipes for adding numbers. If asked to compute 2 + 4, for example, a child might start with the first number and then count upward by the second number: “two, three is one, four is two, five is three, six is four, six.” But multiplication is another matter. It is an “unnatural practice,” Dehaene is fond of saying, and the reason is that our brains are wired the wrong way. Neither intuition nor counting is of much use, and multiplication facts must be stored in the brain verbally, as strings of words. The list of arithmetical facts to be memorized may be short, but it is fiendishly tricky: the same numbers occur over and over, in different orders, with partial overlaps and irrelevant rhymes. (Bilinguals, it has been found, revert to the language they used in school when doing multiplication.) The human memory, unlike that of a computer, has evolved to be associative, which makes it ill-suited to arithmetic, where bits of knowledge must be kept from interfering with one another: if you’re trying to retrieve the result of multiplying 7 X 6, the reflex activation of 7 + 6 and 7 X 5 can be disastrous. So multiplication is a double terror: not only is it remote from our intuitive sense of number; it has to be internalized in a form that clashes with the evolved organization of our memory. The result is that when adults multiply single-digit numbers they make mistakes ten to fifteen per cent of the time. For the hardest problems, like 7 X 8, the error rate can exceed twenty-five per cent.

Now I understand why giving my son copywork for his mutiplication tables works to help retain his "math facts." Knowing 3x7 is a linguistic skill more than a numerical skill.

And, for the record: Evolution is a theory, not a fact. Adaptation is a fact, not a theory.

Weekly Report #2

It was a short week. In fact, it isn't over yet as we still have today to get through.

But I am quite excited about what we have done, this week.

We finished SoTW chapter 9.

We got caught up in Grammer with the boy and he pretty much has his diagramming of subjects and predicates figured out at last.

The girl is up to lesson 127 in FLL and we're now getting into dictation. She's handling it without any trouble, much to my surprise. She was so delighted with the fact she got it right, yesterday, she wrote it again!



I've got over my fear of Memoria Press's Christian Studies 1. The boy continues to astonish me with his grasp of the Bible. It isn't taking a lot to elicit some fairly deep thoughts.

I've switched back to using the Vos Story Bible with sheets from Calvary Chapel for my daughter. She loves this. She hasn't really gone through the Old Testament this way. (We used it for the New last year.) One night this week, she found that I had printed off new sheets--and all of a sudden she had to do them. Never mind it was bed-time! So, I had her Dad read the proper chapter.

Later, I asked her how it went and she pouted, "Daddy wouldn't help me."
"What do you mean?" I asked her.
"He wouldn't spell 'cursed.' He just sounded it out."

Oh dear. Teaching can really change the dynamic between the Princess and her Daddy! (Probably for the better.)

There are just two other things I want to highlight from this week.

My son and I continued on with Aesop A. This week we were to identify sentence types. I was frustrated with the instructions in the teacher's book when it told me to go back through the previous week's model to identify the different sentences as this week's model was written entirely in declarative sentences. What on Earth? I wondered. Why would they do that?

Then it occurred to me--ahh, it's easier to change them! So, I suggested to my son that we re-write Androcles and the Lion using different types of sentences and he was stumped until he took my suggestion to tell the story from Androcles's point of view. We had a great time re-writing it. I'll have to post it tomorrow, though, as he isn't finished typing it up on the computer yet.

Lastly, and most importantly, my son hit a wall with long division. I've spent a lot of time this week over at the WTM boards hashing this out. With the wonderful suggestions from the women there, we are beginning to get through it.


We did some physical exercises that involve crossing the mid-line (mostly a bunch of figure 8's and swaying our arms from left to right and from upper left to lower right.) I wrote his problems on graph paper and pre-drew the subtraction lines. I sat down beside him and worked on each question with him as he went along. It took us 30-45 minutes to do 8 questions, but they were done perfectly, and we "talked through" every single step.

We're going to do that today and every day until he gets impatient with me and just does it himself. I'm not sure the wall is scaled yet, but it is at times like these that I am so grateful to be homeschooling. What public school teacher could possibly have time to do all that? How could he hit that wall and not come away feeling (needlessly) ashamed of himself?

This is exactly where he would give up on school, if he hadn't already. When I brought him home at the end of Grade One he was already calling himself stupid and had zero tolerance for his mistakes. Let's hope he gets over this wall quickly, though. My daughter needs some intense one on one work for three digit subtraction with borrowing!

As for me, I started making up our spreadsheet to plan out the year. I have finally stopped fretting about how behind we are and accepted the fact that the work we have to do is just the work we have to do. I'm still fiddling with it, but I've finally lost the anger and despair I had had about our very long break last fall. So, we're on week 7 of a 40-42 week year. I'm just trying to do my best to make sure the load isn't too heavy during the summer.