Tuesday, July 1, 2008

Why memorize facts?

One day, few years back, my principal called me in to her office. She knew I had been researching "new math" and "fuzzy math" and she had a related question.

It seems that a parent of a younger-aged student had questioned why their daughter needed to learn math facts. The teacher of the girl's class had been working on speed drills for math facts and the father was disputing the need for knowing the facts. My principal wanted to get my take on the subject.

The battle is on-going indeed.

So, is memorization of math facts important? You or your student will be confronted with this dilemma, sooner or later, and we need to be prepared. "New math" tells you your child doesn't need to be forced to do the pencil and paper work of the "drill" of traditional math. Your child needs to learn what "8 X 9" actually means, and he/she can always calculate by drawing groups. But your child will understand how to do it, and that's what is important!

According to an article in the March 14, 2008 issue of The New York Times, a recent report, presented to Education Secretary Margaret Spellings by the National Mathematics Advisory Panel (March 2008), addressed the
importance of mastering the basic facts.

The report stated that it is important for students to master their basic math facts well enough that their recall becomes automatic, stored in their long-term memory, leaving room in their working memory to take in new math processes.

"For all content areas, practice allows students to achieve automaticity of basic skills -- the
fast, accurate and effortless processing of content information -- which frees up working memory for more complex aspects of problem solving," the report said.

According to the NYT, the report found that "to prepare students for algebra, the curriculum must simultaneously develop conceptual understanding,
computational fluency, and problem-solving skills."

The report also said that prekindergarten-to-eighth-grade math curriculum should be streamlined and should focus attention on skills such as the handling of whole numbers and fractions.

Read the entire article here.

By even the 5th grade, the number of steps in problems necessitates that students know those facts quickly so they don't get bogged down in recalculating the facts several times while solving the problem.

The above report stated that by 3rd grade students need to have addition and subtraction facts mastered. By 5th grade, students need to have multiplication and subtraction facts mastered so that they are quickly put to use.

So work with your student on math facts. This is one thing students can do over the summer. Practice, practice, practice.


Barry Garelick said...

Memorization does not go away no matter how high up in math you go. It is not the mark of a backwards program if a math course requires certain formulae to be memorized. Certain trig identities for example are better off committed to memory, even though math reformers would have you believe that if you really need to know something, you can look it up.

Well, OK. Let's look at a typical problem in calculus. A gutter is to be made of a strip of sheet iron 3a inches wide, the cross section being an isosceles trapezoid. Assuming the base of this trapezoid is "a" inches wide, find the width across the top giving maximum carrying capacity.

First of all, this isn't some contrived 'real world' problem; it is a pretty good problem that oomes up in various engineering design situations. Second of all, it requires that you know a lot of things. You have to know what an isosceles trapezoid is. You have to know how the carrying capacity (volume) is calculated; specifically that is a function of the area of the isosceles trapezoid. And you have to know how to compute the area of a trapezoid.

You then have to set up a function to represent the various knowns and unknowns. If you are doing it based on angle of the bend, then you need to know your trig functions. And when you do your computation of area, and then differentiate, you will have to know your differentiation formuale, and how to factor appropriately to get it into proper form for solving.

The higher order thinking step is setting up the equation of area as a function of angle of bend. All the rest is "merely" algorithmic. I put "merely" in quotes because if you have to take the time to look up what reforms consider to be a bother, you will spend far more time than this problem should take. If you know your stuff, you can solve this problem in 5 or 10 minutes.