PROCESS:

Prefrontal cortex recognizes need for data

Math fact data “delivered” to prefrontal cortex

Prefrontal cortex combines fact recall with rules and patterns, resulting in skilled problem solving

Pictures at www,mathnook,com/blog

** Why Fact Games Work **

Readers of this column know that we at www.mathnook.com believe that there is value to rote memorization, but that “skilling, drilling, and killing” students with facts and procedures simply kills kids’ motivation to learn, or even to try. It seems like an impossible dichotomy, but in fact, there is a simple analogy to something we all encounter on a daily basis. Do you have an old computer, a warhorse relic from ten or more years ago? Other than warning you to check continuously for viruses on your XP machine (please don’t pass your viruses to us!), I want you to remember what it is like to try to stream a movie, write music, or develop your own graphics with a machine that was built long before Netflix and the Adobe Creative Suite™.

You are sitting there fuming as your machine keeps saying things like, “Adobe Creative Suite (not responding).” You are tempted to yell at it, “You’re a machine! Stop ‘not responding,’ respond!” Finally, you slam down Ctrl-Alt-Delete and find out that your CPU usage is stuck at 100%. Permit me this geek moment, but I can explain just why this is happening.

Let’s say that your computer has something like 2 gigabytes worth of random access memory (RAM). Adobe Creative Suite™ requires almost all of that for the program to work. The closer you get to full utilization of your computer’s RAM, the more your CPU (central processing unit) takes over the work, which slows your computer down like the carapace on a giant turtle.

Is your child, or your classroom if you are a teacher, trying to compute with too little RAM? If so, the part of the brain that we think is responsible for storage and recall of math knowledge is underutilized, while the parts which should be retrieving the data from centers like the parieto-occipital sulcus, is busy pretending to be RAM. You can buy more RAM quite cheaply for your computer. Why not buy some more RAM for your problem-solving centers to query, by getting the math facts out of the way? Relegating facts to the random-access memory part of the brain frees the prefrontal cortex to organize itself around problem-solving, not fact recall.

For an example, let’s look at the long division algorithm. On the left of the table below, you will find the step, and on the right, the brain processing step that should go into applying stored data. We are going to assume a neurotypical student with at least an adequate storage for math facts and rules.

Step Brain Process

1. set divisor outside the box and dividend inside it Rule recall

2. Estimate how many times the divisor will fit into the dividend, or into the appropriate place value of the dividend Higher-order processing

3. Multiply the divisor by your estimate in step 2 Fact recall; maybe recall of multiplication subroutine

4. Subtract result in Step 3 from dividend Fact recall, application of place value (higher order knowledge) and regrouping rules

5. Repeat (iterate) steps 2-4 until there is no remainder or the desired level of accuracy is reached Higher-order processing, fact recall, and assimilation of rules, facts, and applications.

6. Report the results Mathematical language

Even as I look at this, I’m astonished that some students who manage to become proficient at math remain unable to zap you with “42” when you ask them, “Seven times six?” If you have to work out the staggering number of math facts in every long division problem, by the time you reach algebra, your prefrontal cortex is going to be like that dinosaur computer running Windows XP that we met at the beginning of this entry.

The games at www.mathnook.com don’t claim to train your prefrontal cortex for higher-level functions. A regular visitor to this site will, however, reduce the cognitive load on the part of the brain that needs to send out data requests and integrate the responses into an answer.