Sunday, May 31, 2015

To Memorize or Not - Math Facts

Math facts: Four operations focused on single-digit numbers.  
  • Addition facts: Sums of two single-digit numbers (0 - 9)
  • Subtraction facts:  Reverse of the addition facts
  • Multiplication facts: Product of two single-digit numbers (10 and 11 may be included)
  • Division facts: Reverse of multiplication facts 
I have heard the arguments against forcing a child to memorize math facts: People use calculators, it is just rote, it is more important that a child understand the concept.  I have also met a number of middle schoolers who didn't know their math facts. It is one thing to hit a math wall because of quadratic equations. It is very different to hit that wall because one "really can't subtract too good," to quote a student repeating algebra I.

The National Math Advisory Panel reports that "It is important for students to master basic math facts well enough that their recall becomes automatic, stored in long-term memory, leaving room in their working memory to take in new math process. This frees up working memory for more complex aspects of problem solving. "

So, although memorizing math facts is a bit of work, I recommend children do that work.  Often schools rush through the process, so it requires a bit of summer catch up. Computerized games and flash cards may make the process easier. Students should also practice the facts on plain old worksheets. Why? Because the physical act of writing helps some children learn the facts, and children usually have to write the answers to math facts in class. The Internet is a good place to get free worksheets. Two that I find useful are The Math Worksheet Site and Large Print Math Worksheets.

Some observations:
  • Addition and multiplication facts are easier for most children to learn than subtraction and division. 
  • Memorizing facts does not mean a child doesn't need to learn math concepts. Example: Some children need to be reminded of the concept of multiplication even after they memorize the facts. This is especially true when deciding which operation to use in word problems. Others may only truly understand the concept after they have memorized the facts. Although developmentally they may not have a strong grasp of the concept, they are expected to move on in math because schools usually have a rigid time schedule on curriculum.
  • Consistent use of a skill helps a child learn that skill. 
  • Some children do poorly on math computer games because they have to search for the correct number keys.
  • Much of the protest against learning facts has to do with timed tests and a child's anxiety.
A child with a math learning differences (dyscalculia) often finds it challenging to memorize anything with numbers. The catch 22 is that this child then finds it even more difficult to move forward in math because he is using aids to add or subtract (like finger counting or number charts), rather than memory. This slows down any process requiring more than one step, and makes it difficult to keep track of the steps.  Children, even with a math LD, should be encouraged to work on the math facts. Parents and teachers need to be patient and encouraging in the process. 

Remember learning and using math facts are two separate activities. A recent study showed that as children age they become faster and more accurate at solving math problems, and rely more on retrieving math facts from memory rather than counting. As these shifts in strategy take place the researchers see several changes in the children's brains. The next step in this research is to study how the dyscalculia brain processes math facts and if there is a similar change as the child matures. 

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