Why Memorize?

There is a lot of discussion concerning the memorization of multiplication facts.  Many elementary teachers I know think that if they haven't learned their multiplication facts by a certain age, it really doesn't matter because there are calculators and charts.  Unfortunately, as a high school math teacher I've seen the effects.

I've seen students sit there skip counting their way through 8 x 4  because they don't have fact fluency.  When they have to skip count or stop to use a calculator, it disrupts their flow and they often have trouble learning the process to solve a problem.  They have difficulty factoring, finding GCF and LCM, and fractions which makes it harder for them to pass the math class.

In addition, many students who do not know their multiplication tables, cannot divide, and when tested end up well below grade level.  This makes it more likely students will get further and further behind until they are unable to do high school math.

According to one study done by the Stanford School of Medicine, its the hippocampus in the brain that helps provide scaffolding for learning math fluency when learning moves from counting on fingers to pulling facts from the brain.

There are other studies which indicate that students who do not develop math fluency will continue using less efficient strategies such as counting on fingers thus finding it difficult to move to automatic recall.  There is a developmental sequence when children move from beginning fluency to full fluency.

1.  Finger counting where they add or subtract on their fingers.

2.  Verbal counting strategies where they add and subtract using fingers from the starting number to the answer.  I include skip counting for multiplication and division with this because many of them learned to skip count well but did not move to fact fluency.

3. Decomposing or splitting strategies which allow them to break down facts they might not already know such as 8 x 12 is the same as 2 x 12 x 4.  Too many of my students who arrive in high school do not have this strategy down and haven't been taught to do it.

4.  They are able to retrieve facts automatically from their long term memory.  When they get to this stage, they are able to focus on learning the new material rather than forgetting where they are because they just spent several minutes figuring out 5 x 8.

In addition, if students do not develop fact fluency, they have a higher chance of dropping out, rather than graduating because they struggle and eventually give up but there are things we as teachers can do to help students become more fluent.

One recommended methods to help increase fluency is by using  drill and practice via flash cards, software, or even an app on their computers.  From personal experience, older students tend to prefer the drill practice in the form of a game because they are used to games.

Another method is to use the Cover-Copy-Compare.  The teacher prepares a worksheet with no more than 10 completed problems on the left side of the sheet.  The student studies the problems, then folds the left side over so the problems are now hidden and writes down the work from memory one problem at a time.  They then check their work by comparing it with the original.  If it is correct, they move on, otherwise, they study the problem they missed, cover it and write it down before checking the answer when done.  This step is repeated as often as needed until they get it right.  At this point they move on.  They continue until they have done all the problems correctly.  A student is considered proficient when they can repeat do the same problems three times.

Students can make their own flash cards out of 3 x 5 inch index cards.  If they do it this way, they can work in pairs where one student holds the card up with the answer facing themselves while the other student tries to answer the problem.  They can also access one of those apps which allows them to create their own virtual flash cards and the app tests them so they can do it whenever they want.

I like to set up races where a paper has say 8 problems.  The students are in rows, one behind the other.  I give a paper to the first student in each row face down. When I say go, the first person turns it over and answers the first problem before passing it to the second student who answers the second problems and so on to the end of the row.  If I have fewer students than problems, I sometimes have them send it back down the row to the front until all the problems are answered.  The row with the most correct answers in the quickest time, wins a small prize.

Let me know what you think, I'd love to hear.  Have a great day.