Wednesday, March 23, 2016

Remember the multiplication facts NOT memorize them

My son, a 4th grader, is still struggling with memorizing his multiplication facts. Being his math teacher dad, this kills me. Sorta.

While it is true that he is struggling to memorize his multiplication facts, my real concern is that I'm not entirely sure he understands what multiplication even means. When he comes across a fact that he doesn't know, I'm not entirely sure whether he even knows of a strategy for finding the answer. It appears that his only strategy is based on skip counting. For example when confronted with...

...his primary strategy is a laborious strategy based on skip counting. With his right hand he taps his fingers and counts to six. On his left had he then holds up a finger, indicating he has counted to six once. On his right hand he counts to 12, raising a second finger on his left hand. He continues counting to the next multiple of six on his right hand, while tallying on his left hand until has has reached 7 tallies on his left hand. Essentially, this is a physical version of skip counting...
Clearly, however, this technique is fraught with error, since each hand only has five fingers and he is attempting to repeatedly count six on his right hand, while tallying to seven on his left hand.

I believe the problem is that his teachers have tried to move my son too quickly into memorization without first ensuring he has developed the number sense necessary to achieve fluency. 
Basic fact fluency requires the presence of flexibility, appropriate strategy use, efficiency, and accuracy. (I copied and pasted this from somewhere, but for the life of me I cannot find where.) Clearly, my son's single coping strategy indicates he is neither flexible nor is able to select from a variety of strategies. For example, if one does not immediately know 
then perhaps skip-counting will help...
or try repeated addition using "doubles" to increase efficiency...
or try using an area model with a little bit of the distributive property thrown in... 
or connect the fact to a related known division fact...
Research shows that the way to develop fluency is to increase the student's number sense. 

Memorization does not increase number sense. In fact, the lowest achieving students are more likely to focus on memorization, while the highest achievers focus on strategies based on number sense.

Using this as my premise, I created a system that will give my son more strategies to use for deriving the answer to the multiplication fact if he doesn't already remember it. 

The plan:
  1. Show a flash card and silently count to five seconds. However, give as much time as he needs to answer the question. (Speed is NOT a goal at this point.)
  2. Place the card in one of two piles: "Correct" or "Not Correct/Not in Time"
  3. Continue until 3 flash cards are in the "Not Correct/Not in Time" pile
  4. Using those 3 facts fill in this template

Essentially, the template take those strategies I mentioned above and puts them in a row allowing one to compare and contrast the different strategies. Marzano has long shown that "compare and contrast" is one of the most effective teaching tools.
Of course, the commutative property allows us to think of the same fact in terms of sevens:

 I'm not sure if there will be any value in keeping the completed templates and reviewing them in subsequent days. Research shows that simply re-reading the same information is an ineffective way to learn. I suspect the best idea is to keep the completed template for a day or two and then throw it away. It is likely that my son will have to re-do the same fact another day, but that is okay.

The goals:
  • Focus on strategies and number sense NOT on speed
  • Focus on REMEMBERING not on memorizing

Am I just being a helicopter parent?
Am I needlessly worrying about this?
Will my plan cause more harm than good?

Tell me what you think on the comment section below.