Mastering the Multiplication Table
So many times, I’ve heard middle and high school teachers lament, “My students don’t know their multiplication facts. Didn’t their elementary teachers cover that?”
Yes, they did, but it got stuck in the wrong part of their brain.
It turns out that there are two types of memory: taxon memory and locale memory.[1] Taxon memory is what we use to store things we’ve memorized. Locale memory is for information that makes sense – information that we understand.
The advantage of taxon memory is that it’s fast. If I ask you what is 6x8, you recall it quickly from your taxon memory. You don’t have to add six eight times or draw a six by eight array. The disadvantage of taxon memory is two-fold. First it is finite in scope. There is only so much you can memorize. If I ask you to go to the store and start listing items, after about five or six, you are reaching for a pencil and paper.
Secondly, it is finite in duration. It requires a lot of ongoing practice. Much of grades three and four is invested in memorizing the multiplication table, but after that, we move on to other skills. That’s why our middle school students – who once knew their multiplication facts – now struggle to recall them quickly. Taxon memory fades.
Locale memory is the opposite. It is not fast. You must think about it. Instead of being effortless, like taxon memory, it is effortful. But it is locale memory is also opposite in the other regards as well. It appears to be infinite in scope and duration. There seems to be no limit to how much the human brain can remember when things make sense. And locale memory is “sticky”. It lasts forever.
We’ve all experienced the situation in which we were trying to remember something like the name of a restaurant. We can’t recall it and say, “I forgot the name.” Later, while trimming our toenails, the name jumps back into our head! We didn’t actually forget it; we forgot where we put it. Locale memory lasts forever. Even if the road gets washed out, our synapses can reroute and find a different way to get there.
All that to say, when we tell students to learn their multiplication facts, what they hear is, “I have to memorize 144 unrelated facts.”
My approach is to show students the meaning behind the multiplication table. This encourages storage in long-term locale memory. Then, through consistent practice, it gets stored in taxon memory as well for quick recall, but the anchor always holds in locale memory.
Nice theory, but does it work? The good news is a resounding YES! In just five minutes a day, I was able to help my struggling eighth graders master their multiplication facts. (Boy did that make it easier to teach factoring of polynomials!)
And as a bonus, I showed my students how to use their multiplication table to reduce, add, subtract, multiply, and divide fractions, and how to solve proportions with it as well. They became my fraction experts!
You can learn all about it in my video, “Fast Facts and Fractions” available on my EdStream site. Simply click the button below,
[1] Caine, Renate Nummela, and Caine, Geoffrey. Making Connections: Teaching and the Human Brain. Alexandria, VA: Association for Supervision and Curriculum Development, 1994.
So many times, I’ve heard middle and high school teachers lament, “My students don’t know their multiplication facts. Didn’t their elementary teachers cover that?”
Yes, they did, but it got stuck in the wrong part of their brain.
It turns out that there are two types of memory: taxon memory and locale memory.[1] Taxon memory is what we use to store things we’ve memorized. Locale memory is for information that makes sense – information that we understand.
The advantage of taxon memory is that it’s fast. If I ask you what is 6x8, you recall it quickly from your taxon memory. You don’t have to add six eight times or draw a six by eight array. The disadvantage of taxon memory is two-fold. First it is finite in scope. There is only so much you can memorize. If I ask you to go to the store and start listing items, after about five or six, you are reaching for a pencil and paper.
Secondly, it is finite in duration. It requires a lot of ongoing practice. Much of grades three and four is invested in memorizing the multiplication table, but after that, we move on to other skills. That’s why our middle school students – who once knew their multiplication facts – now struggle to recall them quickly. Taxon memory fades.
Locale memory is the opposite. It is not fast. You must think about it. Instead of being effortless, like taxon memory, it is effortful. But it is locale memory is also opposite in the other regards as well. It appears to be infinite in scope and duration. There seems to be no limit to how much the human brain can remember when things make sense. And locale memory is “sticky”. It lasts forever.
We’ve all experienced the situation in which we were trying to remember something like the name of a restaurant. We can’t recall it and say, “I forgot the name.” Later, while trimming our toenails, the name jumps back into our head! We didn’t actually forget it; we forgot where we put it. Locale memory lasts forever. Even if the road gets washed out, our synapses can reroute and find a different way to get there.
All that to say, when we tell students to learn their multiplication facts, what they hear is, “I have to memorize 144 unrelated facts.”
My approach is to show students the meaning behind the multiplication table. This encourages storage in long-term locale memory. Then, through consistent practice, it gets stored in taxon memory as well for quick recall, but the anchor always holds in locale memory.
Nice theory, but does it work? The good news is a resounding YES! In just five minutes a day, I was able to help my struggling eighth graders master their multiplication facts. (Boy did that make it easier to teach factoring of polynomials!)
And as a bonus, I showed my students how to use their multiplication table to reduce, add, subtract, multiply, and divide fractions, and how to solve proportions with it as well. They became my fraction experts!
You can learn all about it in my video, “Fast Facts and Fractions” available on my EdStream site. Simply click the button below,
[1] Caine, Renate Nummela, and Caine, Geoffrey. Making Connections: Teaching and the Human Brain. Alexandria, VA: Association for Supervision and Curriculum Development, 1994.
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