I was working with some students this week who were learning their “basic facts” in multiplication. These are generally considered to be those one-digit times one-digit problems that we use when we figure out the products of multi-digit problems. I was going over some different strategies and ways of thinking that can be used to help students learn those facts.
There are a number of strategies that can help in the learning of basic facts, but one phrase sums up many of those individual strategies: “Use what you know to figure out what you don’t know.”
This phrase actually applies to FAR more than just the learning of basic facts. The truth, however, is that often we condition students to NOT think for themselves in mathematics. We have a long tradition of teaching by telling: the “here’s how to do it now go practice 50” method. In reality, that kind of math lesson programs students to think that unless someone has told them “the way” to do something (and, of course, they must remember exactly how to follow the directions of “the way”). If they forget, they are stymied and cannot know how to proceed. They remain in their “stuck” position until someone comes to rescue them with “the way”.
It is far better to regularly encourage students with the idea that when they are stuck, they need to stop and think about the things they DO know that can be applied. We might ask questions (and teach them to ask themselves) such as these:
- What might be something similar that you do know?
- If the problem had smaller or simpler numbers, how would you try to solve it?
- Why did you choose to do it that way?
- What is important in the question?
- Is there a pattern?
- Is there a way to record what you have done so far so you a pattern might be noticed?
- Can you think of another way to do that?
- Does this remind you of another problem you have done?
In the case of basic facts, “Use what you know to figure out what you don’t know,” might look like this: a student cannot remember 6 x 8. But 5 x 8 is known. So, knowing that 5 groups of 8 is 40, he need only add one more group of 8 to have the needed 6 groups of 8; thus 40 + 8 = 48 is the solution to the unknown fact.
Students may need practice in doing such strategies, but the important thing is that there ARE strategies to help. It removes the case of having to rely solely on memory and sitting there stuck if memory fails.
What are you doing in your classroom today that encourages students to help themselves when they are stuck? Maybe post the title phrase for them (and model for them how it looks): “Use what you know to figure out what you don’t know.”
Strategies make a difference in student learning!