One student did very well on her baseline test. She was able to get all of the answers correct in a short amount of time, and could easily answer everything up to 10 x 10. This is great, I thought, because she'll really be able to help other students as we work throughout this unit!
Well, we started our unit, and I could tell she would need an extension, as she already was very fluent with her facts. I started giving her harder problems to work on, like 12 x 3, or 13 x 4.
And this was where she shocked me. She stared at me like I had just asked her to build a rocket to the moon. She had no idea how to mentally come up with an answer for these problems.
It didn't take me long to realize that all she had done was memorize the answers to each multiplication problem. She excelled at memorization, but she hadn't developed the number sense to apply what she had learned to other situations.
We want our students to be fluent. But what does fluency mean? According to Math Fact Fluency by Jennifer Bay-Williams and Gina Kling, there are 4 components to fluency:
- Accuracy: The ability to produce mathematically precise answers
- Efficiency: The ability to produce answers relatively quickly and easily
- Appropriate Strategy Use: The ability to select and apply a strategy that is appropriate for solving the given problem efficiently
- Flexibility: The ability to think about a problem in more than one way and to adapt or adjust thinking if necessary (Bay-Williams & Kling, 2019).
My student was accurate and efficient, but she was not flexible, nor could she select a strategy to help her solve the more complex problems I gave her.
Now you might be thinking, "But Jamie-why does this even matter? She had her facts memorized! Most of my students are still figuring out 3 x 7!"
Here's why. Her main strategy is memorization. She doesn't have an underlying conceptual understanding of how numbers work.
We don't ask students to memorize how to say words. We teach them phonics, increase their phonemic awareness, and work with them until they can sound out unfamiliar words independently. We need to be doing the same in math.
So how do we do this? Going back to Math Fact Fluency, here are 4 suggestions on how to increase fact fluency without drills, flashcards, or timed tests.
1. Get a Baseline
Figure out where your students are at using a quick interview. Show students a variety of facts and ask them to tell you the answer, and, more importantly, explain how they figured them out. If they skip count, we know they haven't mastered them yet. If they can recall it automatically, we can check that off as mastered.
Once you have a baseline, you can determine which facts your students need to work on. Bay-Williams and Kling recommend starting with 2s, 10s, 5s, 1s, 0s, and squared facts in that order. If students have mastered those facts you can move on to strategies like doubling, adding a group, subtracting a group, decomposing facts, and using known facts to derive the answer.
2. Use Pictoral Representations
One strategy they recommend is called "Quick Looks." This is where you show students a visual of the math fact or strategy you are trying to teach. For example, let's say you are working on 2 x 7. You would show them a picture that has 2 groups of 7. The trick with this though, is that you would only show it to them for about 3 seconds before hiding the picture.
Then you'd ask them to recall what they saw. You can discuss that there were 7 circles on top and 7 circles on bottom. Two groups of 7 is 14. Could they do it without having to count the individual circles?
The goal is to help students get to a point where they don't have to count each circle but can use what they already know to determine the represented number.
3. Use Story Problems
We're not giving up on word problems at all here. In fact, in the "real world," students are never going to come across random math problems without any context. Every time I've had to use math, it's in the context of something, whether that's food, gas, money, time, etc.
So we ask students to visualize and comprehend what is happening in word problems. If I'm working with a group of students on their 2 multiplication facts, the story problem might be something as simple as "Tamarita has 2 baskets with 8 apples in each one. How many apples are in each basket?"
I'd ask the students to draw a quick representation of what is happening in the story, and then write an equation to match their drawing. Some students might write 8 + 8. That's okay! That is a great way to lead into a discussion about how 8 + 8 = 2 x 8.
4. Play Games!
Games are so much fun to play, and kids enjoy them much more than timed tests. If I'm helping students with their 5s facts, I might have them play Trios, where they'll get practice multiplying by 5.
Just as important as playing the game, however, is the discussion after the game is done. For example, after playing this game you could ask students "What number would I need to roll to get a 35?" or "How could I use 5 x 5 to help me figure out 5 x 6?"
Debriefing the game will help students solidify their thinking, learn from others, and gain strategies that can help them in the future.
If you want to learn more about improving multiplication fact fluency with your students, I highly recommend that you check out Math Fact Fluency. There are so many good ideas there!
