*(Note: This post is a part of a series. For an introduction and index, see Teaching Times Tables)*

Many of my students thought they already knew their times tables, but really what they knew was how to count by multiples of a number. (And some didn’t even know that). If you presented them with a multiplication question, they would all start muttering and counting on their fingers (or making tallies on scraps of paper), and then oftentimes overshoot or undershoot the answer by a multiple. (Sometimes they would be off by one on their answer too, an error I wasn’t able to witness the cause of…)

I explained to my students that they needed to instantly know the answers to their times tables without having to count. I showed them how even a simple multiplication of two, three-digit numbers has 9 times-table facts embedded in it. If they’re slow and inaccurate on their times tables, they’ll never be able to finish harder problems in reasonable time limits.

So I started by having my students build small sets of flashcards by folding and tearing the printer paper that I passed to them:

I quickly found out that this was no good, because as students would lose their cards, there was no fast way to verify that a student had all their cards.

So I moved to creating little grids of times tables, written on a half sheet. The remaining half was split into a small answer key, and then little scraps to cover times tables as they answered correctly.

I had them working in pairs using these materials, quizzing each other on random facts.

It was at this point that I gave them their first test, and they did miserably. (See the following section for the results) It was back to the drawing board, as it were:

Here, I made a grid of times tables on the board and would point to one with my ruler. As soon as I pointed, the class would yell the answer as a group. The number of voices I could hear in the yell would tell me the confidence level of the class. I could move around the grid, finding times tables that were weak, and building them up using the stronger times tables I found.

I started having after-school sessions where we did this. I even started getting my students to lead their peers in the practice. I had them split into groups with leaders, put them all in separate classrooms, and then would just move between the classrooms, keeping them on task and offering words of encouragement and teaching advice.

I found that when I was leading the large group during class time, students could hide in the crowd and avoid participating. So, I would divide the class into two groups, and point to times tables while at the same time pointing to one of the groups to answer. I would move through the times tables, periodically switching which group was answering, making it a game to try to see if I could catch a group unawares.

Curiously, I found students could memorize the answer to a times table by its position on the board rather than the actual math fact. When I sensed that, I started exchanging the positions of the times tables on the board every once in a while, and it prevented students from taking that shortcut.

I would end each practice session by having them write their own set of randomized times tables, and when they finished I would give them a fixed amount of time to write in the answers. This way, they could start to feel the pace they would need to have for their test.

*Next in the Teaching Times Tables series: Measuring Writing Speed*

Great work Kyle! I think all your creativity, perseverance, and insistence on real learning will increasingly pay off! Keep going; we’re with you! DF

Thanks, Dad!

You saying that they memorized the answer by its position on the board really interested me, because I’m not sure I could do that easily (unless it was over the course of multiple sessions unchanged). Do you think their method of learning/understanding is fundamentally different from how we learn?

I doubt its a sign of cultural learning differences… Since I’ve also noticed it happening to me (and my mom notices it with her [American] students). Although I love your thought and think that would be a super interesting question to study… trying map cultural learning characteristics/strengths. Ahh, if only I had teams of people to outsource these questions to!

It can be so strong for me, if I’m not careful, I wouldn’t be surprised if I’d never learn the numbers as long as I could rely on position! But it can also act as great scaffolding to learn the numbers too if you start switching them around, as I did with my students.