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

The test I gave to my students had 120 randomized multiplication questions, and I told them to fill in as many as they could in the time that I gave them.

From my experience testing my students’ writing speed, I knew there was no way to give my students their tests without them trying to start early. So I adopted a sort of “rolling” hand-out and collection method: I’d start my watch, and then weave my way through the rows in my classroom, handing out one test at a time. Then, once the time was up, I would take the same path and collect each test at the same rate.

I meant to give my 8th graders 6 minutes for their test, and my 9th grades 5 minutes, but I made a mistake in my “roll-out” the first time I ran the test, and accidentally gave my 8th and 9th graders 7:00 and 5:34 respectively. When I tested them again a week later, I gave them the same amount of time to make a fair comparison possible between the two tests.

I told them that in order to pass, they would have to get only 60 questions right. That means (for 9th grade), they only had to write one answer every 5 seconds or so. Even the slowest writers could write one answer in about 2 seconds, so I figured 5 seconds would be easy. But nobody in 8th grade and only 2 in 9th grade passed when I gave the test the first time.

So, I gave them a week to study and try the test again. I held after-school study sessions, and a fair number of students came (about a third of each class).

The second time the students took the test, their scores were much better – I had 5 students in 8th grade and 6 in 9th grade score over 60. I wanted to show my students how we could visualize their class’s performance, so I put all their raw scores on the board and showed them how to make histograms. Here’s 8th grade:

And 9th grade:

As you can see, there was a general upward movement in the scores for both classes, although a significant number never reached my target goal of 60 on both tests.

After we finished the histograms, I revealed the students who got the top three scores, had them stand, and we gave them a round of applause. The top score in 8th grade was 76, and my top score in 9th grade was 118.

After making histograms of the raw scores, we made a histogram of their improvement between the two tests:

I told them that this graph was the most important to me, because it shows (in general) how hard students in my classes were studying over the past week. Improvement is much more important than raw score.

It was fun to point out that the top students on the second test (in both classes) were also some of the top most improved. I had the top improvers stand and we gave them a round of applause like the top scorers. My top improvers in 8th and 9th grade improved 47 and 49 points respectively. Excellent work, I must say!

I was happy to see strong female representation in the improvement scores: the top two improvers in my 8th grade class were both girls. (The top three improvers in 9th were guys, but the class has few females to begin with).

For the students that did not meet my 60 point threshold, I allowed them to do an extra assignment to bring their grade up to a passing mark (but made it clear I would not be so nice in the future). For the students that improved 10 or more on their test (students I figured studied), I had them write me 60 randomized multiplication facts on a separate sheet of paper. For the students than improved less than 10, they had to write me 240. I explained to them that if they could not study on their own, I would assign “studying” for them.

*Next in the Teaching Times Tables series: The Importance of Honesty*

So glad you’re writing about all of this, Kyle, because one day you may want to write a book about your teaching adventures. You have great teaching instincts and problem solving skills! Love the histograms.