Love Math equation

By Margie DiPasqua
Math Department
Delaware Technical Community College
Stanton Campus

I thought teaching a certain chapter in my math class had gone really well. My students paid attention to the lectures, did reasonably well on group activities in class, and generally acted like they knew what was going on, even if they waited until the last minute to do homework.

Then test day came. 

My students walked in confident and left dejected. By the time I finished grading the tests I knew why. We both thought everything was going great, when really my students had huge gaps in their knowledge that we were both unaware of until test day.

Formative Assessment to Identify Pitfalls

I always hear about formative assessment, and have used it before in other classes, but hadn’t thought about it with this specific class. It was my first time teaching the class and I was just trying to keep afloat. Then I realized that was exactly the reason I should be doing formative assessment; I didn’t know the pitfalls and misconceptions the students would have before they happened.

For the next chapter, I made a conscious effort to incorporate formative assessment into my lessons. If I don’t write things down, I won’t do them. Likewise, if I think “I’ll do some informal formative assessment in this chapter,” it’ll never happen.

So, I made what I called feedback quizzes for my students. The next chapter covered seven sections and a test in four weeks. I found two good breaking points in the content, where I didn’t mind losing a chunk of time and the students wouldn’t be left hanging in the middle of a class.

At the start of a class, I explained to my students that I was going to give them a feedback quiz, and I was asking them to treat it like a test:

  • No notes
  • No talking to each other for help
  • No asking for help from me (unless it was to clarify directions or a problem)
  • I’ll grade it just like I would a test, but I will also include notes to help figure out why you lost points or get you started if you had no idea how to start a problem.

The only difference from a real test is that it wouldn’t actually count in the students’ course grade.

They spent fifteen minutes on it, I graded it, and we talked about it and reviewed some general issues. We repeated this a few classes later with a different feedback quiz.

In most classes, I build my test reviews based on what students are struggling with on homework and quizzes that are completed at home. However, this particular bunch of students weren’t doing their homework until the night before the test, so I typically didn’t know what they were struggling with until it was too late to help.

Enter the feedback quizzes: I knew exactly what my students were struggling with. Being the number cruncher that I am, I had done an item analysis on each of the feedback quizzes and knew what topics were giving the class trouble. This chapter had six different formulas that students would be given on the test. However, they were ONLY given the formulas. They had to know what every variable stood for and when to use each formula.

Analyzing the Results

On the feedback quizzes almost all of the errors were from using the wrong formula or substituting values into wrong variable. I knew standing at the front of the room and explaining when to use each formula and what all the variables stood for again wasn’t going to help. So I stepped out of my comfort zone and made a Kahoot! quiz to help my students review the formulas.

I gave them different situations and asked which formula they would use. Then, with the results right in front of our faces, we could talk about which one was right and why the other formulas that looked good enough for a couple people to pick them, weren’t quite right. The students were engaged, it wasn’t just me talking, and I actually had one student tell me he didn’t realize how much he knew!

Then, because of the way things fell, spring break happened. I know what you’re thinking, couldn’t you have given the test before spring break and cut out that awesome review? If I hadn’t done those feedback quizzes, I probably would have done that. But I had given a feedback quiz at the beginning of the class just before the review and I knew my students needed more time to process the content and more practice with a lot of the problems. I hoped my students would use spring break to study, complete their homework, and generally not forget everything we had talked about for the last four weeks.

Feedback Quiz for the Win

According to their test scores, that’s exactly what they did (or at least what they did on the last Sunday of spring break). Test scores jumped. Not only did more students pass, students that had scraped by before were earning A’s and B’s.

As much as I’d love to attribute all of that improvement to giving the students those feedback quizzes, in reality it was probably just one of many contributing factors to this improvement. That being said, the quizzes definitely played a role:

  • Writing the quizzes helped me figure what the key concepts were in a class I had never taught before, instead of teaching everything with equal weight and not knowing what to stress.
  • Because of that, I was able to adjust my notes and add in extra examples or more probing questions to think more about important topics.
  • I was more thoughtful in planning the test review because I knew in advance what my students were struggling with.
  • The quizzes helped focus my students too. I had two students who had never come to my office hours before show up with their feedback quizzes to talk about topics they thought they had understood, but that they had gotten wrong on the quiz.
  • Students that already came to my office hours, or stayed after class to ask questions, told me they were happy to have another resource to help them study.

When I shared this idea with some of my colleagues the question I always got was “Do they actually try? I mean, it’s not worth any points.” I was a little scared of this too, but my students tried. I had two or three students who would come in, read the feedback quiz, try one problem and then just give up, even if I encouraged them to try something. But most students generally gave it their best effort.

Before they took their first feedback quiz, I explained that I was trying to help them figure out what they needed to improve on, and to help those students who felt like they got it in class, could do the homework, but weren’t doing as well as they expected on test day. Maybe I just happened to have an exceptional bunch of students, but I think explaining the purpose and how it would help them, even if it didn’t directly affect their grade, was a big motivator.

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