Moving the Chains: Updating What Works and Continuing to Take Things Out for a Test Drive

David Buller

David Buller has been teaching high school mathematics and computer science in Madison, CT for 18 years. Prior to teaching, David spent 15 years working in the information technology arena, where he utilized many of the skills and strategies he now teaches. David and his wife are the proud parents of three grown children, and currently reside in CT with their black lab, “Solo.”


In Part 3 of this three-part series, I spoke about coming up with the idea to look at perception of difficulty with my pre-calculus students. In Part 2, I dug into what happened after I implemented that idea.

As our second unit test approached, I met with Allison again to discuss how we could help students capitalize on their prior personalized learning activities and reflection as they prepared for their assessment.

The next day, I asked students to read their unit 1 reflection and recall how they had answered the question, “What is the one single thing you can do next to improve your performance in Unit 2?” Then, students were asked to identify and record on an index card 1 to 3 actions they could take over the next 48 hours or during their test to improve their performance.

Here are two students’ responses:

perception of difficulty

What I Was Hoping For

Here is next iteration of the Chapter 2 Test Reflection. This time you are seeing the entire assignment. I wanted them to:

  • Follow through on their own promises. Often times they write reflections for the audience of the teacher and not themselves. Letting them review the wisdom of their own insights and revisiting self-identified areas of concerns.
  • Take action before it’s too late. I didn’t want to have students feel like they were a broken record. The point is to build their competence and confidence.

Chapter 2 Test Reflection

Please answer the following questions as completely as possible regarding the Chapter 2 test, and remember, there are no correct or incorrect answers. Responses will only be shared anonymously.

1. Pre-test Preparation

  • What were the Action Items you wrote on your index card to do in the 48 hours leading up to the Chapter 2 test (if you didn’t complete an index card, indicate so and describe what, if anything, you planned to do to prepare for the test)?
  • Did you follow through with the Action Items?
  • Do you think your attention (or lack of attention) to your Action Items impacted your performance on the test?

2. Reflect overall on where you are right now as a mathematician.

  • What behaviors/strategies did you uncover that are working for you?
  • What behaviors/strategies did you uncover that are areas of concern?
  • What Chapter 2 content do you feel that you mastered?
  • What content in chapters 1 and 2 do you feel that you need more growth in?

3. In your Chapter 1 reflection, did you say you needed more work with circle problems? If so, what have you done to improve your understanding of circle problems?

4. What is the one single thing you can do next to improve your performance in Unit 3. Be specific (NOT… I should study more…)?

5. What impact do you think your effort has on your performance in math classes in general, and in this class specifically?

What Happened

  • Between the day of the index card activity and the text, about 40% of of my class came for extra help outside of class. Most of these students had identified getting extra help as an action item, and for several of these students, it was their first seeking help outside of class time.That is significant and satisfying — it is validating the importance of this journey. Yes, it takes time to design and review their reflections but at the same time it creates student ownership that I haven’t seen before at a class level in my 18 years of teaching.
  • For some students, there was tremendous growth in performance from Chapter 1 to Chapter 2 test scores. While I can’t attribute all of the growth to our emphasis on personalized learning, I have no doubt that it had a significant impact.
  • While I de-emphasized the need for students to mark their homework questions as easy or hard, a few students mentioned that they continued to find the exercise helpful, especially as a study aide.
  • Students continued to candidly describe areas of strength, concerns, and next steps. Here’s a sampling of the reflections my students generated. While these statements may be obvious from a teacher’s vantage point, when students come to this realization on their own after analyzing test performance, the statements become powerful.
    • Student 1: My effort impacts my performance a lot in any type of math class because the more work I put in and the more dedication I put into my studies, I do much better with tests and quizzes. In this class specifically, when I pay attention to the problems on the board and say the answers out loud & how I got to that answer, I get much more out of it then just sitting in my seat.
    • Student 2: Conceptual things such as domain I occasionally found myself losing points, along with a slightly weaker background with fractions.
    • Student 3: One thing I can do is be more attentive while going over my work on a test or quiz. There were definitely some mistakes I made that could have easily been avoided. I also have to plug my answers back into the original problem to make sure that it works.
    • Student 4: I definitely want to continue to understand the underlying concepts of how to do the problems because that proved to be very helpful.
    • Student 5: Continue to take notes and do out the example problems and definitely slow down and double check my work. If I don’t understand something I will try to come after school or during my lunch for help.
    • Student 6: I discovered that being more methodical in my approach to a test produced better results.
    • Student 7: My study habits are working for me pretty well based off of my test scores. I changed some of them after the first test and I made a big improvement. I also have been keeping up with the homework which has really been helping.

Where We’re Heading

As we transitioned into chapter 3, I shared with the class my near-term goal of decreasing my involvement in the reflection process. My intent is for reflection to become an automatic, self-directed part of my students’ learning habits.

I also am intrigued by an idea Allison shared with me about “crowdsourcing” helpful strategies, videos given the topics. This was triggered by a student reflection where he commented that it was helpful to watch a video on circles. I was curious to see whether it was one of my videos or something else. So I am planning for students to share and review what was helpful so that I have a broader bank of learning opportunities designed with students for future classes.

Related posts:

Leave a Reply

Your email address will not be published. Required fields are marked *