Students enter college with a variety of backgrounds, and aren’t always sure how they learn best. Despite their best efforts, sometimes they do poorly on their first midterm exam in math, and a lot of the time this is simply because they aren’t used to studying for mathematics. I am inspired by the wonderful book Teach Students how to Learn, as well as the research-backed success of exam wrapper activities for reducing gaps in STEM learning [1]. When teaching a freshman class, I ask the students to complete this reflection after every exam, and (importantly!) follow up with individualized meetings to have the strongest impact I can.

Sample Metacognitive Reflection (done via LMS quiz)

The questions below are designed to help me help you. How can I help you develop a study strategy that works well for college math tests? Some study strategies that work okay in high school don’t work as well in college. For this to be effective, be honest - and I’ll try to help you find a few small things that will improve your learning not only in this class, but in future classes as well! There are no wrong answers to the questions below.

  1. When did you start preparing for this exam?
    • More than a week before the exam
    • Approximately one week before the exam
    • 5-7 days before the exam
    • 2-4 days before the exam
    • 0-1 days before the exam.

  2. Approximately how many hours total did you spend studying for this exam?

  3. What percentage of your test-preparation time was spent in each of the following activities?
    • _____ Reading textbook sections for the first time.
    • _____ Re-reading textbook sections.
    • _____ Reviewing class notes
    • _____ Highlighting important information in textbook/notes
    • _____ Reviewing quiz and homework solutions
    • _____ Redoing old problems from WebWork/homework
    • _____ Redoing old quiz problems
    • _____ Doing practice problems from Midterm 1 Review
    • _____ Doing problems with solutions in the back of the textbook
    • _____ Other (please specify)

  4. Which of the following resources did you use while studying for the midterm?
    • Midterm review packet
    • Midterm review packet solutions
    • Midterm review video
    • Old course recordings
    • Textbook
    • Old quizzes
    • Quiz solutions
    • Old webworks
    • Webwork solutions
    • Peers
    • Tutors
    • Other

  5. Based on your earlier responses, name one to three things you feel you did well at in preparing this exam, and should continue.

  6. Based on your earlier responses, name one to three things you would consider changing when preparing for your next exam.

  7. During what hour should I expect to see you come into my office to talk about this reflection? In particular, email me if none of these times work so we can set up a different time. Notice that I’ve included times that are not my usual office hours in hopes of being able to meet with everyone. During each of these hours, I will meet with students in order of your arrival.

Follow-up

I meet with students one-on-one to talk about any questions they have regarding their exam performance. We meet for maybe 5-10 minutes. I make sure I address any of their questions or concerns about the problems they missed, and then we talk about what they thought they wanted to do differently for the next exam. A lot of the time, their self-assessment is spot on, and they select an activity from the list of activities which they were not doing very much of and choose to do it differently. Other times, I give them a list of effective study strategies from McGuire and ask them to pick one new thing to try from that list before the next exam. Whatever they choose to do, they are assigned to write a short paragraph about it after the next exam, and reflect on whether it helped them.

Results

The last time I implemented exam wrappers, it was optional to complete (I had not yet determined whether I believed it would benefit the students to require it). 18 students chose to complete the reflection following Midterm 1, and 41 chose not to. Of the students who chose to complete the reflection, their Midterm 2 grade was 10 percentage points higher, on average, than their Midterm 1 grade, with 6 students improving their performance by more than 15 percentage points! In contrast, students who did not complete the reflection saw an average improvement of 3 percentage points. This result is statistically significant when taken at face value, but is not controlled for original exam performance (I do not believe I have quite enough data for this purpose).

In their follow-up assignment, students reported that they liked the study techniques they selected and, frequently, would continue them.