Metacognition in a calculus prep course

As usual, fall semester flew by. On Monday, August 28, I met with my two classes for the first time, and on that day we did an activity that I recounted in a Facebook post, where I wrote:

“I followed Stan Yoshinobu‘s wonderful first day lead and asked my students as they met one another (a) what is a hobby or interest that you are good at, and (b) how did you get good at it? Their responses were great, as you can see in the attached photos (1, 2, 3, 4). Besides “practice” being the big winner regarding how they got good, I loved the students who said “have a growth mindset”, “be bad at it for a long time but keep trying”, “worked on my weaknesses”, and “my dad has taught me a lot of things”. We also had a discussion about the most important things to take from a college education (hat tip: Dana Ernst), and students generated great lists there, too, one of which I remembered to take a picture of. Big thanks to all the AIBL folks and other math friends who share their good work to help us get classes off to a great start.”

The course I was teaching was GVSU’s new Math 124: Functions and Models, which is a 5-credit class designed specifically for students who are planning to take calculus but are not yet ready to enter that course.  Nearly all of my students were first-years, and one of my goals was to work specifically with them to help them become not only better students of mathematics, but better students generally.

To that end, beyond the aforementioned first-day activity, I added a new assignment to my courses this semester. I had students broadly tackle “metacognition” by doing a range of reading, listening, and watching experts on the topic of learning. If you are interested, you can read the full details of the assignment, which included some TED Talks and videos on failure (thanks, Stan, and the AIBL folks again), one of my favorite podcasts ever from Sam Harris and Tristan Harris (What is Technology Doing to Us?), reading one of several books (including Dweck’s Mindset, Burger & Starbird’s 5 Elements of Effective Thinking, and Bain’s What the Best College Students Do), and blog posts like Dave Richeson’s “Advice for College Students”.

In the last week of class, students turned in 3-page essays on what they learned about learning. The vast majority of the rest of this post is my students in their own words:

  • I decided to delete all of the social media apps from my phone. … I learned that I was very susceptible to the addiction of getting notifications and having people want to talk to me.
  • Failure is part of learning and it’s only really failure if you don’t learn from it.
  • It is important to learn by failure and work on your weaknesses. I have learned that it takes an immense amount of courage to admit to imperfections and to continue to work on strengthening them.
  • Raising questions personally has been difficult for me to overcome. I know I shouldn’t be afraid to show ignorance and ask if I don’t understand something.
  • The biggest thing I learned from this video is that obstacles and failures aren’t meant to destroy you, they are meant to show that you might need to change the way you’re approaching a problem because it will help you in this moment and later in life.
  • Before doing this assignment, I never thought about which mindset I was or what different mindsets there were.
  • In her book, Dweck states “Remember that having innate talent is not a goal. Expanding skills and knowledge is.”
  • After learning about growth mindset, one practical thing I will do to improve my life is to embrace challenges rather than avoid difficulties.
  • This course has made me realize how important is to have the right mindset. … I learned that if I approached assignments with a mentality that it would be challenging, and would take many hours and lots of patience, I was better off than when I started out being frustrated and feeling sorry for myself.
  • Surface learning versus deep learning was something new that I had never heard of before. After reading Bain’s What the Best College Students Do, he summarized that there are 5 types of college students: 1. The ones who get good grades but do no better than those who get C’s and D’s. 2. The ones who get good grades and become deep learners. 3. The ones who get mediocre grades but learned deeply. 4. The ones who receive bad grades, give up, and depend on the the other. 5. The ones who receive bad grades and tell themselves they’ll get better. I found this interesting because I can see some of these students in my classes. I also realize that surface learning is how I’ve been studying my whole life.
  • Recognizing and understanding your thought process on the path to an important part of success is an important part of continuing your success, however, I believe a more important part is recognizing and understanding your thought process on the path to failure, as it can help you learn and mitigate the decisions that lead to failure. Sitting here, late at night, writing a 3-page essay the day before it is due, I realize that the path to success is not the one I have followed.
  • One thing I want to do better in my learning is to put more effort into my work. This means getting an early start on assignments and studying, as well as going to all my classes. For me to do this, I need to reduce the usage that my phone plays in my life. Instead of being on my phone for hours on end, I should use that time to study or do homework instead.
  • You must go into the unknown to unlock the potential to reach the alternate and more beneficial solutions to a problem … I am seeing that in mathematics especially there is not always one path to the solution, but rather many.
  • The other big idea I took away from this project and math this semester in general is that you are never going to get in trouble for asking for help, and by not asking the only person you’re hurting is yourself because you’re the one who doesn’t understand the information.
  • Through this assignment as a whole I have learned just how importantly my mentality towards school affects my learning, how to find a solution to a problem I may not have planned on answering, and to view every failure as a possibility to try something new.
  • I can confidently say that I’ve learned more than just math in my MTH 124 course. I’ve learned how to be a better student, employee, and even a better person.

I, of course, learned a lot (or was reminded of many things I sometimes forget) through this assignment, too.  Briefly:

  • most college students have a lot to learn about being learners; many of my students reflected on how their high school experience didn’t prepare them very well for college
  • every single human being is afraid of failure, but failure (and learning from it) is essential to living a healthy and productive life
  • things that I tend to take for granted in my students are things I need to talk about with them more:  how to study, how to ask for help, how to grow as a learner, …

A big thank you to all my students from this past semester for the opportunity to work with them, to learn from them, and to hopefully help them take few steps further down the path to success.  I’m also very grateful for their honest and thoughtful essays, which were fun to read at the end of a long and full semester in which I graded a lot of other work.



  1. Good work, Matt! Interesting thinking about grading it. On the one hand, that shows the learners that you really value it, on the other it feels like a weird condition. Regardless, their takeaways are priceless.

    1. John,

      It certainly was different to grade from anything else in the course. I felt like if I didn’t grade it, students wouldn’t do it, in part because in oral evaluations my students consistently tell me “If you don’t grade it, I don’t do it.” That overall issue, of course, is a challenge for a different day.

      I counted the assignment 5% of their semester grade. They completed a cover sheet that itemized what they read/watched/listened to and the time spent. Meeting the specifications there earned full credit (40 points of the 100 overall). For the 60-point essay, I largely graded it on completeness (at least 2.5 pages, not more than 3, with a summary of things they learned and a few practical insights for themselves) and collegiate writing. I also offered to review an advance copy of their work.

      Almost every student in the course completed the assignment, and almost everyone who did earned something close to full credit. I’d be interested to talk about ideas you have for getting students to engage in work like this without grading it.


  2. Sally Smarsty · · Reply

    I love this! I remember taking my first course with you and thinking ‘this is terribly difficult and exhausting! I’m not sure if I can do this!’ I felt frustrated and like a failure for not having the ‘answers’ right away. After a few assignments, I began approaching the work with a different view- yes, this is difficult. It will take you a long time but you are capable. You might not succeed the first time but you’ve found a way that doesn’t work, which has taught you something about your method. That is one thing I always try to pass on to students when tutoring or teaching- math is difficult but don’t let that deter you, frazzle you and cause you to quit. Approach it with the mindset that you have the tools or can find them, you just have to be patient and steadfast and learn how to put them into action. What great lessons you’re teaching first year students!

    1. Thanks Sally! It’s always great to hear from you.

  3. Gord Bramfield · · Reply

    Hi Matt. This was a pleasure to read! Thank you for sharing.

    I am a High School math teacher. I try to do similar things with my students. I truly believe in the power of meta-cognition. I also believe that when students believe in a growth mindset, that is when the real learning begins. However, adopting a growth mindset also requires a certain level of humility and maturity. All too often I see students who say they want to be successful but are not willing to look inwards and reflect on their own practices and habits. The students who are committed to owning their learning are typically the ones who are having a much more positive learning experience. As a learner, you don’t need to be an academic to appreciate the importance of this.

    I take a lot of pride in being able to provide my students with a novel approach to thinking about mathematics and how they learn. It pains me dearly when students don’t reciprocate. For example, and you already mentioned many of the following: Do your home work, come prepared, be an active learner, get help when needed, accept failure as a natural by-product of learning, set goals, manage your time, commit, etc. Many of my students want to go to college or university, but have developed poor learning habits (another discussion piece). As a result, when they leave High School, many are truly ill-prepared for post secondary.

    Matt, thank you again for what you do for your students. They are very fortunate to have you as their teacher.


    1. Gord,

      Thanks for your comments. I think one of the big challenges of teaching is to get more students to reciprocate. And all of us need to keep working to get better at doing so. Clearly you’re doing good things for yours. One thing I’ve learned over the years is that sometimes the impact comes long after the class and so we don’t know about it.

      All the best,

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