Math to the People

This winter 2023 semester, I have been trying something a little different with my Math 099 classes. For those who are not aware, Math 099 is the most basic math course we offer at Alexander College. It is an ‘intermediate algebra’ course covering topics such as solving various types of equations, simplifying rational expressions, and graphing lines and parabolas. It is a course that I have been teaching for a while, but it has always been one that leaves me feeling a little dissatisfied. Attendance has always been low in this course. While the passing rate amongst those students who opt to write the final exam has always been comparable to that in other courses, the fact that half of the students registered will stop attending before the final exam has always made me a little uncomfortable.

In Fall 2022, I had the lowest ever attendance rate I have had in my time teaching Math 099. The last few weeks of class, I had an average of only 4 students attending each class out of a total of 30 students registered. While the number of students who wrote the final exam was significantly higher than that, the passing rate was dismal. Clearly, what I was doing – which was generally the same as what I had been doing for the past 5 years – was not working. It was obvious that I needed to do something differently.

The inspiration for the specific changes I made to my Math 099 course came from the Fall 2022 Professional Development Day at Alexander College. During that PD Day, the keynote speaker was “Anything but Soft: the Value of Transferable Skills in Acion” by Candy Ho. The objective of the presentation was to help faculty at Alexander College better quantify the transferable skills (meaning non-subject-specific skills such as time management, presentation skills, writing skills, etc.) that students are learning in their courses. However, the thing that struck me in the presentation was mainly that my Math 099 students were missing most of these skills. They had a hard time coming to class, had a hard time staying focused during class, seemed to never study outside of class time, and when they did study they seemed to only do it in ineffective ways.

This led me to my hypothesis: that the reason my Math 099 students were performing poorly – and the reason they had always performed poorly – was that they lacked a number of these transferable skills. Since I wasn’t teaching them these transferable skills, they were never able to succeed in my course, even if they took the same course over and over again. In other words, the problem I had in Math 099 was that I was dealing with students who had never properly learned how to learn.

Thus, this semester in Math 099, I dedicated the whole first week of class to trying to teach my students how to learn math. While there was a part of me which resisted giving up time that I could be using to get ahead on the course syllabus, I knew that spending more time covering the material was not going to help my students. I needed to teach my students how to get more out of the class time they had, rather than giving them more of the same.

Before this winter, the first class of Math 099 was spent reviewing the contents of the course syllabus: going over where to get the textbook, assignment instructions, where to find things on the course Canvas page, attendance policies, etc., and then during that first class, students would play a Kahoot! quiz game to test their knowledge of the prerequisite material. Then, in the second class, we would jump right in to reviewing that prerequisite material (in the course syllabus I call this Unit 1: Arithmetic Review).

This winter, I spent the whole first class doing a rather involved interactive Mentimeter presentation. This presentation included most of the topics that I previously would have covered in the first class, but also included a number of additional topics. These additional topics included:

• The percentage of students who failed the course in the previous semester
• Various reason why students had failed in the past (low attendance was at the top of the list)
• How many hours per week students were expected to spend studying
• The way in which mathematical knowledge builds on previous knowledge and its implications (if you fall behind it is really hard to catch up)
• Mathematics as the study of patterns
• Why practice is important when learning mathematics
• The ways in which all of the assigned in-class activities and homework were designed to help students practice

I felt that students were much more engaged in my first class presentation this semester than they had been in previous semesters. I know part of it was because of the interactive elements of the Mentimeter presentation (normally I present by writing in a OneNote notebook on my tablet PC that is projected onto the whiteboard – this is very versatile, but has few ‘gimmicks’). Part of it, though, was also because, when I was explaining how the course was going to work, I was also explaining why I had set up the course in the way I had. I tied every element of the course to the ways in which it would help students study and learn.

In my second class, I re-used the same quiz game on prerequisite material that I has used to give students in their first class. I wanted students – especially those students who hadn’t studied math in years – to have a good idea of where they were starting from in their learning journey. However, rather than moving straight from there into reviewing the prerequisite material, I next moved into a short Mentimeter presentation. While the first class presentation was focused on why studying every week was important, this next presentation was focused more on the difference between ineffective and effective studying. I tried to convey the idea that memorization is a very ineffective way to study math, and that the purpose of repetitive examples is not to memorize the steps used in those examples, but to learn a general rule that can be applied in novel examples.

The final activity in my students’ second class was the creation of a study plan. I asked each student to make a plan for their weekly studying for the semester, and either email it to me or post it in an online discussion forum. On this study plan, students how to indicate:

• How much time they planned to spend studying each week
• What their most important at least important activities were for out-of-class studying
• How much time they would spend on each individual activity
• When during the week they planned to work on each individual activity

It was then only in the students’ third class, at the beginning of week 2 of their course that we actually began working on the material from Unit 1. Even by week 2, I was already seeing a marked difference in attendance and engagement from last semester to this semester. While there could be other explanations for this difference, I hope that the time I spent on helping my students learn how to learn will help them throughout the course and beyond. I hope to make another blog post towards the end of the semester keeping readers informed as to what effects I saw from these changes to Math 099.