math

mathematics for data science#

This was meant to be a “refresher” course for students who might not have had a math class in a while. That said, I teach this class as if students have only had a high school math education.

[Link to course webpage in progress as IU migrates its online assets to an updated platform.]

peer instruction methodology#

In this class, I use peer instruction for the second portion of the class, using TopHat. That is:

  1. Present a question to the class, ask them to give their answer individually, and close their laptop.
  2. They’ll discuss with a pair partner what their answer was, and what their reasoning was.
  3. I present the answer, and an explanation. Essentially giving students the tools they’ll need to address their own writeups.
  4. They discuss with their partner what they got wrong, or how they’d rephrase their reasoning.
  5. Repeat.

interventions#

Below are interventions taken to improve this class over time. My hope is to keep track of what works and what doesn’t.

To assess these interventions, I analyze the results from course assessments at the end of the semester, and compare them to previous semesters. Since most assessment use in my courses are qualitative, I use our institution’s NotebookLM instance to analyze the unstructured text responses. I may also institute a solution of my own using my experience with natural language processing.

Fall 2025

background#

Each week, students in my mathematics course are assigned 8 True/False questions in reference to a notebook like this one, and they are required to write up an explanation for their answer.1 These writeups are meant to give students the opportunity to apply what they learn from the (theoretical) lecture videos and slides each week. The issue is that this creates a “gap between the theory and practice”. In fact, this issue is prevalent in other aspects of our Applied Data Science master’s program. Being able to apply mathematical theory is crucial to the field itself.

Before introducing the intervention, I spent each class meeting reviewing topics from lecture (i.e., the theoretical part of class), trying to address the points that students called out in surveys on Canvas. Clearly, this only addressed one side of the gap (i.e., the theory part), and students reported that the application-based writeups were still unclear. I needed to change the way these class meetings worked on the whole.

intervention#

To address this gap, I decided to organize our class meetings around peer instruction (Mazur, 1997) such that students get the opportunity to practice applying their knowledge through repeated verbal explanation, in class. The aim of this solution is to remove the stress that comes from quiz/writeup “grading” (see my Teaching Philosophy for more on this), and give students a safe place to learn with others.

In particular, after a lecture or review period taking up the first portion of class, I will release the weekly quiz on TopHat. We then run through the steps of peer instruction together (see above). This provides the scaffolding that students will need to connect theory with practice, and write their own writeups more confidently.

outcomes#

So far, the greatest outcome has been student engagement. The peer instruction creates an environment where it becomes only natural for students to interact with one another, and since they’re explaining their own answers, I find it evident that they want to participate. Further, this framework forces students to really think about what they’re learning, and identify any gaps in their understanding.

Otherwise, we can consider the quantitative (and qualitative) data outlined below, with the overarching question: is there still a significant gap between theory and practice? I also will ask about this directly in their course evaluation.

analysis#

More analysis to come …

future efforts (to do)#

  • I’d like to incorporate the peer instruction method into other math-like classes, namely my intro to statistics class. Right now, there are no other classes which have the same “theory-to-practice” issue, but at least this experience has gotten me used to using TopHat, and I do intend to use that in virtually all of my in-person classes.

tools#

Below is a running list of tools I use in this class.

ToolNote
PlayPositHost lecture videos, but also to allow for in-lecture checks for understanding. I use these checks to guide our class meeting review sessions.
HackMDStudents use this to learn how to share their mathematical explanations using LaTeX. It also gives them a great introduction to Markdown syntax, which they’ll be using a lot in the future. Lastly, it has a nice commenting feature which makes feedback easy for TAs and I.
Google ColabI use Colab to host Python code that implements the weekly content into something practical. There are usually visualizations students can use to see what’s going on.

references#

Mazur, E. (1997). Peer instruction: A user’s manual. Prentice Hall.

  1. An example question could be Refer to Situation 1. This matrix also represents an invertible linear transformation. That is, it does NOT “squash” a 4-dimensional vector into a 3-dimensional space. ↩︎