CCT: Course Work

Core Competency 1: Developing Discipline-Related Teaching Strategies (MTH 879, Fall 2024).

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Course taken: MTH/MTHE/CEP/TE 879, Teaching College Mathematics (3 credits), Program in Mathematics Education, College of Natural Science, Michigan State University
Semester: Fall 2024
Instructor: Dr. Jennifer (Jenny) L. Green

Description of the Core Competency

Developing discipline-related teaching strategies means learning how people come to understand ideas in one’s own field and using that knowledge to choose, design, and evaluate teaching practices. For the mathematical sciences, this involves knowing the national guidelines for undergraduate mathematics and statistics teaching (MAA, CUPM, GAISE), understanding the core ideas and habits of mind students should develop, designing tasks that build them, and using research on active learning and assessment to make and test teaching decisions.

I met this competency by completing MTH 879, Teaching College Mathematics, in Fall 2024. The course is built around three questions: (1) How do people learn mathematics and statistics? (2) How do we teach in the mathematical sciences? (3) How do we research and evaluate innovations in teaching and learning mathematical sciences content?

Artifacts

  1. Course syllabus, MTH 879, Fall 2024
  2. Weekly course materials showing the topics and readings covered:
    • Week 1: Introduction to mathematics and statistics education (Hagman 2017; Laursen 2019; Levers for Change 2024; Utts 2015; Zieffler et al. 2017)
    • Weeks 2–3: National recommendations for teaching the mathematical sciences (GAISE College Report 2016; 2015 CUPM Curriculum Guide; MAA Common Vision; MAA Instructional Practices Guide)
    • Weeks 4–5: Core ideas and habits of mind in mathematics and statistics, task design (Tran & Lee 2015; Lee & Tran 2015, SASI Framework; task sets on bivariate data, summarizing data, and probability)
    • Weeks 6–7: Active learning, mathematical microaggressions and microaffirmations (Su 2015; Cawley & Wilson 2023)
    • Weeks 8–9: Article discussions, mathematical proofs and generative AI
    • Weeks 10–15: Student-led seminars

Artifact Rationale

This course content is important because it gave me a research-based vocabulary and set of standards for decisions I had previously made by intuition or by copying how I was taught. The national guidelines (CUPM, GAISE, the MAA Instructional Practices Guide) describe what effective undergraduate mathematics teaching looks like and give me a benchmark to check my own courses against. The task-design frameworks (Tran & Lee; SASI) show how to turn a routine exercise into one that develops reasoning and habits of mind, which is central to how students learn mathematics. The units on active learning and microaggressions/microaffirmations address who feels they belong in mathematics, which matters as much as content coverage. Together, the syllabus and weekly materials show a structured progression from how students learn, to how to teach, to how to evaluate teaching.

Materials Developed During the Course

  1. Lesson plan (final project): Maximal Margin Classifier (PDF). A 90-minute lesson for undergraduates who have completed the calculus sequence. It moves from an instructor-led motivation (classifying spam email), to small-group work on finding separating hyperplanes, to a partner discussion on the meaning and scaling of the coefficients, to a whole-class wrap-up and a hands-on computer activity that exposes the method’s limits on non-separable data.
  2. Student-led discussion: Adult Learners (slides, PDF). A class session I designed and led on teaching adult learners. It contrasts pedagogy and andragogy, introduces Knowles’ five assumptions of adult learners, examines barriers adults face (time, confidence, cost, technology, physical and cognitive changes), and uses Rothwell’s distinction between crystallized and fluid intelligence to ask which teaching strategies work best for adults. The session is built around timed small-group discussion questions rather than lecture.

Rationale for These Materials

  • The lesson plan is the clearest evidence that I can apply what the course taught. It follows a research-based structure (motivate, explore in small groups, discuss, consolidate), puts students to work on the reasoning before the formal result is given, plans what the instructor does while students work, and ends with a task designed to reveal a limitation rather than confirm a recipe. Because the topic connects to my research area (data analysis and machine learning), it is a lesson I can use in my own teaching.
  • The student-led discussion shows that I can research a teaching topic, turn the literature into a session for colleagues, and facilitate active discussion instead of lecturing. Its subject matters for college mathematics: classrooms increasingly include older and returning students, and knowing how adults learn helps me design courses that build on their experience and remove the barriers that keep them from succeeding.

Interpretation / Reflection

When I started this course, I was motivated to learn more about teaching methods and the vocabulary used in discussions about teaching. Earlier that summer I had attended a teaching workshop and realized how unfamiliar I was with many of the terms and ideas. Until then I had mostly designed my classes by intuition or by imitating what I experienced as a student. MTH 879 gave me the foundation I was looking for.

The readings were especially helpful. They answered some of my big questions and left me with new ones, which I think is a good thing. They made me think more critically about traditional teaching methods and when they work or don’t, and one of my goals is to keep asking those questions and looking for ways to improve those approaches.

The class observation stood out the most. I had observed classes before, but always to give feedback to teaching assistants. Observing a full lecture to focus on teaching strategies gave me a new perspective on lesson planning and showed me how much I can learn just by paying attention to the choices an instructor makes.

Preparing and leading the discussion on adult learners changed how I picture my students. Knowles’ principles and Rothwell’s distinction between crystallized and fluid intelligence convinced me that many undergraduates benefit from a blend of pedagogical and andragogical approaches: building on prior knowledge, connecting mathematics to real problems, and breaking abstract reasoning into steps. The lesson plan is where I put these ideas into practice. Instead of presenting the Maximal Margin Classifier as a finished formula, students first ask what it means to separate data, discover that many separating lines exist, and argue about which one is best before the optimization is written down.

Looking ahead, I see myself continuing to teach mathematics and math-related sciences. I enjoy showing students the reasoning behind concepts, and it is rewarding when they finally “get it.” I would also like to work in a research setting that combines mathematics and teaching. To keep growing as a teacher, I plan to attend more workshops, read about teaching strategies, experiment with different methods in my classes, and keep asking students and peers for feedback.