Podcast Summary: Why Is There So Much Math in Science Class?

Hillsdale College K-12 Classical Education Podcast
Host: Scott Bertram
Guest: Dr. Michael Trapeppi, Assistant Professor of Physics at Hillsdale College
Date: April 21, 2025
Duration: ~17 minutes (content, omitting ads/intros/outros)

Episode Overview

This episode explores the question: Why is there so much math in science class? Dr. Michael Trapeppi discusses traditional and classical approaches to teaching science, the pitfalls of rote problem-solving (“plug and chug”), and the philosophical reasons math is central to understanding the natural world through science. The conversation aims to demystify the role of mathematics and encourages educators and students to see science as more than just equations.

Guest Introduction and Background (01:27–03:50)

• Dr. Trapeppi shares his background: undergraduate at Hillsdale (Physics and Math, 2017), graduate study at Ohio State University focused on lasers and optics, and return to Hillsdale as a physics instructor.
• He recalls his high school physics teacher’s creative methods—using cartoon characters and hands-on experiments—as key to his own passion for the field.

  “He would have these cartoon characters that he would print out... and always plop them up on the whiteboard... you'd try to calculate, you know, how far [Donald Duck] is going to fall or something like that.” (03:03–03:26)

How Science Is Commonly Taught: The "Plug and Chug" Model (03:55–07:34)

• Typical science classes rely on textbooks:
  • Teachers present new equations and sample problems (e.g., projectile motion, collisions).
  • Students practice by identifying formulae that "fit" a scenario and substitute in numbers to compute answers.
• This approach, called "plug and chug," is criticized for being:
  • Mindless and mechanical.
  • Focused on answer-getting rather than conceptual understanding.

  “Plug and chug is... just kind of like trying to dig through either your class notes or through the textbook and trying to find what equation matches the problem that you're given... you're not really thinking about why this equation works, why does it fit with your given problem.” (06:09–06:34)

The Problems with Plug and Chug (06:34–07:36)

• Students often pick equations simply because the variables "match," not because they understand their relevance.
  • Teachers see that when students can’t explain their choices.
• This method does not mirror what scientists do in practice.
• It impedes development of scientific reasoning skills necessary for research or real-world problem-solving.

Alternative Approaches: Emphasizing Reasoning and Explanation (07:36–09:42)

• Dr. Trapeppi suggests improving science education not by changing the problems, but by changing how they are assessed:
  • Require students to write explanations for their answers, detailing their methods, assumptions, and reasoning.
  • Go beyond “show your work”; demand clarity and logical structure, as in essay-writing.
  • Encourage checking if their answer makes sense physically (unit checks, reasonable values).

  “You have them explain... these principles apply, and then we derive this equation, and then we check that this equation is, in fact physically possible... and you try to see if the number that you get is actually reasonable.” (08:26–09:20)

• By fostering this approach:
  • Students engage more deeply.
  • They develop habits of scientific thinking and self-correction.

Student Reception and Classroom Impact (09:47–10:50)

• Initially, students may resist this more rigorous, reflective approach—it's harder work.
• Over time, students become more aware when they fall back into mechanical “plug and chug” and begin to appreciate the challenge and depth this method brings.

  “They appreciate the rigor of it and... feel like they understand what's going on. They feel like they're being challenged more.” (10:29–10:39)

Why Is There So Much Math in Science? Philosophical Foundations (11:09–14:59)

• The prevalence of math in science, especially physics, often alienates students.
• The key philosophical insight:
  • Science seeks to uncover underlying order and intelligibility in natural phenomena.
• Mathematics provides a logical structure—a formal language with reasoning—to express, compare, and predict these patterns.
• Notable quotes discussed:
  • James Clerk Maxwell:

    “As students of physics, we observe phenomena under various circumstances and endeavor to deduce the laws of their relations. Every natural phenomenon is... the result of an infinitely complex system of conditions. What we set ourselves out to do is to unravel these conditions to obtain a continually greater degree of clearness and distinctness.” (12:17–12:53)

  • Richard Feynman:

    “Mathematics is not just another language. Mathematics is language plus reasoning; it's like a language plus logic.” (14:11–14:19)

• The remarkable success of mathematical abstraction applied to understanding the physical universe is highlighted as one of the triumphs of the scientific revolution.

Addressing Student Anxiety about Math in Science (14:59–17:08)

• Dr. Trapeppi acknowledges students’ fears about the math in science, especially in physics.
• He encourages reframing:
  • It’s not about just getting good at computations (“don’t judge your success... based solely on your ability to solve problems for a semester”). (15:31–15:44)
  • The real goal is understanding and wielding mathematical tools to clarify ideas about nature.
  • Mastery is a gradual process—success comes not from rote calculation, but from developing clear scientific reasoning.
  • Maxwell quote:

    “The human mind is seldom satisfied and is certainly never exercising its highest function when it is doing the work of a calculating machine... If he can only at last make his ideas clear.” (16:04–16:39)

• Dr. Trapeppi reassures:

  “You have to do the math, but remember that it’s more than just the math. What I care most about is, do you understand the ideas and can you ultimately wield that mathematics to help your ideas become clear?” (16:40–16:56)

Key Takeaways

• “Plug and chug” may yield right answers, but genuine science education requires structured reasoning and explanation.
• Asking students to explain their process in detail leads to deeper engagement and true understanding.
• Math is fundamental to science not as an obstacle, but as a powerful tool for making sense of the natural world.
• Students should aim to understand concepts and develop clarity of thought, not just computational skill—this takes time but leads to lasting scientific literacy.