Why Is There So Much Math in Science Class?

Summary

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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)

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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.

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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)

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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)

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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.

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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.

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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)

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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.

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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)

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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.

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Transcript

[Podcast Announcer]

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[Scott Bertram]

Welcome to the Hillsdale College K12 Classical Education Podcast, bringing you insight into classical education and its unique emphasis on human virtue and moral character, responsible citizenship, content, rich curricula and teacher led classrooms. Now your host, Scott Bertram.

Thanks for listening. The Hillsdale College K12 Classical Education Podcast is part of the Hillsdale College Podcast Network. More episodes at podcast hillsdale.edu or wherever you get your audio. You also can find more information on topics and ideas discussed on this show and at our website, k12 hillsdale.edu.

We'Re joined by Dr. Michael Trapepi and he is assistant professor of physics here at Hillsdale College. Dr. Trapeppi, thanks for joining us.

[Dr. Michael Trapeppi]

Thank you for having me on, Scott.

[Scott Bertram]

Talking today about science, a little about how we teach science, and eventually getting to the question, why is there so much math in science class? Before we begin, tell us a little bit about yourself. You were a student at Hillsdale. You're back teaching at Hillsdale.

Tell us a bit about that journey.

And maybe why you fell in love with science at some point in your life.

[Dr. Michael Trapeppi]

Oh man, that could go on for a while. But so yes, I was a student.

Here at Hillsdale, graduated class of 2017, majored in physics and math, no surprise.

I suppose, and went on to graduate school at Ohio State, which is controversial in these parts, although thankfully we're close enough to the Ohio border that it's not a capital crime.

[Scott Bertram]

Sure, you've got a few friends here, I suppose.

[Dr. Michael Trapeppi]

Yeah. And so there I studied lasers and.

Optics and that's what I did my dissertation work in and then, you know, ended up back here.

So wasn't, wasn't the initial plan, but.

You know, I'm glad to be back.

And so now I teach physics at the college. My normal course load includes our Physics.

100 course, which is kind of the introductory physics course as part of the core curriculum. And then also I teach our sophomore physics majors, Introduction to Waves and Optics.

So yeah, I guess I really fell in love with physics in high school. I had a really good physics teacher.

He was very good at making things down to earth.

And he would have these cartoon characters that he would print out laminate and put magnets on the back of them and always plop them up on the whiteboard and use them and all sorts of examples in. So you'd have like, Donald Duck, you know, running off of a cliff, and you'd try to calculate, you know, how.

Far he's going to fall or something like that.

[Scott Bertram]

Should be the Roadrunner off the cliff, right?

[Dr. Michael Trapeppi]

Yeah, well, I guess I was. Yeah, that's true. Or Wiley Coyote.

[Scott Bertram]

Yeah. Yeah, exactly. Yeah.

[Dr. Michael Trapeppi]

So, yeah, and he also just had a.

He had a storeroom full of just.

Different pieces of equipment that you could use.

And I mean, I remember staying after school and just trying out different experiments in that.

So that's kind of what really got.

Me interested in physics and kind of going on from there.

[Scott Bertram]

So take us inside, say, a typical science classroom. What is a typical way for teachers to address science and present it to the students?

[Dr. Michael Trapeppi]

Yeah, so, you know, typically it's done with, you know, some sort of textbook. And what the teacher will typically do is, you know, cover some section of the textbook. Let's say it's projectile motion or collisions.

Of two objects, and they will introduce the. The topic to class and give some.

Example scenarios and problems, usually write down some equations. And then homework assignments will consist of, you know, kind of variations on those situations, asking the students to solve for some answer. Whether it be like, you know, if we go back to the, the. The roadrunner, Wiley Coyote, you know, if roadrunner is running off of the cliff at, you know, 100 miles per hour or something, and the cliff is, you know, 100ft high, you know, how long does it take for him to fall? Assuming that it's not the cartoon physics, he actually uses the same equations that we do or like in, in collisions, you know, if you've got, you know, one object traveling so fast and it hits another object, what's the final velocities of the two? So problems of that nature, and they usually kind of change out, you know, what information, you know, what information you don't know. And so that is the, the typical situation in science classes. I mean, even in chemistry and biology, it's similar situations, though slightly different context. You may have things like, you know, you have the temperature of water, let's say, and how much energy does it.

Take to get it to a different temperature? That might be a good chemistry question. Or biology related to, like, cell growth and the, you know, given the rate of mitosis or something.

[Scott Bertram]

So what's the problem with that kind of approach. And you. I'm not a science teacher. You introduced me, though, to the phrase plug and chug before we started our conversation. So what's wrong with that approach? And what's wrong with plug and chug?

[Dr. Michael Trapeppi]

Yeah, so. So the problem with it is that for.

For those that don't know.

So plug and chug is kind of this. And it might be the experience that most people have, which is that, you know, as you're trying to solve these problems, what you're often doing 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. And then you're trying to just kind of plug in, stuff numbers into that.

Equation, so solve it and get the answer.

And, you know, that's kind of the. The typical experience. And the problem with it is that it is a little bit mindless. Like, it kind of just turns into you just kind of combing through, you know, the text, and you're not really thinking about why this equation works, why does it fit with your given problem. You're just like, whatever gives me the right answer. You know, we'll go with it. And you see this a lot on the teacher side, too. You ask students, well, why did you pick this equation? It's like, well, I.

You know, this.

This problem had time and this problem, and I knew there was velocity, so I kind of just found a problem that had time, an equation rather, that had time and velocity and kind of stuck it together. And it's like, okay, well, that wasn't the right equation. So it just produces a certain mindlessness, and it. It doesn't set up students for what.

You actually do in science as a.

Researcher, because oftentimes the equation you want or, you know, the way you want to analyze a situation is not just a classic textbook problem problem. So that's the.

That's the issues you run into.

[Scott Bertram]

All right, so if that's not the right way or the way we want to approach it, what are some alternatives? What are some better ways?

[Dr. Michael Trapeppi]

So a better way to do it is just to not necessarily change the.

Problems themselves, but to change how you assess the problems.

So one thing is to, you know.

Instead of just asking for the correct answer, you can have the students write.

Out their explanation for how they got the answer. And, you know, this is a little bit more than just showing work, because that's a little bit of a broad term. And. And sometimes if you tell the students to show their Work. What that means is just kind of a disorganized assembly of numbers and variables kind of tossed about the page. And so, you know, really one way to think about it is, you know, just as in an English class or.

A history class, you, you are asked to write an essay or a short.

Paragraph on some sort of topic. You know, you, you do the same thing that if you're given a problem with, you know, why Wile E. Coyote running off a cliff, you know, you ask them first, let you know, you have them explain. Okay, well, in this situation, these principles apply, and then we derive this equation, and then we check that this equation is, in fact physically possible.

So you do things like units, checks, and that.

And then you, you plug in the numbers and you get an answer, and you try to see if the number that you get is actually reasonable. You know, is, is it taking a tenth of a second to fall 100ft, which seems a little bit unrealistic, or is it taking, you know, five hours.

Which is also unrealistic? You know, we'd expect it to take, I don't know.

I didn't actually do the math, so don't, don't quote me on it. But, you know, like, maybe a minute or something.

It's a little more reasonable there.

So that's just one, one alternative to. And you don't have to change anything about the problems that you assign.

You just have to simply ask the students to kind of explain their reasoning.

More and, and hold them to it. If they, if they don't explain it clear enough, then you tell them that, and you can decide how you want to dock them points and all those logistics. But make it clear that this is, this is the expectation.

We don't want you just mindlessly searching through a book and plugging numbers in.

[Scott Bertram]

So does this generally result also in more engaged and more interested students in the classroom?

[Dr. Michael Trapeppi]

In my experience, it has. Now, they will fight it at first. So for those, for those out there that are excited to try this, I will say they will fight you on it. But what they will find is that after doing it for a while, they, they will know when they're asked to.

Just plug and chug again, if they go into a different class or they.

Go into, you know, later in the semester, and you, you know, don't you, you know, you. Don't you take away the, the, the.

Stringent requirements earlier, they'll, they'll notice when they're just plugging and chugging.

And I've seen that with, with my.

Students, and they they appreciate the. The rigor of it and that they.

They do feel like they understand what's going on. They feel like they're being challenged more.

They're not just being told to kind.

Of do certain problems because that's what's expected of them.

So it is worth it, even though.

It seems like it's. More work, both on the student's part.

And on your part as a grader, trying to go through this, talking with.

[Scott Bertram]

Dr. Michael Trapeppi from here at Hillsdale College. He's an assistant professor of physics about how to teach science. And then the second part of this question we're talking about is, why is there so much math in science class? Where do we begin to explain that?

[Dr. Michael Trapeppi]

Oh, man.

It's a big philosophical question. And kind of the reason my talk is about this is because it's a.

Thing that seems to turn people off.

The most about science class and especially physics. The one thing you get when you tell somebody that you study physics or.

That you're a physicist is that they're like, oh, the math. I just couldn't do it.

Which begs the question, like, why. Why is there so much math in physics class? Like, you know, you don't. You don't worry about it in other classes. So. And I think it. It goes back to this, you know, kind of philosophical discussion about the.

The interplay, these two disciplines.

And here I just have kind of a few quotes from some.

Some physicists on this.

But for one thing, is, what is.

The goal of science? What is it that we're looking for?

And, you know, here James Clerk Maxwell, who is the kind of the father.

Of electricity and magnetism, he came up with the equations that kind of unified electricity, magnetism and optics in the 1800s.

And he says, you know, quote, as.

Students of physics, we observe phenomena under various circumstances and endeavor to deduce the laws of their relations. Every natural phenomena is to our minds, 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. So the idea here is that science is about trying to understand the natural world and understand its. Its principles and ultimately give it some sort of intelligibility.

And that we see so many phenomena and we want to try to understand.

Is there a connection between, you know, objects falling to the ground and the orbits of the planets? Is there a connection between the lightning.

That comes down from the sky and.

The electrical circuitry that we have or static electricity that we Encounter.

So that's kind of the heart of what science is, is going after. And, you know, what mathematics tries to do is give you logical structure. It is kind of this system of axioms that allows you to be able.

To deduce, you know, certain statements and that. And it.

It allows you to work with this. It allows you to work with these.

Concepts in a very rigid manner that.

You know, if you were just trying to kind of think about them more loosely, you'd be prone to kind of not, you know, maybe making a mistake.

Or kind of losing track of terms and that.

So, and it's, you know, to kind.

Of quote Feynman here, Richard Feynman, I should say. He's worked a lot on quantum electrodynamics, which is the.

Basically taking Maxwell's equations and now applying quantum mechanics to them.

And he says that mathematics is not just another language. Mathematics is language plus reasoning is like a language plus logic.

So. And so the reason why this becomes so important in science is that, you.

Know, we want to understand nature, and mathematics gives us kind of logical structures.

And so it just seems very natural.

Then that we want to try to apply these logical structures to nature.

And kind of the astonishing thing since the scientific revolution is that this has been successful, that you can take these.

Mathematically abstract objects and you can apply them to nature and you can learn things about them and you can start to understand the various connections between physical phenomena.

[Scott Bertram]

You mentioned you get this objection in physics and the sciences about this question about math and science. How do you deal with that with students? What do you tell them about sort of getting past that block?

[Dr. Michael Trapeppi]

I would say that it's part of it is just. You have to accept it. It's. Sorry, I don't. I don't have a. There's not a softer way to it, but let's put it this way. It's. You have to deal with a lot.

Of math, but it's not about the math.

So.

And I would say that you should not judge your success in science based solely on your ability to solve problems for a semester like that is not.

The key to science. And that's part of, you know, what. What kind of moving away from this.

Plug and chug model is about is.

That it's, you know, science is about.

More than just taking equations, plugging numbers into them and getting answers. It's about this, trying to understand the structure and the intelligibility of nature.

And kind of. There's a.

There's a great quote by Maxwell about this. This, you know, using mathematics in science. And he says, 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. What the, what the man of science.

Whether he is a mathematician or a physical inquirer, aims at, is to acquire and develop clear ideas of the things he deals with. For this purpose, he is willing to enter long calculations and to be, for a season, a calculating machine if he can only at last make his ideas clear.

So what I tell students is that.

Yes, 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?

And that's a, that's actually a long process.

It's not something that you can just get in just a semester.

You know, it takes, it takes many.

Years to start to get to that process.

But knowing that ahead of time, I.

Think, you know, kind of helps alleviate the pressure of feeling like you need to be a whiz at mathematics to just survive science class or something.

[Scott Bertram]

Yeah. Dr. Michael Trapeppi is assistant professor of physics at Hillsdale College. We talk about teaching science and why is there so much math in science class? Dr. Trapepi, thanks so much for joining us here on the Hillsdale College K12 Classical Education Podcast.

[Dr. Michael Trapeppi]

Thank you.

[Scott Bertram]

I'm Scott Bertram. We invite you to like us on Facebook search for Hillsdale College K12 classical education. You also can follow us on Instagram hillsdalek12. That's hillsdalek12 on Instagram. Thank you for listening to The Hillsdale College K12 classical education podcast, part of the Hillsdale College Podcast Network. More at Podcast Hillsdale Edu or wherever.

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