# What’s Wrong With Algebra-Based E&M?

It’s summer time. For me, that means I’m getting ready for summer classes. Yay! Well, at least I get paid—so that’s good, right? This year, I am teaching the physics for elementary education majors and the second semester of algebra-based physics (electricity and magnetism).

Just to be clear, there are usually two types of introductory physics at the college level. First, there is the calculus-based physics sequence. This course is for physics majors, chemistry majors, math majors…stuff like that. Of course it assumes that the students can use calculus.

The other version is the algebra-based. It does NOT use calculus. The students that take this (at least at my institution) are mostly biology, engineering technology. If you want to consider the course goals, you really need to know who is taking the course.

In order to see the problem with the algebra-based course, let me describe the second semester of the calculus-based course. For this course, I use Matter and Interactions (Chabay and Sherwood, Wiley). It’s a great textbook—here is my review of this textbook from 2014. Here is a short summary of the approach (for the second semester).

• What is the electric field?
• What is the magnetic field?
• How does matter interact with the electric and magnetic fields?
• What is the connection between electric and magnetic fields—Maxwell’s Equations.

For me, it’s all about building up to Maxwell’s Equations. Just to be clear, here are Maxwell’s Equations.

$\oint \vec{E} \cdot \hat{n} dA = \frac{1}{\epsilon_0} \sum q_\text{in}$

$\oint \vec{B} \cdot \hat{n} dA = 0$

$\oint \vec{B} \cdot \vec{dl} = \mu_0 \left[ \sum I_\text{in} + \epsilon_0 \frac{d}{dt} \int \vec{E} \cdot \hat{n} dA \right]$

$\oint \vec{E} \cdot \vec{dl} =- \frac{d}{dt} \int \vec{B} \cdot \hat{n} dA$

Of course there are many different ways to write these equations, however—one thing should be clear. You can’t really grok Maxwell’s Equations without calculus. You need to understand both derivatives, line integrals, and surface integrals.

Now for the algebra-based course. If you don’t have calculus, you can’t really get to Maxwell’s equations. Oh sure, you could do things like Gauss’s Law and Ampere’s law, but it would just be a “how do you use this equation”. Although it’s still true that Maxwell’s equations are sort of magical, without calculus they are just a game.

It’s sort of like teaching long division to 5th graders. Sure, they can learn the process of finding a division value but using the steps—but why? Why use long division when you could just use a calculator? However, if you use long division to understand the number system and division, that’s cool. But it seems that most classes just teach the “how to long divide” without going into the details.

This is exactly where most algebra-based physics textbooks end up. It becomes a giant equation salad. A bunch of equations that have no derivation. Yes, students can be “trained” to use these equations, but I really don’t see the point of that.

I should point out that there isn’t a problem in the first semester of algebra-based physics. A student can use the momentum principle or the work-energy principle without calculus. It’s not a big problem.

OK, so what am I going to do? Honestly, I don’t know. Here are some final thoughts.

• What is the ultimate goal of this course? Why do biology and engineering technology majors take this course? The course goal will shape the course material.
• I have two options for textbooks this semester. They both suck. OK, they don’t actually suck—but they are just a bunch of equations.
• It would be nice to just focus on observable stuff and modeling. Do something like measure current and voltage and produce a linear function relating the two. Oh, how about repeating historical experiments to see where all this stuff comes from?

I’ll keep you updated.

## 2 thoughts on “What’s Wrong With Algebra-Based E&M?”

1. SUSAN BARBER says:

I am wanting you to continue these thoughts. I am having a hard time envisioning these ideas as an AP physics teacher – and my students have no clue where they’re heading in life. Right now my goals are to show that reality can be modeled using math and how to persevere in multistep problems.

2. Paul Lulai says:

Graphical derivations seem to make a bit more sense to students in introductory physics courses than standard mathematical derivations.
I think that physics majors and future PhD students find derivations interesting. Otherwise, most derivations (to a large majority of students) are seen as a continuous “giant equation salad.

Also…

Wondering how r/r^3 went.

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