Recently, a video showing a snappy way to add fractions was shared on the BCAMT listserv. Thankfully, it was panned.

This “butterfly method” also appears in Elizabeth DeCarli’s Ignite presentation, this time to help illustrate that “meaningful representations are greater than cute mnemonics.”

In my previous post, I wrote about one way in which my Math 10 teacher tried to make math memorable for his students. (Yes, I realize that since I still remember this, he was successful.) I also wrote about how this didn’t build any understanding.

As a teacher, sometimes I’d be frustrated/puzzled by what I heard from my students. Negative exponents send numbers “to the basement” (or upstairs if they’re already in the basement). The “Front Door Bomber” has one bomb for each person in the house (the distributive property). Why is a negative times a negative a positive? “When something bad happens to a bad guy, that’s good.”

When something bad happens to a good guy…

But I, too, was guilty.

I’m not talking about the usual suspects, FOIL and SohCahToa. I’m talking about “bacon and eggs”. Secondary math teachers can see slides 3 and 4 below and figure it out. Others probably stopped reading two paragraphs ago.

I imagine my students’ calculus professors being frustrated/puzzled by this. That makes me smile. A little. On the inside.

Aside from being unnecessary, two times out of three it’s incorrect and misleading. For example, in slide 8, is *x* the exponent or the answer?

I’ll no longer use FOIL in my classroom. Through algebra tiles, I’ll emphasize an area model. I’ll have a tougher time letting go of SohCahToa. It does help students memorize the definitions of the three primary trig ratios. However, whenever I asked my Math 10 students what they knew about trigonometry from Math 9, they would just say “It’s that SohCahToa thing”. No mention of big ideas or similar triangles. Suggestions?

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I’ll resist evaluating bacon and eggs.

I will, however, take this opportunity to recruit you to my “name the result of exponentiation” campaign. We have product and sum and difference and quotient. We need a name for the result of exponentiation (and your implicit proposal of “answer” is no good, so don’t even try; logarithm calculations have answers too).

Just to be clear, I hope this post doesn’t suggest that I’m proposing this mnemonic (implicitly or explicitly). Rather, I shared what I once did in my classroom before I saw the error of my ways. I tossed it the last time I taught logarithms. Tossed using PowerPoint in class too.

Above, I meant to refer to slide 7, not 8, but either way, we agree “answer” is no good. “Answer” was chosen because an “a” word was needed to match “and” in the mnemonic. (I can’t take the credit/blame for inventing this. Just for using it.) This is the problem with choosing cuteness over sense-making.

You’re right. It would be nice to have a name for the result of exponentiation. My McGraw-Hill Math 9 text calls 4^2 a power and 16 the value of this power. But we use “power” and “exponent” interchangeably (should we be?) and “value” is no better than “answer”.

Holy crap. We introduce logs as the inverse of exponents by graphing y = 2^x and its inverse on the same set of axes, symmetric to y=x and swapping x and y to get the points on the inverse graph. Then I blame someone other than myself for naming it the log function. I never heard of the bacon stuff, and I’m 35 years in classroom.

I have to object to killing FOIL. When you use complex numbers you get to FLOI. I still like it.

SohCahToa is a tough one, but I fight it hard. I give in well after plenty of exploration and mention it about 2 days before the test. When the mnemonic-loving students angrily say “why didn’t you say that before?” I just stare blankly and say “I just said it now.”

After 14 years, I finally taught Alg 2 last year and stumbled. My honors kids resisted exploration, and I consistently pushed back. But their favorite questions when they made conjectures were “will that always work?” I said yes once, and a kid came up with a counterexample. It was a great learning experience for all of us. But it also taught me to never go there with students.

Even if I know there is a shortcut that will always work, I always shrug it off when asked. Keep em skeptical. Then we’re playing with something for the first time, test, test, test and seek generalization, but always keep an eye out for that counterexample.

The worst thing about mnemonics is not that they almost always fall apart, they don’t encourage understanding, and never justify anything; it’s that they kill curiosity and creativity–two important character traits that too many math teachers out there disregard.

As a student, I have to disagree with you. I never understood math. I still don’t now. In fact, I’m in the middle doing my math homework and needed a refresher on the bacon and eggs thing.

These mnemonics help me to learn and understand what I’m required to do. SohCahToa, when I had geometry, gave me a way to remember how to do the sines, cosines, and tangents. I can still do those to this day. The reasons those students who couldn’t remember anything but SohCahToa wasn’t just because it was a weird acronym. Yes, it was something that stuck in their minds because it was one. But they didn’t remember anything because, let’s be honest, not every teenager cares about remembering every little thing about math! In fact, most of them don’t! Who cares about similar triangles if they’re not using them in day-to-day life? I’m speaking from experience as a teen and from what I hear from classmates daily.

FOIL helps me distribute properly. I’d probably mess everything up without it.

A teacher once explained to use in the absolute oddest way ever how to reduce a weird number under a radical. I can’t reexplain it, but whenever I have to reduce a radical, I got back to that dumb lesson and do the problem right.

For me, these “cutesy” mnemonics actually get me to learn about the math I’m doing. Most people remember things with a dumb rhyme. It’s just how our brains work. And if these rhymes work almost all the time, then what is the harm?

and to answer your question about slide 8, X is supposed to be the base – neither exponent nor answer. Maybe if you actually paid attention to what you were bashing instead of just being cranky about it, you’d understand what it was teaching you. Then again, perhaps you wouldn’t – your brain clearly learns differently than mine!

Students all learn different things ways. Some will understand your area model. Some will understand FOIL. Find out what works best for each student and teach them the way they need to be taught instead of generalizing them all. I guarantee if you work with each student as you can (because again let’s be honest, you probably have 30 kids a class which has been proven too many times to be a bad way of teaching) and teach them in the ways they learn best, you’ll get good results!

After all, you wouldn’t tell a person who needs to SEE how to do it they can only learn through audio-recording. Their performance would fall because their brain can’t understand it that way. That is just how it works.

So please, if a student doesn’t get the math by your area model, teach them FOIL. They might understand it that way and do it right. Everyone’s brain works differently. Work to the student’s needs instead. It’s basic psychology.