Yesterday’s Other Moment Of Clarity:

The Law of Cosines is a beastly formula, which, yesterday, for the first time in five years, I didn’t ask my students to memorize.

I gave them my reasoning: basically, that ten years down the road, ten months, maybe ten days, they’d forget this formula. It’s inevitable. I’d rather them pour their guts into creatively operating the formula than memorizing it, since, in the Google era, that’s an appropriation of resources I could no longer defend.

At the end of my monologue, I wrote the formula on the board and started passing out tests. One student in the front held up her hand, smiling, the Law of Cosines written brazenly across it.

I'm Dan and this is my blog. I'm a former high school math teacher and current head of teaching at Desmos. He / him. More here.


  1. I’ve gotten to the point where I regularly have a “cheat board” – a section of the white board where there are hints and formulas. They stay there for a couple of weeks, until I rotate them out to make room for new hints/formulas.

    I find that by the time I have to erase them, most students have internalized them already…

  2. I came to the same realization the first time I taught an “advanced” class and had to familiarize myself with the formulas that I forgot since high school and college.

  3. I’m sure there are others, but the AP Stats test has never required memorization of formulas. It’s all about, “Yes, but what can you do with that formula? Do you know when to use it and when to use another one?”

    If I need to use the Law of Cosines in my daily work (heaven forfend…) then I know where to find it and what to do with it.

    A lot of good it did me in college stats to memorize the (ridiculous) formula for standard deviation. I mean, does anyone calculate s.d. by hand?!?

    BTW – the same goes for the periodic table and historical dates (other than a select few, perhaps).

  4. It’s actually a bit more intimidating when I go into a test and they give you an equation sheet or make it open book. If you spent time memorizing, you were hoping for a couple points just for writing down the right equation correctly, but having the equation for free takes the wind out of those free-loading sails.

    So the value of “equation dropping” goes down while the value of equation using goes up. Win win. Unless you didn’t study.

    Nice work though, I wonder how much cumulative stress temporarily memorizing things like the law of cosines has caused us. On the other hand, I can still remember the phone numbers of my friends from 4th grade that I dialed by hand, but I don’t really know anyone’s phone number now because it’s in my cell phone. Does it matter? I guess if my cell phone breaks…

  5. I just finished reviewing about 400 vocabulary words that have been plastered on my walls since September. A bunch of the terms are people throughout time period we studied, many of which my students won’t remember next year. Even I had to refresh my memory on some of the words. How am I supposed to convince kids that they need to know all of these concepts, when I find myself in need of a refresher course before their refresher course?

  6. @Steven – I don’t think the internet will break any time soon, so no worries there. And if it does break, then we have bigger issues…

    In my IB math course, students are given a comprehensive formula booklet at the beginning of the year. They are told that it can be used on any test, including the Exam. My rationale: I’m testing your math skills, not your memory skills.

    @Steven again – And, on those IB Exams, you are still given marks for choosing to use the correct formula.

  7. I gave a test/quest/quiz/assessment on the laws of sines/cosines last week. The formulas were up on the screen the whole time. Some of the cherubs thought I forgot to change the slide. :)

    I gave the seniors a sheet on card-stock with the trig identities. Heck, I don’t even remember the half-angle formulas, why should they?

  8. Hmph. Thought I was being pretty subversive here but apparently I’m the last to board this train. Why don’t y’all post more?

  9. Well, we don’t post more because we are just getting around to realizing how awesome a tool blogs are!

    You discovered that years ago, which is why we look up to you and steal so much from you.

    By the way, just started my blog at, and just posted the graphs I used for a graphing lesson.

    Feel free to take a peek and let me know what you think.

  10. TheInfamousJ

    May 15, 2008 - 8:26 am -

    My state gives the Chemistry students a reference tables and I give them one in class as well. Regardless, my students keep asking whether or not they need to memorize the periodic table. :: sigh ::

  11. Brian Cormier

    May 15, 2008 - 11:57 am -

    I have my students memorize the formula when I feel the formula reflects the concept I want them to understand, like area of a rectangle and triangle, and even the pythagorean theorem. Otherwise, they’re just memorizing letters, numbers and symbols in a seemingle arbitrary sequence.

    Furthermore, if you make them memorize the formula and they write it incorrectly, but otherwise plug in and solve correctly, how much credit should they get?

  12. Interesting. In Finland, at the school level resembling high school (classes 10-12, non-compulsory), the students are allowed the benefit of a whole book of formulas and data from maths, physics and chemistry. However, few and far between are the students who actually know how to use it…