Should we teach math in high school? I say no. Now before you get up in arms with a “math is the foundation of the Universe” argument here is what I mean. We should not be teaching math, we should be teaching how to learn math. Look at the average high school math text book, be it Geometry, Algebra I or Pre-Calc. There is a lot of stuff in there. Of all that stuff we math teachers teach in a year how much is retained by the average student? I am talking the average student here, not the kid that is taking 3 honors courses, is applying for MIT and CalTech scholarships and asks those questions in class where all you can say is “give me a day or two to figure this out”. As a guess (with 33 years of experience behind it) 90% of what we teach in math class goes in one ear and out the other. Don’t believe me? Give your usual end of chapter test to a regular class (not the honors kids, most of them are math geeks to some extent and are usually a school minority) on some messy topic. Trig is always a good one or graphing non-linear functions without a calculator. Now a month later surprise the kids by giving a test on the same material. Without even actually doing this you can predict the results. The scores will be lower. Of course the level of retention will vary depending on the kid and the teacher but overall we can assume a significant loss of knowledge. So why are we throwing all this math stuff at these kids when most of it will be gone in a fairly short time? Personally I think it is tradition. It is the way we math teachers have done it forever and that is the way we are going to continue to do it forever. I do not think the results are justifying the means.

Now where did this thought stream come from? Larry Cuban posted this article from the NYTimes. Now I admit I read newspaper articles with a grain of salt, most of the time they are just hype and BS but this one sort of hit a chord. Right now I am teaching a Math II course, primarily geometry and a dash of algebra, to normal every day sophomores. These kids are not into math. They do not like math. Math is boring, confusing, stupid, useless, weird, not connected to the real world, and involves thinking (a skill not high on their list of fun things to do). Looking at what I have them doing most of the time I have to agree 100%. So I have been head scratching on how to fix this course without throwing the baby out with the bath water.

Now many years ago when I was in high school (Had to walk up hill in 3 feet of snow to get to school. Same thing to get home.) when I wanted the square root of 532 to some accuracy better than my slide rule would give I grabbed a CRC book and looked it up in the table or, if a CRC was not handy, I looked in some book for the ugly algorithm to compute square roots. (For those readers educated in the calculator era this may make no sense to you. Find someone with gray hair to explain.) I did not memorize the square root of 532, I looked it up. In the intervening years looking something up has changed. Google was invented. Access to the internet is expected. It seems to me that the teaching of math has sort of ignored these lovely inventions. I am trying to correct this oversight in my Math II class, hopefully without losing the baby.

(There is nothing really new here but I live in Montana. We are a little slow. One school I taught at had a regular announcement that the kids riding their horses to school were responsible for getting their horse manure at the hitching rail in front of the school to the manure pile in the back of the school. No shit. (Slight pun there.))

All the kids have a smart phone and I am expecting them to use it. The traditional math class consists of “here is a formula (or technique) and here are a bunch of practice problems. I am trying to reverse that. Here is a problem, find a formula (or technique) to solve it. This is not as easy as it seems for me. For many years I have followed the usual math teaching trend of putting something fancy on the board, explaining it, working some sample problems and then dishing out the homework so the kids can get the concept sort of in their heads. With the usual results of having to do the whole thing over again the next year for the same kids in the next level class. An example of my new approach is “Find the surface area and volume of the 5 Platonic solids with edge length 6.” No preamble, no board work, just a sheet of paper with the question. “What the heck is a Platonic solid?” they ask. I reply “You tell me.” The phones come out, the heads get together, and someone says “I found it”. I wander around the room. I do not want them to memorize this formula, I want them to be able to find the formula. I do not want to teach them the math, I want them to find the math then I will help them figure it out.

Most of the math taught in high school is not something for day to day usage. It is specialty math. Even something as common as right triangle trigonometry is a specialty math. Those that use it regularly (not sure who they are, maybe the building fields, and math teachers of course) memorize it, the rest of the world just needs to know how to look it up and use it once they have found it.

There is one minor problem with this approach. No phones on the SAT, the ACT, standardized tests, and so on and on. That is where throwing out the baby comes in. Maybe if I can just get these kids to not fear math and convince them it is not the child of Satan by using this “look it up” approach maybe they will collect the fundamental skills that makes math doable.

I have a General Mathematics textbook published in 1939. The chapters look identical to a modern high school/college pre-calc textbook. The old book is thinner and the chapters are more condensed but it teaches the same topics I teach in pre-calc the exact same way my modern textbook does. Just no pretty pictures or politically correct “extra” at the end of each chapter. There is something wrong here. 77 years with no fundamental changes in material or technique. Try that in Computer Science.

March 13, 2016 at 4:11 pm |

I love your approach! As a CS teacher who was terrible in math (took Algebra I 3 times), I feel the pain of your students. Wish I had a teacher like you! I teach CS in much the same way…. let’s jump in the deep end and think about this… I give support along the way with videos, links, mini-lessons. If the project is engaging and challenging and the students want to do it, they always find a way. But putting it all out there first (here’s what for loops do, here’s variable types, here’s dot notation….) seems counter-productive to me. YMMV.

March 15, 2016 at 2:22 pm |

https://www.maa.org/external_archive/devlin/LockhartsLament.pdf

March 20, 2016 at 10:45 pm |

Another view on ways to teach math so students think: http://www.theguardian.com/commentisfree/2016/mar/11/maths-isnt-problem-curriculum-lacking-imagination