I am writing math quizzes today (algebra, trigonometry, pre-algebra and a mixture of maths for an 8th-grade course). This is difficult for me; I am not a mathematically-minded person. I trace this back to extraordinarily poor mathematical instruction starting in 6th grade. I had math teachers who were boondoggled by the fact that I could not understand what they were talking about as we got into more abstract math; each time I asked a question, they explained the problem the same way, with different numbers. They got frustrated when I asked why something worked the way it did, and I got frustrated by their frustration. When I was seven, my favorite subject was math (according to My Book About Me), but by the time I was 12, the love was all gone.
In this article, the authors present practical solutions for fixing math, specifically,
A math curriculum that focused on real-life problems would still expose students to the abstract tools of mathematics, especially the manipulation of unknown quantities. But there is a world of difference between teaching “pure” math, with no context, and teaching relevant problems that will lead students to appreciate how a mathematical formula models and clarifies real-world situations.
Imagine replacing the sequence of algebra, geometry and calculus with a sequence of finance, data and basic engineering. In the finance course, students would learn the exponential function, use formulas in spreadsheets and study the budgets of people, companies and governments. In the data course, students would gather their own data sets and learn how, in fields as diverse as sports and medicine, larger samples give better estimates of averages. In the basic engineering course, students would learn the workings of engines, sound waves, TV signals and computers. Science and math were originally discovered together, and they are best learned together now.
Showing the practical application of the abstract is key in this; algebra goes from something mysterious and complicated to something applicable (but still complicated), a puzzle to be solved to fix something. In designing the trig quiz, I had to look up what, exactly, trigonometry is used for to convince myself of the value of this discipline. This may seem very disrespectful to the math folks in the world, but I mean no disrespect. One current debate in schools is whether or not students actually need all of the math instruction they receive, or if their academic time would be better spent elsewhere. It is important to me that my students get why we learn something, and so I looked up trigonometry's applications to share. The New World Encyclopedia says that trig is used in navigation and astronomy, music theory and oceanography and a host of other fields that range from the fine arts to the physical sciences (see the whole article here, a very efficient basic intro to trig). That is enough for me; life is long, and the categories are broad enough to include several of my students' interests.
If I had a teacher who had taught me to look at math this way, perhaps I would have gone through school with more appreciation of math. As it stands, I limped through college math, barely, and although I am quick with numbers, it requires extraordinary patience and focus for me to understand the topics I am quizzing. Thankfully, this is good for the brain overall, but I would like to make sure students get the point of math. Maybe there are some questions in math that don't have a satisfactory, concrete answer, but I believe I should be able to communicate the value of higher-level math in a way that makes sense. It is not enough to say, "Just do it."
So maybe, with an approach that incorporates practical application, other subjects and traditional practice, math won't be boring. That gets at A+!