Background One of the thoughts I find myself returning to frequently is this: There is the belief shared among high school mathematics teachers that the struggle students have with algebra is that it’s the first time they’re exposed to abstraction. This isn’t true. The first abstraction in mathematics comes at such an early age, and…
Category: Mathematics
Tangents and the Pythagorean Theorem
A common exercise that’s used to reinforce the concept that the tangent of a circle is perpendicular to its radius involves finding the radius of a circle given two measurements which are related to the tangent and the diameter secant. For example, students might be asked to find the radius of this circle: In the…
Spelling and Math
Last night, as part of our learning-play, I asked my five-year-old son how to spell “night”. He told me “nitk”. That got me thinking about math education. English spelling is notorious for its quirks and oddities. In the case of “nitk”, my son told me it was because he knew a “k” went in there…
Radicals and Mixed Numbers
The lesser known of two math memes currently wandering around the Internet involves an interesting equation: \[\sqrt{2\frac{2}{3}} = 2\sqrt{\frac{2}{3}}\] This has spawned at least three discussions I’ve seen so far: What other values is this equation true for? Is this example good or bad for students? What’s with mixed numbers, anyway? I’ll discuss each topic…
Introducing the Spry
Some time ago, the discussion on π being the incorrect number for calculations in trigonometry, in favor of τ (2π), led me to muse about creating a unit to replace the degree, called the wedge and being equal to nearly two degrees (100W = 60°). I found myself musing about the topic again, but I’ve…
Polygon Sets: Doing the Math
In my previous post, I created sets of regular polygons in GeoGebra by setting a parameter of the polygons equal to a constant. In this post, I will show the mathematics for determining the side length given a particular parameter. The values I calculated were side length, radius length, apothem length, area, height, and width….
Polygon Sets
I recently found myself creating a set of regular polygons for a worksheet. I used GeoGebra to create them, and then free-handed the zoom in order to get them consistently sized. This led me to wonder what “consistently sized” would mean when it comes to polygons. There are six basic values of a regular n-gon:…
Reflections on Fractions
I was reading an article on fractions, waiting for students to show up for after-school tutoring. One of them asked me what I was reading, so I told him. He groaned. I asked him what his least favorite topic in mathematics was, and he told me it was fractions. I nodded, saying that I reckoned…
Three Card Monty Hall
Imagine we are playing a game of cards. In this game, there are only three cards in the deck: An Ace and two Kings. I will deal you one card, and I will keep the other two. You win if, at the end of the round, you are holding the Ace. You are not allowed…
Thoughts about the Cracks
An adult friend is getting tested to see if she has a formal neurological problem that would account for her struggles with mathematics. She asked how it could be that she might make it all the way through public education without being tested for such a learning disability (LD). Here were my thoughts; keep in…