First, a riddle… Q. How do you shoot a white elephant? A. With a white elephant gun. Q. How do you shoot a blue elephant? A. Paint him white, then shoot him with a white elephant gun. Back to Units In this TEDx Talk, Randy Palisoc argues that mathematics should be taught as a language. While…
Author: Clio
Zip and Abby
There are a lot of trite websites and apps available for teaching elementary education concepts. And then there are the occasional gems. Zip and Abby, from The Learning Chest, is one of the true gems. The goal of Zip and Abby is not to teach simple “math facts” or to drill on numbers as abstract…
Pizza Math
This gem is timely to my thinking about ratios and units: It seems to have situated itself broadly enough across the Internet that I don’t know if it’s real or a fabrication, but it seems plausible enough. There are, at least, lots of non-teachers who are equally convinced that the question is a trick because,…
Division vs. Ratio
I’ve noticed that the teachers of fractions tend to make a strong distinction between division and ratios, but I haven’t entirely understood why. In my mind, ratios and division are intimately related, even inextricably so. However, my reflections on the abstract unit has brought me to a realization that there is one significant difference between…
Philosophical Natterings: Abstraction
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…
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….