Effective mathematics involves two distinct acts: Parsing and writing mathematical symbols to create meaningful messages Applying an understanding of mathematical relations and objects It seems to me that we have two terms at our disposal: Numeracy and mathematical literacy. It also seems to me that these two terms are used somewhat interchangeably. (“What is numeracy?”)…
Author: Clio
SSA Congruence: Constraints
In my last post, I pointed out that SSA is in fact sufficient for determining all three sides and angles under certain conditions. In this post, I will specify those conditions, with illustrations. Given two noncollinear segments \(\overline{S_1}\) and \(\overline{S_2}\) and angle \(\angle A\), where \(\overline{S_1}\)’s two endpoints are the vertex of \(\angle A\) and an…
Fibs Our Geometry Teachers Told Us: SSA
There is a standard litany of theorems involving proving triangle congruence that has remained largely unchanged since my high school days. I was told that, to prove that two triangles are congruent, we need three pieces of information. The abbreviations were given as SSS, SAS, AAS, and ASA. Astute students would ask about SSA (or…
The Pizza Party
n this post, I’d like to reflect on story problems and the purpose of mathematics education. Consider this problem: Every week, Julie invites some friends over for pizza. Last week, she had four friends over and they ate one whole pizza. This week, she had two more friends over. If she orders two pizzas, how…
Object-Oriented Geometry
In an earlier post, I reflected on the relationship between mathematics, language, and computer programming. One detail of that has been on my mind quite a bit lately, as I’ve been teaching geometry. While early computer programming was heavily reliant on a strong knowledge of mathematics, particularly algebra, I think that programming has evolved to…
“Two Kinds” of Zero: Same But Not The Same?
I recently got into a protracted discussion in which the other person insisted that the fact that the character 0 is used in place value notation is merely a place holder is evidence that zero is not a number, but rather a concept we use to indicate the lack of a number. I have long…
Euclid’s proof of infinite primes
It has been known since at least Euclid’s time that there are an infinite number of prime numbers. Here is his basic proof: Imagine that there is a finite set of prime numbers, P. Let N be the product of all the elements of P, plus 1. N’s factors do not include any element of…
My Muse
I smothered my muse with a down-filled pillow And left her corpse stretched out, Naked and prostrate, On the futon in the spare room. I held her in my dreams for a fortnight, Then discarded the memory, Wretched and withered, To the wraiths that live behind the house. But her siren call kept singing to…
The Rubik’s Cube and task completion
Part of my shtick as a Geometry teacher is the Rubik’s Cube. I have a 3^3 and a 5^3 in my room; I’d had a Void as well, but it’s wandered off (perhaps due to my own doing). The students will distract themselves with the cubes; some of them will ask me to do it….
Your Song
I wrote your song last night In words of sulfur and strychnine Writ in blood on onion skin I set it on fire And watched the smoke curl Up Up Up And Nevermore Now I’m humming the melody Softly to myself Thinking only Of you — ptkh 10.21.14