## Numeracy vs. mathematical literacy

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…

Arenas of mathematical mastery

## 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 $$\overline{S_2}$$…

## 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…

Mathematics

## The Pizza Party

In 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…

## 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…

## “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…

## 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…

Mathematics

## 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…

Education

I’m exploring if it’s possible to create a function in GeoGebra that would take an integer as input and create a simplified radical as output. For instance, it would take $$20$$ as input and return $$2\sqrt{5}$$ as output. I don’t…

## Indeterminate vs. Undefined

Here’s something that seems to confuse many people: $\frac{1}{0} \text{ is undefined}\\ \frac{0}{0} \text{ is indeterminate}$ If some number, any number at all, divided by zero is undefined, then why isn’t zero divided by zero likewise undefined? And what does…

Mathematics

## The Six Basic Trigonometric Functions

I read an article today on the six basic trigonometric functions, and I thought there was a particularly important insight that I wanted to present in my own words. When I was in school, we learned the six basic trigonometric…

## How Many Factors?

A post on G+ Mathematics asks: “How many of the positive divisors of 8400 have four or more positive divisors?” A divisor, or a factor, is an integer which evenly divides another integer; in other words, it is the opposite…

Mathematics