Category: Mathematics
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[mathjax]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…
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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…
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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…
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[mathjax]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…
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[mathjax]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.…
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[mathjax]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 know a way, so if someone does, please tell me. (Edit: There is the SurdText…
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[mathjax]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 “indeterminate” mean anyway? Let’s start with a more concrete question: What is division? Assume we…
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[mathjax]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 functions. Since I’ve been teaching, I’ve noticed that only three of these are emphasized: Sine,…
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[mathjax]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 of a multiple (with the exception of 0). For instance, 8 has the factors {1,…
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Introduction [mathjax]In this entry, I’m going to demonstrate the use of GeoGebra to estimate a value for a fairly tricky trigonometry problem, then illustrate how to find the value using trigonometry and an appeal to WolframAlpha. In so doing, I hope to also illustrate the eight basic standards for mathematical practice within Common Core. Here…