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## The Natural Base e: Thoughts on Teaching

In “Burn Math Class”, Jason Wilkes spends quite a few pages deriving the value of $$e$$. I did not notice him at any point mentioning compound interest. Since we’re currently wrapping up the chapter on exponential functions and logarithms in…

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## Number values and multiple representations

One of the questions my mind keeps returning to is: What is a number? I don’t mean this in a high-level set theory way. I’m not talking about aleph-numbers or other sorts of concepts. I’m restricting my thoughts here to…

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## Speaking English vs Speaking Math

One of the challenges that I see with students learning mathematics is their confusion with what qualifies as the content of mathematics and the language of mathematics. In a famous and enduring article, “Relational Understanding and Instrumental Understanding”, Richard Skemp…

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## Three and a half methods for finding square roots

The easiest way to find a square root in this technological age is to use a calculator. That’s a fine method if what you want to do is simply calculate a square root. However, if what you want to do…

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## It’s Always Monday

In this post, I discuss the Sleeping Beauty problem, which explores how perception can affect assessment of probabilities. First, the video that introduced me to the concept: If you’re not in a position to or would rather not watch the…

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