Mathematics Educators Weekly Newsletter - Thursday, September 29, 2016

Mathematics Educators newsletter

Top new questions this week: Why do we teach complex numbers? In algebra II, USA, we teach our students complex numbers. However, after algebra II, they never use complex numbers until pretty much complex analysis. The whole point of teaching them complex ... algebra teaching applied-mathematics applications complex-numbers   asked by Simple Art 27 votes answered by Ben Crowell 45 votes "Function" vs "Function of ...": how much does it contribute to students difficulties? Most textbooks I've seen (and teachers I've met, myself included) are rather careless about the distinction between variables and functions. For example, when we write $y=f(x)$ we all know that $f$ ... calculus education-research functions   asked by Michael Bächtold 11 votes answered by kcrisman 2 votes Is algebra unnecessarily quadratic intensive? I don't know about all algebra courses, but the following is the basic outline of my algebra years: Alg. I - Lots of linear graphs and solving systems of equations. Alg. II - Lots of quadratics, ... algebra curriculum   asked by Simple Art 6 votes answered by Scott Eberle 2 votes "The following are equivalent" What do you say to the following way of teaching "if" and "the following are equivalent"? Has somebody ever taught it like this? An implication A -> B can be viewed as asserting that B is at least as ... logic terminology   asked by user7213 4 votes answered by Confutus 0 votes Why are proofs by contradiction counterintuitive? And how to make them intuitive? We are tasked to prove $P \implies Q$. So we assume $P$ and are trying to prove $Q$. We assume not-$Q$ ($\neg Q$) and derive a contradiction, establishing $Q$. There ... mathematical-pedagogy proofs logic   asked by Joseph O'Rourke 3 votes answered by dtldarek 2 votes Greatest hits from previous weeks: Why would you teach Calculus before teaching Real Analysis? Let's assume our students are actual aspiring mathematicians. Why would we introduce our students to Calculus rather than Real Analysis? After all, "Calculus is a subset of Real Analysis". He will ... calculus mathematical-analysis   asked by ClassicEndingMusic 19 votes answered by mweiss 51 votes Looking for simple "interesting" math problems that cannot be easily solved without algebra I often find students who dislike algebra. They prefer to work with numbers in solving problems. I believe there are many problems that are hard to solve without algebra. For example: Finding the ... mathematical-pedagogy   asked by kiss my armpit 14 votes answered by Sue VanHattum 23 votes

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