Something I’ve been thinking about is the way we teach students to solve systems of linear equations using substitution. Consider for example the following system of linear equations: y = 3x + 4 and 2y – 3x = 16. Many textbooks would suggest the way forward is to solve one of the equations for a … Continue reading Solve for y and substitute?
Note: This is part 2 in a multi-part series on fractions. In part 1, I discussed two different meanings for fractions, I recommend you start there. The Whole Story Discussing fractions without discussing their associated whole (also called referent unit) can be problematic. The quantity is assumed to refer to some referent unit. However, I … Continue reading Fractions Part 2: The Whole
When I began teaching undergraduates, I mainly taught mathematics methods courses for elementary education majors. Put simply, I taught future elementary teachers how to teach mathematics. For many elementary teachers, fractions is one of their least favorite topics to teach. For many elementary students, fractions is one of their least favorite topics to learn. So … Continue reading Fractions Part 1: They’re Complicated
Teachers typically emphasize two techniques (though there are certainly others) for solving systems of equations: substitution and elimination. The other day I asked my class of prospective middle and secondary teachers to explain why elimination works. I asked this because as I was sitting at my kitchen table that morning, My students were not able … Continue reading Why does elimination work?