When students are learning a new concept we tend to define the concept and give some examples. Consider right angles, we might first define them as angles that are 90 degrees and then show some examples like these: This idea is all about going just one step further by adding in some creative non-examples. Non-examples … Continue reading 180 Ideas: #3 Creative Non-Examples
A small idea to celebrate wrong answers in the mathematics classroom. Continue reading 180 Ideas: #2 Ask for a Wrong
When I was a new teacher I planned my year out with the help of my district and textbook pacing guides. I knew I needed to get through X number of chapters in X weeks. I typically started by mapping out how far I needed to get through by midterm, then I put in the … Continue reading 180 Ideas: #1 The Flex Day
I taught high school mathematics in Orlando, Florida. My first day in the classroom was literally my first day in the classroom. I had earned a B.S. in mathematics with a minor in anthropology at the University of Florida. As a first generation college student, I knew I should go to college, but I wasn’t … Continue reading 180 Ideas: The Premise
Recently, I’ve noticed that we are in the midst of a purposeless, clutter epidemic. It’s hard to trace the start of this epidemic. Perhaps it can be traced back to the rise of Pinterest and easy access to classroom inspiration. In any case, many classrooms are just filled with visual clutter that has little to … Continue reading The Purposeful Classroom
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?
Why this blog now? Continue reading Mathematically Educated