# Tidbits

A small collection of unrelated items.

• My future teachers see things differently than my readership. Readership was strongly in favor of pennies as parts of a dollar, with the dollar being the natural unit. My future teachers were strongly in favor of the penny as the natural unit, and the dollar being composed of pennies.
• Both ideas are correct.
• The results from my classroom ought to at least make us stop and think about the effectiveness of money as the go-to tool for explaining decimals.
• At least one of my students remembers the pennies/dollars conversation as one in which I came out in favor of a dollar being composed of quarters.
• I remember things differently.
• The morning after the temperature conversation I documented recently, it was even colder. I asked Griffin to guess the temperature, with the hint that it was below zero. He guessed -10. It was -7. He had no problem stating that his guess was 3 degrees too cold.
• I had a conversation with Sadie Estrella recently in which she made me wonder, What is the right amount of information for third graders to have about similar shapes?
• I have no idea what the answer to that is, and correspondingly I wish someone would write the geometry equivalent of Children’s Mathematics.
• Friday marks the first of several meetings of a Math Teaching Seminar I am leading with my colleagues that features readings and videos from Keith Devlin, Sal Khan, Dan Meyer, George Polya and Peg Smith (Five Practices, anyone?)
• The ALEKS developmental math curriculum includes (among many others) this topic: “Solving a rational equation that simplifies into a linear equation,” which seems entirely too specific to me and exemplifies what is broken in so much of developmental mathematics.
• My future elementary teachers struggle think explicitly about patterns and struggle to think recursively.
• My College Algebra students think recursively and struggle to think explicitly.
• I do not understand why there are names for arithmetic and geometric sequences, but not for those that are described by a quadratic function on the natural numbers (except special ones like square and triangular numbers).
• If something is free, according to Tabitha, it cannot be described as an extreme case of cheap.