Multiplication is vexation,
The Rule of Three doth puzzle me,

(old nursery rhyme.)

My first years of teaching, I worried my students looked at me much like Ben Stein as the teacher in Ferris Bueller’s Day Off. I cringe to think about the series of monotonous and leading questions I strung together to a room of dazed students slowly wilting in front of my eyes. “Bueller? Anyone?”

NCTM has called for structural and curricular changes in high school mathematics. Learn about how IM’s high school curriculum is aligned with the vision put forth by NCTM to end tracking, implement effective targeted instructional supports, and broaden the focus of teaching high school mathematics beyond college and career readiness.

Supporting high-school students to write detailed, precise proofs is challenging. Learn about some of the design elements that IM used to invite students to a deep exploration of proof.

You will never have to subtract again.

Students sometimes learn about addition and subtraction of integers using integer chips. These are circular chips, with a yellow chip representing +1 and a red chip representing -1. You start with the all-important rule that $1 + (\text-1) = 0$, so you can add or remove a red-yellow pair without changing the number. To calculate the right hand side of the equation in the title, $3 + (\text-5)$, you put 3 yellow chips together with 5 red chips, then remove 3 red-yellow pairs, leaving 2 red chips. So $3 + (\text-5) = -2$. Continue reading “Why is 3 – 5 = 3 + (-5)?”

Having an extended period of time to teach a lesson can be an advantage in a problem-based classroom. Students and teachers can savor the questions that are asked. Activities can breathe in a way that they can’t in a shorter period of time. But questions about planning inevitably arise. We find ourselves asking questions like: Do I simply merge two lessons? What stays? What goes? How do we ensure that we engage our students in the right conversations that will prepare them for the next leg of the journey?

Teaching mathematics is a continuous cycle of identifying where each student is in their learning trajectory and determining meaningful ways in which to build on their current understandings. While we often have little control over students’ mathematical experiences before they walk into our classrooms, we do have complete control of our own learning.

At the end of the day, this wasn’t about focusing on the objective, it was about making the objective meaningful to him.”

Open House night; cue anxiety and sweaty palms! Hope my students’ parents don’t mind.

I just began my seventh year of teaching middle school mathematics. Middle school is a limbo land filled with prepubescent pre-teens, drama, and students trying to find their individual voice without drawing too much attention to themselves (sigh). There are sixth grade boys and girls in my class who are taller than me, 5’9”. Some of the boys have mustaches while others still look like they’re in third grade. It’s a difficult year for the students. This is their last year before moving onto the even weirder, and much more confusing junior high. Students are anxious about this being the last year of elementary school, and so are the parents; maybe even more anxious than their little boys and girls becoming young men and women. I think it is my job to help ease this transition, and to get them excited about what is to come.