Month: June 2017

My New Favorite Term: Abductive Reasoning

June 13, 2017

What is Abductive Reasoning?

I’m going to share my new favorite term: abductive reasoning. Maybe you’ve known about it for years and never told me about it. (If that’s the case, you might be a jerk.) Or maybe it’s new to you too. (If that’s the case, let me know because I’m a little embarrassed I haven’t learned about abductive reasoning until recently.)

To recap, deductive reasoning is about making specific conclusions from general statements (like a math proof). Inductive reasoning is about making generalizations about specific observations (like a science experiment).

By comparison, abductive reasoning is about making your best prediction based on incomplete information.

Abductive reasoning?!?!?! Where have you been all my life? Welcome to my lexicon. Have a seat front and center and let’s talk.

What is Argument? And Emerging from the Rabbit Hole

June 9, 2017

(Update: This post is the second in a series about my learning and thinking about argument and how it relates to our work in the math classroom. Click here to read the first post. Click here to read the third.) Welcome back math geeks! Last week, I was preparing for a workshop facilitating the learning …

Access, Equity, and the Bias of Brilliance

June 2, 2017

A Confession

As a student, math class was mostly about taking notes, practicing algorithms and getting right answers. And I loved it. I really did. I could hide. It was safe and without risk. I was comfortable. “I do; we do; you do” was my jam as a student. More importantly, in this teaching style, I identified as a really strong and talented math student because I learned algorithms and got right answers. That’s what good math students do in class, right? I never had to share my thinking, never had to learn from the thinking of others, never had to challenge the dimensions of my adolescent bubble of insecurity. I never had to share or listen to a classmate share an interesting math question or an elegant solution. I never had to be vulnerable.

When I started teaching, I created the same classroom culture. I was safer as a teacher as well. I could hide. Never take risks. Be comfortable. I was the author of culture in my classroom. They were the factory workforce with one job to do: consume the algorithm and produce right answers. And my teaching aligned to this goal. Employing this style of pedagogy created a silent pact in my classroom: If you sit there and do your job and let me do mine, I will never ask you to take a risk, to challenge the dimensions of your adolescent bubble of insecurity, to share anything unique or interesting about you or your thinking. Time will pass and so will you. We might be bored, but we’ll get through this together without ever knowing each other or our vulnerabilities. Now let’s open up our textbooks and get to work.