It seems like since the very inception of public education in the United States, we have been grappling with what good math instruction should look like. For example, in 1895 John Dewey wrote, “There is no subject taught in the elementary schools that taxes the teacher’s resources as to methods and devices to a greater extent […]
I’ll bet you are wondering two things: What does the title mean? What the heck is a nutria? Today I did a demonstration with a wonderful 6th grade class. We were comparing and ordering rational numbers. I grabbed this lesson from Open Up Resources. (It is an amazing free curriculum, but you might need to […]
I recently received a wonderful email from a mathematical leader at a local junior high school. She had two great questions, so I thought I’d turn my response into this short blog post. I separated her questions with my responses. Read on… 1.) How do we connect the Concrete and Representational to the Abstract in […]
When I teach new mathematical concepts to my students, I always try to use some sort of visual model to make the learning easier. No duh! But what I have noticed is that over the years I have collected an odd assortment of models to teach everything without any theme to all the models. The […]
Recently, I have found myself vociferously advocating for more teachers to use number disks when teaching the four operations of whole numbers: addition, subtraction, multiplication, and division. Clearly my excitement for number disks has not yet rubbed off onto all the teachers I work with, because today I received the following question: Why are disks […]
While nothing can adequately replace the REAL thing, virtual manipulatives play an essential role in a student’s journey towards developing a profound understanding of mathematics. That’s a bold claim! Let’s go a little deeper… You’ve heard of CPA? Concrete – Pictorial – Abstract. Sometimes it is referred to as CRA. (Concrete – Representational – Abstract) […]