By William McCallum “I'm afraid I can't explain myself, sir. Because I am not myself, you see?” Alice in Wonderland. The idea of equivalence in mathematics is tricky for learners, because when we talk about two things being equivalent, for example the fractions...
By Kristin Gray There are some standards I think we do such a great job developing in early elementary, but never revisit explicitly when students learn about different numbers such as fractions and decimals. I blogged about this in reference to even and odd numbers...
By Anna Polsgrove When I first started the Math Methods course at University of California, Irvine, all of my ideas on how to learn math took a complete 180. During the first two months, a million questions swirled in my head as I worked through problems with my...
By William McCallum In everyday language, $\frac{a}{b}$, $a\div b$, and $a : b$ are all different manifestations of a single fused notion. Here, for example are the mathematical definitions of fraction, quotient, and ratio from Merriam-Webster online: Fraction: a...
It was great to see so many of you at NCSM and NCTM. If we missed you, or you weren’t able to attend, read our NCSM and NCTM round-up below. We enjoyed the conversations we had with those of you that are using the IM 6–8 Math curriculum and are looking forward to High...
By Allison Van Voy When I started teaching four years ago, I had no idea how important number sense was to a student’s math understanding. I was fresh out of college, brand new to teaching, and number sense was not a concept I had learned in my math courses. In my...
By Jody Guarino We know instructional materials play a key role in student learning experiences but how do we ensure our students are learning from coherent high-quality instructional materials that engage them in critical thinking and provide opportunities to “do...
By Melissa Greenwald You know it is time for a change when half of the students in class are lost by the third lesson of a new unit. I teach third grade in a charter school in Philadelphia. We use Go Math! and each year I have followed Chapter 8: Understand Fractions,...
By Kristin Gray As a teacher, curiosity around students’ mathematical thinking was the driving force behind the teaching and learning in my classroom. To better understand what they were thinking, I needed to not only have great, accessible problems but also create...
By Jody Guarino As a teacher, I constantly wonder how I can elicit student thinking in order to gain insight into the current thinking of my students and leverage their thoughts and ideas to build mathematical understandings for the class. First, I need a task that...
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