Secret Squares and Stop Signs

28 Jun 2022

I wrote a deeply sad post today. As I went to publish it, I hesitated. Yesterday was my last day of school, and instead of ending with sadness, I'd like…

Understanding Negative Numbers: In Praise of Tiny Games

1 Feb 202217 Jun 2022

"Is this right?" Inaya asked me, pointing to the equation she'd recorded on her paper: 5 + (-8) = -13 We are one week into our 7th grade unit on…

“Look! I showed my work!”

8 Sep 20218 Sep 2021

It's surreal to be back at my school, in person, after 18 months away. I feel a tremendous sense of vertigo when I look around at this place that is…

How Much Is Enough: Using Student Feedback to Reflect on Practice

28 Jun 202112 Jul 2021

Do students need to finish every problem? When I have asked this of colleagues, everyone has responding with a resounding no! Definitely not!Not every student needs that much practice.It's okay…

Caterpillar Math

20 Jul 202020 Jul 2020

This spring, my children fell madly in love with insects. Ants. Bees. Butterflies. We read books. We went exploring outside with magnifying glasses. We developed elaborate pretend play rituals based…

Assessments: Capturing a Moment in Time

20 Feb 20205 Feb 2022

It can be tempting to overgeneralize what we learn from an assessment. See how that second grader drew tally marks to solve 54 + 28? He's a direct modeler. He…

Everyone Gets A Handful: Preschoolers Explore Division

28 Jan 20205 Feb 2022

One bag of cheese puffs. Four hungry children. My two children -- ages 4 and 2 -- had been playing with friends -- ages 4 and 8 -- when my…

Problem Based Lesson #3: Learning From One Another in Grade 4

9 Jan 202026 Jun 2020

This is a post in a series about problem based instruction in fourth grade -- centering on a series of lessons classroom teacher Claire* and I taught about symmetry. This…

Building Mental Representations

25 Nov 201917 Nov 2019

"Sabrina is fascinating. She will look at a problem for three minutes, not appearing to be thinking about it at all, and then come up with the correct answer," her…

Using Instructional Routines to Inspire Deep Thinking

21 Oct 20195 Feb 2022

Originally published on the Illustrative Mathematics blog (October 13, 2019). We want students to think about math deeply. Creatively. Analytically. Instead, what often happens is that students race towards quick solutions. So…

Listening to Early Understandings of Division: “12 ÷ 5 is either -3 or 0”

20 Aug 20195 Feb 2022

This blogpost is a part of the (2019) HUMANIZING MATHEMATICS CONVENTION: Virtual Conference on Humanizing Mathematics hosted by Sam Shah and Hema Khodai___ I love, love listening to early understandings…

Students Surprise Us: Interviews with Juliet

20 Jun 201919 Jun 2019

Have you ever had a student just gloriously prove all your assumptions wrong? Things move so quickly in a school. In order to grapple with the pace of our days,…

The Cookie Recipe: Learning Math from Students

1 Apr 20195 Feb 2022

Fourth grade teacher Alicia and I have a beautiful habit of doing math together when planning. We try out problems, and anticipate ways we think students.* *This work is made…

Mathematical Connections in a Kindergarten Science Unit

18 Mar 201915 Mar 2019

"I'm sorry, we're only loosely doing math today," Jessica apologized as I walked into her kindergarten classroom. "We're deep into our structures unit in science, and I'd like to keep…

“I see the same hands”: Dealing with Discretionary Spaces

12 Feb 201912 Feb 2019

The teacher frowned as she looked out at her 25 students, only 3 of which had their hands raised -- the same three students who always had their hands raised."I see…

What does it mean to be “struggling” in math class? (Eduardo’s Story)

5 Feb 20195 Feb 2019

It was a sea of dots. Eduardo's work for 47 + 27 Over and over again, for both computational and story problems, third grade student Eduardo drew dots. Eduardo's work,…

Presuming Competence: Using Clinical Interviews to Support Classroom Instruction

13 Nov 201827 Nov 2018

"She's not on an IEP, but she's struggling in class. What should I do?" I don't know the student -- Alejandra, or Ali, for short -- very well, so I arranged…

Keeping a Straight Face

9 Aug 201810 Aug 2018

This is my contribution to the Convention of Mathematical Flavors organized by @samjshah2. He put a call out for presenters to ponder the "mathematical flavor" of their classrooms How does your class move…

Cultivating a Listener’s Mindset — with ELs

10 Jun 20186 Feb 2022

In a post last January, I wrote about how the "mental load" teachers carry can impact their ability to listen to their students. ...but listening is critical. It's especially critical when…