Posts

Mathematical Tools

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It's so interesting to me when micro-themes start to emerge from my Twitter feed. Most recently, I've noticed many of my tweeps grappling with the use of mathematical tools, both the ones we would consider more traditional like hands-on manipulatives, and the high tech devices, apps, and programs that are more recently showing up in math classrooms. This morning, Malke Rosenfeld posted this question:
This seems like a simple question, but it's an incredibly important one to consider. I think about the word "tool" and how it's really the name of a category of objects we use in certain ways to achieve certain outcomes and not a precise description of any one object. When it comes to math, what makes an object (or representation, or strategy) fit into the category of "math tool"? My simplest answer is that if we are able to use something to support our mathematical thinking in a way that wasn't possible without it or in a way that makes a strategy …

Reflections from a teacher educator, Part 1

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Tonight was officially the last class of the semester teaching my first math methods course. I have lots of feelings about this... a sense of accomplishment and relief among them. It was a hard semester, y'all. I poured my heart and soul into these 34 (34!!!) men and women who are on their way to becoming teachers, and I am so proud of *most* of how it all played out.  Overall, I feel really positive about how I organized and implemented the course, but like many professionals, I tend to have some symptoms of imposter syndrome alongside the feelings of pride and excitement. The first time one of my students called me Professor I almost ugly-laughed right in his face - me!? A professor?! Surely I'm not important enough to be called that. But as I consider the reflections my students shared with me this afternoon in a finals week fro-yo shop office hours session, my feelings of inadequacy are slowly subsiding as they are replaced with a bit of disappointment... not in myself or …

Precision Over Perfection: My First Ignite Talk!

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I had the amazing honor of being asked to do an Ignite Talk at the NCSM Annual Conference this year in San Antonio. If you're unfamiliar with the format of Ignite, here's a crash course: 10 speakers, each get 5 minutes and 20 auto-advancing slides. Terrifying? Yes. Exhilarating? That too.

















Ignite speakers are asked to speak about something they're passionate about - something that "ignites" them. I chose to speak about privileging precision over perfection as we listen to and support students' mathematical ideas. Here's what I wanted to say (and here's the video link where you can watch what I actually said under pressure - ha!)



My mom tells a story about me when I was 3 years old. I was drawing her a picture with what she describes as “meticulousness”, drawing each band of the rainbow carefully, precisely, with the colors in the “correct” order, whatever that is. All of a sudden, she saw me grab a black crayon and scribble all over the whole thing in f…

My Math Autobiography

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What better way to start 2017 than to finally write my math autobiography! I am preparing to teach my first math methods course for pre-service teachers this coming semester, and I look forward to sharing this with my students and hearing theirs. Thanks, @TracyZager for the inspiration to finally nail this down.

My first memory of math in elementary school is from 3rd grade. It was January, and I had returned from winter break to a new school. The first thing I saw when I walked into the classroom on my first day was a bulletin board with a road on it. At equal intervals along the road were pit stops – “Land of 2s,” Land of 3s”, “Land of 4s”… all the way to the “Land of 12s”. Each student had colored their own car and as they mastered math facts, they moved along the road. The furthest car was in the “Land of 6s” and I immediately knew that leaving everyone in my dust on the multiplication road was going to shape my identity in my new class. I loved math because I was good at it, and t…

This Math Was Made for Talking: Targeting Math Discussions

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As a visiting teacher, I love to ask students what they think a “number talk” might be. It’s usually silent at first, and then a brave soul will say something like, “Is it when you talk…about numbers?” Their faces light up when that profound idea is confirmed. I have been in countless elementary and middle school classrooms in the last few years both observing and facilitating Number Talks (Sherry Parrish, 2010), and I am part of an amazing team that has trained over 1,000 teachers on their implementation since 2013. Number talks are changing how teachers and students interact with mathematics by opening up the discourse in the classroom to more than just a volley between teacher, student, teacher, student. They invite students to construct and consider multiple strategies for a single problem or string of related problems, and serve as formative assessment for teachers who want to know how their students are thinking about a problem. While these “open strategy sharing” conversations…

Spatial Structuring: a Public Service Announcement

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I'm knee deep in writing an article about an area lesson I taught to rising 4th graders in summer school a couple weeks ago and, as usual, something totally unexpected and profound has emerged as I take a closer look at student work. I wanted to do a quick post today as a shout-out to the importance of spatial structuring for students who are being asked to think about multiplication in terms of arrays and area.

In the lesson, students were given two tasks related to area. The first task was to find different rectangles with an area of 12 square units, where students were given 12 square units to build their rectangles and then asked to draw pictorial representations on a square grid. The second task was to determine the area of a table given only enough square units for two side lengths and to draw a representation of their thinking on a blank sheet of paper (for an amazing read on the power of a blank sheet of paper, check out Tracy Zager's blog). There was a startling corre…

Mission: Partition #MTBos

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Let's play a game. It's called "What math does this assess, and is that the math the standard calls for?" Wordy, I know, but it's a game worth playing as we consider how to make assessments actually assess what we need them to. The item below comes from a 1st grade benchmark exam, and is tagged as an assessment of standard 1.G.3, with no other items assessing this standard. Before I give you the text of the standard, we're going to play the first part of the game: what does this assess?

Some teachers' answers to "What math does this assess?": Understanding of the phrases "half of" and "quarter of"Ability to color "one part" of a shapeLow level assessment of identifying a part of a shape (not necessarily understanding of equal parts)And now for the next part of the game: "Is that the math the standards call for?" Here's the full text of the standard:  1.G.3 Partition circles and rectang…