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RME 2011 presentation and resources

At the RME 3 conference, we gave a presentation on a quadratic functions unit that we designed using principles of RME.Title:"Length times width equals area" and "Line times line equals parabola":...

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Beyond "Rise over Run"

ICME-12 Workshop and sharing group on slope and linear functionsMichael Matassa and I were honored to conduct a workshop and sharing group at the ICME-12 conference in Seoul, South Korea on July 11,...

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RME 4: Beyond rise over run: Contexts, representations, and a learning...

I was excited to facilitate this workshop at RME 4 in Boulder on September 29, 2013. Even thought the title, abstract, and slide design is very similar to the ICME talk, a lot has changed in my...

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NCTM 2014: Beyond rise over run!

Research talk and gallery workshop for teachers    Again, similar titles to my previous presentations, but again, a lot has changed in my thinking around our study of slope in 2012. At NCTM 2014, I...

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CCTM 2014: Beyond Rise over Run: Activities to invent and connect slope's...

Slope has five—count 'em, five—faces. Students shouldn’t focus on just one or two, and in this session, neither will we! Instead, we'll explore realistic and meaningful activities and a learning...

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CTR 2015: Using models to do and learn math

At the Courage to Risk 2015 conference, Mark Semmler, Cindy Ritter and I gave three talks about how models help students do and learn mathematics. CTR is a conference for special education...

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RME-5: Opening plenary: An orientation to Realistic Mathematics Education

My colleagues and I from the Freudenthal Institute US gave this opening plenary at the Fifth International Conference on Realistic Mathematics Education. If you're wondering what RME is all about, look...

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RME-5: Emergent modeling: From chains of signification to cascades of artifacts

I gave this talk at the Fifth International Conference on Realistic Mathematics Education in Boulder CO.It's a somewhat theoretical talk.Abstract:Emergent modeling is a key design principle in RME. The...

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NCTM 2016 research session: The intertwinement of activity and artifacts in...

In RME, mathematics is understood as both an activity and as the product of that activity. In other words, it's a unidirectional relationship: activity produces products. Often, the activity is...

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NCTM 2016: Modeling your way to understanding with Realistic Mathematics...

Raymond Johnson and I facilitated a session on RME for high school teachers at NCTM 2016.In this session we discussed the unique way that "modeling" is conceptualized in RME (as organizing rather than...

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Reinventing fractions and division as the are used in Algebra: The power of...

     In this paper, Michael Matassa and I explore a problem of practice that we experienced as algebra teachers. Namely, we noticed that students in algebra often struggled with division when the...

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MEA/MFT 2016 - Beyond Rise over Run!

Slope is more than just “steepness” or “rise over run.” Slope has five—count 'em, five—faces. Students shouldn’t focus on just one or two, and in this session, neither will we! We'll explore a sequence...

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NCTM 2018: Building meaning into algebra equations

Raymond Johnson, David Webb, and I facilitated a session at NCTM 2018 in Washington DC.In the session, we introduced two models for algebra equations, discussed how each model reveals a different...

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Montana Educator Conference 2018: Making Algebra Meaningful

This session is based on my work as an algebra teacher and research. I also drew on ideas that my colleagues Raymond Johnson and David Webb presented at NCTM.The session focused on how to make...

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NCTM 2019: Making logarithms meaningful through progressive formalization

Logarithms are often seen as one of the most complicated and abstract concepts in secondary mathematics.Consider these problems. Even for those who can solve the problems using abstract procedures,...

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Montana Educator's Conference 2019: Making logarithms meaningful through...

(This is similar to the session that David Webb, Raymond Johnson, and I facilitated at NCTM, 2019)Logarithms are often seen as one of the most complicated and abstract concepts in secondary...

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Making algebra meaningful: The area model from arithmetic to algebra (and...

We'll offer this session on Saturday 4/24/2021 as part of the NCTM Virtual Annual Meeting, 2021. Here are the slides for the session: 

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NCTM 2022: Making meaning of systems of equations with contexts and...

 Students often learn techniques for solving systems of equations, like substitution and elimination. However, these are often learned as procedures without meaning. Students may also see...

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