## Math Ed Said

**May 13**: The first time I saw "WODB" (Which One Doesn't Belong?) mentioned on Twitter, I wasn't quite sure what to make of it. But when you see it in action, skillfully facilitated, you get it. Tracy Zager shared with us "Straight but Wiggled," in which a bunch of first graders make sense of ideas like "diamond," "straight," and "vertiwiggle." If you're familiar with Paul Cobb et al.'s work on the emergence of sociomathematical norms in classroom group activity, it makes it extra interesting to see what happens here.

*Shared by: Tracy Johnston Zager, Ilona Vashchyshyn, Bridget Dunbar, Malke Rosenfeld, Kent Haines, Simon Gregg, David Butler, Mark Chubb, John Golden, A. O. Fradkin, Bryan Anderson, Laura Wagenman, Pat Power*

**May 14**: If you're looking for Ignite talks from the 2016 NCTM Annual Meeting, or prior meetings, you can find them at The Math Forum.

*Shared by: Suzanne Alejandre, Peg Cagle, The Math Forum, Tracy Johnston Zager, Amie Albrecht*

**May 15**: It's a return appearance for the Ontario Math Links, this time for the week ending May 13th, 2016.

*Shared by: David Petro, Mary Bourassa, Matthew Oldridge, Kyle Pearce, Jon Orr, Ryan Smith, Cathy Yenca*

**May 16**: Jon Orr describes "Double Clothesline – Solving Equations," a very nice approach to understanding solving equations. Instead of a balance or algebra tiles, this uses double number lines in a way that gives more focus to the quantitites, rather than choosing or performing operations.

*Shared by: Jon Orr, Shelley Carranza, Kyle Pearce, David Petro, Alex Overwijk, Pam Wilson, Lisa Lunney Borden, John Gibson*

Dan Meyer |

**May 17**: Dan Meyer is thinking about the

*informal*that supports the

*formal*understanding, which he illustrates in the post "Blue Point Rule." This is familiar territory for those of us who study Realistic Mathematics Education and its approach of

*progressive formalization*. RME uses the terms "informal," "preformal," and "formal," and what Dan's wrestling with is what I'd call the "preformal" in RME. It's important that we call it out because it's really tough to make that last transition from a preformal model or conception to the use of a formal equation or rule. Dan's collecting "Before I ask for (Formal X), I ask for (Informal Y)" statements, some of which hint at common models used in RME.

*Shared by: Dan Meyer, Bridget Dunbar, Jon Orr, Imtiaz Damji, Chris Mueller, Carrie Diaz Eaton, Mark Chubb, Nancy Terry, Jamie Duncan, Michael Fenton, Eddi Vulić, Rob Horcher, Missy Stringham, Levi Patrick, Rob Horcher, Jessica Faurote, Regan Galvan, Tim McCaffrey, Martin Joyce*

**May 18**: There were 14 more shares of Dan's "Blue Point Rule" post, but I didn't want that post to completely overshadow this post by Matt Larson, which also got (re)tweeted a lot on the 17th and 18th. "NCTM Is Its Members" talks about NCTM understanding the needs of its members and what they're doing to meet them. I'm pretty excited about some of the directions NCTM is going, and they're moving a bit faster than I expected when I was thinking about these issues a while back. If you have feedback and ideas for Matt and NCTM, be sure to go to the post and leave them. You can see what other people have said and Matt's replies, and it looks like a pretty good discussion so far.

Matt Larson |

*Shared by: Lisa Henry, Amanda Jansen, TCM - NCTM, NCTM, NCTM - MT, April Pforts, UNL NebraskaMATH*

**May 19**: The

*Chalkbeat*story "How one Tennessee school district is getting students excited about math" describes number talks in a 1st grade classroom.

*Shared by: John Golden, Melissa Soto, Donna Boucher, NCTM, Gary Petko*

## Around the Math Ed Web

A few more links popped up this week that I think are too good to pass up:- "Modeling With Mathematics" is a
*Teaching Channel*post by Elham Kazemi and Kendra Lomax that uses the lesson structure of Three-Act Tasks to focus on modeling. - "Statistical Literacy: Simulations with Dolphins" is a (free for now!)
*Mathematics Teacher*article from Jeremy Strayer and Amber Matuszewski that describes a six-phase structure for statistics lessons using simulations.

In the Global Math Department last week, Tracy Zager gave a talk called, "How Do They Relate? Teaching Students to Make Mathematical Connections." Next week, Yana Weinstein and Cindy Wooldridge will talk about "Improving Math Education with Interleaved Problems by Global Math Department."

**Deadlines**: NCSM Annual on June 1 and RUME on August 19th and December 2nd (for posters).

## Research Notes

The June 2016 issue of ZDM has arrived, with the theme*Cognitive Neuroscience and Mathematics Learning — Revisited After Five Years*:

- Potential applications of cognitive neuroscience to mathematics education by Bert De Smedt, University of Leuven, and Roland H. Grabner, University of Graz
- Measuring fraction comparison strategies with eye-tracking by Andreas Obersteiner and Christine Tumpek, Technische Universität München
- EEG-based prediction of cognitive workload induced by arithmetic: a step towards online adaptation in numerical learning by Martin Spüler, Carina Walter, Wolfgang Rosenstiel, Peter Gerjets, and Korbinian Moeller, Eberhard-Karls University Tuebingen; Elise Klein, RWTH Aachen University
- Electrophysiological markers of newly acquired symbolic numerical representations: the role of magnitude and ordinal information by Rebecca Merkley, Andria Shimi, and Gaia Scerif, University of Oxford
- Exploring mental representations for literal symbols using priming and comparison distance effects by Courtney Pollack, Sibylla Leon Guerrero, and Jon R. Star, Harvard Graduate School of Education
- Does solving insight-based problems differ from solving learning-based problems? Some evidence from an ERP study by Roza Leikin, Ilana Waisman, and Mark Leikin, University of Haifa
- Brain activity associated with logical inferences in geometry: focusing on students with different levels of ability by Ilana Waisman, Mark Leikin, and Roza Leikin, University of Haifa
- The neural correlates of health risk perception in individuals with low and high numeracy by Stephan E. Vogel, University of Graz; Carmen Keller, ETH Zürich; Karl Koschutnig, University of Graz; Gernot Reishofer, Medical University of Graz; Franz Ebner, Medical University of Graz; Simone Dohle, ETH Zürich; Michael Siegrist, ETH Zürich; and Roland H. Grabner, University of Graz
- When errors count: an EEG study on numerical error monitoring under performance pressure by Frieder L. Schillinger, University of Göttingen and University of Graz; Bert De Smedt, University of Leuven; and Roland H. Grabner, University of Graz Erratum
- Comparison of perimeters: improving students' performance by increasing the salience of the relevant variable by Reuven Babai, Laura Nattiv, and Ruth Stavy, Tel Aviv University
- Cognitive neuroscience and mathematics learning: how far have we come? Where do we need to go? by Daniel Ansari and Ian M. Lyons, The University of Western Ontario
- Neuroscientific studies of mathematical thinking and learning: a critical look from a mathematics education viewpoint by Lieven Verschaffel, University of Leuven; Erno Lehtinen, University of Turku; and Wim Van Dooren, University of Leuven

*Teaching and Teacher Education*:

- Positioning in identifying narratives of/about pre-service mathematics teachers in field practice by Reidar Mosvold and Raymond Bjuland, University of Stavanger

*Mathematics Education Research Journal*:

- Developing students' functional thinking in algebra through different visualisations of a growing pattern's structure by Karina J. Wilkie, Monash University, and Doug M. Clarke, Australian Catholic University
- Learning to teach upper primary school algebra: changes to teachers' mathematical knowledge for teaching functional thinking by Karina J Wilkie, Monash University
- Patterns of non-verbal social interactions within intensive mathematics intervention contexts by Jonathan Norris Thomas, University of Kentucky, and Shelly Sheats Harkness, University of Cincinnati
- Using the Fennema-Sherman Mathematics Attitude Scales with lower-primary teachers by Lixin Ren, University of Nebraska—Lincoln; Jennifer L. Green, Montana State University; and Wendy M. Smith, University of Nebraska—Lincoln
- Examining equity of opportunities for learning mathematics through positioning theory by Sandi L. Tait-McCutcheon and Judith Loveridge, Victoria University of Wellington

*AERA Open*:

- Side Effects of Motivational Interventions? Effects of an Intervention in Math Classrooms on Motivation in Verbal Domains by Hanna Gaspard, University of Tübingen; Anna-Lena Dicke, University of California, Irvine; Barbara Flunger, University of Tübingen; Isabelle Häfner, University of Tübingen; Brigitte M. Brisson, University of Tübingen; Ulrich Trautwein, University of Tübingen; and Benjamin Nagengast, University of Tübingen

*Urban Education*on a week-to-week basis for math ed articles, but recently a few caught my eye, so here's what I found published either this year or in upcoming issues:

- Constructing and Role-Playing Student Avatars in a Simulation of Teaching Algebra for Diverse Learners by Tingting Ma1, Texas A&M University; Irving A. Brown, Siemens Technical Learning Services; Gerald Kulm, Texas A&M University; Trina J. Davis, Texas A&M University; Chance W. Lewis, University of North Carolina-Charlotte; and G. Donald Allen, Texas A&M University
- Two Views of Culture and Their Implications for Mathematics Teaching and Learning by Lynn Liao Hodge, The University of Tennessee, and Paul Cobb, Vanderbilt University
- Accountability as a Design for Teacher Learning by Ilana Seidel Horn, Vanderbilt University

## Math Ed in the News

Do you remember that thing I put in last week's news section? No, you didn't, because there*wasn't a news section*! Somehow it slipped by unnoticed. But here's some news for you this week:

- Creators of EngageNY Start New Archive of Free Common-Core Materials (Education Week)
- Ontario teachers colleges now require students to review elementary school math (CBC News)
- Elite Math Competitions Struggle to Diversify Their Talent Pool (Education Week)

## Math Ed in Colorado

The highlight of my week was attending the Colorado Mathematics Awards at the Grant-Humphreys Mansion in Denver. Organized by Richard Gibbs, David Carlson, and the CMA steering committee, this event recognizes students for outstanding performance in MATHCOUNTS, the American Mathematics Contents 8, 10, and 12, Moody's Mega Math Challenge, the USA Mathematics Olympiads, the American Regions Mathematics League, the William Lowell Putnam Mathematical Competition, the International Contest in Modeling, the Interdisciplinary Contest in Modeling, and some teaching awards. Whew, did I remember them all? It was great to see students ages middle school through college all being recognized for their outstanding work, and the fact that Colorado has a special event that brings all these people together is really something to be proud of.The packed house at the Grant-Humphreys Mansion for the 2016 Colorado Mathematics Awards |

While it was great to join everyone in this event in its 21st year, I think a big challenge going forward is to make sure opportunities to participate on math teams and in math competitions gets spread across all of Colorado. As a former MATHCOUNTS kid from a 5200-person rural town in Iowa, I noticed that most of the awardees were students from large, high-SES schools on the Front Range. I realize I only saw the winners, not all the participants, but the small-towner in me would love to see some students there representing places like Gunnison, Ordway, and Walden. Geographic diversity is one of a number of struggles concerning math competitions, so if you'd like to expand the opportunity to participate in math competitions at your school, let me know and I'll see if I can get you connected to people who can help.

In the News:

- Legislature: State bill would help rural school districts attract, keep teachers (Fort Morgan Times)
- Teaching the Power of Diversity in the Classroom has the Power to Change Lives (Huffington Post; features Elizabeth Ramos Torres, a high school math teacher from Parker)

- Jonathan Brendefur is hosting the Developing Mathematical Thinking Institute (DMTI) in Denver from August 2-5, 2016. One workshop is targeted at grades K-2 and the other on grades 3-8.
- Sheridan, Colorado, teacher Julie Sweetman is facilitating some self-directed, online math classes about the CCSS Standards for Mathematical Practice through the Dominican University of California. There are other math classes available there as well.
- And let me mention (once again) the two NCTM summer institutes this summer in Denver:
- July 18-20: Algebra Readiness Institute (6-8)
- July 21-23: Number and Operations Institute (Pk-5)

- Platte Canyon High School in Bailey, CO, needs a math teacher for grades 9-12. At this time, the schedule includes Algebra 1 and several honors classes, including Precalculus. Bailey is a beautiful, small mountain community about an hour southwest of Denver and PCHS enrolls about 300 students. Class sizes are in the twenties or lower. Please apply to www.plattecanyonschools.org.
~~Lake County School District in Leadville is looking for a 7th and 8th grade math teacher. If you are interested in joining a math department that combines Jo Boaler's work with Expeditionary Learning while living in a small town in the mountains, this job is for you. More information and an application can be found at their website~~. (Update 5/23: Position filled!)