This Week in Math Ed: December 30, 2016

Here it is, TWiME 52, the last of the year. I didn't know how far I'd get when I started, and there were times during the year I wasn't sure it was worth continuing. But I'm glad I stuck with it, and I plan to continue in 2017. Big thanks to all of you who have read and shared it!

Math Ed Said

December 23: For a second day in a row, "The High-School Mathematician's Crutch Is Not Allowed in Most Colleges" was the most-shared link on my math ed Twitter list.

Shared by: Michelle Russell, Robert Talbert, Anthony Purcell, Earl Samuelson, Shauna Hedgepeth, Amy Hogan, John Golden, Dan Anderson, Dan Allen

December 24: How cool (and very last-minute) was this? Paula Beardell Krieg took images from math teachers on Twitter and created "Last Minute Wrapping Paper."

Shared by: Mike Lawler, John Golden, Malke Rosenfeld, Simon Gregg

December 25: Yes, people were sharing links on Christmas Day. In this case, they were linking to more links, specifically these from the Ontario Math Links blog for the week ending December 23rd.

Shared by: Kyle Pearce, Bridget Dunbar, Mary Bourassa, David Petro

December 26: In Episode 1621 of the Math Ed Podcast, Samuel Otten interviewed Megan Taylor about her JRME commentary, "From Effective Curricula Toward Effective Curriculum Use."

Shared by: Egan Chernoff, John Golden, Samuel Otten

December 27: Did you hear about Tracy Zager's new book, Becoming the Math Teacher You Wish You'd Had? People were talking about it on the 27th (when they weren't talking about Carrie Fisher).

Shared by: Andrew Gael, Crystal Lancour, Jill Gough, John Golden, Sahar Khatri, David Coffey, Dan Meyer

December 28: Kyle Pearce wrote, "Exploring Fraction Constructs and Proportional Reasoning." It's a post rich with all sorts of part-whole relationships, number line placements, concrete and visual representations, and operations.

Shared by: Crystal Lancour, Dan Allen, David Petro, Mark Chubb, Kyle Pearce, Matthew Oldridge

Annie Fetter at Innov8 2016

December 29: Suzanne Alejandre, Max Ray-Riek, and Annie Fetter, while working fall conferences for The Math Forum, posted bulletin boards in common spaces titled "Ask the NCTM Community." Suzanne's blog post here lists the questions and responses written on those boards, which has prompted maybe the best and most active comment section I've seen to any blog post in a long time.

Shared by: Megan Schmidt, Casey McCormick, Suzanne Alejandre, The Math Forum, Earl Samuelson, Gary Davis, Max Ray-Riek

Around the Math Ed Web

A quick check on the Global Math Department shows these recent and upcoming sessions:

• December 13: Favorite Tech Tools with Julia Finneyfrock, Julie Reulbach, and Shauna Hedgepeth
• December 20: "I'm Not a Math Person" - Identity and Its Impact on Math Success with Nicole Bridge
• January 3: Creativity and Curiosity in the Math Classroom with Zachary Herrmann

I found a tweet from NCTM that says there will be a #TCMchat, #MTMSchat, and #MTchat in January on the 11th, 18th, and 25th, respectively, but no details about the articles. I also learned that one person used #TCMchat over the holiday while watching Turner Classic Movies.

Research Notes

The January 2017 issue of Educational Studies in Mathematics is out:

• Interactions between defining, explaining and classifying: the case of increasing and decreasing sequences by Lara Alcock, Loughborough University, and Adrian Simpson, Durham University
• Agency and assemblage in pattern generalisation: a materialist approach to learning by Francesca Ferrara and Giulia Ferrari, Università di Torino
• Comparative analysis on the nature of proof to be taught in geometry: the cases of French and Japanese lower secondary schools by Takeshi Miyakawa, Joetsu University of Education
• Mathematics education in Lebanon: gender differences in attitudes and achievement by Ketty M. Sarouphim and Madona Chartouny, Lebanese American University
• The association of precollege use of calculators with student performance in college calculus by Yi Mao, Harvard T. H. Chan School of Public Health, Tyreke White, Harvard College, Philip M. Sadler, Harvard-Smithsonian Center for Astrophysics, and Gerhard Sonnert, Harvard-Smithsonian Center for Astrophysics
• A study regarding the spontaneous use of geometric shapes in young children's drawings by José Domingo Villarroel and Olga Sanz Ortega, University of the Basque Country UPV/EHU
• Rupture or continuity: The arithmetico-algebraic thinking as an alternative in a modelling process in a paper and pencil and technology environment by Fernando Hitt, Université du Québec à Montréal & Universidad Michoacana de San Nicolás de Hidalgo; Mireille Saboya, Université du Québec à Montréal & Universidad Michoacana de San Nicolás de Hidalgo; Carlos Cortés Zavala, Université du Québec à Montréal; and GRUTEAM

Three more articles have been added to the March 2017 issue of The Journal of Mathematical Behavior:

• Playing the believing game: Enhancing productive discourse and mathematical understanding by Shelly Sheats Harkness, University of Cincinnati; and Bethany Noblitt, Northern Kentucky University
• How can emphasizing mathematical modeling principles benefit students in a traditionally taught differential equations course? by Jennifer A. Czocher, Texas State University
• An exploratory study on student understandings of derivatives in real-world, non-kinematics contexts by Steven R. Jones, Brigham Young University

Some journals seemed to hurry up to get their last 2016 issue out before the end of the year. For the International Journal of Science and Mathematics Education, they jumped to put out both their January and February 2017 issues. Here's the math-focused articles:

• Graphic Comprehension and Interpretation Skills of Preservice Teachers with Different Learning Approaches in a Technology-Aided Learning Environment by Harun Çelik and Hüseyin Miraç Pektaş, Kırıkkale University
• Format Effects of Empirically Derived Multiple-Choice Versus Free-Response Instruments When Assessing Graphing Abilities by Craig Berg, University of Wisconsin-Milwaukee; and Stacy Boote, University of North Florida
• Prospective Middle School Mathematics Teachers' Covariational Reasoning for Interpreting Dynamic Events During Peer Interactions by Seçil Yemen-Karpuzcu, Middle East Technical University; Fadime Ulusoy, Kastamonu University; and Mine Işıksal-Bostan, Middle East Technical University
• An Investigation of Pre-service Middle School Mathematics Teachers' Ability to Conduct Valid Proofs, Methods Used, and Reasons for Invalid Arguments by Esra Demiray, Hacettepe University; and Mine Işıksal Bostan, Middle East Technical University
• Understanding Linear Function: a Comparison of Selected Textbooks from England and Shanghai by by Yuqian Wang, Durham University; Patrick Barmby, University of the Witwatersrand; and David Bolden, Durham University
• Adults' Use of Mathematics and Its Influence on Mathematical Competence by Christoph Duchhardt, University of Bremen; Anne-Katrin Jordan, University of Bremen; and Timo Ehmke, Leuphana University of Lüneburg
• Development of a Framework to Characterise the Openness of Mathematical Tasks (Erratum) by Joseph B. W. Yeo, Nanyang Technological University
• School–University Action Research: Impacts on Teaching Practices and Pupil Learning by Iiris Attorps and Eva Kellner, University of Gävle
• The Role of Parental Math Anxiety and Math Attitude in Their Children's Math Achievement by Akanksha Soni and Santha Kumari, Thapar University
• Students' Emotions in the High School Mathematical Class: Appraisals in Terms of a Structure of Goals by Gustavo Martínez-Sierra, Autonomous University of Guerrero; and María del Socorro García-González, Research Center of Advanced Studies of the National Polytechnic Institute of Mexico
• Modelling in Primary School: Constructing Conceptual Models and Making Sense of Fractions by Juhaina Awawdeh Shahbari, University of Haifa & Al-Qasemi Academy - Academic College of Education & The College of Sakhnin; and Irit Peled, University of Haifa

Whereas IJSME got out in front of 2017, AERA just squeezed out the March 2016 issue of the Review of Research in Education. It's a bit confusing, but RRE is really only published once a year, so the "March" timing is irrelevant. This year, there is one math-related article by Alan Schoenfeld, and it's a survey of the field — and open access!

• Research in Mathematics Education by Alan H. Schoenfeld, University of California, Berkeley

Here's the newest from the January 2017 and February 2017 issues of Teaching and Teacher Education:

• Teacher learning in the context of Lesson Study: A video-based analysis of teacher discussions by Maria Vrikki, University of Cambridge; Paul Warwick, University of Cambridge; Jan D. Vermunt, University of Cambridge; Neil Mercer, University of Cambridge; and Nicolette Van Halem, University of Utrecht
• Mathematics teachers' motivations for, conceptions of, and experiences with flipped instruction by Zandra de Araujo, Samuel Otten, and Salih Birisci, University of Missouri

For the Twitter crowd, there are some familiar faces in the latest Journal of Urban Mathematics Education:

• Absence of Diversity in Collegiate Upper-Level Mathematics Classrooms: Perpetuating the "White Male Math Myth" by David W. Stinson, Georgia State University
• The Importance of Communities for Mathematics Learning and Socialization by Erica N. Walker, Teachers College, Columbia University
• To Rectify the Moral Turpitude of Mathematics Education by Brian R. Lawler, Kennesaw State University
• A Critical Dialogue: Continuing the Conversation about "The Collective Black and Principles to Actions" by Bryan Meyer, Escondido Union High School District
• Reflecting on the Dialogue Regarding the Mathematics Education of English Learners by Zandra de Araujo, Erin Smith, and Matthew Sakow, University of Missouri
• A Framework for Understanding Whiteness in Mathematics Education by Dan Battey, Rutgers; and Luis A. Leyva, Vanderbilt University
• An Intersectional Analysis of Latin@ College Women’s Counter-stories in Mathematics by Luis A. Leyva, Vanderbilt University
• Striving Toward Transformational Resistance: Youth Participatory Action Research in the Mathematics Classroom by Mary Candace Raygoza, University of California, Los Angeles
• Negotiating Perceptions of Tracked Students: Novice Teachers Facilitating High-Quality Mathematics Instruction by Emily Joy Yanisko, Urban Teachers at Johns Hopkins University
• Book Review: Radical Reconfiguring(s) for Equity in Urban Mathematics Classrooms: Lines of Flight in Mathematics and the Body: Material Entanglements in the Classroom by Susan O. Cannon and Kayla D. Meyers, Georgia State University

Math Ed in the News

The theme this week seems to be "teach math through music/philosophy/news/anythingotherthanmath."

• Iowa City students finding math in music (The Gazette)
• Central A&M students get jump on college math (Herald & Review)
• Teach Kids Philosophy, It Makes Them Better at Math (NY Mag)
• Fourth grade class learns math using The News (The News)

Math Ed in Colorado

I only have two reminders, which I'll keep short:

• The online standards review system is open until February 17.
• Registration for Math on the "Planes" is open and applying for a scholarship is encouraged.

This Week in Math Ed: December 23, 2016

I'm still catching up, so here are stories that were popular the week before Christmas. I'm saving other items for the next post, so you'll have to wait!

Math Ed Said

December 16: It's a Desmos holiday sweater!

Shared by: Shelley Carranza, Mike Maki, Stephanie Ling, Carolyn Spencer, Kathy Henderson, Melinda Lula, Ashley Bingenheimer, Andrew Shauver, Julia Finneyfrock, David Petersen, Desmos.com

December 17: In an interview with Carol Dweck in The Atlantic called "Don't Let Praise Become a Consolation Prize," we explore some of the ways growth mindset should and shouldn't be used.

Shared by: Patrick Honner, Marcie Lewis, Rebecca Gasper, Marilyn Burns, Chi Klein, Steven Strogatz, Ayodele Harrison

December 18: "How Big is 'Big'?" is another great post from Mark Chubb. It's difficult to develop number sense with large numbers, and in this post Mark explores some activities that can help or hinder the development of big-number sense.

Shared by: Mark Chubb, Andrea Ogden, Brandi Moore, Jamie Garner, Matthew Oldridge, Margie Pearse, Laura Wagenman

December 19: Dan Meyer asked us to makeover a system of equations.

Shared by: Jamie Duncan, Carolyn Spencer, George Woodbury, Nat Banting, Zach Cresswell, Denis Sheeran, Michael Welch, Amy Hogan, Matthew Oldridge, Rob Horcher, Dan Meyer

December 20: Progress continues on the Illustrative Mathematics curriculum.

Shared by: Ron King, Ashli Black, Andrew Gael, Sadie Estrella, Kristin Gray, Robert Kaplinsky, Geoff Krall, Kate Nowak, Judy Keeney, Vanessa Cerrahoglu, Joanie Funderburk, David Petersen, Mike Steele, Bowen Kerins, Nik Doran, Illustrative Maths

December 21: There's a companion website for Tracy Zager's new book, Becoming the Math Teacher You Wish You'd Had.

Shared by: Tyler Anderson, Sara VanDerWerf, Genni Steele, Mary Gambrel, Vanessa Cerrahoglu

We might have been debating this in 1966.

December 22: "The High-School Mathematician's Crutch Is Not Allowed in Most Colleges" appeared in The Atlantic, and struck me as something that might have appeared more at home in 1986 or 1996 than 2016. We have a standard to "use appropriate tools strategically," but this article seems to seek for something closer to all-or-none. In 1986 my teachers were telling me I needed to master arithmetic because I wouldn't always have a calculator with me. My teachers were usually right, but on this point, they were wrong. I do always have a calculator with me — and it makes phone calls!

Shared by: Dan Meyer, Egan Chernoff, Brittany Cuchta, Steven Gnagni, Christopher Danielson, Vicki Carter, Andrew Gael, Matthew Oldridge, OCTM, Nick Gerhard

This Week in Math Ed: December 16, 2016

I'm in catch-up mode again, having been busy with mid-December travel for PARCC followed by the holidays. I was also slowed by some changes to Nuzzel that caused the code I wrote about in October to stop working. It took a while to figure out, but I think things are in working order again. If you're curious about the fix, it's mostly a matter of passing a valid session cookie to Nuzzel so it gives me the logged-in version of the site.

Math Ed Said

December 9: Just as it did on December 8, Graham Fletcher's "The Progression of Fractions" tops the list.

Shared by: Denise Gaskins, Jeremiah Ruesch, Michael Jerrell, Kristin Frang, Stephanie Holloway, Farshid Safi, Andrew Stadel, Shelley Carlisle, Bridget Dunbar, Jamie Duncan, Andrew Gael, Allison Peet, Cathy Yenca, Jill Gough, Tim Stirrup

December 10: A March 2014 post by Robert Kaplinsky was most shared on the 10th. In "Why Does Depth of Knowledge Matter?" Robert shows how some changes to the depth of knowledge of some circle area problems resulted in drastic changes in student scores.

Shared by: Sue Wilson, Shauna Hedgepeth, Regan Galvan, Brandi Moore, OCTM

Commentary: Ever since I read and wrote about Jack Schneider's chapter about Bloom's Taxonomy in his book From the Ivory Tower to the Schoolhouse, my first thought about Bloom's Taxonomy has been, "That's not what Bloom had in mind when he designed it." Therefore, now when I hear about Webb's DOK, I think, "What did Webb have in mind when he designed it?" On my to-do list for 2017 will be to dig into the origins of DOK by reading Webb's original piece, Criteria for Alignment of Expectations and Assessments in Mathematics and Science Education. It's not that I think we're misusing Webb's DOK. I just think we gain by knowing about the origins of ideas, that's all.

December 11: Another older story resurfaced on this day, this time "Why Understanding These Four Types of Mistakes Can Help Us Learn" by Eduardo Briceño in KQED's MindShift blog. By looking at both high and low intentionality and learning opportunities, Eduardo describes the risks and rewards of making mistakes.

Shared by: Jack Brown, Clint Chan, DeAnn Huinker, Richelle Marynowski, Ruth Knop, Peg Cagle, Jamie Garner, Jill Gough, DeAnn Huinker

December 12: Christopher Danielson appeared in the MiddleWeb blog with "How I Learned to Love Middle School Geometry." I can see where Christopher is coming from here, as I tended to prefer learning/doing geometry as a student, but found algebra preferable to teach.

Shared by: Mark Chubb, Evelyn Lamb, John Golden, Megan Schmidt, Christopher Danielson

December 13: When I think of bloggers who got my attention by surfacing in TWiME, Joe Schwartz might be first on my list. He appears again with a post called "Emily," in which he uses the engagement and understanding of one unassuming student, Emily, as a benchmark for his teaching.

Shared by: Chris Hunter, John Golden, Chris Kalmbach, Marilyn Burns, Michael Pershan, Joe Schwartz

December 14: Dan Meyer encourages math education conference organizers to consider traditionally underrepresented speakers. In his post, "The Bureau of Non-White Dude Math Education Keynote Speakers," Dan suggested about forty quality, non-white-male speakers, and asked for more suggestions in the comments.

Shared by: Andrew Stadel, Jennifer Lawler, Sara VanDerWerf, Sue Wilson, Life LeGeros, John Berray, Megan Schmidt, Bryan Meyer, Laura Wagenman, Jose Vilson, Cathy Yenca, Martin Joyce, Kimberly Goff, Lisa Bejarano, Matt Vaudrey, David Coffey, Tracy Johnston Zager, Farshid Safi, Keith Devlin, Carrie Muir, Robert Kaplinsky, Dan Meyer

December 15: The conversation continued around Dan's "The Bureau of Non-White Dude Math Education Keynote Speakers."

Shared by: Nicole Bridge, Bethany Sansing-Helton, Kyle Pearce, Sahar Khatri, Theodore Chao, Jonathan Osters, Sara VanDerWerf, Laura Wagenman, Toya J Frank, Annie Perkins, Kate Owens, Ilana Horn, Ethan Weker, Mike Flynn, Matthew Oldridge, Heather Johnson, Jason Merrill, Evelyn Lamb, Kate Nowak, Amy Hogan, Audrey McLaren, Andrew Browning-Couch, Bridget Dunbar, Jill Gough

Commentary: TODOS had a critique of Dan's post:

The construction of this list is an example of white-male privilege, many names missing on this list. https://t.co/dplVbKDl7f

— TODOS (@todosmath) December 16, 2016

Would not have the hubrias to create such a list and post it. https://t.co/9CXpxBuSSZ

— TODOS (@todosmath) December 16, 2016

Dan Meyer at ASSM 2016, literally on a platform.

TODOS is an organization I respect, and their (from "them" or the individual representing them) response took me to the sticky place I think of as, "You're being an ally wrong." Dan's primary platform is as a well-known speaker in math education, and he used that platform in an attempt to promote others. It reminded me a bit of the #CancelColbert fallout, when Colbert used his platform — political satire on TV — to illustrate the absurdity of Washington NFL franchise owner Daniel Snyder's foundation to support American Indians. For me, that turned into "You're being an ally wrong," although the Colbert situation is clearly quite different than Dan's. In the responses to Dan and TODOS, I tried to heed the advice of Bryan Meyer, which was, "Let's listen." In this instance, the conversation fizzled before I felt we got away from the "you're being an ally wrong" place. Maybe my takeaway is that you can't say "Dan used his platform" without claiming that it's "Dan's platform," and using it without claiming it is something privilege itself doesn't allow me or Dan to do. What comes after that? I'm not sure.

Lastly, it does not escape me that I'm a white male discussing this in a post that is highlighting posts made almost entirely by other white males. Not all weeks are like this, but this one was.

Everything Else

I have two more posts to write, so I'll save research, news, and other happenings for the second one, which I hope to have out before it's no longer 2016.

This Week in Math Ed: December 9, 2016

Hello from Chicago! I'm in the greater O'Hare airport area this week working on PARCC rangefinder review for the upcoming 2017 testing window. "Rangefinder review" is that stage in the assessment process where we prepare the student work examples that will be used to train scorers to deal with the range of answer responses they're likely to see on each PARCC exam. For me, the best part of this has to be the variety of student work I'm being exposed to across a series of items.

Math Ed Said

December 2: People were sharing concerns related to a Politico story about Betsy DeVos, who is slated to be the U.S.'s next Secretary of Education.

Shared by: Ethan Weker, Chris Stapel, Avery Pickford, Siri Anderson, Elizabeth Statmore, Jose Vilson, Karen King

December 2016 GMD Webinars

December 3: The Global Math Department announced three webinars for the month of December. People shared.

Shared by: Chris Shore, Julia Finneyfrock, Julie Reulbach, Nicole Bridge, Global Math

December 4: Remember, TWiME isn't the only summary of the week's happenings in mathematics education. You can also check out the Ontario math links, such as this well-shared post from last week.

Shared by: MathDDSB, Nita Cochran, Marissa W, Jon Orr, Mary Bourassa, John Gibson, Kyle Pearce, Matthew Oldridge, David Petro

December 5: Most of us couldn't attend CMC North, but Dan Meyer posted the "#CMCMath Opening Keynote Address, 'Practice Problems'," that he did with Shira Helft, Juana de Anda, and Fawn Nguyen.

Shared by: Siri Anderson, Ilona Vashchyshyn, Dan Meyer, Jeremiah Ruesch, CMC - CA MathCouncil, Bridget Dunbar, Mike Flynn, Tyler Anderson, Fawn Nguyen, Suzanne Alejandre, Michael Pershan, Elham Kazemi, Heather Johnson, Tracy Johnston Zager

December 6: Tuesday was Global Math night, so pepole shared the link to that night's talk, "Clothesline Math: The Master Number Sense Maker" by Andrew Stadel and Chris Shore.

Shared by: Casey McCormick, Andrew Stadel, Christopher Danielson, Shauna Hedgepeth, Judy Larsen, Denis Sheeran, Pam Wilson, Global Math, Tracy Johnston Zager, Lisa Bejarano, Jill Gough, Jessica Bogie, Karen McPherson, Alison Hansel, Deborah Boden

December 7: Ben Orlin is back for more Math With Bad Drawings, this time with "Viral Math News Stories."

Shared by: Denise Gaskins, David Butler, Ilona Vashchyshyn, Ben Orlin, Dan Bach, Kathy Henderson, Shauna Hedgepeth, Keith Devlin

December 8: As you can see from the long list of names below, Graham Fletcher's Making Sense Series of progressions videos has garnered a well-deserved following. In his latest installment, Graham describes "The Progression of Fractions."

Shared by: Mark Chubb, Melinda Knapp, Dan Allen, Kat Hendry, Laura Wagenman, Christina Tondevald, Chris Kalmbach, Rhonda, Jon Orr, Christina Sherman, Tyler Anderson, Jenni Clausen, Rosa Serratore, Math Coach Rivera, Michael Pershan, Martin Joyce, Jedidiah Butler, Nerissa Gerodias, Dave Lanovaz, Daniel Luevanos, Helen J Williams, Jennifer Lawler, MathDDSB, Simon Gregg, Donna Boucher, Janice Novakowski, Rebecca Price, John Golden, Tracy Johnston Zager, Graham Fletcher

Around the Math Ed Web

#TCMchat comes on Wednesday, December 14th. The focus will be the article "Relational Thinking: What's the Difference?" by Ian Whitacre, Robert C. Schoen, Zachary Champagne, and Andrea Goddard.

Last week's GMD talk was mentioned above, and this week's is "Favorite Tech Tools" with Julia Finneyfrock, Julie Reulbach, and Shauna Hedgepeth.

The Mathematics Leadership Programs at Mount Holyoke College has arranged for an online course starting in January 2017 that brings together many well-known math ed people from Twitter. Titled "Effective Practices for Advancing the Teaching and Learning of Mathematics (K-12)," the course features 10 sessions with 10 instructors: Kaneka Turner, Graham Fletcher, Elham Kazemi, Zak Champagne, Kristen Gray, Dan Meyer, Tracy Zager, Mike Flynn, Fawn Nguyen, and Andrew Stadel.

TNTP is taking nominations and applications for their Fishman Prize. The prize honors 100 inspiring public school teachers each year for their ability to create challenging and engaging classrooms for all of their students. Four winners receive $25,000 and six finalists receive $1,000.

Research Notes

The March 2017 issue of The Journal of Mathematical Behavior includes:

• Teacher attention to number choice in problem posing by Tonia Land, Drake University
• Integer comparisons across the grades: Students' justifications and ways of reasoning by Ian Whitacre, Florida State University; Beti Azuz, San Diego State University; Lisa L.C. Lamb, San Diego State University; Jessica Pierson Bishop, Texas State University; Bonnie P. Schappelle, San Diego State University; and Randolph A. Philipp, San Diego State University

The Fall 2016 issue of the Journal of Mathematics Education at Teachers College is out:

• Thinking in Patterns to Solve Multiplication, Division, and Fraction Problems in Second Grade by Patricia Stokes, Barnard College
• Incorporating the Use of Writing-to-Learn Strategy in Grade 10 Mathematics Lessons: The Students' Perspectives by Zuhairina Suhaimi, Sayyidina Ali Secondary School; Masitah Shahrill, Universiti Brunei Darussalam; Khairul Amilin Tengah, Universiti Brunei Darussalam; and Nor'Arifahwati Haji Abbas, Universiti Brunei Darussalam
• Teaching the History of Tracking Time with Technology by Margaret Fitz, Miami University
• Creativity and Insight in Problem Solving by Laura Golnabi, Teachers College, Columbia University
• Some Thoughts on Doctoral Preparation in Mathematics Education by Robert Reys, University of Missouri

Math Ed in the News

Oh, Canada, you're getting a lot of attention in the math ed news! The recently released PISA results are fueling a lot of nation-sized self-reflection this week.

• Knowledgehook raises $1.25 million to empower math teachers with technology (BetaKit)
• Sask. government responds to province's low math education ranking (News Talk 650 CKOM)
• Canada has one of the best education systems in the world, so why can't we stop debating discovery math? (National Post)
• Education minister moves to boost Alberta students' math grades (CBC News)
• Mass. shines on global test, but math scores slip (The Boston Globe)
• What America Can Learn About Smart Schools in Other Countries (The New York Times)

Math Ed in Colorado

Online Standards Review System Extended Until Feb. 17

As CDE continues to develop its plan to guide the upcoming standards review and revision process, the department is actively seeking feedback on the Colorado Academic Standards from all interested parties. In November, CDE launched an online standards review system which enables all Coloradoans to provide specific feedback on each and every expectation within all 10 content areas of the Colorado Academic Standards. To provide sufficient time for meaningful feedback, the department has extended the timeline to provide feedback to Friday, February 17, 2017.

The results of the feedback received through the online system will inform the department's planning for the upcoming review and revision of the standards, required by Senate Bill 08-212, known as Colorado's Achievement Plan for Kids (CAP4K). The law requires a review and revision of the Colorado Academic Standards on or before July 1, 2018 and every six years thereafter.

In early 2017, CDE will provide comprehensive information about the timeline and phases of the standards review and revision process as well as information about how to become involved.

The online standards feedback system can be found at http://www.cde.state.co.us/standardsandinstruction/casreview.

PARCC Released Items

PARCC has released a new set of items for grades 3-8. These are items that have been used on operational test multiple times and were slated for retirement, and the set of items approximates the content coverage of a typical test. High school items should be released in early 2017.

Math on the "Planes"

Registration for next February's conference is open. The focus will be Tier 1 and Tier 2 interventions for K-5 math students, with Dr. Karen Karp as the workshop leader. CCLD encourages you to apply for a Mikkelson Mathematics and Science Teachers Scholarship to cover the costs, as MOTP attendees from outside the metro area are eligible for travel, lodging, and registration reimbursement.

This Week in Math Ed: December 2, 2016

Thanks for everyone's patience as I cut TWiME short for the weeks ending November 18 and November 25. This week I'm caught up again with all the latest research and happenings in math ed.

Math Ed Said

November 25: Twitter traffic on my math ed Twitter list was light and scattered on Black Friday. The most-shared story ended up being the NY Times piece, "In Scotland, Trump Built a Wall. Then He Sent Residents the Bill."

Shared by: Kay Endriss, Dan Bach, Margie Pearse, Keith Devlin, Karen King

November 26: Continuing the post-(U.S)-holiday weekend, five folks were sharing this fun linguistics piece from the NY Times originally published in 2013: "How Y'all, Youse and You Guys Talk." For the record, my answers (which I answered with the words I used where I grew up) indicated I was most similar to speakers in Des Moines, IA; Madision, WI; and Rockford, IL, which is pretty much exactly the area I'm originally from.

Shared by: Kathryn Freed, Megan Schmidt, Mary Williams, Shauna Hedgepeth, Marilyn Burns

November 27: I'd seen balance puzzles like this on paper, but thanks to some friendly sharers on Twitter I now know that EDC has "SolveMe Mobiles" online.

Shared by: Fred G. Harwood, Martin Joyce, Dan Allen, Andrew Gael, Math Coach Rivera, Mark Chubb, Robert Kaplinsky

November 28: Illustrative Maths asked teachers to blog about how they use IM tasks, like some teachers did with the "G-GPE Squares on a coordinate grid" task.

Shared by: Vanessa Cerrahoglu, Melissa Haun, Jennifer Wilson, Nita Cochran, David Petersen, Kate Nowak, Lisa Bejarano, Nik, Illustrative Maths

November 29: Robert Kaplinsky wrote, "What's the Difference Between Honors and Regular Math Classes?" Only once in my teaching career did I teach honors vs. non-honors sections, and in hindsight the difference between the two was pretty lame and largely an artifact of the school's schedule.

Shared by: Greg George, Jennifer Lawler, Rosa Serratore, Travis Lemon, Alison Hansel, Robert Kaplinsky

November 30: Writing in The Atlantic, Timothy Walker asked, "What Happens When Finnish Educators Teach in America's Public Schools?" The responses from several Finnish teachers who moved to and taught in the United States claim teaching in the U.S. is more restricted and rushed.

Shared by: Glenn Kenyon, Tyler Anderson, Stephanie Ryon, Mike Maki, Keith Devlin, Kate Fisher, Shelly Gibson, Russell West Jr.

December 1: Many of the math ed organizational Twitter accounts were promoting a webinar on December 5th titled "Collective Action to Develop Awareness: Equity and Social Justice in Mathematics Education." This is part of a quarterly webinar series on equity and social justice sponsored by NCSM, TODOS, AMTE, and NCTM.

Shared by: CMC - CA MathCouncil, TODOS, CMC - CA MathCouncil, Bryan Meyer, USU TeachMath, Mark Ellis, TCM - NCTM, NCTM - MT, NCSM

Around the Math Ed Web

I kept the last two TWiME posts (11/18 and 11/25) short in order to catch up following some busy traveling and holiday weeks, but in that time I attended Innov8 and took a lot of photos of the action there. In short, I was impressed with the conference and the mix of regular sessions, team time, and opportunities for small group conversations with experts in the Innovation Lounge.

The most recent big conference event was last weekend's conference of the California Mathematics Council — South. #CMCmath tends to be a large and impactful event, so be on the lookout for conference recaps, video of the opening keynote, and visit the CMC-South conference pages for information and resources.

Note the changes in NCTM's Wednesday night chats this month: There will be a #TCMchat on December 14th around the article "Relational Thinking: What's the Difference?" by Ian Whitacre, Robert C. Schoen, Zachary Champagne, and Andrea Goddard. If you missed them, the most recent #MTchat is Storified here and the #MTMSchat is Storified here.

Here are the two most recent Global Math Department meetings:

• "Turn That Lesson Upside Down" with Kate Nowak
• "Reaching the Whole Range" with Henri Picciotto

And the next GMD meeting:

• "Clothesline Math: The Master Number Sense Maker" with Andrew Stadel and Chris Shore

The Mathematics Leadership Programs at Mount Holyoke College has arranged for an online course starting in January 2017 that brings together many well-known math ed people from Twitter. Titled "Effective Practices for Advancing the Teaching and Learning of Mathematics (K-12)," the course features 10 sessions with 10 instructors: Kaneka Turner, Graham Fletcher, Elham Kazemi, Zak Champagne, Kristen Gray, Dan Meyer, Tracy Zager, Mike Flynn, Fawn Nguyen, and Andrew Stadel.

Did you know it's Computer Science Education Week? What are you going to code/build/connect/engineer? What about your students?

Research Notes

Ready for March 2017? Elsevier's way of publishing new papers on a rolling basis means we're already seeing articles slated for the March 2017 issue of The Journal of Mathematical Behavior:

• Preservice teachers' pictorial strategies for a multistep multiplicative fraction problem by Jae M. Baek, Illinois State University; Megan H. Wickstrom, Montana State University; Jennifer M. Tobias, Illinois State University; Amanda L. Miller, Illinois State University; Elif Safak, Florida Gulf Coast University; Nicole Wessman-Enzinger, George Fox University; and J. Vince Kirwan, Kennesaw State University
• Looking back to the roots of partially correct constructs: The case of the area model in probability by Gila Ron, Tel Aviv University and Ohalo College; Tommy Dreyfus, Tel Aviv University; and Rina Hershkowitz, Weizmann Institute of Science

Ilana Horn at the 2016 Innov8 Conference

Here's what's new in the Juanary/Feburary 2017 issue of the Journal of Teacher Education:

• A Taxonomy of Instructional Learning Opportunities in Teachers' Workgroup Conversations by Ilana Seidel Horn, Vanderbilt University; Brette Garner, Vanderbilt University; Britnie Delinger Kane, University of Colorado Denver; and Jason Brasel, University of Michigan
• Mathematics Anxiety: One Size Does Not Fit All by Kathleen Jablon Stoehr, Santa Clara University

I like the look of this slate of articles in the December 2016 issue of The Elementary School Journal:

• Does the Value of Dynamic Assessment in Predicting End-of-First-Grade Mathematics Performance Differ as a Function of English Language Proficiency? by Pamela M. Seethaler, Lynn S. Fuchs, and Douglas Fuchs, Vanderbilt University; and Donald L. Compton, Florida State University
• How Teacher and Classroom Characteristics Moderate the Effects of Four Elementary Math Curricula by Roberto Agodini, Plainsboro, NJ; and Barbara Harris, Mathematica Policy Research
• Content-Focused Coaching: Five Key Practices by Lynsey Gibbons, Boston University; and Paul Cobb, Vanderbilt University
• Influence of Writing Ability and Computation Skill on Mathematics Writing: The Elementary School Journal by Sarah R. Powell, University of Texas at Austin; and Michael A. Hebert, University of Nebraska-Lincoln

The December 2016 issue of the Mathematics Education Research Journal includes:

• Experiencing teaching and learning quantitative reasoning in a project-based context by Tracey Muir, Kim Beswick, Rosemary Callingham, and Katara Jade, University of Tasmania
• Influence of proportional number relationships on item accessibility and students' strategies by Michele B. Carney, Boise State University; Everett Smith, University of Illinois; Gwyneth R. Hughes, University of Wisconsin; Jonathan L. Brendefur, Boise State University; and Angela Crawford, Boise State University
• Primary teachers notice the impact of language on children's mathematical reasoning by Leicha A. Bragg, Sandra Herbert, Esther Yoon-Kin Loong, Colleen Vale, and Wanty Widjaja, Deakin University
• What secondary teachers think and do about student engagement in mathematics by Karen Skilling, King's College London; Janette Bobis, The University of Sydney; Andrew J. Martin, University of NSW, Kensington; Judy Anderson, The University of Sydney; and Jennifer Way, The University of Sydney
• A design study to develop young children's understanding of multiplication and division by Brenda Bicknell, University of Waikato; Jenny Young-Loveridge, University of Waikato; and Nhung Nguyen, Open Polytechnic
• Curriculum enactment patterns and associated factors from teachers' perspectives by Ji-Won Son, University of Buffalo; and Ok-Kyeong Kim, Western Michigan University

Three more articles have appeared in Pythagoras:

• Where is the bigger picture in the teaching and learning of mathematics? by Satsope Maoto, Kwena Masha, and Kgaladi Maphutha, University of Limpopo
• A square in drag as concrete universal; or, Hegel as a Sketchpad programmer by Zain Davis, University of Cape Town
• Proportional reasoning ability of school leavers aspiring to higher education in South Africa by Vera Frith and Pam Lloyd, University of Cape Town

Math Ed in the News

I looked for articles and was generally disappointed. If you read anything, I suggest getting caught up with the results of the latest TIMSS test. This EdWeek article covers the highlights. You can take a deeper look with this NCES report or this webinar:

Math Ed in Colorado

Mathematics Design Collaborative

Last week I joined math teachers and leaders for a meeting of the Mathematics Design Collaborative, a CEI-led effort that includes teachers from Thompson School District, Jeffco Public Schools, and Montezuma-Cortez. The collaborative serves to support high-quality formative assessment and classroom discourse, using tools like the Shell Center's formative assessment lessons and Achieve the Core's coaching tool. If you'd like to know more or be put in touch with the right people at CEI, let me know.

Colorado Math Leaders

The next CML meeting will be Wednesday, December 14 from 9:00-12:00 in Harrison School District 2, Colorado Springs.

CDE Launches Online Standards Feedback System

The Colorado Department of Education (CDE) is currently developing its plan to guide the upcoming standards review and revision process and is actively seeking the input of all interested parties to inform its planning process. In addition to the general standards perception survey that was open in October and November, CDE has launched an online standards review system. Unlike the perception survey, the online standards review system will enable all Coloradoans to provide specific feedback on each and every expectation within all 10 content areas of the Colorado Academic Standards. The online system will accept feedback from Wednesday, Nov. 9 through Friday, Dec. 30. The online standards feedback system can be found at http://www.cde.state.co.us/standardsandinstruction/casreview.

The results of the survey and feedback received through the online system will inform the department's planning for the upcoming review and revision of the standards, required by Senate Bill 08-212, known as Colorado's Achievement Plan for Kids (CAP4K). The law requires a review and revision of the Colorado Academic Standards on or before July 1, 2018, and every six years thereafter.

In early 2017, CDE will provide comprehensive information about the timeline and phases of the standards review and revision process as well as information about how to become involved. This will begin robust public engagement throughout the state and through social media. If you would like to receive regular updates on the standards review and revision process, you can sign up here: https://www.surveymonkey.com/r/standardsupdate.

PAEMST 2017

The nominations are now open for PAEMST awards for 7-12 math teachers to be awarded in 2017.

Math on the "Planes"

Registration for next February's conference is open. The focus will be Tier 1 and Tier 2 interventions for K-5 math students, with Dr. Karen Karp as the workshop leader. CCLD encourages you to apply for a Mikkelson Mathematics and Science Teachers Scholarship to cover the costs, as MOTP attendees from outside the metro area are eligible for travel, lodging, and registration reimbursement.

This Week in Math Ed: November 25, 2016

I'm again keeping this TWiME short as I catch up from conference travel and the Thanksgiving holiday. Thankfully, I remembered to grab all the most-shared posts before that data slipped away from me!

Dan Meyer at the 2016 ASSM Annual Meeting

November 18: For what I assume is a limited time, you can download the Mathematics Teacher article, "Increased Participation and Conversation Using Networked Devices" by Christopher Danielson and Dan Meyer.

Comment: Seeing Dan and Christopher's name on this article gave me the sudden thought, "It's like they're the George Immerzeel and Earl Ockenga of the 2010s." This will only amuse you if (a) you are really knowledgeable about late-70s calculator research or (b) you went to the University of Northern Iowa, as I did, and either knew or knew of these people.

Shared by: Bethany Sansing-Helton, Taylor Belcher, Dan Meyer, Lorraine Males, NCTM - MT

November 19: I'm not sure why a post from July suddenly made the rounds in November, but a number of people were sharing "Research Shows Students Learn Better When They Figure Things Out On Their Own," a post written by Martin Buschkuehl on the MIND Research Institute blog.

Shared by: Laura Wagenman, Kit G., Brian Errey, Rusty Anderson, Taylor Belcher, Becca Phillips, Annie Forest, Alex Overwijk, Margie Pearse

November 20: In a post that would serve well as a case study for teacher discussions, Kim Van Duzer wrote "Tape Diagrams, Big Feelings and other Predicaments of Teaching."

Shared by: Lynsey Gibbons, Ilona Vashchyshyn, Kent Haines, Tyler Anderson, Sadie Estrella, Simon Gregg, Michael Pershan, Tracy Johnston Zager

November 21: Ian Sample in the Guardian wrote a richly-presented article called "Magic numbers: can maths equations be beautiful?"

Shared by: Francis Su, Gary Davis, Egan J Chernoff, Nita Cochran, Simon Gregg, Steven Strogatz, Keith Jones, Geoff Wake, Marcus du Sautoy, Nerissa Gerodias

November 22: Using a nice mix of numberless word problems and a notice/wonder setup, Kristen Gray describes a classroom activity with "Help Kids Understand Math Problems: Take Away The Numbers And the Question!"

Shared by: J. Brown, Margie Pearse, Math Coach Rivera, Laura Wagenman, Rusty Anderson, Amanda Jansen, Kristin Gray

November 23: People were taking an interest in the nominee to become our next Secretary of Education and shared this brief Q+A from Betsy DeVos.

Shared by: Karen Gartland, Josh Fisher, David Hallowell, Dan Anderson, Ilana Horn

November 24: Charles Blow's NY Times opinion piece, "No, Trump, We Can't Just Get Along" struck a nerve with a number of math educators.

Shared by: Annie Perkins, Earl Samuelson, Keith Devlin, Elizabeth Statmore, Bill Thill, Mike Anderson, Eddi Vulić, Karen King, John Allen Paulos, Ματτ, Peg Cagle, Sahar Khatri, Ilana Horn, Kay Endriss, Keith Devlin

This Week in Math Ed: November 18, 2016

I'm so far behind! Going from Innov8 one week to a holiday the next week wasn't good for blogging productivity. Please excuse my tardiness and this abbreviated version of TWiME.

November 11: Geoff Krall gave us "What does it mean to be problem based? An attempt to unwind 'PrBL.'" I appreciate when someone sets their assumptions aside about what we think we know and attempts to define/explain the thing in a more useful way.

Shared by: Kit G., Brian Marks, Carmel Schettino, Wendy Rose Aaron, Erika Bullock, Nicole M. Joseph

November 12: Folks were sharing a "Manifesto on the Teaching of Mathematics" written by Viktor Blåsjö, a Ph.D. candidate at the University of Utrecht. If you're going to think deeply and write about the teaching of mathematics, I can think of few better places in the world than Utrecht.

Shared by: Maria H. Andersen, Fred Feldon, Matthew Oldridge, Jennifer Lawler, Joshua Bowman, Dan McQuillan, Steven Strogatz

November 13: Kristin Gray came up with a way to help teachers prepare to do number talks in their classrooms that she calls "Number Talk Karaoke."

Shared by: Jody Guarino, Jamie Garner, Laura Wagenman, Max Ray-Riek, Lindel, Jana Sanchez, Laura Wagenman, Joe Schwartz, Kristin Gray

November 14: The AMC 8 competition happened on November 15th, so people were sharing a link with information about all the AMC competitions.

Shared by: Jennifer Lawler, TODOS, NCTM, POWER Org Math, John Golden, Malke Rosenfeld, MAA

Matt Larson at the 2016 Innov8 Conference

November 15: In his President's Message, Matt Larson made some really good points in "The Need to Make Homework Comprehensible."

Shared by: Juli K. Dixon, Denise Spangler, Sarah Bush, Christie Madancy, NCTM, Matthew Beyranevand, Greg George, Chris Kalmbach, Matt Larson

November 16: Reflecting on the CMC South conference, Tracy Zager builds from a talk by Megan Franke that highlighted the idea of "Springboarding" directly from counting to problem solving for young learners. There are some great examples in the post, and those of us who teach higher grades might be pleasantly suprised at what students are capable of when they're giving the right opportunities.

Shared by: Lisa Melton Pizzuto, Rosa Serratore, Denise Gaskins, Elham Kazemi, Janice Novakowski, Becca Lewis, Tracy Johnston Zager

November 17: Dan Meyer brings up "Engagement in Math: Three Places to Start" with some basic advice on gaining students' interest.

Shared by: Kit G., Levi Patrick, Brian Bushart, Robert Kaplinsky, Simon Gregg, Jennifer Blinzler, Christy Vehe

As I mentioned, I'm keeping this short in an effort to catch up!

Innov8 and Positive Directions for NCTM

I recently attended NCTM's inaugural Innov8 Conference in St. Louis. NCTM promised a different kind of conference, and I would say they delivered — assuming attendees took advantage of the options beyond the usual keynotes, sessions, and exhibit hall.

Conference Content

For those of you interested in the content of the conference, I apologize for keeping this part brief. The theme of the conference was "Engaging the Struggling Learner" and speakers did better to stick to the theme than I expected. The opening keynote with Juli Dixon and her daughters Alex and Jessica was wonderful. The focus of the talk was Alex's struggle to overcome the effects of a stroke she suffered in 6th grade. I'm horribly underselling the talk, and underselling Alex and Jessica, but I will make this point: As much as I want to call both of them extraordinary, I won't. For as impressed as I was with them, I didn't want to leave thinking they were "exceptional," as in "not like all the others." I wanted to leave, hopefully along with everyone else, thinking that all struggling learners were just as amazing as Alex and Jessica, and Alex and Jessica were just as amazing as other struggling learners. In that way, I think the keynote really did hit the key note.

Juli, Jessica, and Alex Dixon

Thursday morning we experienced a rotation of keynote speakers. For me, Amanda Jansen was up first to discuss "rough draft talk," an approach that emphasizes to students that thinking out loud, making mistakes, exploring multiple solutions, and revising our thinking is all a normal part of doing mathematics. Next up was Karen Karp, who had us face the reality that too many struggling learners get worksheets and tricks rather than sound, research-based strategies. Karen recommended checking out the math Practice Guides published by IES, and I will. In fact, let me put them right here so you will, too:

• Teaching Strategies for Improving Algebra Knowledge in Middle and High School Students (Related Resource)
• Teaching Math to Young Children (Related Resource)
• Improving Mathematical Problem Solving in Grades 4 Through 8
• Developing Effective Fractions Instruction for Kindergarten Through 8th Grade
• Assisting Students Struggling with Mathematics
• Encouraging Girls in Math and Science

Fawn Nguyen

Last to go was Fawn Nguyen, who stressed productive struggle and choosing high-quality tasks. She had some comments about resisting tracking in her school, and dealing with upset parents, that I think really resonated with other teachers in the room. Before the conference was over, I saw Peg Smith (for the first time, somehow), dipped in and out of Jo Boaler's talks, and got some good stuff out of Melissa Boston's session involving resources from NCTM's Principles to Action Professional Learning Toolkit. I find PtoA's effective teaching practices to be right-sized descriptions of practice, and I like seeing different ways they can be used to improve the planning and analysis of teaching.

Conference Format

More than the conference content, I was specifically drawn to Innov8 by NCTM's attempt to shake up their typical conference format. To be sure, Innov8 had typical keynotes and sessions and attendees could make the conference feel like a regular NCTM regional conference if they wished. But what set Innov8 apart (and makes me more likely to return) were its more novel features, Team Time and the Innovation Lounge.

I attended primarily as a member of the board of the Colorado Council of Teachers of Mathematics, and I was joined by three other board members who all had an interest in learning about the conference. In this way we were a team, but not exactly the kind of school-based team NCTM had designed the conference for. The Innov8 schedule had multiple times set aside for teams to tackle what they identified as a "problem of practice," and the researcher in me really wish I could have sat in with some of the groups to see what they identified as their problem and how they thought they might go about tackling it.

NCTM Board Member Cathy Martin in the Innovation Lounge

I thought the Innovation Lounge was the highlight of the conference, and I wonder if others felt the same. In the Innovation Lounge, conference attendees had ample opportunities to come face-to-face with experts in math education in a variety of formats. There was the Book Nook, where attendees could sit with authors to discuss their books, and the Innov8 Bar, where experts in various topics (assessment, motivation, productive struggle, and MTSS) offered advice to groups of 1-8 people seated around a high table. There was also a place for telling teaching stories, getting Twitter and blog advice, and talking to people from The Math Forum.

Matt Larson at the Innov8 Bar

I admit, when I saw NCTM President Matt Larson at the Innov8 Bar talking to a single person, or Jo Boaler overflowing the Book Nook with about 150 people, I wondered if the format was really working. In hindsight, though, I think the format was working just fine. There are some details NCTM needs to work out, but overall I think these issues are reflective of the very hard work NCTM faces in making a personal connection to its members. I feel good that the person who got solo time with an NCTM President will renew their membership and be a more active NCTM member, and in general, NCTM made a positive impression on those who spent some time in the Innovation Lounge. In the future, I think NCTM can do more to let attendees know who some of these experts are and why they're worth talking to. A little bit of celebrity can go a long way.

A large crowd gathered for Jo Boaler's book talk

Positive Directions for NCTM

Two years ago I published a post describing what I saw as NCTM's grand challenge: to shift their focus away from providing content to members and towards providing services, even as their membership shifts from older and more loyal members to younger teachers who are less likely to join organizations. I made some suggestions: Be less faceless as an organization, find teachers where they are, spend more time listening, build a thank you economy with your members, play matchmaker, and guide teachers towards mastery. Here are a few ways I see NCTM moving in these directions:

• Conferences: The Innov8 Conference had ample amounts of face-to-face time between NCTM board members and other representatives, and I hope it served to facilitate a lot of listening at an organizational level. Similarly, the Annual Meeting in San Francisco featured small-group gatherings between major speakers and attendees. Although conferences are geographically and temporally limited, NCTM needs to make the most of these opportunities for the members dedicated enough to attend.
• Twitter Chats: In the last few months we've seen NCTM establish a regular schedule of Wednesday-night chats that bring authors of articles in NCTM teacher journals (Teaching Children Mathematics, Mathematics Teaching in the Middle School, and Mathematics Teacher) together with teachers and other math educators for an hour on Twitter. By having authors engage directly in the chats, there are great opportunities for personal connections between experts and members. NCTM is making the articles free to download to help facilitate participation, and I think the upside for NCTM in terms of membership will exceed any potential downside from lost journal subscriptions. Despite the dedication and enthusiasm from math teachers on Twitter, it remains a relatively small audience, but just like conferences, NCTM is working to meet its members where they are.
• Reaching Out to Critics: I've seen several examples in the past two years of NCTM recruiting teachers (Lisa Henry and Graham Fletcher come to mind) critical of the organization to provide feedback and take active roles within the organization. I don't have the inside knowledge of how these arrangements have been made or the extent of the involvement, but I see so many benefits from this. As members we still don't get much of a window into the workings and disagreements of the NCTM Board of Directors, but it looks good when members can disagree with the organization and then be given a platform to have those ideas heard.

The effects of these changes might not be large, at least not yet, but I think they're steps in the right direction. I do wonder how much my perception of the organization is shaped by my own involvement and the number of relationships I've built with people I see as part of NCTM. Some of the suggestions I made, like playing matchmaker and guiding teachers towards mastery, don't yet seem to be part of NCTM's plans. I know NCTM has entertained ideas related to certifying/credentialing members for their knowledge and skills, but that's a big step that comes with more risks than the efforts they're currently taking.

Lastly, one moment of Innov8 made a big deal to me: At the last minute, I stopped in the NCTM book store to pick up some books. At the register, the NCTM staff member said, "Oh, you're Raymond Johnson!" It was Tracy Cullen, NCTM's communications manager, and the person usually behind the NCTM Twitter account. I realize that the NCTM social media accounts need to represent the organization, not the individual tasked with running them, but I felt a great sense of satisfaction to meet the person doing the hard work of engaging members across multiple accounts and often non during 9-5 hours. So if you're reading this: Hi, Tracy, and thank you!