Let's Get Elizabeth Fennema an NCTM Lifetime Achievement Award

Elizabeth Fennema

I've never met Elizabeth Fennema and she retired long ago. But I know her body of work, and I believe she's conspicuously absent from NCTM's list of Lifetime Achievement Award winners. I've mentioned this on Twitter in the past in the hopes that someone who worked with her would snap to action, but this year I'm taking matters into my own hands and coordinating a nomination. And I'm giving you a chance to help me.

I'm assembling a letter of nomination and resume in a Google Doc that is open to public comments. Beyond this, I need up to 5 letters of recommendations. If you want to write one of the letters, let me know at raymond@mathed.net. I'll be recruiting a few potential letter writers personally, but will take any help people wish to offer. I encourage you to sign this petition in support of her nomination, and I'll collect names from this petition and include them as co-signers of the letter of nomination.

If you don't know Elizabeth Fennema or why she deserves an NCTM Lifetime Achievement Award, keep reading for a short biography of her below. You can also read her biographies on Wikipedia and the University of St. Andrews. And don't forget to review and contribute to the letter of nomination, resume and petition.

Elizabeth Fennema Biography:

Elizabeth Fennema is an Emerita Professor of Curriculum and Instruction at the University of Wisconsin-Madison. Her active career in mathematics spanned about 40 years, starting as a graduate student at UW-Madison in the 1960s, then as a faculty member until the mid-90s, then continuing in retirement as an emerita professor.

Fennema is known for two field-changing bodies of work, either of which alone would be worthy of lasting recognition. First is her work about gender in mathematics. After publishing a review of gender differences literature in JRME in 1974, she teamed with Julia Sherman to produce what are now known as the Fennema-Sherman studies. With methodological rigor and new measurement tools (the Fennema-Sherman Scales), the pair redefined knowledge and perspectives on the intersection between gender and achievement in mathematics, showing that under-performance by females was sociocultural in nature and a function of opportunity, and not due to differences in biology.

In the 1980s, Fennema combined with Thomas Carpenter and others for another grand body of work, now known as Cognitively Guided Instruction and summarized for teachers in the book Children’s Mathematics. The research program was a model for applying new theories of constructivism to children’s mathematics learning, and took equally seriously the development of professional development to empower teachers to use their findings to improve elementary mathematics education. Few, if any, mathematics research programs to date have been as comprehensive, rigorous, and beneficial to the field of mathematics education as CGI.

NCTM’s book Classics in Mathematics Education Research (2004) contains articles representing both of these bodies of work (Fennema & Sherman, 1977; Carpenter, Fennema, Peterson, Chiang, & Loef, 1989), making Elizabeth Fennema the only author with two articles recognized as classics in mathematics education. According to citation counts in Google Scholar, Fennema has authored 7 articles or books that have been cited over 1000 times. Searching the JSTOR archives of the Journal for Research in Mathematics Education for “Fennema” yields 431 results, putting her ahead of her contemporaries Thomas Romberg (332 results) and Douglas Grouws (379 results), both NCTM Lifetime Achievement Award recipients. Fennema served NCTM as the chair of the Research Advisory Committee in the late 1970s and was on the JRME editorial panel from 1977-1979, in addition to editing a number of books co-published by the council in the 1980s and 1990s. Fennema has been awarded for her work by the American Educational Research Association and the Association for Women in Mathematics Education, holds an honorary doctorate from Mount Mary College, and was named a member of the National Academy of Education in 1997.

Coherence Gap Spreadsheet

I'm overdue in getting this out into the wider world, but I've developed a spreadsheet that incorporates all the coherence connections found in the Coherence Map and adds to that instructional time data about how many lessons and hours a math curriculum spends on each standard. Yeah, it's a lot. But as I talked to math teachers and leaders at the end of last spring, I felt there were a lack of tools available that incorporated both coherence and instructional time, and my solution was a big Excel workbook with lots and lots of rows of lesson data, some long VLOOKUP formulas, and some conditional formatting to make the results readable. If you geek out over spreadsheets and math curriculum planning, I think you'll like it.

The lesson data comes from EngageNY for K-5 and Illustrative Mathematics for Grades 6 through Algebra 2. I didn't have any special preference for one set of curriculum materials over any other (and neither does the State of Colorado), but both of these are open educational resources with lesson alignments and time estimates, so I used them. You can substitute time data in for whatever materials you'd like, but be warned that you're looking at 3500+ rows of data, so either bring a team of people with you or learn to write some code that scrapes data from publishers' websites and formats it for you. (I chose the latter.)

With the help of a pivot table and some lookup functions, what this spreadsheet allows you to do is indicate some percentage of coverage you thought each standard has gotten (if making sense of past curriculum decisions) or will get (if planning for future curriculum decisions). In return, the spreadsheet reports back to you how much instruction for each standard is left unfinished, and how much future instruction (following arrows in the Coherence Map) might be at risk. Just be mindful that the spreadsheet is like a lot of models—wrong, but possibly useful. The instructional time estimates might be flawed, not everything aligns as neatly as I'd like, the data may not really reflect your materials or pacing, and the crude way the coverage formulas work might just be wrong. So if it gives you some data that you just know is flawed, then maybe it is. But if you're patient with it, and you aren't afraid to look beyond the conditional formatting color scheme and dig more deeply into why instructional time is allocated where it is, then I think this spreadsheet can give you something to work with as you make decisions about your curriculum planning.

This was one of my on-the-job projects as math specialist for the Colorado Department of Education, so CDE is hosting the spreadsheet itself. Head on over to the Coherence Gap Spreadsheet page to download the latest version of the file. I also urge you to watch the tutorial video, which I'll also embed here. I kept it as short as I could at 12 minutes, and if you're already familiar with the Coherence Map you can skip the first 2:00.

If you have any questions about the spreadsheet, please let me know. And if you modify the spreadsheet to make it better or more inclusive of more curriculum materials, I'd really like to know about that, too.

This Week in Math Ed: January 4, 2019

I'm back! I'll remember 2018 for finishing two enormous projects: The revision of the Colorado Academic Standards (where I had a hand in all 12 content areas, not just mathematics) and the completion of my dissertation and my Ph.D. It really became necessary to set aside this blog (and a whole lot of other things) to get those done. When 2019 is over, I hope to remember it as the year life resumed some sense of normalcy.

I'm going to make some tweaks to my previous TWiME format. Most notably, I'm not going to apply more editorial discretion instead of simply resharing whatever happened to be the most popular link on Twitter each day. Sometimes what is popular isn't what's best, and what we see on the internet is already controlled by enough half-baked algorithms without me, a human, trying to act like a half-baked algorithm myself. If you want raw data about what's popular, you can look the same place I look, my Nuzzel feed for my MathEd Twitter list. I think I'll also allow myself more flexibility week-to-week instead of thinking I need a certain amount of research, news, events, etc. in each post. With that said, let's get on to it, shall we?

Math Ed Said

As a preservice teacher, my advisor, Bonnie Litwiller, told us to read decimal numbers properly, i.e., read "5.43" as "five and forty-three hundredths." I'm a stickler about a lot of mathematical language, but I wasn't sold on this one. Sara Van Der Werf's post, "Small Change, Big Difference part 1. Why you should eliminate ‘POINT’ from your vocabulary" made me rethink my position about this because it makes such a compelling argument for how our language helps students build their understanding of place value and the base-10 number system.

George Woodbury read a lot of books last year and summarized the best in the post "Top 5 Education Books I Read Last Year". George seems to like reading about student learning and most of the books on this list were new to me.

Kyle Pearce and Jon Orr have a podcast? When did this start? Less than a month ago, it turns out, so if you're just finding out now, like me, you haven't missed very much. It's called "Making Math Moments that Matter" and the first few episodes have focused on curiousity, sensemaking, and mentoring.

Get Involved

On Tuesday, January 8, Sara Vaughn, Martin Joyce, Morgan Stipe, and Jen Arberg will lead the Global Math Department with a discussion of their experiences with the Open Up Resources 6-8 math curriculum.

Dr. Robert Berry, NCTM President

Dr. Robert Berry, President of NCTM, will hold a President's Message webinar on Wednesday, January 9 at 7pm EST. Register now to attend. While you're at it, check out NCTM's webinar archives to see what else you might have missed.

The first #TCMchat of 2019 will be Wednesday, January 9 at 9pm EST. The topic will be the article "'Sliding' into an Equitable Lesson" by Kelley Buchheister, Christa Jackson, and Cynthia Taylor.
The application deadline for the Teacher Leadership Program at the IAS/Park City Mathematics Institute (PCMI) is Tuesday, January 15. This is a professional development program best suited for teachers of grades 5-12. Teachers of lower grades may apply but should be aware of the emphasis on mathematics in the program. Applicants to TLP must spend at least 50% of their time as classroom teachers. You'll need a resume and reference letters, so don't put off your application until the last minute! To learn more, you can go to the website and you may want to review this Global Math Department session from last month.

The PAEMST application cycle is open! Outstanding grade 7-12 teachers of mathematics, science, computer science, technology, and engineering can be nominated any time before March 1, 2019. Those teachers accepting their nomination have until May 1, 2019 to submit a completed application.

Are you interested in becoming a reviewer for EdReports.org? If so, you can apply now on their website.

Math Ed in Colorado

Celebrate Teacher Appreciation Day with the Buffs and a basketball game on Thursday, January 10th! CU Boulder alums and friends of the School of Education are invited to a pre-game reception and can get discounted tickets to the basketball game.

Math on the "Planes" is coming February 22-23! This year's facilitator is Steve Leinwand and the event will be held in Adams 12. You can register on the CCLD website and those needing a scholarship to cover registration costs are encouraged to apply through the Mikkelson Mathematics and Science Scholarship Fund. The deadline for scholarship applications is January 18, 2019.

RME 6: Opening Keynote - Moving from Disowning to Owning Realistic Mathematics Education

Frank Eade, Ministry of Education, Cayman Islands

David Webb, School of Education, University of Colorado Boulder

Frank Eade

The point of this keynote was to describe Realistic Mathematics Education from the experience of two of its strongest proponents, Frank Eade of the Cayman Islands and David Webb of the United States. With Grand Cayman as a new location for this conference, and many educators coming to an RME conference for the first time, the keynote was designed to describe experiences that any math teacher could relate to.

Frank described his early experiences as a math teacher in the UK. There were influences of New Math from the US, and a sense that things could be changing, but the expectation was to teach traditionally. David's early experiences as a teacher, teaching high school in 1980s Los Angeles, was that instruction was largely teacher-oriented. People talked about group work, but not without much of a sense of purpose. People focused on procedure and problem solving only came at the end after the procedures had been learned.

David Webb

Frank began to learn about dilemmas with students' mathematical experiences. For example, if you ask students to put 0.375, 0.7, and 0.32 in order, many students will say 0.375 is the smallest because it has thousandths, and thousandths are the smallest. Frank read this in research and didn't want to believe it, so he tried it with his own students. They replicated the research, revealing to him that he'd been totally unaware of their misconceptions. He talked to them about why they believed what they did, and got answers like "It's a bit like negative numbers --- the smaller it is, the larger it is." David knew he could organize his entire curriculum around a procedural textbook and hand out worksheets. Students didn't seem to mind and figuring out how to do group work seemed like an uphill battle. Change meant fighting the didactical contract students had formed with their math teachers over many years.

Frank's first experiences with RME came when he visited the University of Amsterdam and some schools there. He observed 7/8 students comparing 2/3 to 3/4. He figured students would answer as his would -- that the fractions were the same because in each fraction you could add one to the numerator to get the denominator. Instead, he saw students drawing pictures and using those pictures to argue their reasoning. The only student he observed who reasoned incorrectly was someone who recently moved there. He started to become a convert. David entered graduate school after 7-8 years of teaching and ended up at Wisconsin with Tom Romberg. His assignment as a grad student was to align every activity in Math in Context to the NCTM Curriculum Standards. There were 30 MiC units, so it was a lot of work, but it gave him a detailed look at RME's approach to curriculum design. Sometimes he was in disbelief about the kind of reasoning that was expected of students before procedural understanding had developed. But as he observed students in classrooms, he became a believer as students approached problems informally but expressed all the reasoning they would need to understand the problem formally.

Frank and David describing models and progressive formalization

Frank's experience with RME curriculum design was part of a MiC pilot. A teacher who was supposed to try a unit for 3 weeks ended up stretching the unit for 10 weeks because kids were so engaged in all the mathematical reasoning -- and because they all had a lot to learn about how to implement and pace a different kind of curriculum. This led to multiple grant-funded projects both to develop new curriculum and to study its implementation. David's experience with design in RME came at the end of the MiC project as focus shifted to implementation and assessment. He had the opportunities to travel the country and offer PD and learn from teachers who needed support to understand the principles of RME and, maybe more importantly, to redefine the roles of teacher and learner in their classrooms.

3A + 2P = $9.20

1A + 2P = $5.20

Frank gave the above problem to a group of students with experience with RME, but they were scared of the symbolic notation. Then one student in the room said, "Wait, it's hats and umbrellas!" (a problem in Math in Context) and the rest of the class caught on and they were able to reason with the mathematics. They had seen the hats and umbrellas problem 2 years before, but the reasoning had stuck with them. David's work with assessment bridged the divides between RME and formative assessment. It was yet another way to rethink what it meant for students to understand mathematics. David began to promote the use of the assessment pyramid, even for teachers to think about how they arrange the bulk of their assessments they use in their classrooms. "Students are capable of solving fascinating problems -- we just have to ask them."

Frank was talking to his wife about math and asked her to explain how she got an answer to a particular fraction problem. She said, "I cheated. I imagined it, but I know I'm supposed to find the common denominator." Here in the Caymans, Frank has worked with students who have struggled but are now seeing the math in their worlds in new ways. RME isn't totally different from other approaches to mathematics, but some distinctions are useful. It's important for teachers to see their role in orchestrating students' mathematical experiences, and not just facilitate. The use of models is fundamental to RME's design, and teachers need to understand that approach to be successful.

When Frank introduced RME to the Caymans, he first visited every classroom to get a sense for the current state of math education on the islands. Staff turnover tends to be high in the Caymans. He found that many children didn't have a sense of shopping and the values of things, so those were opportunities to work those contexts into the curriculum. Students needed more support, so they introduced Mathematics Recovery. Interventions outside the classroom were far more fruitful in helping students because teachers struggled with interventions within the classroom. They employed lesson study to help teachers understand how lessons could be taught, and to address their own experiences with traditional instruction. At the end of primary in 2011, only 25% of students were expected and only 5% were above. At the end of primary in 2018, 62% were expected and 25% were above. That said, Frank says there is great danger in looking at scores like this too much, as we don't want teachers to become too focused on exam success as a measure of achievement.

This Week in Math Ed: February 2, 2018

I think I have a new plan: Since going through news, research, and Colorado events (in addition to daily Twitter updates) are quite a lot of work to do every week, I'll just highlight each one once a month. Something like this:

• First Friday of the month: Research Report
• Second Friday of the month: Around the Math Ed Web (events)
• Third Friday of the month: Math Ed in the News
• Fourth Friday of the month: Math Ed in Colorado

I might move some things around, but this one-feature-weekly in addition to the Math Ed Said review of Twitter activity seems like a good idea.

Math Ed Said

January 26: James Tanton wrote a wonderful piece on Medium, "Just teach my kid the <explitive> math." I'd guess most math educators have found themselves in these kinds of conversations (even within one's head) and Tanton's version is one of the more articulate versions I've seen.

Shared by: Jenise Sexton, Pam J. Wilson, Chris Hunter, James Tanton, Bridget Dunbar, Katherine Bryant, Jennifer Wilson, Christine Klynen, Cathy Yenca

January 27: Other people must agree with my enjoyment of Tanton's article because more decided to share it on the 27th. Here it is, again: "Just teach my kid the <explitive> math."

Shared by: Scott Leverentz, Barbara Rock, John Colgan, Nerissa Gerodias, Sunil Singh, Ben Blum-Smith, Chris Brownell, Alison Hansel, Bridget Soumeillan, Gregory Taylor, Matthew Oldridge, James Tanton, Laura Kinnel

January 28: How fun! Here in "Equations I Have Known" Joe Schwartz cataloged a number of the ways students use the notation for operations and equality before they've attended to the level of precision we expect from someone who has mastered these conventions. Some are quite common, like run-on equations (1x2=2-1=1), but others might be new to you.

Shared by: Amie Albrecht, Mark Chubb, Heidi Fessenden, Cathy Campbell, Chrissy Newell, Lisa Bejarano, Kit, Chris Kalmbach, Simon Gregg, Marilyn Burns, Jim Doherty, Rene Grimes, Heidi Allum, Joe Schwartz

January 29: As a first-year teacher resisting the mid-'90s feel-good, self-esteem pushes in education, I was convinced that my students (before I'd even had a chance to teach them!) would feel good about math if they were successful at it, and not the other way around. I gradually learned that it wasn't that simple, and new research from Stanford is helping us better understand how a positive attitude toward math predicts math achievement in kids.

Shared by: Laura Wagenman, Jani Nelson, Georgina Rivera, Christopher Rohde, Lara Francisco, Christina Moore, Camsie McAdams, Judy Larsen, Andie Ogden, Rosa Serratore, Kim Webb, Jo Boaler

January 30: More people shared the story, "Positive attitude toward math predicts math achievement in kids."

Shared by: Rosa Serratore, Regina Barrett, Nick Harris, Jennifer Lawler, Chris Brownell, Linda Braddy

January 31: I so appreciate David Bressoud's relentlessness when it comes to calculus education reform. Here he is on The Conversation with "Why colleges must change how they teach calculus." Part of this article talks about the SEMINAL project, which my advisor David Webb works on as part of his role at CU Boulder and on behalf of the Association of Public Land Grand Universities.

Shared by: Eddi Vulić, Robert Cop, David Butler, Jennifer Lawler, Lybrya Kebreab, Heather Johnson, Egan J Chernoff

February 1: More people helped spread the word about the Desmos Teaching Fellowship.

Shared by: Ed Campos Jr, Jocelyn Dagenais, Ron King, Audrey McLaren, Nerissa Gerodias, David Sabol, Julia Finneyfrock, Sadie Estrella, Nanette Johnson, Jennifer Fairbanks, Explore MTBoS, Lisa Bejarano, Emily Campbell, Sara VanDerWerf, Robert Kaplinsky, Molly Daley, Mary Bourassa, Daniel Luevanos, Zack Patterson, Jon Orr, Patty Stephens, Kathy Henderson, Tom Snarsky, Dan Anderson, Lybrya Kebreab, Jedidiah Butler, Matthew Baker, Bob Lochel, Eli Luberoff, Chris Lusto, Bryan Anderson, Jocelyn Dagenais, Desmos.com

Research Report

Educational Studies in Mathematics

ESM published both their January and February issues since my last Research Report on January 5.

• Why Johnny struggles when familiar concepts are taken to a new mathematical domain: towards a polysemous approach by Igor' Kontorovich
• Conflicting frames: a case of misalignment between professional development efforts and a teacher’s practice in a high school mathematics classroom by Einat Heyd-Metzuyanim, Charles Munter, and James Greeno
• Power and identity in immigrant parents’ involvement in early years mathematics learning by Miwa Aoki Takeuchi
• Culture and ideology in mathematics teacher noticing by Nicole L. Louie
• Mediating primary mathematics: theory, concepts, and a framework for studying practice by Hamsa Venkat and Mike Askew
• Inverse function: Pre-service teachers’ techniques and meanings by Teo Paoletti, Irma E. Stevens, Natalie L. F. Hobson, Kevin C. Moore, Kevin R. LaForest
• Book review: Baruch B. Schwarz and Michael J. Baker (Eds) (Foreword by L. B. Resnick with F. Schantz) (2017) Dialogue, Argumentation and Education: History, Theory and Practice by Keith Weber
• Developing mathematical fluency: comparing exercises and rich tasks by Colin Foster
• Order of operations: On convention and met-before acronyms by Rina Zazkis and Annette Rouleau
• The role of perceptual similarity, context, and situation when selecting attributes: considerations made by 5–6-year-olds in data modeling environments by Aisling Leavy and Mairead Hourigan
• The influence of theoretical mathematical foundations on teaching and learning: a case study of whole numbers in elementary school by Christine Chambris
• Book review: Anthropomorphizing mathematics education Review of Hauke Staehler-Pohl, Nina Bohlmann, and Alexandre Pais (Eds). (2017). The disorder of mathematics education: challenging the sociopolitical dimensions of research. 329 pp. by Bharath Sriraman

Mathematical Thinking and Learning

This issue focuses on mathematics learning and computational thinking.

• On MTL's Second Milestone: Exploring Computational Thinking and Mathematics Learning by Lyn English
• Computational Literacy and "The Big Picture" Concerning Computers in Mathematics Education by Andrea A. diSessa
• Group Theory, Computational Thinking, and Young Mathematicians by George Gadanidis
• The Dynamic Geometrisation of Computer Programming by Nathalie Sinclair and Margaret Patterson
• Cultivating Computational Thinking Practices and Mathematical Habits of Mind in Lattice Land by Christina (Yu) Pei, David Weintrop, and Uri Wilensky

International Journal of Science and Mathematics Education

Both the January and February issues of IJSME have been published since the last Research Report.

Patricio Herbst presenting at the 2014 NCTM Annual Meeting

• A Framework for Assessing Reading Comprehension of Geometric Construction Texts by Kai-Lin Yang and Jian-Lin Li
• The Importance of Multiple Representations of Mathematical Problems: Evidence from Chinese Preservice Elementary Teachers' Analysis of a Learning Goal by Rui Kang and Di Liu
• Engaging Primary School Students in Mathematics: Can iPads Make a Difference? by Annette Hilton
• Will Teachers Create Opportunities for Discussion when Teaching Proof in a Geometry Classroom? by Ander Erickson and Patricio Herbst
• Effects of a Mathematics Cognitive Acceleration Program on Student Achievement and Motivation by Teukava Finau, David F. Treagust, Mihye Won, and A. L. Chandrasegaran
• Exploring Young Children's Understanding About the Concept of Volume Through Engineering Design in a STEM Activity: A Case Study by Do-Yong Park, Mi-Hwa Park, and Alan B. Bates
• Reification in the Learning of Square Roots in a Ninth Grade Classroom: Combining Semiotic and Discursive Approaches by Yusuke Shinno
• Preservice Middle and High School Mathematics Teachers' Strategies when Solving Proportion Problems by Muhammet Arican
• The Relationship between Pre-service Mathematics Teachers' Focus on Student Thinking in Lesson Analysis and Lesson Planning Tasks by Rukiye Didem Taylan
• High School Students' Motivation to Learn Mathematics: The Role of Multiple Goals by Chi-hung Clarence Ng
• Pre-service Mathematics Teachers' Noticing Skills and Scaffolding Practices by Hulya Kilic

Journal of Mathematics Teacher Education

• Mathematics teacher's knowledge, knowledge-based reasoning, and contexts by Salvador Llinares
• Audible conversational affordances and constraints of verbalizing professional noticing during prospective teacher lesson study by Julie M. Amador and Ingrid S. Carter
• More than meets the eye: patterns and shifts in middle school mathematics teachers' descriptions of models by Michelle H. Wilkerson, Alfredo Bautista, Roger G. Tobin, Bárbara M. Brizuela, and Ying Cao
• Assessing key epistemic features of didactic-mathematical knowledge of prospective teachers: the case of the derivative by Luis R. Pino-Fan, Juan D. Godino, and Vicenç Font

Fields Mathematics Education Journal

• Teaching and learning mathematics through error analysis by Sheryl J. Rushton

Technology Innovations in Statistics Education

• Dynamic Data in the Statistics Classroom by Johanna Hardin