This Week in Math Ed: January 29, 2016

Math Ed Said

January 22: "Draw the Kitty" by Jonathan Claydon was the most popular post last Friday, and I'm pretty sure it being Friday might have contributed to the popularity of the post. Thanks to Jonathan, Andrew Gael, Glenn Waddell, Gregory Taylor, and Taylor Belcher for sharing.

Doug Clements presenting at the 2011 RME Conference
January 23: A host of people including Matthew Oldridge, Jo Boaler, Keith Devlin, Susan Davidson, Richelle Marynowski, Tim Hudson, and Trena Wilkerson retweeted Doug Clements's share of a research article, "Developing Multiplication Fact Fluency."

January 24: Dave Radcliffe, James Cleveland, Dylan Kane, Michael Welch, and Mikael Johansson shared Ta-Nehisi Coates article in The Atlantic, "Bernie Sanders and the Liberal Imagination."

January 25: Dan Meyer, Geoff Krall, Megan Schmidt, Dave Radcliffe, Mark Chubb, Jedidiah Butler, and Jana Sanchez shared Christopher Danielson's "Parent Letters." Here Chris looks at how a report from a commercial math practice app helps parents understand an arithmetic strategy as well as their child's performance.

January 26: Pick from three: (1) Jon Orr's "Better Questions – Two Truths & One Lie" (shared by Laura Wheeler, Shauna Hedgepeth, Bridget Dunbar and Jana Sanchez); (2) the Quartz story "An NFL Player Was Just Accepted to the Math PhD Program at MIT" (shared by Steve Phelps, OCTM, George Woodbury, and Egan Chernoff); and/or (3) Joe Schwartz's "What I'm Looking For" (shared by Joe, Patrick Honner, Michael Pershan, and Josh Fisher).

January 27: NCTM announced a new conference called "Innov8" and 16 members of my MathEd Twitter list had something to say about it or gave it a retweet: NCTM, Travis Olson, Diane J. Briars, Stephanie Iacadoro, Matt Larson, Teaching Children Math, Emily Campbell, Amanda Jansen, Bridget Dunbar, Dan Meyer, John SanGiovanni, Bridget Dunbar, Mathematics Teacher, Jessica Faurote, Farshid Safi, The Math Forum, and David Keller chimed in. Details about the event are to come, but there are some sure signs here that Innov8 will not just be another version of the annual meeting or the regional conferences as they are currently designed.

January 28: Cal Armstrong, Michael Pershan, Matt Enlow, Bridget Dunbar, Eddi Vulić, Sendhil Revuluri, Dylan Kane, and Dan Goldner shared Ben Blum-Smith's "Lessons from Bowen and Darryl." It's a great post that should get teachers thinking about the intentionality of their teaching, including how problems are chosen, how students are grouped, and how we can strategically call on students to share their ideas.

Complimenting Ben's post is one called "Planning Lessons" by David Wees, which was shared by 6 people on Thursday.

Around the Math Ed Web

The 2016 conference of the Association of Mathematics Teacher Educators (AMTE) is currently underway. I'm seeing some quality activity on the #AMTE2016 hashtag, so go there to follow along.

In the Global Math Department, this week's topic was "Using Direct Measurement Videos to Learn to Make Mathematical Models," presented by Peter Bohacek. Next week's topic is "Google Apps for Education in the Math Classroom."

At the Mathematics Educators StackExchange, recent topics have looked at the use of the terms "specific" and "particular," working with polynomials, accepting late homework, and innumeracy.

In the Google+ Mathematics Education (K-12) Community, recent posts have looked at John Hattie's work and Josh Fisher, as usual, has kept busy sharing blog posts.

Research Notes

Three new articles and a book review have recently appeared in Mathematical Thinking and Learning:
By far, the article above that instantly grabbed my attention was the "Shortcomings" article by Gravemeijer et al. I really want to give it a more proper summary in the coming days, but to do that you really need to know Sfard (1991), which is another article I've been meaning to give a proper summary. In short, however, Gravemeijer et al. say this: Reform math isn't working as well as it should, and it's not because traditional is better — and we have evidence to back that up. Rather, reform mathematics is struggling because we're too task-focused, especially in how we make student performance on particular tasks the goal of student understanding. True conceptual understanding needs to go beyond tasks, and focus on students' mastery of mathematical phenomena as processes and objects, as Sfard described in 1991.

Here's another new math-related article in Teaching and Teacher Education that I think I missed:
Lastly, and not quite new for 2016, is a great exchange between Danny Martin and leaders of NCTM. If Principles to Actions was the most important document in math education last year, then this is the most important discussion of that document, captured in the Journal of Urban Mathematics Education:

Math Ed in the News

Math Ed in Colorado

The Colorado Math Leaders met on Tuesday in Colorado Springs. It was my first time meeting the group, although there were a few familiar faces there. We had excellent discussions around NCTM's Principles to Actions and we're looking to hold our next meeting on February 23rd.

The next session of the Northern Colorado Math Circles are on Monday, February 22nd. Contact Gulden Karakok or Delia Haefeli for more information or to RSVP.

The next CCTM board meeting is this Saturday, January 30th. I'm looking forward to meeting everyone!

The Math on the "Planes" conference, presented by the Colorado Council for Learning Disabilities is coming up on February 26-27.

This Week in Math Ed: January 22, 2016

Math Ed Said

My MathEd Twitter list has passed 1300 members and 150 followers. Here's what the list members have been talking about in the past week.

Jason Zimba presenting at the 2015 NCTM Annual Meeting
January 15: Diana Suddreth, Illustrative Maths, Katherine Martin, Shauhna Feitlin, and Kate Nowak shared a post by Jason Zimba on the "Common Core Watch" blog titled, "Can parents help with math homework? YES." This post is written in response to recent headlines suggesting that math education is best left to teachers, and provides some advice for parents who might not be familiar with the curriculum their children are using.

On a personal note, I find conversations about parent help on homework interesting and, frankly, a bit foreign. Growing up, getting homework help from my parents just wasn't a thing. They didn't offer, I didn't ask, and even thinking about it now I still feel like my parents instructing me on my homework would have been as weird as me standing over their shoulders at their jobs instructing them how to do their work. This had implications for me as a teacher, as on more than one occasion I struggled to deal with parents simply because I underestimated the involvement they wanted in their child's education. I consider it just one more example of how teaching is difficult when you struggle to shake yourself from the idea that you just need to do for your students what was done for you when you were a student.

January 16: Mike Lawler, Simon Gregg, TJ Hitchman, and Kate Owens were all talking about how to fold a dodecahedron into a cube. This is a richly multimedia post, complete with animated GIFs of folding shapes and videos of kids working with a Zometool set to demonstrate how the two shapes fit together. (Fun fact I just learned: The Zometool offices are just a few miles down the road from me in Longmont, CO.)

January 17: Oh boy. Michael Welch, Jose Vilson, Ματτ, Shannon Houghton, Michael Welch, Taylor Belcher, Kate Nowak, Joshua Bowman, Jessica Faurote, Robin Hosemann, and Megan Schmidt shared a link to the story, "My year of terror and abuse teaching at a NYC high school," published in the New York Post. Many people retweeted Doug Robertson, who summarized the story thusly:

January 18: It's a 3-way tie! Shauna Hedgepeth, Kent Haines, Bridget Dunbar, and Elizabeth Statmore shared Elizabeth's post, "Algebra 1 Inequalities – A minor 'How People Learn' unit". Meanwhile, Lorraine Males, Eddi Vulić, Chris Lusto, and Dan Meyer shared Dan's post, "[Makeover] Marine Ramp". Lastly, Jocelyn Dagenais, Larry Sizemore, Brian Bushart, and Kasi Allen shared "Practical Ways to Develop Students’ Mathematical Reasoning." Without summarizing these, I'll just say that the quality across these posts is outstanding.

January 19: It's bigger than the last one! Gary Davis, Learning Maths, ATM, Dave Radcliffe, Better Maths, and Avery Pickford shared either a news story or the announcement of our brand-new largest known prime number.

January 20: People like to share Ben Orlin's bad drawings. This time it's "The Number Line: A Journey," shared Thursday by Simon Gregg, Paula Beardell Krieg, Denise Gaskins, Alison Hansel, and Ben Orlin himself. This one might have bad drawings, but the entertaining narrative more than makes up for it.

January 21: Three posts were most-shared on Thursday, but the one that got my attention was Rachel Lambert's "Developing meaningful mathematics goals for IEPs," shared by Bridget Dunbar, Tracy Johnston Zager, Tina Cardone, Fawn Nguyen, and Andrew Stadel in preparation for #SwDMathChat. The post makes some very good suggestions for writing IEP goals that reflect mathematical practices rather than merely requiring a certain number of right answers on a certain kind of repetitive exercise. The other most-shared posts were about Desmos's new features in Activity Builder and calls to submit to the MTBoS Activity Bank.

<soapbox>My one piece of critical feedback for the latter: it's great to submit a "good math activity" but I want to keep pushing people to articulate and work with criteria for why something is good — and none of us should be satisfied with the simple thumbs-up, likes, or 5-star systems we might see on any of the other repositories. Furthermore, as a community, we shouldn't put the blame for this on the makers of the repositories. When we, as lesson and activity authors, make it standard practice to articulate and use shared criteria for activity quality, then the repository builders will have something powerful to work with.</soapbox>

Global Math Department

This week's GMD meeting featured Ryan Seth Jones work on statistical variability in a talked titled, "Conceptual Understanding is Not Enough! Supporting Students to See Statistics as Epistemic Tools." Next week's meeting looks at video-supported measurement scenarios and mathematical modeling.

Research Notes

Samuel Otten released a new episode of the Math Ed Podcast. His guest? Himself! (Why not? It's his show, after all.) In this episode, Sam talks about a new article in ZDM that he co-authored with Chris Engledowl and Vickie Spain, "Univocal and Dialogic Discourse in Secondary Mathematics Classrooms: The Case of Attending to Precision."

I was excited to see Elham Kazemi, Hala Ghousseini, Adrian Cunard, and Angela Chan Turrou's Journal of Teacher Education article, "Getting Inside Rehearsals: Insights From Teacher Educators to Support Work on Complex Practice." I should say more about this article when I get around to following up on my "Madness to Our Methods" post from last fall, but for now, I want to acknowledge it for being a well-framed article that pushes the conversation about practice-based teacher education a bit further by really focusing on the roles of novice teachers and teacher educators and how they interact in the context of rehearsing practice. I think the scenarios described here (all of which are math activities) are things that existed in my imagination when I thought about practice-based teacher ed, but I lacked any empirical basis for really thinking about how as a teacher educator I might facilitate rehearsing a practice.

I also looked at "Exploring a Structure for Mathematics Lessons that Initiate Learning by Activating Cognition on Challenging Tasks" which has been added to the slate of articles for the March issue of The Journal of Mathematical Behavior. (See last week's TWiME for the previously-added articles.) My first thought was, "Is this going to be any different than Stein, Smith, et al.'s cognitive demand?" Yes, it's different, but related. The Australian authors (Peter Sullivan, Chris Borcek, Nadia Walker, and Mick Rennie) draw upon a somewhat different body of literature than you might typically see in a Smith & Stein-based article, but their lessons were designed similar to what is typically found in Connected Mathematics, citing Lappan, Fey, Fitzgerald, Friel, and Phillips (2006), the CMP2 Implementing and Teaching Guide. The researchers were interested in lessons where initial tasks were quite engaging and demanding, as opposed to more traditional lessons in which simple problems were practiced first before working towards problems of higher difficulty. Overall, Sullivan et al. found success with the lessons, as most teachers rated them positively for what students learned and were able to contribute during the lessons. Time management of the lessons did not always go to plan, which is no surprise for those of us who have taught such lessons. Students did show improvement from their pre-test to post-test, but this was not an experimental or quasi-experimental study that compared the focus students to any others using different lesson structures. For this reason, this research isn't by itself going to answer really big questions about how we teach mathematics, but it can sit comfortably with the body of evidence that promotes a more student inquiry-oriented type of teaching.

Other articles appearing in JMB's March issue that I didn't mention last week are Pedemonte and Balacheff's "Establishing Links Between Conceptions, Argumentation and Proof Through the ck¢-Enriched Toulmin Model" and Huang, Barlow, and Prince's "The Same Tasks, Different Learning Opportunities: An Analysis of Two Exemplary Lessons in China and the U.S. From a Perspective of Variation."

A quick look through the February issue of the International Journal of Science and Mathematics Education seems to have quite a bit more science than math, but here's a quick rundown of what's new:
Lastly, five new articles in the February 2016 issue of the Journal of Mathematics Teacher Education:
Patricio Herbst presenting at the 2014 NCTM Research Conference
Can you take just one more article? Here's one from the Journal of Teacher Education by Erin Turner (University of Arizona) and Corey Drake (Michigan State University): "A Review of Research on Prospective Teachers' Learning About Children's Mathematical Thinking and Cultural Funds of Knowledge"

Math Ed in the News

Math Ed in Colorado

Colorado Math Leaders (CML) are meeting in Colorado Springs on Tuesday, January 26th. This will be my first meeting, and I'm anxious to meet everyone and see a few familiar faces. I believe our main topic is Principles to Actions, and I can't think of too many other relevant publications that I'd rather talk and hear others talk about.

Northern Colorado Math Circles are on January 25th at UNC for 5th-8th graders. Find Ross Hall 2090 from 5:30 to 7. RSVP to Gulden Karakok or Delia Haefeli by noon on Monday, January 25th. The next sessions for teachers and students will be on Monday, February 22nd.

The next CCTM board meeting is Saturday, January 30th. I had a great meeting with CCTM President Joanie Funderburk on Wednesday, and I look forward to working with her and the rest of the people with CCTM. In case you missed it, the Winter 2016 issue of the CCTM Journal is available, and I'm happy to say that I'm a co-author with Frederick Peck, Jessica Alzen, and Derek Briggs on an article that talks about some of our learning progression-based growth measurement work, specifically the tools we used with teachers to guide the analysis of student work and the quality of assessments. See the CU-Boulder CADRE website for more information about this work or feel free to contact me.

Feeling around in the dark to understand the elephant of local control

The view from my new office.
Educationally, Colorado is a "local control" state, and I know this because I've heard many people say it. I once read something that said "there are only six local control states," and I assumed Colorado was one of them. (I also assume many more than six states would claim to belong on the list.) The document did not list the states or describe the difference between local and not-quite-local. But by all other accounts I've seen and heard, Colorado is a local control state.

Today was my first day in my new job at the Colorado Department of Education, and at almost every turn I was reminded of Colorado's status as a local control state. Before I go further, let me be clear: I see many positives in local control and generally favor it. I appreciate that historically and politically we've entrusted our schools to the communities they serve, and I cherish my rural school experiences where the tight bonds between the school and the community generate a special sense of pride and responsibility.

Local control is not to be confused with insular, however. I've never known a school district where teachers and district officials didn't seek resources and guidance from outside their boundaries. In my new job, I'm now one of those outsiders who can offer some of those resources and guidance. But as an employee of the state, I have to be rather careful about the resources and guidance I give, lest anyone be confused about whether control lies with the state or with the school district.

It's a bit awkward, as you might expect. And it's becoming apparent to me how local control influences the things a CDE employee decides they can and cannot say is, well, a little arbitrary. Maybe arbitrary isn't the right description, but rather there's some socio-normative set of unwritten rules guiding all this that aren't 100% logical. For example, we believe local districts have the power to make curriculum decisions, not the state. But what does that mean? For me, I know without a doubt this means I have no power as a state employee to require that a district, school, or teacher use a particular set of textbooks. Okay, that's clear to me, but can I recommend a textbook, while plainly stating that textbook choices are not the state's decision? Again, this is something we expressly avoid at CDE because we don't want to give districts the impression that they're not in control of their curriculum. Let's make this even fuzzier: If someone asks me what textbooks I've personally used and why I chose to use them, can I answer? I certainly hope so, as I'd feel silly not answering the question. But with my answer, I have to be cautious that what I say is not construed as some kind of state endorsement of a particular textbook. Why? Local control, that's why.

Yet, there are numerous areas where we, the citizens of Colorado and our elected representatives, have decided the state should have control. The state dictates sets of academic standards, which are accompanied by all sorts of supporting documents. The state also requires the administration of assessments that measure student performance towards those standards, and by law the results of those assessments are used to hold local educators accountable. Whether I approve or disapprove of these things is irrelevant in the current discussion, because I only name them to illustrate how the state has control over things that might not be textbooks or curriculum, yet have undeniable influence over local educators' choice of curriculum and related materials. We still claim to have a system of local control, but it shows that local vs. state control of schools is beyond a simple binary classification.

I'm reminded of a pair of sessions I attended at the Realistic Mathematics Education Conference in 2013. The first was from several people from CDE, who presented a series of standards implementation materials they developed in cooperation with local educators. The second presentation came from national curriculum developers from The Netherlands, who showed their new integrated STEM curriculum materials. Both groups sincerely wanted high-quality educational experiences for students, but CDE illustrated the more traditionally American approach of building out documents and tools to support local decision-makers, instead of developing student-facing curriculum materials, as seen in The Netherlands. Dutch schools are not required to use materials developed by their national curriculum office, so you can say there's still an element of local control there. But at a national/state level they do experience a broader set of options for what they produce for schools, and these options are supported by a different political and cultural climate than we generally find in the United States.

Without belaboring the issue much further, I hope by now you get a little sense of the tension I'm feeling in my new position. I'm grappling with my new role and how my actions and words will be shaped by issues of local control, this elephant in the dark room that I felt my hands on all day. A lot of "what-ifs" came to mind, and some of them yield unsatisfactory possibilities. I'm frustrated by thoughts of continually almost doing curriculum work, and I don't think anyone wants to produce supplementary documentation just for the sake of producing it. With what I currently see offered for mathematics from CDE, there's a lot of value in the details, but it's a pretty overwhelming mass of stuff at first (and second) glance. That's not going to change overnight, but for me, after Day 1 on the job, I think the best thing I can do is think openly about this and to explore the boundaries of what is reasonable and possible. Ultimately, I serve the teachers and educators of Colorado, and for now, I can be honest about the thought I put into these things, even if I don't anticipate easy answers anytime soon.

A day in the life of a Ph.D. candidate

7:30 Wake up, roll over, and begin my day by checking email, Twitter, Google+, and RSS feeds.

8:15 Actually get out of bed and get ready for the day.

9:00 Sit at desk and start working. Listen to Science Friday podcasts on 2x speed in the background. My first task is to apply for a travel grant I'm hoping will help get me to NCTM. Task #2 is to follow up on some other travel funding I applied for.

9:45 Snack.

10:00 Prepare expense report and receipt for student infographics I printed for Inquiry Hub. It amazes me how much technology I use even for a simple task like this: Taking a picture of the receipt with the Microsoft Office Lens app on my phone, uploading it as a PDF to OneDrive, using Adobe Reader to fill out and digitally sign the expense report (with a password saved in LastPass), and using BitTorrent Sync to sync OneDrive to my Linux desktop, where I save files and do most my work. Science Friday has given way to Leo Laporte's The Tech Guy podcasts.
A glimpse of what I have in Pocket Casts

10:30 Work on a new "This Week in Math Ed" post. I was smarter this week and started writing earlier in the week as I saw some of the posts.

11:30 Lunch.

11:45 I'm back to work and reviewing recent research. I pause the podcasts to help me keep focus as I'd like to get through a few articles in a relatively short amount of time.

1:00 Break. So much for getting through multiple articles quickly. I started one and decided it wasn't a good fit for the post, then dug too deep into the next and ended up summarizing it on the Wiki.

1:20 Back to the research and writing.

3:15 I finally wrap up the blog post and send it out on Twitter and Google+. Time for another break.

3:45 Email wrangling. In 30 minutes I manage to delete, archive, reply to, or otherwise act upon about 40 emails, which only leaves me with about 100 unread. Try as I might, I've never quite developed habits that keep me at or very near inbox zero.

4:15 Dig into some administrative stuff to follow-up on some of my teaching duties from last semester. I told myself I'd get it done the first week back, and the last minutes of that first week are here.

5:00 I keep working, but turn on Tech News Today to catch some of the day's tech news.

6:00 Dinner time. Watch the Daily Tech News Show to get even more tech news. I'm still not done with the 4:15 task, but I set it aside for awhile.

Wisconsin won 1 match tonight. Ask Northwestern fans -- it could be worse.
7:00 On the bike. I aim for an hour of activity every day, and many days that means I'm on my exercise bike for an hour in the evening. Today I planned it this way so I could watch the Iowa-Wisconsin wrestling dual meet while I pedaled. Today's ride went about 20 miles, which puts me at 289 miles so far this year.

8:00 I finish watching the wrestling meet and send some email. I'm running out of steam at this point so everything I do seems to take longer.

9:45 Wrap up the 4:15 task, which thankfully had little left to do.

Bill Penuel-approved reading.
10:00 I concede that there's not just much productivity left in me today. Like too many days, I finish and think, "Where could I have found time to work on my dissertation?" In this case, I really thought I'd get through my mid-day blogging faster than I did. Writing now wouldn't go well, so I'll settle for some reading. Tony Bryk's book was delivered yesterday, and if I'm lucky I'll stay awake long enough to get through 10 pages.

This Week in Math Ed: January 15, 2016

Math Ed Said

January 8: NCTM, Regan Galvan, Math for America, and Bridget Dunbar tweeted this Chalkbeat story about New York City having specialized math teachers as a strategy to improving algebra readiness. I think this approach has some real promise (there's probably research on the effectiveness of elementary math specialists, but I don't know it), and I wish them luck figuring out what I imagine will be some tricky staffing and logistical issues to make it happen. Interestingly, Redwood Falls, Minnesota, plans on doing the exact opposite.

January 9: Suzanne Alejandre, Tina Cardone, Ashli Black, Diana Suddreth, Anna Blinstein, Bowen Kerins, and OCTM were all talking about the Park City Math Institute's Teacher Leadership Program. Applications are due TODAY, and good luck to all those who applied!

Jo Boaler presenting at the 2015 NCTM Annual Meeting
January 10: Jo Boaler's Hechinger Report article from last May, "Memorizers Are the Lowest Achievers and Other Common Core Math Surprises", was made the rounds Sunday thanks to Ilana Horn, Robert Talbert, Sara VanDerWerf, Andrew Gael, Dan Anderson, and George Woodbury. Here, Jo encourages us to be more patient with the learning of mathematics rather than marching through memorization and fact drills on a race to calculus.

January 11: The blogosphere is abuzz with Week 1 of the 2016 MTBoS blogging initiative. Tina Cardone, Gregory Taylor, Jon Orr, Kristina Danahy, Kyle Pearce, and Danielle Reycer were all busy on Monday sharing, resharing, and/or encouraging people to share blog posts.

January 12: Teaching Children Math, NCTM, Richelle Marynowski, Fawn Nguyen, and UCTM shared "Practıcal Problems: Using Literature to Teach Statistics", an article in the NCTM elementary journal, Teaching Children Mathematics. This was one of the most-shared links all week long, and for good reason: the activities in NCTM's teacher journals tend to be very well written and edited, and this article was both free and was the focus of the first #TCMchat on Twitter. The authors of the TCM article, Mairéad Hourigan and Aisling Leavy of Mary Immaculate College, Ireland, have several related publications here and here in the journal Teaching Statistics.

January 13: Egan Chernoff, Andrew Shauver, Josh Fisher, and Katherine Bryant shared Ben Orlin's "Simplify," the latest in his series of Math With Bad Drawings. Having done a few (tens of thousands) "simplify" problems myself, I've come to see "simplify" to mean, "re-write this according to the convention your teacher/student/reader would expect or appreciate." Ben takes this further and uses the idea of "paraphrasing" to emphasize that many of our symbol manipulations are transformations on objects whose value remains the same.

January 14: The most-shared link of the day pointed to a Storify of Tuesday's #TCMchat, but coming in 2nd was a story at Quartz titled "The Stanford professor who pioneered praising kids for effort says we’ve totally missed the point". "Mindset" has been perhaps the biggest education buzzword of the past couple of years ("practice" or "practices," as nouns, are another) and this article and the comments from Carol Dweck remind me of two things: (1) Uri Treisman's 2014 NCTM Research Conference plenary in which he said that it's a "parlor trick" to shift away from a fixed mindset for a short time, but lasting change is something we have a lot still to learn about, and (2) this SMBC comic from last week. Thanks to Elizabeth Statmore, John Golden, Mr. Harris, Denise Gaskins, Anna Hester, Avery Pickford, and Ron King for sharing.

Research Notes

I spent time this week curating a list of journals to follow and organize their RSS feeds. As much as I'd like to mention or describe all the research that crosses my path, there's just no way I can keep up with all of it. I'll do my best to choose 2-3 new articles this week, give them a quick looking-over (studying and understanding an article in-depth can take hours), and summarizing a bit here.

Educational Studies in Mathematics has already published new issues for January and February.

Csaba Csíkos at the University of Szeged, Hungary, published "Strategies and Performance in Elementary Students' Three-Digit Mental Addition" in ESM. Working with 78 4th grade students, Csíkos wanted to explore students' less-routine approaches to mental calculation in terms of strategy, speed, and accuracy. Bottom line? He didn't see as much of a relationship between strategy, response time, and success rate on tasks as you might think, although that might have been due to limitations in the study. I won't go on about it here, but I've summarized more of this article on the Wiki.

In Teaching and Teacher Education, Beth Clark-Gareca at Teachers College wrote, "Classroom Assessment and English Language Learners: Teachers' Accommodations Implementation on Routine Math and Science Tests." Working with 213 Pennsylvania elementary teachers, her findings are humbling: 65% of teachers said they weren't sure about the WIDA scores or proficiency levels of their ESL students. Ninety-six percent of teachers surveyed claimed fluency only in English. Overall, however, teachers did make the most test accommodations for students at the beginning and intermediate levels of English language proficiency. Additional time on assessments was a common accommodation, with one-on-one help, a translator, and dictionaries were less commonly used. Tests that included the native language of the test-taker were rarely used. ELL students who were not also identified as needing special education services often got fewer language accommodations as students receiving special education services.

The Journal of Mathematical Behavior is in the process of publishing their March issue, with these articles so far:
The above research represents maybe half of the tabs I opened in the past week as I found new articles, but I'm stopping here for this week! Also, math ed folks that do great work in the journal world but have horrible Google search results make me sad. (If RateMyProfessor or some such site ranks higher than your faculty page, you have a problem.)

Math Ed in the News

Did I miss anything? If so, feel free to mention it in the comments!

New year, new job

Exciting news! Starting January 19, I will be the new mathematics content specialist for the Colorado Department of Education (CDE). Whenever people would ask me about what kinds of jobs I might be interested in doing after grad school, I always mentioned this one or ones like it. It's a mixture of curriculum work, policy, assessment, teacher education, and communication — all the things I've focused on during my time as a graduate student. Of course, there's only one such job in the state of Colorado, so it was my good fortune that the job came open (relatively) near the end of my time as a graduate student. To help ease the transition, CDE is generously allowing me to start the job part-time while I complete work here at CU-Boulder. Thankfully, my new colleagues at CDE are well-aware of the challenges of finishing a Ph.D. and are willing to be flexible so that I can complete my degree. As educators I think we're all on the same page when it comes to helping students (even a supposedly grown-up one, like me) see their program through to the end.

What will the new job mean for this blog and my other online activities? If I have anything to say about it, the blogging, tweeting, Google-plussing, etc. will only get better. (I may even have to venture more frequently into Facebook for my professional use, as well as LinkedIn.) As a researcher (even the graduate student kind), there's a large expectation to share with others in the research community. But in this role as math specialist, I plan to make sharing of research, policy perspectives, projects and collaborations, etc. part of my full-time work, with the goal of bringing it to math educators across Colorado and beyond. I look forward to sharing more of the great work I see teachers doing, along with the hard-earned lessons we collectively learn along the way. I also look forward to bringing more transparency to a state agency. Yes, there are a few things I can't say on the job (for example, in Colorado the state doesn't tell school districts what curriculum to use), but to the extent I can keep sharing, I will!

This Week in Math Ed: January 8, 2016

Last year was not a productive blogging year for me, so I hope this post is the first of many in which I recap the goings-on in the mathematics education community. I see two benefits of doing this: (1) I can help others by finding, curating, and annotating the enormous amount of everything that might be of interest to us in the mathematics education community, and (2) it will encourage me to keep up and engage with more of the best stuff being shared and published. I've thought of doing this in newsletter or podcast form, but I'll start with blog posts until I get some traction.

Math Ed Said

I may follow fewer than 200 people with my @MathEdnet Twitter account, but over the years, I've amassed a MathEd Twitter list of nearly 1300 people. I curate the list pretty carefully by only adding people who appear to primarily tweet about math education and related issues. (Know someone who should be on the list but isn't? Tell me!) Here are the most-shared links from people on the list over the past week:

January 1: Ryan Ruff, Matthew Oldridge, Gary Davis, Chi Klein, and Bridget Dunbar were all sharing Jo Boaler's latest article in The Atlantic, The Math-Class Paradox. In the article, Boaler says we should work harder to focus on the learning that can happen in math classes, and less on student performance. Like other pieces Boaler has written over the past few years, this encourages us to steer clear of excessive assessment, timed tests, and pedagogy that gives students the impression math is all about facts and rules.

January 2: Federico Chialvo, Markus Sagebiel, John Golden, Katrina Hall, and Bridget Dunbar all shared Dan Meyer's blog post, "I'm gonna use my formula sheets and that's the only way I'm gonna do stuff". Dan highlights a recent New York Times piece in which a deposition by an expert witness becomes very uncomfortable when the witness isn't able to do what should be an easy mathematics problem.

January 3: Cathy Yenca, Lisa Bejarano, Jennifer Fairbanks, Mary Bourassa, Megan Schmidt, and Tina Cardone shared the ExploreMTBoS kick-off of their 2016 blogging initiative. (For more on the MTBoS and math educators on Twitter, see the Math Ed Wiki.) The post includes some simple to-dos for both new and experienced bloggers to help everyone start the new year right.

January 4: Danielle Reycer, Tina Cardone, Bridget Dunbar, Graham Fletcher, James Cleveland, Fawn Nguyen, George Woodbury, Michael Pershan, and Sadie Estrella all shared Kate Nowak's plea to "Please be more boring" described in Kate's post, In Defense of Unsexy. Kate says that while finding novel tasks that are high in cognitive demand has become increasingly easy, we're lacking high-quality but lower-demand tasks that address fundamental concepts. Basic stuff. The post is worth reading for her Mario Batali vs. Rachel Ray analogy.

Tracy Zager presenting at the 2015 NCTM Annual Meeting
January 5: Michelle, Ruth Parker, Josh Fisher, Denise Gaskins, Larry Sizemore, Shauna Hedgepeth, Brian Anderson, Kate Nowak, David Coffey, Dan Meyer, Simon Gregg, Brian Bushart, Tim Hudson, and Christopher Danielson all shared Tracy Johnston Zager's excellent post, My Criteria for Fact-Based Apps. In her post, Tracy addresses a problem I've focused on for some time now in my dissertation work: While teachers and others have little trouble telling you what curriculum materials they like or dislike, it seems more difficult for people to clearly articulate the criteria they use for determining if something is good. Tracy does exactly this in her post, describing three criteria she uses when looking at fact-based math apps. This post gets my early vote for blog post of the year, and I hope others will follow Tracy by trying to articulate their criteria for choosing or recommending curricular materials.

January 6 and 7: Brett Gilland, Eric Milou, Keith Devlin, Kevin Moore, John Golden, Rachel Lambert, John Pelesko, Dylan Kane, Steve Phelps, Tracy Zager, and I made this comic from Saturday Morning Breakfast Cereal the most linked-to post for two days running in my MathEd list. We laugh to keep from crying, right?

If you're looking for something else to read that was popular in the past week, try Matt Townsley's list of Top 10 Standards-Based Grading Articles. I won't say SBG is a panacea for all our educational ills, but I've tried various formations of it myself and encourage teachers to thoughtfully experiment with their grading and feedback systems in ways that put more attention on student performance on tasks and less on students' ego.

Research Notes

The Journal for Research in Mathematics Education (JRME) was first to cross my path in the new year with a new issue.

Richard Kitchen and Sarabeth Berk from the University of Denver wrote a research commentary about the challenge of using computer-assisted instruction to help students — particularly low-income students and students of color — meet the learning goals described in the Common Core state standards. The authors are concerned that schools and teachers will rely too heavily on technology for their mathematics instruction, despite shaky and inconclusive research regarding computer-aided instruction. I highly recommend reading their commentary, which is currently free for all to read on NCTM's site.

Charles Hohensee at the University of Delaware wrote a brief report called Teachers' Awareness of the Relationship Between Prior Knowledge and New Learning. At its most basic level, constructivism tells us that students' prior knowledge shapes their new learning. Honensee used a series of interviews with eight teachers to see if teachers noticed relationships between prior knowledge and new learning. Teachers were pretty good at identifying when students did or did not use their prior knowledge to learn something new, but it was less clear that teachers were aware of backward transfer, or how the new learning was influencing prior knowledge. What's backwards transfer? Here's an example from algebra: Students learn how to combine like terms and often do so with little difficulty. But then some short time later, students are introduced to solving equations and suddenly some struggle with basic "simplify" exercises because now they are trying to "do the same thing to both sides," even if there are no "sides" in the expression they're simplifying. Whereas solving equations should give students more practice and understanding of combining like terms, for some students this "backwards transfer" is unproductive and leads to errors. Hohensee has several examples: graphing speed-time graphs confuses students about distance-time; learning about exponential function growth confuses students about linear functions; multiplying and dividing integers confuses students about adding and subtracting; scientific notation confuses students about metric conversions; and complex fractions confuse students about unit rate. The more we learn about these problematic areas of backwards transfer, the better we can help prepare teachers to deal with them when they happen.

Lyn English at the Queensland University of Technology and Jane Watson at the University of Tasmania wrote Development of Probabilistic Understanding in Fourth Grade. Working with 91 Grade 4 students over 3 years, the authors designed a number of activities to help students better understand the relative frequency of possible outcomes.

Martin Simon, Nicora Placa, and Arnon Avitzur of NYU described a 2-year teaching experiment in their article, Participatory and Anticipatory Stages of Mathematical Concept Learning: Further Empirical and Theoretical Development. This article adds to what Tzur and Simon (2004) theorized about participatory and anticipatory stages of concept development, which attempts to help us understand why students can "get" something one day when they're engaged in an activity, but yet "forget" something the next day when they're asked to refer to what they learned. The article is mostly theory-focused, but it comes with hopes that by better understanding what is normally just chalked up to "forgetting" we'll be able to apply this knowledge in classrooms.

The open access journal Numeracy also published new articles in the new year, including:
Remember, Numeracy is open access so you can read any of these articles for yourself. Jumping into research can be rough if you're not used to it, but just do what we graduate students do: muddle your way through the best you can and then talk it out with others.

Whew! All this and I didn't get to other happenings, such as the MAA Joint Meetings in Seattle, the new year in the Global Math Department, or recent posts in the Google+ Math Education community. If you have suggestions, let me know!