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!

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