Sunday, April 19, 2015

A Few Thoughts from NCTM 2015 (#NCTMBoston)

As I sit in the airport with lots of thoughts in my mind, I figured I should deal with a few before taking off. I need my head a little clearer if I'm going to shift my focus back to grad school work. In no particular order, and by no means a complete list:

In preparing and giving my own talk, I became increasingly aware that focusing on mathematical tasks affords us lots of opportunities (looking at cognitive demand, CCSS alignment, task language, cultural relevance, adaptation strategies, etc.) but we're going to have to think beyond tasks if we're going to tackle the issue of curricular coherence. I think Anna Blinstein said it best:

I have some thinking to do about this, too. Unfortunately, that's about all I think I have. I've looked at the EQUiP rubrics and they're a step in the right direction, but the challenge of coherence needs to be met with a stronger toolset if we want to tackle this at scale. It's probably a good thing that NCTM president-elect Matt Larson is concerned about this, too.

Not talking the same language, but talking different languages similarly?
I spent the first half of the week around researchers and the second half around teachers. Parts of conversations really aren't that different. You're just as likely to hear a researcher say something like, "My research builds off an approach and findings found by Scholar X who published in Journal Y" as you are to hear a teacher-blogger say, "My teaching builds off an approach and findings found by Blogger X who published on Site Y." In this way, the research and teaching community differs by the literature they draw upon, but is quite similar in their willingness and ability to build on others' work. I see a lot of promise here, and it's making me think that the MathEdnet Wiki needs to open up to put more blogger literature side-by-side with traditional academic literature. I don't see many good reasons for Michael Pershan's approach towards giving hints to not be mentioned alongside similar ideas Stein and Smith's 5 Practices, for example.

Beyond Twitter
Thinking about how we build and bridge communities is important, but I need to balance my critiques and commentary about using Twitter with a broader and more positive message about other available tools. A couple times during the week I heard the question asked, "Do you use Twitter?" and the response was "No" or even "I refuse." Some of those times I feared the message was, "You either use Twitter, or you don't. There's nothing else." I should work a little harder to push people to maybe ask, "Do you use social media or math resources online?" and have better knowledge of non-Twitter ways to engage with math ed folks online. (The lack of a network-neutral hashtag is still a nuisance, though.)

Task Analysis and Adaptation
Geoff Krall's adaptation talk was really good, even if the task analysis was limited to "likes" vs. "dislikes." Then again, maybe I'm just jealous because my rejected presentation was about some specific and useful things to look for when analyzing tasks. I'm pretty sure there was just only so much Geoff could tackle in an hour.

Tricks Nixing
I knew about the book Nix the Tricks but hadn't had any direct interactions with Tina Cardone. I think she's my new math-teacher-blogger-writer-twitter-er crush, or at least one of a half dozen or so that I met in the past week. Check her out if you haven't already.

Time to board a plane.

Saturday, March 14, 2015

Education, Neuroscience, and Tangled Webs We Weave

I'm far from the first to point this out, but some of us in the education game hold some ill-informed beliefs about the brain and what it should mean to us as teachers. These are known as "neuromyths" and there's even an organization, the International Mind, Brain and Education Society, working to improve how educators use knowledge from neuroscience. A study by Dekker, Lee, Howard-Jones, and Jones (2012) in the Netherlands found that when given 32 statements about the brain, 15 of which were myths, on average teachers believed in about 50% of the myths. I doubt teachers in the United States would fare any better, given what I see about left brain vs. right brain, "learning styles," and "only use 10%" nonsense.

Even though there is more communication than ever on peer-reviewed brain research, a lot of that communication distorts the science and ends up spreading or creating new neuromyths (Howard-Jones, 2014). What does that distortion look like? I present to you two examples, where something I saw on social media referring to the brain ended up linking back to research with claims that looked quite different.

Example One: "Your Brain Grew"

Yesterday +Joshua Fisher  pointed out this tweet:
Being sensitive to neuromyths, I admit I poked a little fun at this tweet-length, out-of-context claim. Rightly, +Paul Hartzer called me out and suggested I search for some context, such as this:

I immediately went for the "growing evidence" link, which took me to this:

As this was a review of two studies, I dove down to the reference section and tracked down the research. The first, by Moser et al. (2011), had this abstract:

How well people bounce back from mistakes depends on their beliefs about learning and intelligence. For individuals with a growth mind-set, who believe intelligence develops through effort, mistakes are seen as opportunities to learn and improve. For individuals with a fixed mind-set, who believe intelligence is a stable characteristic, mistakes indicate lack of ability. We examined performance-monitoring event-related potentials (ERPs) to probe the neural mechanisms underlying these different reactions to mistakes. Findings revealed that a growth mind-set was associated with enhancement of the error positivity component (Pe), which reflects awareness of and allocation of attention to mistakes. More growth-minded individuals also showed superior accuracy after mistakes compared with individuals endorsing a more fixed mind-set. It is critical to note that Pe amplitude mediated the relationship between mind-set and posterror accuracy. These results suggest that neural mechanisms indexing on-line awareness of and attention to mistakes are intimately involved in growth-minded individuals' ability to rebound from mistakes.
This sounds familiar to those who know things about growth vs. fixed mindsets, and shows that growth mindsets are associated with some brain activity that we don't see with fixed mindsets. So maybe brain "growth" doesn't happen to everyone. The second article, by Downar, Bhatt, and Montague (2011), is even more neuroscience-y:

Accurate associative learning is often hindered by confirmation bias and success-chasing, which together can conspire to produce or solidify false beliefs in the decision-maker. We performed functional magnetic resonance imaging in 35 experienced physicians, while they learned to choose between two treatments in a series of virtual patient encounters. We estimated a learning model for each subject based on their observed behavior and this model divided clearly into high performers and low performers. The high performers showed small, but equal learning rates for both successes (positive outcomes) and failures (no response to the drug). In contrast, low performers showed very large and asymmetric learning rates, learning significantly more from successes than failures; a tendency that led to sub-optimal treatment choices. Consistently with these behavioral findings, high performers showed larger, more sustained BOLD responses to failed vs. successful outcomes in the dorsolateral prefrontal cortex and inferior parietal lobule while low performers displayed the opposite response profile. Furthermore, participants' learning asymmetry correlated with anticipatory activation in the nucleus accumbens at trial onset, well before outcome presentation. Subjects with anticipatory activation in the nucleus accumbens showed more success-chasing during learning. These results suggest that high performers' brains achieve better outcomes by attending to informative failures during training, rather than chasing the reward value of successes. The differential brain activations between high and low performers could potentially be developed into biomarkers to identify efficient learners on novel decision tasks, in medical or other contexts.
Now we're talking about some brain activity, but the results aren't so simple. Take-away? A group of doctors who performed well on a task had brains that appeared to respond better to failure, while low-performing doctors didn't. Also, don't overlook the last bit: This study is less about finding better teaching than it is about identifying biomarkers that indicate who might be more easily taught. That's an important difference — teachers don't get to scan kids in fMRI machines and only teach the best of the lot.

Example Two: Common Core is Bad for Your Brain

Last year Lane Walker pointed me to this claim in a post on LinkedIn:

Curious (and very skeptical), I followed the link to find this:

That post was referencing this article on Fox News:

A search for the actual research took me to an article by Qin et al. (2014) with this abstract:

The importance of the hippocampal system for rapid learning and memory is well recognized, but its contributions to a cardinal feature of children's cognitive development—the transition from procedure-based to memory-based problem-solving strategies—are unknown. Here we show that the hippocampal system is pivotal to this strategic transition. Longitudinal functional magnetic resonance imaging (fMRI) in 7–9-year-old children revealed that the transition from use of counting to memory-based retrieval parallels increased hippocampal and decreased prefrontal-parietal engagement during arithmetic problem solving. Longitudinal improvements in retrieval-strategy use were predicted by increased hippocampal-neocortical functional connectivity. Beyond childhood, retrieval-strategy use continued to improve through adolescence into adulthood and was associated with decreased activation but more stable interproblem representations in the hippocampus. Our findings provide insights into the dynamic role of the hippocampus in the maturation of memory-based problem solving and establish a critical link between hippocampal-neocortical reorganization and children's cognitive development.
As I suspected, the neuroscience really had nothing to do with Common Core or how to teach math. It just found out which part of the brain became more active as children increase their ability to do things from memory. That should sound exciting if you're a neuroscientist, but pretty useless if you're a teacher.

Why We Have Theories of Learning

Like a predictable telephone game, you can see how research gets distorted as it morphs its way through news articles, blog posts, and social media posts. You could criticize me for not quite backtracking all the way to the source, as I'm only referring to abstracts and not digging deeply into the research described and cited in the articles themselves. To take that last step, frankly, requires more of a neuroscience background than I possess. I don't expect that of myself, and wouldn't expect a teacher to do that, either. Daniel Willingham wrote about this a few years ago, and acknowledged the role of institutions like schools of education to collectively make sense of such research and make it useful for teachers. There are people like Jo Boaler who are doing this work. I admire her for taking on the challenge of making complex ideas understandable and appealing to a wide audience of educators, and I'm sure every day she thinks hard about what messages she has to craft and how she has to craft them. It's tricky work.

My hope for teachers is this: When you hear claims about the brain and what they mean for your teaching, be skeptical. Avoid the possibility that you'll be fooled by the next big neuromyth. Realize that a lot of neuroscience relies on placing individuals in an fMRI machine and observing their brain activity while they perform a task. Is that cool science? You bet it is. Does this kind of research capture the context and complexity of your classroom? It does not.

Instead, understand and appreciate why education and related fields have theories of learning that don't rely on knowing what the brain does. In general, theories of construcivism don't go into detail about what's happening at the synapse level, nor do they need to. Cognitive theories use schema to theorize what's going on in the head, but no fMRI machines are necessary. Situated and sociocultural theories of learning gain their usefulness not by trying to look inside the learner's head, but rather outward to that learner's environment, the tools they use, the communities they participate in, and how culture and history shape their activity. So teachers, focus on that — focus on the culture of your classroom, how your students participate, and the learning community you support. Focus on how a carefully constructed curriculum, well-enacted, supports a trajectory of student learning. It will get you much further than neuromyths.


Dekker, S., Lee, N. C., Howard-Jones, P., & Jolles, J. (2012). Neuromyths in education: Prevalence and predictors of misconceptions among teachers. Frontiers in Psychology, (Oct), 1–8. doi:10.3389/fpsyg.2012.00429 Retrieved from

Downar, J., Bhatt, M., & Montague, P. (2011). Neural correlates of effective learning in experienced medical decision-makers. PLoS ONE. doi:10.1371/journal.pone.0027768 Retrieved from

Howard-Jones, P. A. (2014). Neuroscience and education: Myths and messages. Nature Reviews Neuroscience, 15, 817–824. doi:10.1038/nrn3817 Retrieved from

Moser, J., Schroder, H., Heeter, C., Moran, T., & Lee, Y. (2011). Mind your errors: Evidence for a neural mechanism linking growth mind-set to adaptive posterror adjustments. Psychological Science, 22(12), 1484-1489. doi:10.1177/0956797611419520 Retrieved from

Qin, S., Cho, S., Chen, T., Rosenberg-Lee, M. Geary, D., & Menon, V. (2014) Hippocampal-neocortical functional reorganization underlies children's cognitive development. Nature Neuroscience, 17, 1263-1269. doi:10.1038/nn.3788 Retrieved from

Thursday, March 12, 2015

NCTM's Grand Challenges and Opportunities in Mathematics Education Research

Last summer, the NCTM Research Committee asked members to identify grand challenges in mathematics education (written about here and here), and today they've published their findings in the Journal of Research in Mathematics Education. First thing's first: If you're not a JRME subscriber your access to the article is blocked by a paywall. Sadly, this feels like another case of NCTM's reluctance to move past old models of publishing and communication, leaving teachers interested in the grand challenges to feel like second-class NCTM members, begging for a handout from the privileged NCTM research community. I've written about my concerns and suggestions for NCTM's relationship with its members, so here I'll just focus on the key points found in today's report. Ready to be inspired? Slow your roll, turbo. You might want to prepare yourself to be a bit puzzled, if not disappointed.

The report begins by placing the concept of a "grand challenge" in the hands of researchers:

Mathematics education researchers seek answers to important questions that will ultimately result in the enhancement of mathematics teaching, learning, curriculum, and assessment, working toward “ensuring that all students attain mathematics proficiency and increasing the numbers of students from all racial, ethnic, gender, and socioeconomic groups who attain the highest levels of mathematics achievement” (National Council of Teachers of Mathematics [NCTM], 2014, p. 61). Although mathematics education is a relatively young field, researchers have made significant progress in advancing the discipline. As Ellerton (2014) explained in her JRME editorial, our field is like a growing tree, stable and strong in its roots yet becoming more vast and diverse because of a number of factors.

Next the report talks about the purpose of grand challenges and their development and use in other fields. In some ways, it reminded me of the spread of the standards movement: "Math has standards, we should too!", except now it's "The National Academy of Engineering has grand challenges, math ed should too!" Then the report spends four paragraphs talking about Hilbert's problems and how they influenced the last 100-plus years of research in mathematics. The report shifts back to the present, summarizing grand challenges in other disciplines. Readers at this point are likely getting anxious, sensing that their grand challenge lies just ahead.

But wait! What's the criteria for a grand challenge again? The report slows to grind away at feedback about how a "grand challenge" was defined in the initial survey. Saying a grand challenge is "doable," for example, wasn't specific enough for some concerned respondents. Okay, point taken. Nobody wants a grand challenge that can't be met. (Ahem...NCLB...100% proficiency targets. Been there, done that.) So now, we prepare ourselves for the challenge...

But first, let's talk about three themes of responses the committee got from the math ed community. Let me be clear: These aren't the challenges, just the themes describing a body of suggested challenges:

  1. Changing perceptions about what it means to do mathematics.
  2. Changing the public’s perception about the role of mathematics in society.
  3. Achieving equity in mathematics education.

I was hoping to have a strong, positive reaction to these, but I fear my inner cynic took over: "In a nutshell, survey respondents argued our grand challenge for the future is to finally win the math wars that we've been fighting for the past 25 years." The details that followed this list, while short, were thoughtful. My inner cynic quieted down. We do need public support for improved ways of teaching mathematics. We do need to conceive of equity and teaching that goes beyond simply narrowing the achievement gap. All good things. But like I said, those were just themes. So now, I stand ready for the distillation of those themes to form itself in the shape of a grand challenge. So the winner is...

Will you settle for a "hypothetical" grand challenge instead? NCTM suggests this as a mere example: All students will be mathematically literate by the completion of eighth grade, accompanied with this disclaimer:

Our example is only meant to illustrate how a Grand Challenge could satisfy the criteria listed in the previous section; we are not suggesting that it is necessarily a Grand Challenge we should pursue.

There are then six paragraphs describing the attention and importance given to literacy (the read-and-write text kind) and how we should give the same attention and importance to mathematical literacy. But this isn't the grand challenge. It could be, but it's not. Unless we decide it is. Which we haven't.

What we need next, says the report, is to think about the process we need to draft grand challenges. The design researcher in me says, "Yes, this is how to do this. We asked for grand challenges, got input, and now we're going to make revisions to our thinking and ask for more input, and it's going to be better input the next time around." I get it. But readers expecting a call to action might think NCTM is just calling a big, frustrating "Do over!" on the process. Here's NCTM's proposed plan, which they encourage people to critique: Engage many voices. Give people opportunities to draft the grand challenges and comment on drafts written by others. Engage in conversations online (!) and at conferences. Avoid just handing this work to a committee. So expect to see the NCTM Grand Challenge Grand Tour coming to a town near you — they'll have sessions in Boston at the Research Conference and Annual Meeting, as well as at AREA, AMATYC, AMTE, the Benjamin Banneker Association, EONAS, MAA, NCSM, PME-NA, TODOS, WME, regional NCTM meetings, and online venues. (Forgive me for not spelling out all the organizations. I figure if you don't know what it is, you're probably not attending.) I found this bit interesting:

The NCTM Research Committee will also convene a diverse group with a wide variety of expertise to review all submitted challenges, write additional challenges, vet them according to the criteria set forth in the invitation, and provide opportunities for the field to comment on them.

That sounds a bit like a hand-picked committee working in conjunction yet parallel to all the work described above. There's little detail, but I think NCTM better be clear about how the work of this committee will be weighed against the suggestions of the broader community. So, are we ready? Psyched? Ready to push that boulder back up the hill? I hope not, because the last section, while probably necessary, is a bit of a downer.

The Research Committee knows that a grand challenge — if and when we have one — will have consequences for researchers:

Any time a representative group of people is given an opportunity to identify Grand Challenges for an entire field, there is a moral obligation to consider the associated risks and weigh them against the potential benefits. The risks associated with creating a document that identifies our field’s Grand Challenges could be significant, yet we hope to minimize the risks by acknowledging and addressing them throughout the process.

What are the risks? Some people's research and work will get privileged over others. Funding will get reallocated. Journals will rethink what should and should not be published. The groups we consider to be "stakeholders" in math education could change. In some cases, people's feelings might get hurt; in other cases, careers could be threatened. I know this sounds overly dramatic, but the tenure and promotion game for academic researchers can be a rough one, and the research committee knows that. It still struck me as odd to see this "inside baseball"-type discussion near the end of the report, but it might comfort some and give fair warning to others.

So that's it. NCTM's grand challenge was not, and will not be, the "we asked, you answered" kind of process that some of us might have expected. I guess you could call that the bad news. If you were ready to jump to collective action, you're going to have to wait. But there is good news: If you are looking to give your input, it looks like you'll have multiple opportunities. And now that the task ahead is defined more clearly, we can think not just of possible challenges, but the ways we'll organize ourselves to tackle those challenges. To me, the key to the former will be the latter.


Stephan, M. L., Chval, K. B., Wanko, J. J., Civil, M., Fish, M. C., Herbel-Eisenmann, B., … Wilkerson, T. L. (2015). Grand challenges and opportunities in mathematics education research. Journal for Research in Mathematics Education, 46(2). Retrieved from

Friday, October 3, 2014

NCTM's Grand Challenge

This post first appeared at CLIME Connections. I thank Ihor Charischak (@climeguy) for reaching out and encouraging me to think more deeply about these issues, and for letting me repost this here.

The Old and the New

NCTM has a generation gap problem.

What Dan was noticing at the 2013 NCTM Annual Meeting may not have been just about age, but age is a big part of it. During a session at the 2014 NCTM Annual Meeting, Jon Wray reported that the median age of an NCTM member is 57.5 years. 57.5 years! I personally have a fondness for NCTM veterans and enjoy the history of mathematics education, but a median of 57.5 is big when compared to the current distribution of teacher ages, where we see a median age closer to 40-42 and a modal age of about 30:

(Source: Ingersoll, Merrill, & Stuckey, 2014)

This age difference is noteworthy for NCTM because older generations, like those in the upper half of NCTM's membership, tend to be relatively loyal to their institutions. But that's not the case for younger generations that now comprise the bulk of new teachers. Millennials often fail to find relevance in institutions, or they share in Generation X's tendencies towards institutional mistrust. Claims like these are symptomatic of NCTM's challenge:

It's not that Millennials don't value the power of being organized — they just tend to use the internet and social media to organize rather than rely on help from established organizations. An increasing number of math teachers are using Twitter and other social networks to organize themselves in both less- and more-formal ways. There might be no better example of self-organization than "Twitter Math Camp," an institution-free math conference where attendees tend to be young, connected, and not members of NCTM. (Attendees also tended to be very white and male, even more so than for the profession as a whole. That's a challenge for TMC and our social networks.)

The degree to which NCTM understands the changing needs of its membership is not entirely clear. On the one hand, NCTM does have an organizational social media presence (Twitter, Facebook, and LinkedIn) as well as blogs and social media accounts for their teacher journals (TCM, MTMS, and MT). Yet, not so long ago, members of NCTM's Research Committee appeared unaware that such tools could be used for connecting with teachers. In a 2012 report, the committee's recommended strategies for reporting research to teachers focused on journal-based publications and conferences. There were zero mentions of the internet, the WWW, blogs, social media, virtual teacher communities, or anything that would have distinguished their recommendations from plans NCTM might have formulated in the 1980s or before. While the committee's recommendations for how research gets reported in their journals and at their conferences might be sound, an assumption that math teachers will be loyal journal-reading, conference-attending members is not. NCTM's grand challenge is not to refine how well it preaches to its choir.

Thankfully, NCTM is not monolithic and some clearly understand the challenge NCTM faces in being relevant to the various needs of young math teachers. Peg Cagle is one of the better-connected members of NCTM's Board of Directors (Jon Wray is another), and if you click through to see the replies to Peg's question, you'll see a lot about what teachers want and what they feel NCTM is currently providing.

Beyond Content

In 2010 Google's Eric Schmidt famously claimed that every two days we create as much information as we did from the rise of civilization through 2003. While the accuracy of such a statement is difficult to establish, there's no doubt that we are awash with content.

Included in all this content are materials for math teachers, such as curriculum materials, lesson plan sites, instructional videos, test generators, and other teachers' reflections on their practice. What's more, this content is cheaper, more abundant, and more accessible than ever before. When math teachers perceive NCTM mostly as a provider of journals and conferences, NCTM risks becoming just another (and more expensive) content source in a vast sea of content sources. The quality of NCTM's resources certainly helps their cause, but we shouldn't ignore the possibility that people sometimes settle for good enough when they can get something easily at low or no cost. For all its journals and all its conferences, NCTM's game can't be to out-content the rest of the internet.

The internet has spawned many disruptive innovations and NCTM is one of many institutions facing challenges in this content-rich era. Traditional news media is similarly challenged to attract younger subscribers/readers/viewers who are accustomed to using the internet as an abundant source of news coverage, much of which is localized, specialized, and free. We've seen traditional news organizations experiment with variations of familiar revenue strategies, such as targeted advertising and freemium subscription models, but some think it's time for a more fundamental shift in how news media serves the public.

One of my favorite thinkers on the future of news is Jeff Jarvis, a journalism professor, blogger, and podcaster. Recently, Jeff has been working to answer the question, "Now that the internet has ruined news, what now?" Jeff has partly given his answer to this question in a five-part series (1, 2, 3, 4, 5) on Medium as he writes his way towards a new book due out in November. At the core of Jeff's vision is a service-oriented journalism based on relationships, where content is just a means to that end, not the end itself. Journalists would position themselves to work closely with communities, privileging community knowledge instead of acting as the content authority and gatekeeper. Social media would be a key tool for building and maintaining these relationships, as Jeff describes in this selection from Part 2 of his essay:

Now we have more tools at hand that enable communities to communicate directly. So perhaps our first task in expanding journalism’s service should be to offer platforms that enable individuals and communities to seek, reveal, gather, share, organize, analyze, understand, and use their own information — or to use the platforms that already exist to enable that. The internet has proven to be good at helping communities inform themselves, sharing what’s happening via Twitter, what’s known via Wikipedia, and what matters to people through conversational tools — comments, blog posts, and tweets that, never mind their frequent banality and repetition and sometimes incivility, do nevertheless tap the cultural consciousness.

To be clear, Jeff isn't saying journalists should just be replaced by the public sharing of information. Journalists can add value to the community's knowledge by raising new questions, adding context, bringing experts into the conversation, fact-checking, and performing other duties long-associated with quality journalism. What's different, says Jeff, is that "simply distributing information is no longer our monopoly as gatekeepers and no longer a proper use of our scarce resources." Content doesn't go away, but it takes on a supporting role for journalists focused on maintaining personal relationships with their community and its members.

I may be overestimating the similarities between challenges faced by news organizations and by a professional teaching association. But where visions for the future are concerned, I think Jeff Jarvis's service-oriented, relationship-based model for journalism may also be a promising model for NCTM. When I re-read Jeff's essays and mentally substitute "NCTM" for "journalism" or "news," I start to imagine a different kind of NCTM focused on privileging and coordinating the knowledge and relationships of a community of math teachers, one in which journals and conferences are merely seen by members as means, not the ends.

What Now for NCTM

I may be guilty of armchair quarterbacking. I also may be guilty of underestimating how much NCTM members already feel part of a strong professional community built on relationships. During the same panel at which Jon Wray mentioned NCTM's median age was 57.5, he also proudly expressed that he thought of NCTM as a collection of members he could refer to as "we" or "us." That's great for Jon and like-minded members, but that's not where NCTM's grand challenge lies. The challenge is with those who see NCTM as an "it" or a "they," likely young teachers who only associate NCTM with conferences they might not attend and publications they might not read.

I do not profess to be an expert in relationship-building, nor do I believe there to be easy answers. That's part of what makes this a grand challenge. That said, here are a few ideas for moving forward:

  • Don't be faceless. NCTM's blogs and social media accounts are a good start, but to build strong relationships we need to associate with each other as individuals, not as product titles. For example, instead of a @MT_at_NCTM Twitter presence to represent the journal, NCTM needs the editors and authors of Mathematics Teacher to represent themselves online as individuals. The same goes for board members, NCTM staff, and anyone else who identifies with the organization. It's easier to build trust with a person than a brand, and in my two years of helping teachers develop criteria to identify quality resources, I still don't think any indicator of resource quality matters more to a teacher than to have a recommendation from an individual they trust.
  • Find teachers where they are. Perhaps a time existed when it would have made sense for NCTM to build its own social networking site, but that time has passed. We should leverage the networks that already exist and find the teachers there. Some math teachers already use social media for professional reasons and would be easily engaged by NCTM. Other teachers of mathematics, who may only use social media for personal reasons, number in the tens and potentially hundreds of thousands. They may or may not be NCTM members, or regularly interact with other teachers online, but they exist. NCTM needs to organize its membership so that we seek these teachers out, show them that we care, and offer our support.
  • Don't just push, listen. The most common behavior I currently see in NCTM's social media streams is pushing content. To again use @MT_at_NCTM as an example, instead of just pushing out a daily link to an article or calendar problem, show that you're listening to the community. Talk to teachers about what they need and want. Use the journal to respond to these needs and show the community that you're listening. When there's a new article to share, arrange for the authors to engage in discussions and Q&As around what they've written. Again, engage as individuals, and use the @MT_at_NCTM account (and likewise, the other journal social media accounts, blogs, etc.) to highlight and point people to these community interactions.
  • Build a thank you economy and know your members. NCTM should take a few pages from Gary Vaynerchuck's playbook and establish a "thank you economy" with its members. Gary's current business is helping brands with their marketing, focusing more on listening and thanking than with pushing and closing deals. The language Gary uses in his keynotes is NSFW and his message is bold. Here's a 10 minute version and hour-long version of Gary's talks. (Note that these are 3-4 years old but still sound cutting edge. On Gary's clock, that means the next big thing is probably already here.) Gary is a big believer in knowing your customers and using that knowledge to show how much you care. Imagine an NCTM that used social media to know more about you as a teacher — the subjects you were teaching, the textbooks you have, the length of your class period, nuances in your state and local standards, etc., and used that information to help you in ways very specific to your needs. That kind of listening and caring about teachers as individuals builds loyalty.
  • Play matchmaker. At both the AERA and NCTM Annual Meetings this year I heard someone say something like, "We need a for connecting teachers who want to work together" or "We need a website that connects teachers who want to work with researchers." Along with knowing teachers well enough to match them with relevant content and material resources, NCTM should know enough about its membership to connect members with each other.
  • Guide teachers towards mastery. In a 2001 article in Teachers College Record, Sharon Feiman-Nemser discusses what a continuum of teacher education might look like if it began with preservice teachers and continued through the early years of teaching. This continuum would need mentorship and induction programs better than what we have now and, most importantly, someone to coordinate teacher learning across university and school boundaries. For math teachers, NCTM might be the organization that could make this happen. If NCTM knew the strengths and weaknesses of teacher preparation programs, and of individual graduates, and knew more about those individual teachers' needs and experiences, they could position themselves as the facilitator/provider of high-quality, ongoing professional development for teachers. Examples: Maybe I'm a new teacher hired to teach 7th grade, but I student taught with 11th graders — NCTM could build my 1st-year PD around video cases with 7th graders. Maybe my teacher education program was strong in its approach to formative assessment — NCTM could provide support in furthering my practice instead of starting back at the basics. Maybe I switched states for my new teaching position — NCTM could help me better understand how teaching math is different in my new place, and what's worked well for other teachers making a similar move. Yes, this is that big data stuff that scares some people, but I'm not sure the size of the data matters much when it leads to something genuinely helpful.

These are just some ideas. Others will have different perspectives on NCTM's challenges and possible ways to meet them, but I hope this either starts or adds to conversations about math teaching as a profession and we should value in our professional organizations. While I understand why some teachers aren't members of NCTM, I think math teaching is a stronger profession with a strong NCTM. It's a better "we" than a "they." This stronger NCTM lies in a new generation of math teachers, ones who I believe are willing to connect and collaborate as part of an organization committed to forming relationships with them and amongst them, not just providing content to them.

Thursday, August 28, 2014

On Major Problems and Grand Challenges, Part 2

Prompted by NCTM's call for "grand challenges," in my last post I looked back at Hans Freudenthal's 1981 "Major Problems" paper. We've made progress in the past 30+ years, and we should recognize that. But that doesn't mean other challenges don't await us, and in this post I'll look at some suggestions made by some fellow bloggers. If this looks like "armchair challenging" it's probably because it is, rambling commentary and all.

Before I continue, it's worth noting that all four bloggers I found writing on this topic are white males. (And I am, too.) If this doesn't bring to mind a grand challenge for the future of math education, I don't know what should.

Robert Talbert: Grand Challenges for Mathematics Education

Robert's first suggestion is to develop an open curriculum for high school and early college. Sure, we've had many curriculum projects, but I can't say I've seen many that try to seamlessly span high school and college. It makes me realize that textbook companies typically package things in ways that align with the jurisdictions of district decision-makers, but there's really no reason it has to be that way.

We currently have some open curriculum projects that might give us a start on this challenge, such as the Mathematics Vision Project out of Utah and the EngageNY materials from New York. I say "give us a start" for two reasons: neither set of materials are very mature (and thus quality can be suspect) and such a project should plan for the evolution and improvement of the materials over time.

Side story: I was having dinner this summer with a retired mathematics education professor and she was telling me about her experiences volunteering to help tutor kids at a local high school. Our conversation went like this:

Her: "I didn't recognize the materials they were using, but they're a mess. It's something they found online and I don't know who put it together, but it looks like different people wrote adjacent lessons and never talked to each other, because there were big jumps from one topic to another with no explanation."

Me: "Let me guess. Are the materials from New York?"

Her: "No, Utah."

Me: "That was my second guess. And your guess about different people writing different lessons without much coordination is a very good guess of what probably happened."

Robert's second and third challenges involve the creation and use of concept inventories for mathematics, like the force concept inventory (FCI) for physics. I hear this get discussed occasionally and I'm aware of some efforts for inventories in calculus and statistics, but they aren't nearly as well recognized or used as the FCI. What's the advantage of having these inventories? They tend to make for great pre-post tests for a course or to judge if a particular teaching approach is better for students' conceptual understanding. Last week I attended a talk by Stephen Pollock who talked about his work in physics education research and the improved results we're getting in CU's physics program. The FCI played a key role in that progress, as it allowed professors to self-monitor their courses and compare their results to others who were attempting to improve their teaching. These kinds of standardized assessment tools could be equally useful and powerful in mathematics departments, especially when used in a self-monitoring sort of way instead of the all-too-common external-and-top-down-accountability-enforcing sort of way.

Robert's last recommendation is to have a preprint server for math education research. As he notes, this is a road we've tried to go down before and we didn't get very far. I don't think the problem has nearly as much to do with policy or categories of the arXiv as it does with the lack of a "preprint culture" in mathematics education. What I learned in those previous preprint discussions, and in my observations as a developing scholar, is that math educators regularly and happily share work in progress — with a select group of people. In math ed, there doesn't seem to be widespread faith in anything like Linus' Law, the open source software dictum that says, "With enough eyeballs, all bugs are shallow." I think the math wars led to a lot of distrust, and some of it is very rational. It's safer to only share preliminary work with a few scholars who share similar methods and theoretical frameworks, and then refine the work after peer review before publication in a journal whose readership is likely to understand the work. Maybe it shouldn't be this way, but to move forward we're going to have to confront some of these beliefs.

Patrick Honner: My Grand Challenge for Mathematics Education

Patrick described in some detail a single grand challenge: "Build and maintain a free, comprehensive, modular, and adaptable repository of learning materials for all secondary mathematics content." It's worth reading his post and the comments. This challenge hits close to home for me because it touches on my own research, including the difficulty of coordinating distributed curriculum development and the infrastructure needed to support the customization of curriculum.

I've always been intrigued by the concept of "modular and adaptable" curriculum materials. Personally, I thought I did my best work as a teacher when I offloaded my curriclum to a high-quality textbook that I'd been trained to use. That's an anathema to many math teachers who take improvisation of curriculum to be a sign of quality teaching. (It's not, by the way. There can be good and bad improvisation, just as there can be good and bad offloading.) I tried writing my own curriculum for a while and found it exhausting and ineffective. In a couple hours per day, I just couldn't create from scratch anything that I thought was as good as the texts coming from university-based curriculum teams with decades of experience and millions of dollars of funding. Go figure. I got better results when I leveraged the rigor and coherence of a text that integrated topics, contexts, tools, and routines across its lessons and units.

With enough effort, however, Patrick's recommendation could lead to a set of materials that are both modular and coherent. I've always seen these in opposition, a sort of "textbook paradox." I speculate that teachers who value being able to adapt and improvise with their curriculum will resist or find ineffective those textbooks built around coherence. It's relatively straightforward to replace a lesson in a very traditional textbook that relies on an isolated set of examples and practice problems. But for reform-based materials, such as IMP, CPM, and Everyday Math, skipping around in the textbook can lead to trouble. Saxon texts, for that matter, with their use of "incremental development," should make a teacher think twice before skipping or improvising a lesson. Thus, the paradox: teachers who want to improve the quality of their curriculum materials probably have an easier time adapting materials that are lower quality to begin with, but if they start with higher-quality materials, adaptation can sacrifice coherence and make adaptation more difficult.

Adaptation can still be done with any curriculum, but it takes skill. Currently, that skill must come almost entirely from the teacher, as the texts aren't smart enough to know what you've been skipping. Take Patrick's challenge far enough, however, and maybe we could have a curriculum that is smart enough to know what you've used and not used. Imagine a statistics curriculum that automatically modifies tasks to use a preferred data set, or a system that reminds you that you should probably include a lesson and practice with mean absolute deviation prior to teaching standard deviation. Or, for algebra, imagine a system that let you decide whether to teach exponential functions before or after quadratics, with the curriculum being smart enough to recommend appropriate modeling tasks. When I helped a school pilot Accelerated Math in 1999 and used the exprience as my student teaching action research project, I really thought we were on the cusp of a wave of "smart curriclum" that would help build coherence into teacher-adapted curriculum. We're not there yet, but a challenge like the one Patrick describes could get us much closer.

David Wees: Grand Challenge for NCTM

David's grand challenges focuses more on people than materials: "Develop a comprehensive, national professional development model that supports the high quality mathematics instruction they have been promoting for many years." ("They" refers to NCTM.) David breaks this challenge into bullet points around the development and scaling of "core practices."

I'm a firm believer in this idea. I get resistance from those who love the creative and spontaneous aspects of teaching, but I think that learning to teach should involve the learning and practicing of key teaching practices. Thankfully, there are some very good people working in this area. Until recently, their efforts were somewhat scattered and referred to with such names as "high-leverage practices" or "ambitious teaching." Thankfully, at AERA this past spring, many of the heavy hitters doing this work came together to address the need for a common language around these practices and supporting their development and use. For a good idea of what a list of core practices might look like, check out the Teaching Works project from the University of Michigan. I have a hard time finding anything on that list that doesn't seem essential to quality teaching, and it reminds me that the list is really the easy part. The real work comes in developing those practices in preservice and inservice teachers, and I'm glad that David had his mind on that development when he articulated his grand challenge.

Bryan Meyer:

Bryan's challenge isn't math-specific but it could help a lot of math teachers. Our expectations for teacher collaboration exceed our opportunities, and changing this involves a lot of people and resources. In some countries there are limits to how many student contact hours a teacher can have because they are expected to be collaborating with or observing other teachers for several hours each day. What if we did that in the United States? We'd have to seriously rethink our resources. Suppose you currently teach six periods a day with about 24 students in each class. What if you only taught four periods with 36 students in each class, and you had the extra two periods to work with other teachers to ensure your instruction in those four periods was better? (For those of you who already have 36 students in your classes and are working out even larger classes in your heads, I'm sorry.) Or, instead of changing class sizes, what if salaries were lowered to accommodate the hiring of extra teachers?

While these questions suggest difficult choices, they do seem like questions that could be answered with adequate research, and maybe there exists some research already that could help us answer them. Still, research in education isn't always very effective at changing school cultures or how resources are allocated. I don't want to sound too pessimistic, but I'm thinking that Bryan's challenge is going to have to focus as much on understanding and developing cultures of collaboration amongst teachers as it would scheduling and resource allocations.

Parting Thoughts

While it may have been personally beneficial for me to put a couple thousand words into a grand challenge I thought about on my own, I realize that our best hopes for meeting a grand challenge come when we share and push each other's ideas. As a student of curriculum and instruction, I find much to like in Robert and Patrick's thoughts about curriculum and David and Bryan's thoughts about instruction. There's some really meaty stuff there.

I've also tried to think about what wasn't mentioned as a challenge. Nobody said, "I really think we need to better understand how students think about ratio/functions/number/proof/etc." While people are hard at work on such questions, I don't think there's any widespread perception that a lack of research in specific areas of student mathematical understanding is what is holding us back. (If there's a challenge I should be writing about, it's about the dissemination and use of this information.) I'm also happy to see that people weren't writing challenges involving new sets of academic standards. It's rather unfortunate that so much energy is being put into debating Common Core when it seems quite likely that standards account for little of the variability in student outcomes. We have a list of stuff we want students to learn. Fine. I'm ready to focus more of our efforts on the learning, not the list.

Lastly, to touch briefly on the challenge I hinted at near the top of this post, I didn't see any equity-focused grand challenges. I think I speak for Robert, Patrick, David, and Bryan when I say we all believe in achieving equitable participation and outcomes in mathematics education. Then again, we can't just say that and expect equity to come about by accident. There are elements of each challenge mentioned that could be used to promote equity, but it's going to take a more explicit focus than we've given it. In fact, maybe the first step is to significantly change the representation implied when I say "we." It seems simple enough, but privilege has a way of producing thoughts of "for" and "to" instead of "with," and that's a challenge for the kinds of people and organizations who pose challenges.