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.

Wednesday, July 30, 2014

On Major Problems and Grand Challenges, Part 1

Last month the NCTM Research Committee asked its members to help it identify the grand challenges for mathematics education. Grand challenges, said NCTM, (a) are hard yet doable, (b) affect millions of people, (c) need a comprehensive research program, (d) are goal-based with progress we can measure, and (e) capture the public's attention and support. I'm a month too late to contribute to NCTM's survey, and before blogging my thoughts into the wider conversation I thought I should look back at someone else's previous attempt. Maybe I'd gain some perspective on what grand challenges are and how persistent they might be.

Hans Freudenthal (Wikimedia Commons, CC-BY-SA)
In 1980, Hans Freudenthal gave a plenary address at ICME that later turned into an article in Educational Studies in Mathematics titled, Major Problems of Mathematics Education. I've briefly summarized the article on the MathEd Wiki and here I'll note the progress I think we've made on Freudenthal's 11 problems.
  1. Freudenthal believed we "need[ed] more pardigmatic cases, paradigms of diagnosis and prescription, for the benefit of practitioners and as bricks for theory builders" (p. 135). In the case of arithmetic, which was Freudenthal's example, I think Cognitively Guided Instruction (CGI) is very much the kind of thing Hans was looking for.
  2. Freudenthal wanted us to more carefully consider how people learn and observe their learning processes. I think several decades of teachers' awareness of constructivist theories of learning has changed how most people think of learning, and newer work in the area of teacher noticing puts fine points on what teachers notice and why.
  3. How do we design curriculum and instruction around progressive formalization? There is always more to learn, but the Freudenthal Institute in the Netherlands has now worked on this for decades and the frameworks for curriculum design are well-established.
  4. How do we retain and leverage mathematical insight? Freudenthal wrapped this into the conceptual vs. procedural debate, one that's still very much alive. However, I think we have better examples of productive approaches to this problem, and some research results (the BEAR project work at Berkeley comes to mind) showed that more focus on the conceptual didn't come at the expense of procedural facility. Still, this problem gets wrapped up in people's beliefs about mathematics and the teaching and learning of mathematics, and those beliefs sometimes aren't swayed by current evidence.
  5. How do we reflect on our learning? This is another problem we now know much more about, particularly due to Schoenfeld and his work on metacognition.
  6. How do we develop a mathematical attitude? This is still a challenge, and not just because some students say they don't like math. I think this problem might be closest to what Jo Boaler is currently trying to change with her focus on mindsets in learning mathematics.
  7. How do we coordinate students working together when the are at different levels of learning? Many teachers and scholars have worked quite hard on this problem and I feel like most teachers now see the benefit of heterogeneous ability groups. For more, I'd suggest Ilana Horn's book, Strength in Numbers.
  8. How do we create contexts for mathematizing? I think there's been a wealth of work in this area, from work based in Realistic Mathematics Education, work on word problems like that from Verschaffel, Greer, and de Corte, and, most recently, Dan Meyer's work. I could go on, as there are many more examples, and perhaps future work will give us a clearer picture about which contexts work best and why.
  9. Can we teach geometry by having the learner reflect on spatial intuitions? Maybe it's my lack of expertise in geometry education research, but I really don't know where we stand on this problem. Freudenthal seemed to be reaching in his article on this problem, and maybe a more tangible articulation of the problem would have helped me better judge any solutions we might have.
  10. How can technology increase mathematical understanding? Freudenthal admitted not being tech-savvy even in 1981 (he used "the ballpoint" as an example of technology that changed instruction, and not in an obviously historical way), but I think we now have numerous examples of tech that helps increase understanding. We also have a lot of examples of tech that doesn't, and I'm sure Freudenthal would have seen problems in our ability to judge the good from bad.
  11. How do we use a holistic approach to educational development for change? In his native Netherlands, Freudenthal would likely be pleased today to see his colleagues' commitment to design-based, participatory approaches to research. We have some of that here in the U.S., too, but we also struggle for a "scientific" approach to finding "what works" based on experimental studies. We also have too much faith in how standards affect change; if Freudenthal thought curriculum development for change was a wrong perspective, surely he'd think the same about standards. Those things are just part of a much bigger picture.
Looking at this list, I think we have a lot to be proud of. Even though Freudenthal's article wasn't some sort of directive or command to fellow and future math education researchers and teachers, many people over many years worked so we'd have some answers to these questions. Still, there's a gap between ''what the field of math ed knows'' and ''what a teacher does with this knowledge, if they know it," which hints at what might be a grand challenge of its own. I'd like to get to that, but in a later post. Next, I'll look at some of the grand challenges that I've seen others post on the web in response to NCTM's call for input.

Sunday, June 8, 2014

Schneider's From the Ivory Tower to the Schoolhouse, Chapter 5: Ideas Without a Foothold

In the first four chapters of From the Ivory Tower to the Schoolhouse: How Scholarship Becomes Common Knowledge in Education, Jack Schneider details how four ideas (Bloom's taxonomy, multiple intelligences, the project method, and Direct Instruction) traversed the gap between the education research world and K-12 classrooms. Now, in Chapter 5, he identifies counterparts to each idea that failed to make the leap: Krathwohl's taxonomy for the affective domain (the sequel to Bloom's Taxonomy for the cognitive domain), Sternberg's triarchic theory (which paralleled multiple intelligences), Wittrock's generative learning model (see Michael's post), and the behavior analysis model (similar to Direct Instruction in more ways than one). If my personal experience is any indication, Schneider has chosen these well, as I knew as a teacher about all the ideas in Schneider's first four chapters (to various degrees, anyway) but can't say I knew any of the four ideas compared in Chapter 5. To be honest, Chapter 5 served as my proper introduction to these latter ideas — not only did I not know of them as a teacher, I can't recall having learned about them in grad school, either.

In his review of Chapter 5, Michael Pershan takes the position that even though he hadn't heard of Wittrock's generative learning model, surely there existed some path by which he was at the tail end of some chain of Wittrock's influence. I think this is probably true; while teachers might only recognize Piaget and Vygotsky by name, the rise of the study of cognition and how we construct knowledge is the result of the work of many scholars, not just two. I think this falls under Schneider's concept of perceived importance: Piaget and Vygotsky seem important because so many scholars built upon their work, even if the scholars in that crowd remain nameless to us.

Still, it's difficult to say this is good enough. Even though it's not possible for a teacher (or anyone!) to have a direct connection to all available research, shorter paths would be preferable to long ones. I agree with Michael: teachers would likely benefit from knowing Wittrock and his work. But to what degree?

One of the things we learned from Schneider's first four chapters is that familiarity sometimes does not breed fidelity in education research. This felt most true in the multiple intelligences chapter, where some consultants seemed to play fast-and-loose with Gardner's theories, and I imagine the teachers who sat through those workshops or read those books played even faster-er and looser-er with multiple intelligences. Should we be worried that a little bit of knowledge is indeed a dangerous thing in education research?

I would be more worried if not for one thing: constructivist theories of learning tell us that not only to bits of knowledge matter, they're the stuff upon which more knowledge is constructed. In fact, there's a particular learning theory that addresses this called knowledge in pieces, and, if you can find it, it's worth reading Andy diDessa's 1988 chapter by that title. This should be of particular interest to Michael as the theory gives a nice way of explaining misconceptions, whether they be the ones we see in students or the ones we see teachers make when research finds its way to them by vague and indirect paths. In short, misconceptions aren't just the acquisition of "wrong" knowledge that needs to be confronted with "right" knowledge. Rather, knowledge in pieces says learners systematize their pieces of knowledge. What we think of as a "misconception" can be explained as a system of knowledge built upon pieces of available knowledge. The pieces aren't "wrong" and neither is the system, but as more pieces of knowledge get added we expect the system to adapt and become more sophisticated. Now, I admit that my understanding of the theory might be short a few pieces, but I think the key to wrapping your head around it is to force yourself to think knowledge exists with the learner, and nowhere else. Knowledge gets constructed from experience, not with the acquisition of knowledge from an external source. (See also: radical constructivism.)

Opening quote from diSessa's 1988 chapter

This leads us back to one of the ideas Michael mentioned in his post: teachers need exposure to research followed by opportunities to engage with the research more deeply. Teachers will take the pieces of knowledge they have — whether gained from teaching experiences, experiences engaging with research, or elsewhere — and systematize that knowledge in variously sophisticated ways. What we need, then, are opportunities for teachers to further systematize their knowledge. I'll talk about that in my next post, a review of Schneider's recommendations for improving research-to-practice.

Note: Michael Pershan (@mpershan) and I are reading Jack Schneider's book From the Ivory Tower to the Schoolhouse: How Scholarship Becomes Common Knowledge in Education. Our previous posts:


diSessa, A. A. (1988). Knowledge in pieces. In G. Forman & P. B. Pufall (Eds.), Constructivism in the computer age (pp. 49–70). Hillsdale, NJ: Lawrence Erlbaum Associates.

Sunday, June 1, 2014

Schneider's From the Ivory Tower to the Schoolhouse, Chapter 4: Direct Instruction

The fourth chapter of Jack Schneider's From the Ivory Tower to the Schoolhouse: How Scholarship Becomes Common Knowledge in Education represents a needed turn in the overall narrative of the book. As a bonus, this chapter will likely keep me from throwing around the phrase "direct instruction" in unintended ways.

Schneider's previous three chapters focused on Bloom's Taxonomy, multiple intelligences, and the project method. Each of those cases seemed to rely heavily on Schneider's constructs of philosophical compatibility and transportability. In other words, fidelity of implementation didn't seem to matter much: teachers adoption of the research seemed tied to their freedom to interpret and implement the research in whatever way they saw fit. In more than a few instances, Schneider leaves the reader to question if the research has been implemented with any fidelity at all, or if teachers are adopting it in name only.
In this chapter, titled Lessons of Last Resort, Schneider tells the story of Direct Instruction. I've heard and used the term direct instruction (little "d" little "i") to simply describe teaching as telling, but it has a more specific research heritage exending back 50+ years. The researcher there from the beginning is Siegfried Engelmann, seen here:

Unlike Bloom's Taxonomy, multiple intelligences, and the project method, Englemann's Direct Instruction works (with the research to show it) when teachers are philosophically compatible with the method and they implement it with fidelity. The actual effectiveness of research wasn't addressed in Schneider's first three chapters, but it is here because it's one of the big reasons for Direct Instruction's success.

This success isn't something that makes some progressive educators very comfortable, as they resist the scripted nature of the curriculum. These progressive educators are usually in schools where illiteracy and innumeracy isn't a persistent problem, and they're given autonomy to choose other, more philosophically compatible curriculum and methods. (To be clear, just because Direct Instruction has been shown to be effective, that doesn't mean it's the only effective thing, or the most effective. Also, it should go without saying, showing something to be "effective" is a tricky business, even when we agree what "effective" means.) But in schools where illiteracy and innumeracy persists, often in low-income schools with underrepresented populations and difficulties finding skilled teachers, Direct Instruction is more popular. Schneider addresses the issue of philosophical compatibility:
In addition to its effect on teacher authority, scripting also promised to reduce the responsibilities of those in classrooms. Working with a program like Direct Instruction, teachers would no longer be responsible for lesson design, for expertise about children, or for the task of dealing with the uncertainty of classroom life. As Direct Instruction promoters put it on their Web site: "The popular valuing of teacher creativity and autonomy as high priorities must give way to a willingness to follow certain carefully prescribed instructional practices." And as Englemann put it: "The teacher is a teacher—not a genius, an instructional designer, or a counselor. The teacher must be viewed as a consumer of instructional material." Engelmann saw this aspect of Direct Instruction as occupationally realistic, and he may have been right. But reducing teacher responsibility also raised serious philosophical compatibility issues insofar as it threatened teacher professionalism. (p. 122)
You might be reading this right now and saying to yourself, "No way. I'd never use this stuff." That's the philosophical incompatibility talking. There's reasearch for that, too: reform curricula might be good, but the results aren't nearly as good when placed in the hands of a traditional teacher. I believe vice-versa has been found to be better, but still not as good as reform curriculua with reform teachers. But where do we draw the line between philosophical compatibility and the need for teachers to be open minded? To be learners? As professionals, when should our philosophies give way to what we can gain from research, regardless of compatibility?

I don't have an answer for this question, but perhaps Michael Pershan (@mpershan) will have some thoughts in his reply. If you haven't been following along, we've been reading the book together and here are our posts so far: