NCTM Puts up a Sign

NCTM President Matt Larson wrote an essay last week titled “Curricular Coherence in the Age of Open Educational Resources.” As I read them, the big takeaways are:

  1. Coherence in curriculum is important.
  2. A curriculum is more than just a sequence of activities.
  3. Activities that are downloaded from the Internet vary in quality and often undermine curriculum coherence.
  4. If you’re going to download activities anyway, then download them from NCTM’s lesson site or download them in learning communities where there might be more accountability for coherence.

I’ll co-sign all of the above. I hadn’t thought about collaborative lesson planning as insurance against incoherence. That’s clever. All of that said, I’m disappointed at how much of the essay obliges teachers and how little of it obliges publishers.

It reminds me of desire paths.

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Desire paths occurs when people walk off the path you pre-determined and create their own. They create another route because it satisfies their needs better than yours did. In that situation, you have options. You can post signs directing people to stay on the path. You can hire security to make sure people stay on the path. Or you can admit that you messed it up on your first try and pave the desire path.

NCTM is putting up a sign.

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Aside from a brief mention of sympathy for teachers who “lack highly engaging, high-cognitive demand tasks or lessons,” the essay doesn’t acknowledge the desire that leads to online activities.

It isn’t as if many teachers are eager to spend nights and weekends cobbling together a curriculum from scratch. What gives? I asked teachers about their desire. Most prominently they want materials a) that are engaging, b) that are scaffolded appropriately, and c) that create high cognitive demand. A large number of them don’t think their core curriculum is particularly coherent.

I appreciate Larson’s leadership and support NCTM’s interest in coherent mathematical experiences for kids. But if teachers – especially at secondary levels – had access to resources that offered those features above, I suspect the desire lines, and consequently NCTM’s sign, would be unnecessary.

So an open question: What would it mean to pave the desire path here? Now that we’re at the point where people are tromping across the lawn, marching towards online activities, what would it look like to say, “Okay,” and then pave that path for teachers.

Recommended. Tyler Auer’s analysis.

Also recommended. The comments of the essay, where Larson is taking questions and adding commentary, including what appears to be an answer to my open question above.

Featured Comments

Please read Matt Larson’s comment.

Michael Pershan:

While Matt’s piece didn’t rub me the wrong way, it does seem to me that treating this as a challenge for people who want to influence what teachers do is going to be a better framing than trying to convince teachers to change their online patterns.

Steve Weimar:

One of the projects that the Math Forum at NCTM is beginning to plan within NCTM concerns the idea of an online collaboration space and supporting repository through which the community can move along the continuum from sharing good tasks to identifying and playing with sequences and instructional practices that lead to the engagement, depth of understanding, rigor, and competence we all seek for our students.

Patty Miloro:

Curricula coherence is my biggest struggle. I work in a small charter high school and we have not purchased a commercial math curriculum. Instead of only 20% of my time spent planning, I am lucky to have the freedom to spend lots of time attempting to develop a cohesive unit by vetting online materials. This autonomy is both wonderful and terrifying.

Henri Picciotto:

One way NCTM might help with both coherence and quality is to offer a really-core curricular framework (as opposed to the much-too-massive CCSSM), and within that offer curated links to high-quality online materials. A positive contribution along those lines would be a lot more useful than anxiety-provoking warnings about coherence.

Elizabeth Statmore:

One last deep thought — I sure am getting tired of being blamed for the incoherence of standards and curricula that are way above my pay grade. Unfortunately, the way all of this has been set up (or not set up), everything rolls downhill into my yard.

Jason Slowbe:

Perhaps the “next big opportunity” for NCTM is in connecting members online around its quality content. NCTM’s average member age is 55 years and fewer teachers are buying memberships, opting instead for free online connectivity with other teachers that is still quite good overall.

About 
I'm Dan and this is my blog. I'm a former high school math teacher and current head of teaching at Desmos. More here.

20 Comments

  1. Thank you Dan for your comments. NCTM is not saying, “keep off the online activities.” NCTM is neither arguing that teachers should avoid online materials, nor should teachers only use online materials from NCTM. What NCTM is arguing for is that those materials be selected wisely to ensure they fit within a coherent curriculum. I certainly agree that many teachers are drawn to, or pushed to, on-line materials as a result of the quality of the materials they are provided by their school district, but I don’t equate a curriculum with just a publisher’s text either.

    Clearly there is work for traditional publishers and other curriculum providers to do to improve the quality of the materials they offer teachers. I believe collaboration is needed, not a guarantee, and expands well beyond curriculum coherence. Effective teacher collaboration can also serve the goal of equity by ensuring that the experiences of two different students in the same school and course with two different teachers don’t experience widely different learning opportunities. For example, a focus on procedures in one class versus a focus on reasoning and sense making supporting the development of procedures in another, simply because each teacher selected his/her own curricular activities. These different approaches, as a consequence of isolated curriculum selection, can result in vastly different learning opportunities for students. As a profession we need to do more to collectively and collaboratively reach each and every student.

    On a side note I think these conversations within the community are a sign of its strength. By engaging in these conversations we iteratively better understand one another’s perspectives and improve our practice. Thank you.

  2. Curricula is headed towards becoming digital interactive documents. Consequently, both publishers and teachers will have the opportunity to polish and customize at will. Given any grade level, all vested parties should be obsessing about how to keep things fresh and coherent. The beauty about digital curricula is that we can make potentially seamless transitions from what is considered outdated to new contexts relevant to our students. “Editions” will no longer exist, but rather “Updates”. I know first hand that the piecemeal approach teachers take poses risks to learning progressions for both student and class, but hopefully our digital innovations will afford us to stay nimble and productive within the curricula landscape.

  3. Thanks, Dan, for highlighting Matt Larson’s recent President’s Message. It is an important message and I was glad to see NCTM make a strong statement about curricular coherence, which is often overlooked in discussions about high-quality mathematics tasks. It is nice to see NCTM out front on issues such as this, which is what you have been encouraging in previous posts..

    Your response, however, seemed to misinterpret some of Larson’s comments and seemed, to me at least, a bit defensive. Larson was not saying, “Don’t use online activities!” Far from it. As such, I thought your “Keep off the grass!” analogy was over the top. Larson was simply saying that using online materials — even great tasks such as those you discuss here — should be done carefully and thoughtfully. That’s a fair and needed warning. A collection of great tasks does not necessarily make for a great curriculum. You, Karim Ani, and others who have promoted the use of rich mathematics tasks have acknowledged that before.

    As for publishers, while the publishing industry is changing, previous waves of improved mathematics curriculum materials did not originate from publishers. Support from NSF and foundations provided much of the catalyst needed to promote new developments in mathematics curricula, with publishers following later. Unfortunately, such support is no longer forthcoming. NSF retrenched years ago under political pressure from the “Math Wars” and foundations either are uninterested in mathematics curriculum development or are putting their support behind “personalized learning” programs that show little or no promise to actually help students learn mathematics.

    If we want to see the development of new models for mathematics instructional materials, we’d be better off pressuring NSF to get back into supporting instructional materials development than putting our faith in publishers or venture capitalists. That way, next-generation curriculum developers like you (and others) can get the needed support to create the new materials we all would like to see. As has happened before, publishers will follow suit, once they see the demand for these new of materials.

    In any case, I applaud Larson and NCTM for raising an important issue and emphasizing the importance of curricular coherence. And thanks for pointing people to Tyler Auer’s thoughtful comments about Larson’s message.

  4. I love the questions and many threads winding around these days concerning curriculum and online community.

    One of the projects that the Math Forum at NCTM is beginning to plan within NCTM concerns the idea of an online collaboration space and supporting repository through which the community can move along the continuum from sharing good tasks to identifying and playing with sequences and instructional practices that lead to the engagement, depth of understanding, rigor, and competence we all seek for our students.

    This activity could be situated in or near formal publishing ventures that can highlight, polish and sustain particularly attractive paths that emerge. As we have merged, NCTM seeks to more fully and obviously embrace both of these dimensions, the formal side of publishing and policy in concert with the professional community.

    For our part, maybe we are focused less on paving and more on providing water, restorative gathering spots, cartographers, guides, lighting, beautiful albums of glorious hikes taken, etc.

    And we are looking to collaborate with others in the endeavor, so hopefully this and other related conversations will continue and coalesce. I encourage folks to let us know if they are interested in collaborating, in big ways or small.

  5. Btw, it’s interesting to read the tweets responding to Dan’s query about reasons why teachers download or write their own instead of using textbooks and to note the difference in language from the language of coherence. The primary critiques of the textbook that stuck with me were: too procedural and micromanaging, not supportive enough of inquiry and the Practices side of the equation, too hard to work with, etc.

    Yes, there was some mention of the lack of coherence in textbooks also, but I wonder if coherence isn’t a secondary and less visible dimension, where in the classroom we are more focused on the readily identified factors affecting the quality of the engagement. And, because coherence runs under the surface in some sense and is very difficult to achieve, we may underestimate its impact on the experience, the way in which organization designed for an overarching effect and an investment in enabling the learner and teacher to realize fully the benefits of prior learning and skill building can pay off as the year(s) go on. Or maybe it’s just plain difficult for it to have such effects.

  6. Marty Gartzman:

    As such, I thought your “Keep off the grass!” analogy was over the top.

    That signage was too glib for the good of my point, perhaps. My point is that NCTM is posting a sign pointing towards coherence, rather than considering the origins of the desire path and paving a better one. Other metaphors are equally meaningful to me here: horses out of barns, dams bursting, genies out of bottles.

    Steve’s & NCTM’s initiative sounds like it offers teachers one or multiple frameworks for their curriculum planning – synthesizing online, traditional, and other sources. I’ve been skeptical about online lesson planning, but that might be a light-enough framework that people will buy in.

  7. Here is a small tool that I think I want. I think NCTM/Math Forum could help develop it, and I think it’s an example of the sort of way I want NCTM to be in the business of tending to the online infrastructure of teacher’s online work.

    (Also, apologies if you’ve heard this before. I’ve been yammering about this for a while, but I have had trouble communicating my excitement to others. Can’t tell if it’s because the idea sucks or if because I’m a troubled visionary ahead of my time.)

    Is there a way to create bundles of lessons online and easily share those bundles online? I don’t think there is, and I often want to do this.

    Would such a tool if it were designed well — easy to make, easy to read, lightweight, easy to read, easy to edit — would it change how teachers collect and share curriculum? Could it be a nudge in the right direction?

    This feels like a design problem for the math teacher web. I’m encouraged that the Math Forum/NCTM seems interested in this design problem. While Matt’s piece didn’t rub me the wrong way, it does seem to me that treating this as a challenge for people who want to influence what teachers do is going to be a better framing than trying to convince teachers to change their online patterns.

  8. Hi Dan,
    Curricula coherence is my biggest struggle. I work in a small charter high school and we have not purchased a commercial math curriculum. Instead of only 20% of my time spent planning, I am lucky to have the freedom to spend lots of time attempting to develop a cohesive unit by vetting online materials. This autonomy is both wonderful and terrifying. What if my learning progressions aren’t what they should be? Am I missing anything? Am I overemphasizing the mundane? Am I spending enough time on what I should? Should I use more Dan Meyer tasks!!!??
    I often scoff at commercially produced curriculum programs, but that is because I resent the pressure from districts to follow the pacing guide to the letter! However, your blog post reminds me that “cobbling a curriculum together from scratch” ain’t so easy. We haven’t purchased a math curriculum mostly because of the cost, but also because I do think that we have fallen into the trap that Auer describes; only “lazy or beginner” teachers use curricula and good teachers create their own materials. As a matter of fact, the initial math competencies that were proposed for our school largely ignored the recommendations of Common Core for that same reason. My belief is that Common Core is good, at least as good as any other set of standards that came before and certainly that will come in the future, repackaged with a new name. It is the knee-jerk, standardized test reaction to it that has been the problem.
    Anyway, I can appreciate what Larson had to say and it was a good reminder to me that my attention to scaffolding and coherent learning progressions is right on.
    Really enjoy your blog!
    Patty

  9. jennifer furuglyas

    September 2, 2016 - 6:07 am -

    I am not certain of the point that Matt Larson is trying to make; or rather, that it needs to be made at all. “What NCTM is arguing for is that those materials be selected wisely to ensure they fit within a coherent curriculum.” What is it you think most teachers do Mr. Larson? I seek materials that engage, expand, and fit into my curriculum. No one else, and certainly not the publishers, is doing it for me. There is no time scheduled in my day to collaborate with other teachers of my courses. Emails usually suffice, but are definitely not enough. Teachers across the board are trying new things in the classroom every day to see what works and what doesn’t. And what works for some does not necessarily work for all. Effective teacher collaboration has traditionally been the downfall for most schools. For ours, primarily, it is a financial issue. Our schedules are packed as much as they can be with classes and supervisions. Between planning, grading, helping students, and administrative b.s., there is little time for collaboration. But teachers know this already. The district would need to pony up the $$ and provide more teachers so that we would have more time built in to work together. NCTM cannot solve this problem. I do like using their stuff sometimes though :).

  10. I too read Matt’s post as discouraging teachers from incorporating materials they find online. I agree with Jennifer: teachers are smart enough to find and use materials that fit into their classes.

    I’m all for coherence, but it should not trump all other concerns. Most textbooks are reasonably coherent, within their worldview, but any particular lesson they offer may or may not fit a given teacher’s class at a given time. Escapes from the textbook are often how teachers break from the mind-numbing “this is how you do it, now practice in silence” routine.

    One way NCTM might help with both coherence and quality is to offer a _really-core_ curricular framework (as opposed to the much-too-massive CCSSM), and within that offer curated links to high-quality online materials. A positive contribution along those lines would be a lot more useful than anxiety-provoking warnings about coherence.

    As I wrote on Matt’s blog: Teachers! If something in your textbook is not working, don’t be afraid to try something else!

  11. I’ve added several comments to the body of the post. Thanks, Patty, Steve, Matt, Michael, and Henri.

    Michael:

    Is there a way to create bundles of lessons online and easily share those bundles online? I don’t think there is, and I often want to do this.

    Whenever I ask a question like this around Desmos, I tend to get the response, “How far would Google Docs get you?” What are you looking for that existing solutions, however clunky, don’t provide?

  12. Michael Paul Goldenberg

    September 2, 2016 - 9:26 am -

    Posted at the NCTM site:

    Better to have tried (something off the beaten path) and “failed” (the lesson-as-taught doesn’t grab the brass ring of high levels of student engagement, participation, and insight/learning/growth) than to never have tried at all (thereby settling for the usual, generally dull and highly-directive activities of most commercially produced textbooks. 

    Now, having probably mixed too many metaphors in an attempt to get the cliche to fit, let me suggest that the fundamental issue is never the materials but always the teacher. A teacher who downloads, finds in another book than the official text, pulls from the latest issue of one of NCTM’s teacher journals, or takes from the colleague across the hall a lesson-as-written and mindlessly applies it to his/her own classrooms will generally do no better (and generally worse) than the original implementation/design of said resource. Garbage in, garbage out? Of course, the given lesson may be a good deal above the level of garbage, but it can’t be a magical elixir, either, that miraculously works with every student in every class as taught by any teacher whatsoever. No such animal exists. 

    What’s needed is both teachers who have been taught how to interrogate lessons in the light of their particular students, their own strengths and weakness as practitioners of the art and craft of mathematics teaching, and lessons that are offered up with reflection on the various “moves” within the lesson and the components thereof. That is, the person(s) posting these lesson frames need to draw back the curtain on how they came to craft them as they did and why they think doing things in a particular way makes sense, keeping in mind that it’s unlikely that everyone, perhaps not even ANYONE, who is giving the proper reflection to such matters will agree 100%. And so there might well be reason to post “alternative hypotheses and conclusions” about how a lesson might be done, much like we expect from intellectually honest publishers of educational and other social science research. One size does NOT fit all, even if a limited bit of experimenting with one’s own practice suggests that it does. 

  13. Upon further reflection, I believe there are even greater battles being fought for coherence.

    Because standards and standardized tests were rolled out ahead of aligned commercial or open-source curricula, many districts have chosen to “roll their own” curriculum. Because of the disparities between and among different teacher and learner audiences, most of these efforts result in Frankenstein-monster-style curricula, in which Lesson A is stitched to Unit B and wrapped in language from Curriculum C.These are mashed together by mid-level people who are not curriculum experts in an attempt to create coherence through common printing, binding (or through PDF generation), and legal proclamations.

    As a result, we have even less coherence than before.

    I appreciate Dan’s perspective about the six-year time cycle for conventional commercial curricula.

    In my classroom, *I* am the common element. I am also the one who gets yelled at if students and families have a bad experience due to incoherent curricula. This makes me the de facto editor of bad curricula — regardless of where they come to me from.

    For this reason, it feels insane to me to suggest that I *not* be resourceful in the MTBoS in the service of greater coherence for my students. I assure you this is a major pain in my butt, but I am determined to use it as an opportunity to become a clearer and more effective teacher for and with my students.

    One last deep thought — I sure am getting tired of being blamed for the incoherence of standards and curricula that are way above my pay grade. Unfortunately, the way all of this has been set up (or *not* set up), everything rolls downhill into my yard.

    Grumpily,

    – Elizabeth (@cheesemonkeysf)

  14. If it chooses to do so, NCTM is uniquely positioned to merge the powers of collaboration (online activities) and coherence (NCTM content) as a truly valuable member benefit.

    The emergence of online communities like the #MTBoS has created challenges for NCTM, particularly on the content production and membership fronts. NCTM past president Linda Gojak said “NCTM is no longer in the standards-writing business”, notably with its 1989-2000 publications. Throughout its history and especially since 2000 NCTM seems to have focused on producing quality peer-reviewed content through its various publications (including P2A recently) and conferences, but less on the connectivity that empowers online communities.

    Perhaps the “next big opportunity” for NCTM is in connecting members online around its quality content. NCTM’s average member age is 55 years and fewer teachers are buying memberships, opting instead for free online connectivity with other teachers that is still quite good overall.

    A pivot may be in order. NCTM could make its high quality resources more freely available to attract new followers, but offer members an integrated ecosystem built to sustain collaboration, resource modification and implementation of high quality content wherever that content may be found: NCTM, online or elsewhere.

    “Paving a new path” indeed.

  15. Dan:

    Whenever I ask a question like this around Desmos, I tend to get the response, “How far would Google Docs get you?” What are you looking for that existing solutions, however clunky, don’t provide?

    I’m not entirely clear why I hate doing this on google docs, but I do. I need to do some soul searching to figure out why, I think…

    run soulsearch.exe

    Docs is the tool that I use, at the moment, to handle this stuff. Geoff’s curriculum maps do a great job of collecting curriculum, and they use docs.

    One issue is that docs are clunky to load and to view. I don’t feel as if they are capable of capturing my “vision” for a unit or something. I’m reluctant to link to a google doc from my blog. (Partly because it’s not published. It’s hanging out in a folder. I assume that, at some point, I’ll screw up and delete it by accident, as I’ve done to various important google docs numerous times already.)

    Another thing about docs: they aren’t searchable. I know, I know, now we’re getting into Better Lesson territory, but so far Desmos has been handling that problem pretty well with the curated search.

    Maybe y’all can let users make Desmos activity bundles and treat those the same way as you treat activities? And, if that goes OK, you can give us a labs experiment where we can include things besides Desmos activities in the bundles? (And then, eventually, ditto with courses???)

  16. Johanna Langill

    September 2, 2016 - 6:05 pm -

    I’m so tired of people confusing uniformity with coherence. Coherence comes from lots of communication, and too many people assume that we can shortcut to coherence by imposing uniformity of curriculum or experiences. I believe coherence is grown, not delivered, even if you have a good base to work from. (I love Oakland’s core curriculum.)

  17. Great communication thread, as always.
    I think we are all agreeing that Matt Larson’s response, “What NCTM is arguing for is that those materials be selected wisely to ensure they fit within a coherent curriculum” is, in fact, what we are encouraging teachers to consider. Working across grade levels, I know how easy it is for an ES teacher to turn to Pinterest to find a ‘fun’ or appealing product, pre-made – especially considering they are busy planning similarly engaging activities and tasks for multiple subject areas. For those of us that get to focus on math only, we might have our readily available, go-to math websites and resources. With that in mind, how do we create that path that supports all teachers across grade levels, AND explores so many of those resources already out there? How might make those connections to the Teaching & Learning Practices in Principles to Actions? Teachers already use Dan Meyer’s 3 Act Task and NCTM’s problem bank as resources when planning for learning. Further, the work NCTM is doing around Activities with Rigor and Coherence (the newly aligned ARCs) is encouraging – I’m looking forward to inviting our teachers to use it as a resource.

    In short, I actually think we mostly talking about the same thing here… the question is, how do we all get around the same table, to have that conversation? How do we get the path design going?

  18. I spent over 16 years building a tool with my partner to help students learn math. We released the tool online for teachers and their students to use at no charge. NCTM had no interest in our tool (it’s an online Socrates tutor covering over 580 different problem types in math from pre-algebra through pre-calculus. Feel free to check it out at useusinclass.com – full privacy for students and not even advertising to teachers or students).

    Only use what they promote? They didn’t even have the courtesy to even respond to us…

  19. JM ivler:

    I appreciate your persistence in working on improving how we engage students and apologize that NCTM did not respond to you. As I indicated in a previous post, NCTM does not recommend that anyone only use NCTM materials. While NCTM does not endorse products, we do provide opportunities for teachers to share, learn about, and discuss methods and resources as part of collective and collaborative professional growth. Under the Math Forum, we are working to increase these opportunities for teachers. Teachers and math educators sharing and discussing methods and resources are the foundation of our journals and our conferences similarly focus on sharing the expertise and work of teachers.

  20. This post takes me back to an earlier post Dan wrote about sharing lessons.
    How are we as a community developing a shared quality criteria? Perhaps this energy should be spent in investing in teacher’s understanding of what makes a task:
    1. mathematically coherent
    2. of sufficient richness to encourage sense-making
    3. appropriate to my context at the moment

    Creating great content is difficult, but so is using that content if I don’t understand the math, the context and the kind of questions I should be asking students to respond to their thinking. Our path will always be determined by our own context, but naming what is necessary and sufficient as a community? That’s what will help us learn to be learners about mathematics in schools.

    The concept then of collaborative lesson planning might start to address this need, but only if it is followed with reflective revision. What student thinking was revealed through the task? What student thinking was obscured? Was there mathematics worth discussing that arose from the work (generalizations of patterns, new tools/strategies, etc)?