RYSK: Boaler's The Development of Disciplinary Relationships: Knowledge, Practice and Identity in Mathematics Classrooms (2002)

This is the 22nd in a series describing "Research You Should Know" (RYSK)

Today Geoff Krall (@emergentmath) posed this on Twitter:

It's a cycle I've seen before, and you probably have, too. Students struggle on complex tasks (or, far worse, we just assume they'll struggle without giving them the opportunity) so we opt for the "back to basics" approach and change our mathematical practices to include a lot of repetition on lower-level, procedural tasks. We convince ourselves that this is the right thing until either the students tune out, or underperform, or both, and then we bark about "raising the bar" and the cycle begins anew.

Geoff's cycle reflects knowledge and practice, but I wanted to dig a little deeper into the idea of "student resistance." Jo Boaler (@joboaler) found herself in a similar position after she'd done some studies that linked reform-oriented practices to a more flexible and robust form of mathematical knowledge, but felt there were some stronger links to make between knowledge and a student's mathematical identity, or the way they see themselves as and becoming knowers and do-ers of mathematics.

Boaler described this process in an article titled The Development of Disciplinary Relationships: Knowledge, Practice and Identity in Mathematics Classrooms, published in 2002 in the journal For the Learning of Mathematics. You can find a preprint of the article on Boaler's faculty website, but I took the time tonight to add a summary of the article to the MathEd.net Wiki:


My takeaway from reading this particular Boaler article is that while both traditional and reform approaches can result in student learning, the attention to student identity and affect in the reform approach shapes student learning in a way that makes the knowledge more useful in more situations, or, in the relative absence of knowledge, gives students both the disposition and a set of practices to make mathematical progress. When students get caught in Geoff's "Cycle of Low Performance," it's not that they aren't learning. Instead, they just don't see their knowledge as particularly valuable, nor do they see themselves as active users of that knowledge. As teachers, we need to design our classrooms and activities in ways that give students opportunities to have some authority over their mathematical ideas if we expect them to use their knowledge productively.

The MathEd.net Wiki

Today I'm announcing a project over a year in the making, the MathEd.net Wiki.

The project has its roots in my own attempts as a graduate student to connect the literature I engage in. Tools like Zotero and Mendeley helped me organize PDFs and references, but I really wanted something that could help connect literature and citations together. Several times I tried setting up a wiki to do this, but each time it felt disorganized and overwhelming. As I prepared for my comprehensive exams in the fall of 2012, I finally found an organizational system for the wiki I thought I could sustain. I've been quietly contributing to it as a private side project ever since, and now feel it's reached the critical mass it needed for me to stay committed to it — and to make it public.

One of the things that drove me to graduate school was a desire to engage in the academic scholarship of my profession. Unfortunately, that's not easy to do as a teacher — either the literature is behind paywalls or inaccessible without a way to get the background knowledge needed to understand it. Usually both. When I started the "Research You Should Know" series on this blog, I hoped I could make some small dent in that problem. But blog posts still didn't let me make all the connections between the literature that I wanted to make. I wanted something that was less linear, and I think this wiki could be that thing.

Having read about similar specialized wikis, I know most fail to meet the expectations of their creators. I'm keeping my expectations modest. It's still a side project. (I have to finish my PhD program sometime, right?) It's a work in progress, and always will be. I don't expect dozens of contributors, although I'd really enjoy having at least a few. I don't expect the simple act of having access to more research to revolutionize anyone's practices. You deserve access to it, but alone it won't solve all our problems. I'll keep contributing to it, and I encourage you to visit the wiki, read the welcome message, and browse around a bit. I would love to get feedback, so either leave a comment or send me an email with your ideas!

Why I Blog

In preparation for her featured NCTM presentation next April, +Kate Nowak is asking why we blog. I also have an NCTM presentation about teachers and social media use, so everybody helping Kate is helping me, too. (That's part of why we blog.)

I think I had my first website in 1996, and I joined Blogger (back in the pre-Google Pyra Labs days) in 2001. I didn't have an education-specific blog until 2009, but any nervousness about self-publishing content to the web had long passed by then. So to answer Kate's questions...

Q1: What hooked you on reading the blogs?
A1: I was the sole full-time math teacher at a small rural school when I attended the 2008 NCTM Annual Meeting in Salt Lake City. Suddenly I found myself talking to members of the National Math Panel, math education professors, and teachers from all over. I'd forgotten what it was like to be part of the larger mathematics education community, so after I got home I tried reaching out to that community in support of my own teaching. I subscribed to Mathematics Teacher and the Journal for Research in Mathematics Education, and while the articles in JRME looked interesting, I quickly got the feeling they weren't written for me. When I searched the internet for information on mathematics education, I found most scholarly articles behind paywalls — another sign that what was out there wasn't meant for me. All those academics that made me feel welcome in Salt Lake City now made me feel shut out of my own profession.

But where journals failed me, blogs succeeded. +Shelly Blake-Plock's "TeachPaperless" blog was very interesting to me, and I was very impressed by Stacy V on Twitter, as she tirelessly searched for and replied to students who expressed their math frustrations via tweet. It was around that time I started following +Dan Meyer and +Cassandra Turner, and when I started graduate school in the Fall of 2009 I had decided that I wanted to use my blog to bridge the research world and the practice world.

Q2: What keeps you coming back?
A2: In many ways, the blogs are my bridge back into the practice world, which, if you allow it, can feel as distant from the research world as the distance feels to teachers looking across the gap from the other direction. I admit that I find myself less interested in the content of any one blog or post, and more interested in the general nature of the conversation and how that represents math teaching as a profession. (If you're wondering how my talk will likely be different from the other math-teacher-blogger sessions at NCTM, this is it.)

Q3: If you write, why do you write?
A3: I'm in a very privileged position; I have access to great people and great literature and I get to think about mathematics education as my full-time job. I feel a responsibility to share. I benefit personally from greater social capital, as now people introduce themselves to me at conferences and tell me they've read my blog. But as a student who is funded by Colorado taxpayers, tuition-paying students, and the National Science Foundation, I hope those funders would be pleased to see me writing and sharing online.

Q4: If you chose to enter a room where I was going to talk about blogging for an hour, what would you hope to be hearing from me?
A4: Like it or not, Kate, you're in a position to steer conversations beyond your own. I think there's a low bar to be a blogging teacher, but a rather high bar to be a really good one. For example, some teachers blog to reflect on their own practice. But are those reflections just casual, or more serious, in a Zeichner-Liston reflective teaching sort of way? Some teachers share resources. Do they try to describe the qualities of those resources? What measures/attributes do they use? So, Kate, if you're going to talk about teacher blogging, make sure you go beyond blog/noblog. Frame participation along a spectrum from novice towards expertise, and steps you'd suggest good bloggers take to get even better.

Trained in First Aid

I was at a conference recently and, much to my embarrassment, I got a rather bad paper cut. As luck would have it, the woman sitting to my right said she was an ER nurse and she offered to help. But then a young woman on my left said she had just finished an intensive five-week course to become Trained in First Aid. With a mixture of innocence and confidence, she asked me, "Could I test out my new skills?"

I appreciated the young woman's eagerness so I accepted her offer. She set about mending my finger with a few first aid supplies she kept in her bag.

As she mended my finger she described the process: "Apply pressure with sterile gauze to stop the bleeding, clean the wound, apply an antibiotic, then bandage neatly and securely to ward off potential infection." Her process looked like what I pictured other healthcare professionals doing in that situation, so I was happy.

"Is that how they taught you in the first aid class?" I asked.

"Yes, we practiced how to stop bleeding and fix cuts many times. I learned how to fix all kinds of things," she replied confidently.

I looked to the nurse for her approval. "Is that how you learned to fix paper cuts?" I asked, hoping my tone didn't come across as too condescending. Her reply began with a "Yes" but continued in detail about the benefits and potential problems with different kinds of antibiotics, how to determine when cuts need stitches, and then she started using some medical terms I didn't know. My mind wandered in the jargon, thinking she misunderstood my reference to a simple paper cut. I asked again, "But my paper cut...what this nice girl did should fix it, right? Can I consider myself healthy?"

That unfortunately struck a nerve with the nurse: "Being healthy is not a matter of 'fixing' things. I didn't spend four years getting a nursing degree and many more hours in professional training to learn how to 'fix' things. The notion of being 'healthy' is a very big idea, and there's no such thing as 'perfect health.' I'm just one part in large system dedicated to people's health care needs, and helping patients help themselves is more important than anything I could pretend to 'fix'."

The nurse's tone made me uncomfortable so I turned back to the eager young woman, now neatly putting away her first aid kit. "How do you see yourself as a healthcare worker?"

"I guess I haven't thought about it that much. I just want to help people when they're sick or hurt," she sweetly replied.

"Have you thought about being a nurse or doctor someday? I really liked your bedside manner," I said.

"No, not really. I just took the first aid class so I could work at a summer camp for disadvantaged kids. I've always liked working with kids, and the experience will look good on my resume when I apply to graduate school."

"Medical school?" I pressed.

"Probably not," she said. "My dad is a doctor, but I'm really hoping to pursue business or law."

What a shame, I thought to myself. We'd be better off as a society if eager young people trained in first aid were always there to help, especially for those people without much access to health care. For many people, I thought, a young man or woman like this could help with many things we typically leave up to nurses and doctors who require longer and more expensive training.

The session ended and we filed towards the exit of the conference center. Just as we approached the doors I heard a loud explosion from across the street. I was stunned and confused and saw both the nurse and the young woman running outside to help. Through the smoke and debris on the street, I saw a few dozen injured people making their way out of a restaurant. The young woman rushed to one of the first ones out, a man with a cut on his arm. First aid kit in hand, she began the same practiced procedure she used with me to clean and cover the injured man's wound.

I looked for the nurse, but she hadn't stopped at the first few people she saw. Instead, she was busy putting people in groups: she directed people with cuts to gather together in the street, while those too injured to walk were carried down the sidewalk to relative safety. There was a small group of people nearby who appeared to have suffered burns, and the nurse was attending most closely to three people who were having trouble breathing. She spotted a man carrying a first aid kit and I heard her yell, "Take that over there," pointing to the group with cuts. "Get some people to help you apply pressure to the wounds." I joined the man in helping people tend to their lacerations, following the same steps the young woman had just used minutes before when helping me with my paper cut.

Sirens from multiple directions got louder and as the EMTs arrived both the young woman and the nurse described the situation. I heard the young woman talk about people who were bleeding while EMTs pressed her for more detailed information. The nurse, on the other hand, was able to give very short, specific directions to the EMTs using medical terminology I didn't understand. When she had used that jargon with me I had been unimpressed, but in this context it took on urgently needed usefulness and carried a mark of professionalism.

As the injured were treated and rushed away to a nearby hospital, I thought about the eager young woman Trained in First Aid. I don't think I had misjudged her — she did what she had been trained to do and provided valuable help. With more training and experience, I saw no reason she wouldn't be able to triage victims and respond with the level of professionalism I'd seen from the ER nurse. What I had misjudged, however, were the demands of people needing help. Had I been in that restaurant, I probably would have suffered far worse than a paper cut.

Accidents can happen anywhere. People need quality health care everywhere. For the eager young woman to be part of a long-term solution, she'd need to commit to far more than five weeks of first aid training and a summer at camp. But that wasn't her plan. To me, that means she and others like her are unlikely to be part of a solution. That doesn't mean she's part of the problem, but there is a problem when we fail to believe and invest in well-trained, experienced nurses and doctors. The ER nurse was right: health care needs come both big and small, and it's not about providing a 'fix.' Health is a process, and health care needs to be a system to support that process. Needs run deeper than paper cuts, and we can't expect to meet them all with eager young people Trained in First Aid.

RYSK: Cobb, Zhao, & Visnovska's Learning From and Adapting the Theory of Realistic Mathematics Education (2008)

This is the 21st in a series describing "Research You Should Know" (RYSK).

It's Open Access Week (#OAweek) so I thought it would be fitting to use this "research you should know" post to highlight one of my favorite open access articles in mathematics education, Learning From and Adapting the Theory of Realistic Mathematics Education by Paul Cobb, Qing Zhao, and Jana Visnovska. Because the article is open access, I get to be less interested in summarizing it and more interested in giving you a reason to read it.

Realistic Mathematics Education (RME) is a theory for the design and development of mathematics curriculum. It is still deeply rooted in the Netherlands, where Hans Freudenthal greatly influenced mathematics instruction there with his belief that mathematics was a human activity, and that activity was characterized by mathematizing the real or readily imagined world. ("Realistic" comes from the Dutch phrase "zich realiseren," which in English means "to imagine.") This mathematization can be thought of in two ways, horizontal and vertical: "horizontal mathematization involves going from the world of life into the world of symbols, while vertical mathematization means moving within the world of symbols" (Freudenthal, 1991). Hans Freudenthal died in 1990 but his work continues, primarily at the Freudenthal Institute for Science and Mathematics Education at the University of Utrecht in the Netherlands.

There have been four primary avenues where RME has established itself in the United States. The first is with the middle school curriculum series Mathematics in Context, which grew from a partnership between mathematics education researchers at the University of Wisconsin (primarily Thomas Romberg) and researchers at the Freudenthal Institute. The second is the K-8-focused work of Mathematics in the City, which primarily brought together Cathy Fosnot from the City College of New York and Maarten Dolk of the Freudenthal Institute. The pair also wrote most of the Young Mathematicians at Work book series. The third place where RME is established in the U.S. is here at CU-Boulder, home of Freudenthal Institute US and its director, David Webb. David worked on the Mathematics in Context project at Wisconsin, and brought FI-US with him to CU-Boulder. The fourth place I recognize RME having a significant influence in the United States is in the work of Paul Cobb, particularly in his long research partnership with Koeno Gravemeijer, a researcher from the Freudenthal Institute. Cobb and Gravemeijer spent more than a decade working and publishing together, and that work did a lot to strengthen ties between RME as a design theory and theories in the learning sciences.

Like any idea or theory, RME has limitations. Over its 40+ years of existence it's proven to not be a static thing (van den Heuvel-Panhuizen, 2002), and this article by Cobb, Zhao, & Visnovska describes some of the important ways their work has both informed and been influenced by RME. They describe three adaptations: the first involves accounting for classroom activity and discourse in RME, the second acknowledges the mediating role of the teacher in making curriculum modifications and adaptations, and the third looks at how RME can focus on teacher learning, not just student learning. For details, I'll let you read the article for yourself at http://educationdidactique.revues.org/276. If you have any questions about the article or RME, leave a comment, find me on social media, or email me. We RME folks want to spread the word!


Freudenthal, H. (1991). Revisiting Mathematics Education: China Lectures. Dordrecht: Kluwer.

van den Heuvel-Panhuizen, M. (2002). Realistic Mathematics Education as work in progress. In F. L. Lin (Ed.), Common Sense in Mathematics Education: Proceedings of 2001 The Netherlands and Taiwan Conference on Mathematics Education (pp. 1–39). Taipei, Taiwan.

RME4: Webb's Opening Remarks

Opening Session - Friday, September 27, 2013

David Webb - Executive Director of Freudenthal Institute US and Associate Professor of Mathematics Education, University of Colorado Boulder

David Webb
David Webb welcomed us to the 4th International Realistic Mathematics Education Conference (#RME4) by addressing a shift in organizational structures. What used to be simply the Freudenthal Institute in the Netherlands is now the Freudenthal Institute for Science and Mathematics Education, and its American counterpart, Freudenthal Institute US, is now part of a larger CU-Boulder effort known as the Center for STEM Learning. These shifts reflect a desire to not just have cooperation between mathematics and science disciplines, but a perceived need to create innovative new STEM curricula along with the supporting frameworks, teacher education, and professional development to support it. Webb announced that earlier in the week that FISME and the Center for STEM Learning had formally agreed to collaborate, although we'll have to wait and see how this collaboration takes shape.

At its core, RME is a set of principles for curriculum design. It is sensible, then, to seek common ground in mathematics and the sciences for ideas upon which we can design curriculum. Some of that common ground is found in how we reason in math and science, and Webb offered these four activities:

  • Recognition of patterns
  • Making conjectures from observation
  • Reasoning from evidence
  • Generating new evidence

From these, we can think about how we consider the acts of modeling, problem solving, generalizing, and proving in both math and science. There are similarities and differences, and these things are meant as a starting point, not a definitive list. Perhaps the most fundamental RME principle is that of progressive formalization (see here for an example), so we must also think about how informal contexts can be used in both math and science, as well as the preformal models and representations that support more formal kinds of student thinking. Webb encouraged us to consider these RME traditions as we stretched ourselves beyond our usual disciplines, and with that the conference was underway.

NCTM Annual Meeting Fee Frustration (Updated 9-18)

I was recently informed by NCTM that my proposal to speak at the 2014 NCTM Annual Meeting was accepted. That's the good news. Unlike last year, when the conference was held in my backyard of Denver, I hesitated to accept NCTM's invitation to speak because of the costs involved. Registration fees, hotels, and transportation add up alarmingly quickly, especially for a graduate student getting by on a modest stipend and student loans.

Today I decided to accept the invitation and proceeded through NCTM's multi-step process. Step 1 was to accept, which was done with a quick login and a few clicks. Step 2 was to register for the conference. The registration fee for lead speakers is $281. Okay, but what are the fees for regular attendees? Here are the fees listed at http://www.nctm.org/researchconf/:

Fees at http://www.nctm.org/researchconf/, current as of 9/17/13.

Do you see what I see? If I were a regular NCTM member, the full, early-bird fee would be $345, which means the $281 speaker fee represents a $64 discount. That's a nice way to show your appreciation to speakers, isn't it? But what about student NCTM members? My full, early-bird fee is $172, which means the $281 speaker fee represents a $109 penalty.

Why is this? Does NCTM want to discourage students from presenting? I doubt it, but unless they get their fee structure sorted out that might be the result. I've emailed NCTM about this issue, and I hope they reply sensibly.

While I'm ranting, here's a selection of other things about this process that makes me mean:
  • Silly me did Step 1 before Step 2, which mean I accepted before checking out the speaker fee. Even worse, NCTM warns you that accepting then cancelling puts you in the NCTM doghouse and decreases the chances that any future proposals get accepted.
  • Too many policies at http://www.nctm.org/speak/neworleans/ disappoint me, such as:
    • Remember that recording of Steven Leinwand's talk I posted from the last Annual Meeting? That apparently is (or will be) against NCTM's wishes, as they state: "Written permission to tape or record presentations must be obtained directly from the speaker involved at least thirty days before the NCTM Annual Meeting & Exposition. The request must contain a statement indicating the intended use of such a recording or videotape. The person making the request should also inform the NCTM Headquarters Office in writing at least two weeks prior to the NCTM Annual Meeting & Exposition." I had Leinwand's permission to post the recording, but didn't get that permission from him in advance.
    • If you aren't a lead speaker, but a co-speaker, your registration rate is $344. Yes, a $1 discount compared to the regular, early-bird registration rate. That's like leaving your waitstaff a nickel tip. I'm assuming this higher fee applies to students, too.
    • Speakers must submit a written request to use any art related to the Annual Meeting. I can't imagine there's any real risk to just letting registered speakers download that from the password-protected speaker's website.
    • NCTM's idea of "going green" is to pick up your program book when you register so they don't have to mail it to you. This wouldn't have struck me as strange 10 years ago, but it sure does now. Why not try this, NCTM: Tell everyone that program books will be available electronically, and those wishing a paper copy can pay an extra $5 with their registration. That way you'll have an estimate of how many copies to print, and be "going green" 2014-style.

UPDATE! (Wednesday, September 18)

I received a reply this morning from Michael Barbagallo, Senior Manager of Member Services at NCTM. He said I can pay the student rate and not the speaker rate, but their system does not currently give me a way to register as a student until registration opens to everyone in November. For now I should confirm I will present (which I've done) and book my hotel room (uhh...can I just bring a tent and a sleeping bag to New Orleans?), then NCTM will sort things out in November when I register for the conference. It sounds like there's no automated way to do this and according to Mr. Barbagallo, "we have few students who speak." To that, I say to grad students: I know the culture of academia and research tells us that presenting at research conferences deserves higher priority than presenting at teacher conferences. Cultures can be changed and good things often come when they are challenged.

Teaching Statistics: Textbook Considerations

I have the pleasure of teaching an undergraduate basic statistics class this fall for the third consecutive year. It's not a class I had any specific preparation to teach, but I've tried to make up for that by becoming familiar with some of the statistics education literature, bolstering my content knowledge (although I doubt it will ever be as wide or deep as I'd like), getting access to good resources, and being mindful of the needs of my students.

First, it would help to know a little bit about the course. Most strikingly, the class only meets once a week on a Thursday from 4:30 to 7. If you're used to teaching 180-day school years, you really have to wrap your head quickly around the idea that you're only going to see these students 15 times before finals. Also, despite the class being taught in the School of Education, it's not required of any education students. Instead, the class consists mostly of students from two majors: Sociology and Speech, Language, and Hearing Sciences. Honestly, most of them admit to avoiding math classes, but they usually need the stats class to apply for graduate school. As for the content of the course, here is how it is described in the university catalog:

Introduces descriptive statistics including graphic presentation of data, measures of central tendency and variability, correlation and prediction, and basic inferential statistics, including the t-test.

And that's it. As someone who works almost daily with the Common Core State Standards, building a course around such a sparse description would be quite a challenge, especially for a first-time instructor. When I talked to Derek Briggs about teaching the course, he advised that I use his preferred text, Statistics by Freedman, Pisani, and Purves. I'd recently used Agresti and Finlay's Statistical Methods for the Social Sciences for my qualitative methods courses, and while that book suited me pretty well, I was open to something different so I ordered the Freedman text for my class.

In hindsight, the Freedman text was fine, and the Agresti text would have been fine, too. Both were decently well-written and had plenty of problems to assign, but that's the thing — I was looking for a text that offered considerably more than explanations followed by problem sets. I really wanted something that supported students working together in groups during class, making sense of the material as we went along.

One book that had gotten my attention was Workshop Statistics: Discovery with Data by Rossman and Chance. I recognized Beth Chance's name immediately from some of the stats education literature I'd read, and felt good that this text would offer what I was looking for. I used the text last year and was not disappointed, and will be using it again this year. Below is a summary of some of the reasons I like Workshop Statistics.

Context Continuity

In the front matter of the book, Workshop Statistics contains a list of activities by application — in other words, they've categorized all the problems by context and indexed exactly where those contexts get used. The list of related problems appears again with each problem in the text (inset in picture above), so it's easy for me or my students to refer back or forward to where that context appears. I believe in teaching mathematics rooted in context when possible, so I found this an especially helpful way of finding problems that might be relevant or interesting to the students in my class.


Every topic (lesson) in the text opens with some preliminary questions. Some involve data collection, which is great, but at the very least it gives students an opportunity to consider a question and how we might answer it. If Dan Meyer has made anything clear, it's that we shouldn't teach math as finding answers to questions that nobody has bothered to ask.

In Brief

The end-of-topic summary certainly isn't unique to this text, but the "You should be able to" statements are very handy for writing objectives for standards-based grading. (I hope to write about my SBG approach in a future post.)

Online Supports and Simulations

Besides both online instructor and student resources, the text uses a number of custom applets that often really help illustrate some of the concepts in the course. Some are Java, but a number have been converted to JavaScript for use on more platforms. I've avoided having students use software beyond a spreadsheet, and some of these applets have saved us from having to purchase SPSS (expensive!) or trying to use R (steep learning curve!).


The in-class activities use some interesting contexts and support groups working together. If anything they can be a bit over-scaffolded, but that relieves me from having to lecture much and I can spend most of my time going group-to-group in the classroom and dealing with questions more intimately.


There are a number of smaller things that I'm fine with, although they aren't deal-makers or deal-breakers. The pacing of the text is good — if we cover about two topics a week, we finish the text and pretty much everything one would expect in a basic statistics course. The order of the topics is sensible, too. Typically, it makes sense to put descriptive statistics before inferential statistics, and to work from one-variable stats to two-variable stats. This book is no different. Some texts put linear regression earlier, and where probability should land in a book seems to be negotiable. The placement of those topics in this book is fine for this course and the progression from topic to topic was very manageable.

Other than my first day activity, I haven't written much about teaching stats, but look for me to change that this semester.

Starting the Standards Era: NCTM and the 1980s (Part 6 of 6, Focusing the Council on Standards)

(See Part 1, Part 2, Part 3, Part 4, and Part 5 of this six-part series.)

The successful release of the 1989 NCTM Standards paved the way for the release of the next two NCTM standards documents, the Professional Standards for Teaching Mathematics (1991) and the Assessment Standards for School Mathematics (1995). While neither received all the attention of the 1989 Standards, a change in administration in the federal government and changing attitudes at private foundations meant money for later Standards-based projects was more easily obtainable.

In order to provide teachers and district-level mathematics specialists a clearer vision of what Standards-guided lessons would look like, the NCTM launched a project called the Addenda Series, with a committee chaired by Bonnie Litwiller of the University of Northern Iowa1. Although initially intended to produce just a few books a year for one or two years, the project eventually produced 22 books in five years, covering all grade levels K-12. Each book in the Addenda Series provided a set of lesson plans that a teacher could use directly in his or her classroom, offering some of the specificity lacking in the original Standards. The Addenda Series also supported NCTM financially, as it became their most profitable set of publications (S. Frye, personal communication, April 19, 2013).

In order to focus all the NCTM publications on the Standards, a deliberate effort was made by the editors of NCTM's journals to acquire and publish articles that cited the Standards (Lindquist, 2003, p. 837). Authors of research articles that did not refer to the Standards were asked as part of the peer review process to refocus their writing to include the Standards. With this de-facto policy in place, soon nearly every article listed the Standards as a reference. Somewhat ironically, the Standards themselves contain a reference list of only 27 sources (NCTM, 1989, pp. 257-258).


The creation and publication of the NCTM Standards is generally recognized as the event that launched our current era of standards-based reform. Given the rapidity with which educational reforms come and go, such a lasting impact from a document published almost 25 years ago deserves to be well-understood by education policymakers as well as teachers and other education stakeholders. The most significant positive, negative, and fortunate aspects of NCTM's Standards process can be summarized as:


  • Leadership desired an organization-level policy influence.
  • Working groups possessed expertise and represented diverse stakeholders.
  • Goals were set conservatively in an effort to broaden public acceptance.
  • Drafts of the Standards were sent to a very wide audience for review and commentary.
  • Standards were promoted through a massive public relations campaign.


  • Despite seeking consensus, reconciliation with the most vocal critics in the mathematics community has yet to happen.
  • The working groups lacked writing talent.


  • A well-timed "crisis" came in the form of A Nation at Risk.
  • NCTM membership rebounded in the mid-80s before the Standards project had an opportunity to put the organization in greater financial jeopardy.
  • Attitudes about the federal government's role in education, as well as national efforts like the Standards, became more favorable after the end of the Reagan Administration.

It's evident that NCTM's leadership in standards-based educational reform didn't come without a sizeable bit of good fortune. The shifting of any number of events by a year or two might have jeopardized the entire process, or relegated the Standards to be that "book on the shelf" to which few paid much attention.

When compared to the Common Core State Standards, a few significant differences stand out to me. First, the NCTM Standards were created largely for the purposes of comparing and judging curriculum, whereas the CCSSM were created as student learning targets and as part of a larger accountability structure. The NCTM Standards were not grade-level specific like the CCSSM, nor were they ever "adopted" wholesale by states or districts. Instead, the NCTM Standards became a foundation for states and districts to write their own standards, and the CCSSM represents the effort to de-duplicate the efforts of states by having a single, agreed-upon set of standards. Although not without their detractors, standards efforts on this scale do have the potential to drive positive change and anchor collaboration between educators across states and districts. Time will tell if any lasting effects of the CCSSM measure up to those of the NCTM Standards, and how.


Lindquist, M. M. (2003). My perspective on the NCTM Standards. In G. M. A. Stanic & J. Kilpatrick (Eds.), A History of School Mathematics (pp. 819-842). Reston, VA: National Council of Teachers of Mathematics.

National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: Author.

National Council of Teachers of Mathematics. (1991). Professional standards for teaching mathematics (p. 196). Reston, VA: Author.

National Council of Teachers of Mathematics. (1995). Assessment standards for school mathematics (p. 102). Reston, VA: Author.

  1. Bonnie Litwiller was my academic advisor and twice my methods professor while I was an undergraduate mathematics major at UNI. 

Starting the Standards Era: NCTM and the 1980s (Part 5 of 6, Making a Draft Widely Available for Review; Publishing and Promoting)

(See Part 1, Part 2, Part 3, and Part 4 of this six-part series.)

So far this series has described the first three of six characteristics of the policy process I outlined in Part 1. This installment will look at the next two characteristics. Despite their shorter descriptions, both were critical in NCTM's effort to have the Standards see wide adoption.

Making a Draft Widely Available for Review

There was one aspect of the Standards draft review process that had significant policy implications. Instead of just sending drafts to a limited number of outside experts, as is often the norm in such cases, NCTM sent out 10,000 copies of the 1987 draft to more than fifty other groups with interests in mathematics education (McLeod, 2003, p. 779). Every single page of the draft contained room for comments, and the working groups received comments by the thousands. Not only did such wide distribution create anticipation for the final draft, the NCTM garnered the support of sixty organizations whose names were printed in the opening pages of the final draft (NCTM, 1989, pp. vi-viii). Listing as endorsers the American Mathematical Society, the American Statistical Association, the Mathematical Association of America, and the Mathematical Sciences Education Board helped moderate the opinion by some that mathematicians were excluded from the Standards writing process.

In the end, the Standards incorporated the perspectives of many people and organizations, but not without compromise. Building consensus while being provocative is a tricky balance, something to which Michael Apple (1992) applied the term "slogan system," meaning they were

a statement of goals that was specific enough to provide direction to the field, vague enough to be acceptable to most mathematics teachers, and novel enough for its vision to catch the attention of the many different groups having a stake in mathematics education. (McLeod, 2003, p. 783)

Publishing and Promoting

While the public relations campaign undertaken by the NCTM to promote the Standards may not have been notable from Mary Lindquist's perspective as a writer (see the difference between her four characteristics and my six in Part 1), it certainly deserves attention as a matter of policy. Without a massive effort, the immediate and lasting policy influence of both the NCTM and the Standards would have certainly been reduced. By the time of publication in March 1989, the total expense of the Standards project had reached approximately $1,000,000, far exceeding the initial estimate of $258,000 (McLeod et al., 1996, p. 44). Included in the million-dollar total was $200,000 in expenses paid to public relations firms. Without this and continuing effort, the worry was that the Standards would be resigned to "sit on shelves" (Lindquist, 2003, p. 840), where all but a few curious graduate students would ever look at them again.

The public relations efforts had all the signs of a six-figure expense (McLeod et al, 1996, pp. 15-16). First, NCTM leadership, including President Shirley Frye and Tom Romberg, were coached to improve their ability to positively present themselves and to handle tough questions gracefully. They then hosted a press conference in Washington D.C. for about 200 members of the media. NCTM leaders made appearances on the Today Show and other major news programs and Astronaut Sally Ride was brought in to help by lending her endorsement. A video featuring jazz musician Wynton Marsalis describing the Standards was "shown over 6000 times by 121 television stations, reaching an audience in the millions" (McLeod et al., 1996, p. 64).

Perhaps most significant was how many copies of the Standards the NCTM had arranged to give away. Unlike the Agenda's relatively short 30 pages, the Standards were 258 pages in length. Still, the NCTM gave away a copy to each one of their 51,000-plus members, as well as anyone and everyone who might have influence but wasn’t an NCTM member. Judith Sowder, Standards Coordinating Committee chair, remembered:

The mailing lists were enormous. The NCTM lobbyist took [the Standards] around personally and handed them to members of Congress. Certainly every dean of sciences, every chair of a mathematics department, every math coordinator, high school principal, and elementary school principal who was on our mailing lists got one. We sent to PTA presidents, school board presidents, and on and on and on. Every mailing list that could possibly be used was used. (McLeod et al., 1996, p. 63)

While the size of this giveaway represented a huge cost to NCTM, it was necessary to ensure widespread adoption. Fortunately for NCTM and their budget, by 1995 more than 258,000 copies of the Standards had been distributed, including the giveaways, and the $25 cost per purchased copy made up for the lost revenue and helped pay for the expenses of the project (McLeod et al., 1996, p. 63).

Now that NCTM had written, published, and promoted the Standards, the last important piece was to make sure they played a part in future efforts. In Part 6, we'll look at how the NCTM focused efforts around the Standards, and I'll wrap up the series with some reflection.


Apple, M. W. (1992). Do the standards go far enough? Power, policy, and practice in mathematics education. Journal for Research in Mathematics Education, 23(5), 412-431. doi:10.2307/749562

Lindquist, M. M. (2003). My perspective on the NCTM Standards. In G. M. A. Stanic & J. Kilpatrick (Eds.), A History of School Mathematics (pp. 819-842). Reston, VA: National Council of Teachers of Mathematics.

McLeod, D. B. (2003). From consensus to controversy: The story of the NCTM Standards. In G. M. A. Stanic & J. Kilpatrick (Eds.), A History of School Mathematics (pp. 753-818). Reston, VA: National Council of Teachers of Mathematics.

McLeod, D. B., Stake, R. E., Schappelle, B. P., Mellissinos, M., & Gierl, M. J. (1996). Setting the standards: NCTM's role in the reform of mathematics education. In S. A. Raizen & E. D. Britton (Eds.), Bold ventures: Case studies of U.S. innovations in mathematics education (pp. 13-132). Dordrecht, The Netherlands: Kluwer.

National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: Author.

Starting the Standards Era: NCTM and the 1980s (Part 4 of 6, Establishing and Supporting Working Groups)

(See Part 1, Part 2, and Part 3 of this six-part series.)

NCTM's standards-writing process began in 1986 when the Council proposed the creation of a Commission on Standards, chaired by Tom Romberg, and four working groups: grades K-4, 5-8, 9-12, and evaluation. Each working group was chosen for its expertise and consisted of six people, generally a mix of mathematics teachers, state and district math supervisors, mathematics professors from major university mathematics departments, and mathematics education researchers (Lindquist, 2003, pp. 826-827; McLeod, 2003, pp. 772-773). The working groups were somewhat conservative, as radical suggestions would likely make for a less marketable policy recommendation. John Dossey, then president of NCTM, remarked that each group included

somebody who had been around and had a lot of experience – who could represent not a traditional view, but someone who understood the status quo well, who understood the dangers of change, and who was a worker for change, but who knew that you could not just flip a switch and have it happen. (McLeod et al., 1996, p. 46)

While expertise and diversity are generally key ingredients in a policy-making process, a quality that may have been overlooked was the recruitment of quality writers. While some members of the working groups had written textbooks, "neither writing experience nor the ability to produce polished prose was a criterion for selection, and the writing teams often struggled to produce high-quality text" (McLeod, 2003, p. 774). Writing quality was an unexpected struggle during the almost two-year process of writing the Standards.

Although the working groups were tasked with writing standards focusing on mathematical content, they were also mindful of equity issues – including how the inclusion of equity statements might help or hinder the adoption of the Standards. Christian Hirsch, chair of the 9-12 working group, remarked:

I think a careful look at the Standards would show that, in the case of the high school mathematics curriculum, there were two issues that the Standards politically decided not to take a stand on. One was the issue of tracking, and the other was the issue of whether the mathematics studied each year at the high school should be an integrated or unified curriculum, as opposed to a curriculum that was subject-matter oriented each year: algebra, geometry, advanced algebra. That decision was very conscious, in that we felt that we needed to identify in the Standards what we believed at the time in history to be the most important mathematics that all students should have the opportunity to study. And that in itself was advancing thinking on the curriculum quite a ways, because if one looked at the curriculum of the 1970s and 1980s, there was a marked contrast between the mathematics that was in college prep programs and the mathematics that one found in general math, consumer math, remedial courses. We felt it was most important to get out on the table (and over time gain acceptance for) the notion that all kids should be studying different mathematics, rather than getting the Standards caught up in a heated debate over how that mathematics could be organized and made available to students – that is, through sequences of courses that may or may not be tracked. (McLeod et al., 1996, pp. 56-57)

With the exception of a small grant from the AT&T Foundation for $25,000, NCTM chose to finance the writing of the Standards themselves, despite having recently been in significant financial difficulty. The organization had seen its membership fall from 82,000 in 1968 to 56,000 in 19831, and the loss of revenue forced the Board of Directors to consider a proposal to eliminate NCTM's publication program (McLeod et al., 1996, p. 20). Despite the risk of bearing the responsibility for the Standards total estimated cost of $258,000 (McLeod et al., 1996, p. 42) former Executive Director James Gates claimed "the proposal [to fund the Standards] was not submitted to either NSF or the U.S. Department of Education, so that no claims could be made that the federal government had funded the development of curriculum and evaluation standards" (Gates, 2003, p. 742). In addition, the self-funding of the Standards and the decision to not write textbooks, as had been the case during the new math era, afforded the working groups relative independence from textbook publishers. The "corrupting process" (McLeod et al., 1996, p. 33) of working with textbook publishers was a shared concern among the working groups, explained by Arthur Coxford in his chapter in A History of School Mathematics:

Publishers tend to be concerned with the 'bottom line,' whereas curriculum developers desire to try new ideas and organizations. Editors for publishers listen carefully to state textbook adoption committees and to teachers in the field. Neither of these groups was demanding radically different curricula in the 1980s. In fact, they often recommended retaining topics (Cramer's rule or computation using logarithms, for example) long after the usefulness, mathematical or in application, of the topic had diminished. Often it seemed such recommendations were based on an individual's opinion rather than the result of a careful analysis of needs. (Coxford, 2003, p. 613)

While self-funding did afford the working groups a degree of independence and James Gates' statement is at least partially true, the reality of the situation is that the federal government had very little, if any, money to give for a project like the Standards. In 1982, the Reagan Administration has stripped all K-12 funding for mathematics and science from NSF's budget (McLeod et al., 1996, p. 25). Moreover, the same Reagan Administration that had recently sought to dismantle the U.S. Department of Education in the name of local control was not likely to award large sums of money for the development of a national set of curriculum standards. NCTM had applied for a sizable amount of other private money, but the AT&T grant was the only one awarded. Clearly the organization had no other real options but to pay for the Standards itself and use the independence to its advantage, including spinning the effect of that independence as a policy tool.

In Part 5 of this series, we'll look at how NCTM collected and incorporated feedback about the Standards and the measures they took to promote the published draft.


Coxford, A. F. (2003). Mathematics curriculum reform: A personal view. In G. M. A. Stanic & J. Kilpatrick (Eds.), A History of School Mathematics (pp. 599-621). Reston, VA: National Council of Teachers of Mathematics.

Gates, J. D. (2003). Perspective on the recent history of the National Council of Teachers of Mathematics. In G. M. A. Stanic & J. Kilpatrick (Eds.), A History of School Mathematics (pp. 737-752). Reston, VA: National Council of Teachers of Mathematics.

Lindquist, M. M. (2003). My perspective on the NCTM Standards. In G. M. A. Stanic & J. Kilpatrick (Eds.), A History of School Mathematics (pp. 819-842). Reston, VA: National Council of Teachers of Mathematics.

McLeod, D. B. (2003). From consensus to controversy: The story of the NCTM Standards. In G. M. A. Stanic & J. Kilpatrick (Eds.), A History of School Mathematics (pp. 753-818). Reston, VA: National Council of Teachers of Mathematics.

McLeod, D. B., Stake, R. E., Schappelle, B. P., Mellissinos, M., & Gierl, M. J. (1996). Setting the standards: NCTM's role in the reform of mathematics education. In S. A. Raizen & E. D. Britton (Eds.), Bold ventures: Case studies of U.S. innovations in mathematics education (pp. 13-132). Dordrecht, The Netherlands: Kluwer.

National Council of Teachers of Mathematics. (2013). NCTM at a glance. Retrieved from http://www.nctm.org/about/content.aspx?id=174

  1. Membership began to rebound in 1984. NCTM's membership grew to 118,000 in 1995 (McLeod et al., 1996, p. 20) and currently stands at 80,000 members (National Council of Teachers of Mathematics, 2013). 

Starting the Standards Era: NCTM and the 1980s (Part 3 of 6, Meeting a [Perceived] Need)

(See Part 1 and Part 2 of this six-part series.)

"Exactly where the Agenda's call for action might have led without the appearance of a new crisis is not clear" (Fey & Graeber, 2003, p. 553). If the research and public sentiment regarding mathematics education had looked positive as the country moved into the 1980s, there would have been little need for the NCTM to flex its new policy muscles. But that wasn't the case. Instead, growing concern over the state of math education would give the NCTM a reason to put the Agenda for Action into action.

In the late 1970s, the NSF funded a series of surveys and case studies to determine a baseline of the nation's mathematics performance. The case studies indicated that most classrooms were still exhibiting a traditional view of mathematics and showed little influence of the new math efforts of the 1960s (McLeod, 2003, p. 757). Furthermore, early results from the National Assessment of Educational Progress (NAEP) raised doubts that students were able to perform anything but the most basic mathematical tasks.

Less publicly visible but yet of concern to mathematics educators was the continued trend towards "basic" math textbooks. In particular, the claims of outspoken textbook author John Saxon "became a preoccupation of NCTM leaders" (McLeod, 2003, pp. 760-761). Saxon (1982), in a three-page Phi Delta Kappan article, made boisterous claims about the effectiveness of his textbooks. The article lacked a description of how (or if) the treatment and control groups were randomized, what textbooks were used by the students in the control group, how the assessment used to measure students' learning was constructed, and failed to use any real statistical tests. It did, however, include the address of the publisher and the cost of his textbook, as well as statements like, "A general scanning of the scores suggests that gifted students who used the normal textbooks were severely damaged and that less gifted students who used the normal textbooks were destroyed" (p. 484).

NCTM’s Research Advisory Committee (RAC) fielded concerns over Saxon's claims, some requesting censure of Saxon's texts and others requesting further research regarding the effectiveness of the Saxon texts. John Dossey, NCTM president from 1986-1988, recalled that "RAC members felt that it was inappropriate for professional groups to censure material, especially in the absence of an agreed-upon set of standards" (McLeod et al., 1996, p. 31). Concurrently, NCTM's Instructional Issues Advisory Committee (IIAC) was considering the creation of a document that could be used by schools when selecting textbooks. Jim Fey, an IIAC member at the time, said, "There was some concern from several places that textbooks, and therefore curricula, were being driven by non-professional considerations, political log rolling, and so on" (McLeod et al., 1996, p. 31). The RAC and IIAC were already considering such a textbook selection document in the spring of 1983 when a much more public educational crisis would demand the attention of the NCTM.

In April the National Commission on Excellence in Education (1983) published A Nation at Risk: The Imperative for Educational Reform. This critical document used Cold War-era language combined with threats of losing our nation's economic competitiveness to assert that it was imperative that schools change to meet the nation's growing needs. A Nation at Risk convinced many that an increase in the amount rigorous coursework required in schools, specifically in mathematics and science, should be a top national priority. While there is substantial evidence suggesting that the nation wasn't any more "at risk" than it ever had been (Berliner & Biddle, 1995), the perception of risk was more important than the truth.

By the end of 1983, two small conferences were held to determine the math education community's response to A Nation at Risk. Only sixty-eight people attended in total, with only six people attending both conferences (McLeod, 2003, p. 767). One of those six people was Tom Romberg, the University of Wisconsin professor who would later be named chairperson of the NCTM Standards Commission. Among the recommendations to come out of those conferences was the organization of a group who could write a set of guidelines specifying qualities of a proper mathematics curriculum (Romberg & Stewart, 1984).

Romberg remembered that "A Nation at Risk served primarily as a spark plug, a starting point for people" (McLeod et al., 1996, p. 27). Others downplayed the influence of A Nation at Risk. Mary Lindquist claimed "The Standards came mainly from within mathematics education rather than as a reaction to A Nation at Risk or federal policies" (McLeod et al., 1996, p. 37). The deciding measure of A Nation at Risk's impact might be found in the Standards themselves, in the first line of the first paragraph of the Introduction: "These standards are one facet of the mathematics education community's response to the call for reform in the teaching and learning of mathematics" (NCTM, 1989, p. 1). The footnote for that sentence contains the statement "See A Nation at Risk."

NCTM had prepared itself to take a stand on matters of policy and now they had their greatest opportunity. In Part 4 of this series, we'll look at how NCTM organized itself to write the Standards, and the risks they took and avoided in doing so.


Berliner, D. C., & Biddle, B. J. (1995). The manufactured crisis: Myths, fraud, and the attack on America’s public schools (p. 414). New York, NY: Basic Books.

Fey, J. T., & Graeber, A. O. (2003). From the New Math to the Agenda for Action. In G. M. A. Stanic & J. Kilpatrick (Eds.), A History of School Mathematics (Vol. 1, pp. 521-558). Reston, VA: National Council of Teachers of Mathematics.

McLeod, D. B. (2003). From consensus to controversy: The story of the NCTM Standards. In G. M. A. Stanic & J. Kilpatrick (Eds.), A History of School Mathematics (pp. 753-818). Reston, VA: National Council of Teachers of Mathematics.

McLeod, D. B., Stake, R. E., Schappelle, B. P., Mellissinos, M., & Gierl, M. J. (1996). Setting the standards: NCTM‟s role in the reform of mathematics education. In S. A. Raizen & E. D. Britton (Eds.), Bold ventures: Case studies of U.S. innovations in mathematics education (pp. 13-132). Dordrecht, The Netherlands: Kluwer.

National Commission on Excellence in Education. (1983). A nation at risk: The imperative for educational reform. Washington, D.C. Retrieved from http://www2.ed.gov/pubs/NatAtRisk/index.html

National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: Author.

Romberg, T. A., & Stewart, D. M. (Eds.). (1984). School mathematics: Options for the 1990s. Retrieved from http://www.eric.ed.gov/ERICWebPortal/detail?accno=ED250196

Saxon, J. (1982). Incremental development: A breakthrough in mathematics. Phi Delta Kappan, 63(7), 482-484. Retrieved from http://www.jstor.org/stable/20386409.

Starting the Standards Era: NCTM and the 1980s (Part 2 of 6, Asserting a Policy-Minded Orientation)

From the NCTM's inception in 1920 until the 1960s, the organization "played an important but usually secondary role" (McLeod, Stake, Schappelle, Mellissinos, & Gierl, 1996, p. 18) in mathematics education policy. NCTM's primary role "focused on supporting mathematics teachers through the exchange and promotion of good ideas, not through its influence on educational policy" (McLeod, 2003, p. 759), and many NCTM leaders thought it was best to avoid "positions that might be opposed by some of its members" (McLeod et al., 1996, pp. 18-19). Therefore, during the Sputnik-era calls for reform in the late 1950s and the "new math" era of the 1960s (Fey & Graeber, 2003), organizational leadership from NCTM was insignificant.

Fueled by the battles over the new math and events of the mid-1960s, attitudes at NCTM began to change:

Although the attempt to change school mathematics during the new math era was not very successful, the idea that an activist professional organization could have an impact on society still had some appeal. The change from passive to more active stances was a topic of discussion for many professional organizations during the 1960s and 1970s. Opposition to the war in Vietnam was one source of these discussions. As academics became involved in teach-ins and other protests against the war, there was a natural spread of their concerns into the domain of professional organizations. (McLeod, 2003, p. 758)

NCTM's hands-off policy stance changed in 1966 when the Board of Directors voted to be more willing to assert its position on controversial issues. Reflecting on his thirty-one years (1964-1995) as NCTM Executive Director, James D. Gates (2003) characterized the decision and its effects: "It was a bold step for the Council, to take actions that were more visible in the public sector, leading to the development and distribution of position statements, the publication of guidelines and standards, and testimony before congressional committees" (p. 747).

While the NCTM struggled to use its new policy-minded powers during the 1970s (Fey & Graeber, 2003), the critical turning point came with the election of Shirley Hill as NCTM President in 1978. Joe Crosswhite, NCTM president from 1984-1986, remarked that, "Prior to Shirley's time, you couldn't interest an NCTM president in having a national presence in Washington – an NCTM presence" (McLeod et al., 1996, p. 19). Shirley Hill explained that she

felt a certain frustration that we weren't being listened to seriously enough outside our own circles....I remember attending some meeting of the presidents of like organizations in Washington, DC, in the 1970s and noticing the frequent absence of the president of one of our sister organizations. It turned out that he was being escorted by his staff government relations expert in visits to members of Congress. At that time his organization seemed to be very influential in the establishment of federal programs. I thought that we in NCTM should be doing more of these things. I thought that we and most of our sister organizations were being a little naïve about government relations and public relations at that time. (McLeod et al., 1996, pp. 19-20)

In addition to hiring Richard Long, a former lobbyist for the International Reading Association (McLeod, 2003, p. 760), two documents published by NCTM during this time mark NCTM's emerging policy perspective. The first was actually a republishing of a position paper of the National Council of Supervisors of Mathematics (NCSM), a sister organization of the NCTM. The paper, A Position Paper on Basic Mathematical Skills (1977), was notable because instead of refuting the "back to basics" theme of school mathematics in the 1970s, it co-opted the language and redefined the meaning of "basic skills" for NCSM's and NCTM's own purpose (Fey & Graeber, 2003, p. 552; McLeod, 2003, p. 761). With this action, NCTM and NCSM showed that both organizations understood the importance of controlling the vocabulary and discourse in educational policy.

The second document published by the NCTM solidified their stance as a policy influencer. The Agenda for Action (1980) was the product of NCTM's Committee for Mathematics Curriculum for the 1980s, chaired by George Immerzeel of the University of Northern Iowa. While only about thirty pages in length and containing eight somewhat non-specific recommendations, the Agenda was NCTM's most prominent and powerful policy document to date, and "laid the groundwork for a major reform effort that continued through the end of the twentieth century" (Gates, 2003, p. 741). Shirley Hill described the context for the Agenda at her 1980 presidential address:

In the 1960s we learned that curriculum change is not a simple matter of devising, trying out, and proposing new programs. In the 1970s we learned that many pressures, from both inside and particularly outside the institution of the school, determine goals and directions and programs....A major obligation of a professional organization such as ours is to present our best knowledgeable advice on what the goals and objectives of mathematics education ought to be....In my opinion, we are approaching a crisis stage in school mathematics. Policy makers in education are not confronting the deepest problems because the public and its representatives have been diverted by a fixation on test scores....We are still battling an excessive narrowing of the curriculum in the name of "back to basics." (Hill, 1980, pp. 473-476, as cited in McLeod et al., 1996, pp. 24-25)

Furthermore, in the introduction of the 1983 NCTM Yearbook, The Agenda in Action, Shirley Hill described the NCTM's implementation of the Agenda in five categories:

  1. Public relations.
  2. Political action.
  3. Support for local efforts.
  4. Collection and dissemination of model programs.
  5. Production of guidelines and instructional resources.

Certainly the first two items in the list would have been far less likely to appear even ten years earlier. The words and actions of Shirley Hill clearly demonstrate the policy orientation NCTM had asserted by the early 1980s. But a willingness to affect policy and an opportunity to affect policy are two different things, and that opportunity would come soon enough. In Part 3 of this series, we'll look at the events that set NCTM to work on the Standards.


Fey, J. T., & Graeber, A. O. (2003). From the New Math to the Agenda for Action. In G. M. A. Stanic & J. Kilpatrick (Eds.), A History of School Mathematics (Vol. 1, pp. 521-558). Reston, VA: National Council of Teachers of Mathematics.

Gates, J. D. (2003). Perspective on the recent history of the National Council of Teachers of Mathematics. In G. M. A. Stanic & J. Kilpatrick (Eds.), A History of School Mathematics (pp. 737-752). Reston, VA: National Council of Teachers of Mathematics.

Hill, S. (1983). An agenda for action: Status and impact. In G. Shufelt & J. R. Smart (Eds.), The
agenda in action
(pp. 1-7). Reston, VA: National Council of Teachers of Mathematics.

McLeod, D. B. (2003). From consensus to controversy: The story of the NCTM Standards. In G. M. A. Stanic & J. Kilpatrick (Eds.), A History of School Mathematics (pp. 753-818). Reston, VA: National Council of Teachers of Mathematics.

McLeod, D. B., Stake, R. E., Schappelle, B. P., Mellissinos, M., & Gierl, M. J. (1996). Setting the standards: NCTM's role in the reform of mathematics education. In S. A. Raizen & E. D. Britton (Eds.), Bold ventures: Case studies of U.S. innovations in mathematics education (pp. 13-132). Dordrecht, The Netherlands: Kluwer.

National Council of Supervisors of Mathematics. (1977). Position paper on basic mathematical skills (p. 4). Minneapolis, MN. Retrieved from http://www.eric.ed.gov/ERICWebPortal/detail?accno=ED139654

National Council of Teachers of Mathematics. (1980). An Agenda for Action: Recommendations for School Mathematics of the 1980s. Reston, VA. Retrieved from http://www.nctm.org/standards/content.aspx?id=17278

Starting the Standards Era: NCTM and the 1980s (Part 1 of 6, Where Curriculum and Policy Meet)

The Common Core State Standards might be the current story, but to gain a broader perspective of this "standards era" of educational reform we would be wise to look at where the era got its start. Over the next six posts, borrowing generously from the work of Douglas McLeod and others, I'll attempt to tell the story of how the National Council of Teachers of Mathematics (NCTM) created the first widely-recognized set of curriculum standards, and the policy process that developed along the way.

NCTM's publication of the Curriculum and Evaluation Standards for School Mathematics (1989) stands as the landmark event that launched our nation's current era of standards-based educational reform1. While the effect of this effort led to a new period of reform in school mathematics, marked by new textbooks and materials and what has come to be known as the "math wars," the process undertaken by NCTM in writing the Standards has been both praised and panned by critics. Diane Ravitch (1995) claimed the Standards "emerged from a successful consensus process that included many classroom teachers and the nation's leading mathematics educators.... [They are] an example for emulation" (p. 57). Roy Romer (1995), then the Governor of Colorado, said the Standards "were arrived at correctly, from the bottom up. They represent the best thinking in the country, collectively" (p. 67).

Critics were far tougher on NCTM and the process for writing standards for school mathematics. Ralph A. Raimi, a prominent figure in the math wars, claimed that whenever he was asked to help write or review math standards, he'd send the following recommendation:

If your standards were composed without the significant participation of mathematicians, let me advise you to go down to your best state university and find a professor of mathematics, at least 40 years old, who is willing to help you. He need not have heard of Piaget and Bruner, and he might very well be of such a personality that you would never trust him in a fifth grade class, but he should be an English-speaking American who himself has gone through our public school system, and he should be a genuine mathematician who has published at least a handful of research articles in the refereed professional journals of pure or applied mathematics. (Not journals of math education; you have such people in your department of education already.) Find out that this mathematician is willing to devote a few days to your project. Give him a copy of the Fordham Foundation report on the state standards to read....Then give him a copy of your own state's draft standards and ask for written commentary. Then use it. (Raimi, 2000, p. 57)

Raimi's suggested process for writing or reviewing mathematics standards might have some admirers, but it does not reflect the process undertaken by most standards-writing groups who wish to have a lasting impact on education practice and policy. Because the NCTM Standards have had an influence lasting now over twenty years, this series of writings will examine the specific process undertaken by NCTM that led to the publication of the Standards in 1989.

The Standards as a Policy Process

A review of the literature describing the NCTM's efforts can be undertaken from multiple perspectives. Teachers of mathematics might be most interested in the content of the Standards themselves, along with the contrasting arguments that influenced the curricular content emphasized and de-emphasized by the Standards. Historians of education might wish to study the development of the Standards as a sequence of events set in the context of greater educational and societal movements. Those who participated in the writing of the Standards bring yet another perspective of the process, such as that of Mary Lindquist, a member of the Grades K-4 working group that wrote the Standards. In Lindquist's chapter of NCTM's A History of School Mathematics (2003), she describes the effort to develop and promote the standards as having "four fundamental characteristics:"

  1. Accepting responsibility for standards.
  2. Establishing and supporting working groups.
  3. Making a draft widely available for review.
  4. Focusing the Council on standards.

Although any review of the NCTM's standards-writing process will probably be more alike than different, to gain a broader, policy-making perspective, this series of posts will be organized into six areas that share much similarity with Mary Lindquist's fundamental characteristics:

  1. Asserting a policy-minded orientation.
  2. Meeting a (perceived) need.
  3. Establishing and supporting working groups.
  4. Making a draft widely available for review.
  5. Publishing and promoting.
  6. Focusing the Council on standards.

The addition of the first two areas acknowledges that efforts to impact policy are: (a) generally conscious efforts undertaken by an organization and (b) most successful when done in response to a perceived crisis. The fifth area, publishing and promoting, describes the sometimes extraordinary effort an organization must take to make their message heard and to make it lasting.

In Part 2, we'll look at how and why NCTM decided to assert itself in the education policy arena.


Lindquist, M. M. (2003). My perspective on the NCTM Standards. In G. M. A. Stanic & J. Kilpatrick (Eds.), A History of School Mathematics (pp. 819-842). Reston, VA: National Council of Teachers of Mathematics.

National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: Author.

National Council of Teachers of Mathematics. (1991). Professional standards for teaching mathematics (p. 196). Reston, VA: Author.

National Council of Teachers of Mathematics. (1995). Assessment standards for school mathematics (p. 102). Reston, VA: Author.

Raimi, R. A. (2000). Judging state standards for K-12 mathematics education. In S. Stotsky (Ed.), What’s at stake in the K-12 standards wars (pp. 33-58). New York, NY: Peter Lang.

Ravitch, D. (1995). National standards in American education (p. 223). Washington, D.C.: Brookings Institution.

Romer, R. (1995). Explaining standards to the public. In D. Ravitch (Ed.), Debating the future of American education: Do we need national standards and assessments? (pp. 66-72). Washington, D.C.: Brookings Institution.

  1. Although NCTM’s Curriculum and Evaluation Standards for School Mathematics is just the first in a set of three publications, with the second two addressing the teaching (NCTM, 1991) and assessment (NCTM, 1995) of mathematics, this first document is the most well-known and is frequently referred to simply as the Standards

RYSK: Dewey's The Child and the Curriculum (1902)

This is the 20th in a series describing "Research You Should Know" (RYSK).

In my last RYSK post, I joined some other math teachers in discussing Richard Skemp's Relational Understanding and Instrumental Understanding (1976). Skemp's is a classic article that wrestles with a duality; in Skemp's case, the distinction between math for procedural skill versus a deeper mathematical understanding. For this meeting we turned the clock back further to Dewey's The Child and the Curriculum (1902), another classic article struggling with a duality in learning.

As D. C. Phillips (1998) noted in his review of The Child and the Curriculum, Dewey had a particular passion for dualisms, addressing more than three dozen of them in Democracy and Education (1916) alone. As Skemp and many others have shown, dualisms can be a starting point towards building a more nuanced understanding, as "neither is the world divided into a series of polar opposites, nor is it one" (Phillips, 1998, p. 404). Somewhere in between the opposites and the same lies the understanding many of us seek.

The Child and the Curriculum presents a particular dualism that very much persists to this day: should education be rooted in content, or in the needs and wants of the child? In Dewey's time, the push for a content focus was seen in the report by The Committee of Ten, not totally unlike how we currently push for content with documents like the Common Core State Standards. Dewey, like Skemp, also uses the metaphor of the map, using it to describe the logical versus psychological ordering of subject matter. Again, we still struggle with this duality today; last November Jere Confrey remarked at a conference, "There are some parts of the common core standards that I would express as mathematicians’ thought experiments," meaning we often guess how mathematical understanding is developed based on the structure of the mathematics instead of research on how children actually learn. These, of course, are not opposites, but they aren't the same, either.

Most of our discussion used Dewey as a prompt for thinking how Dewey's words more than a century ago frame modern challenges in education. (Reading Dewey seems particularly good for this kind of activity.) I was joined by +Nik Doran+Bryan Meyer+Nat Banting, and +Chris Robinson was feeding us ideas in the chat as we went along.

I plan to have more of these discussions, and hope we can get into some literature that really addresses research in math education versus some of these more theoretical or philosophical pieces. If you have suggestions for articles to read, please add them and vote them up or down in Google Moderator!


Phillips, D. C. (1998). John Dewey’s The Child and the Curriculum: A century later. The Elementary School Journal, 98(5), 403–414.

NCTM Denver 2013: Final Thoughts

Despite my flurry of blog posts during and immediately following this year's NCTM Annual Meeting, I fell short of recapping the last of the sessions I attended or summarizing some of my thoughts about the week. After my last post two months ago I needed to refocus on finishing a very busy semester — in less than two weeks I managed to give a presentation, write six papers, and tackle a digital pile of backlogged grading. Following that I just wanted to enjoy some calm and quiet, and I've done just that. Now on to the recapping:

Meyer's Tools and Technology for Modern Math Teaching

Annual Meeting - Saturday, April 20, 11:00 am

Dan Meyer - Stanford University and mrmeyer.com

I was one of many who turned out for Dan Meyer's session, which focused on why teachers should be using technology to capture, share, and resolve perplexity. What's perplexity? Dan described it as "not confusion" but a "wanting to know, thinking you're able to know." Dan is careful to differentiate perplexity from engagement, as we've all been engaged in something that was simply tedious or boring.

"I'm about THIS big."
This kind of perplexity describes a particular state of mind, one with more promise than the traditional definitions that describe perplexity as full of uncertainty and difficulty. However, when Dan speaks of "capturing" and "sharing" complexity, he's not so much describing a state of mind as he's describing the kinds of phenomena that provoke the asking of mathematical questions accompanied by an eagerness to mathematize. I'm hoping as Dan and others go forward we develop some sort of theoretical basis for these phenomena, or at very least, a useful classification system that can aid in task design. For example, I see the phenomena of scale frequently in Dan's work, provoking questions like "How much might the big blue bear weigh if it were a real, live bear?"

For capturing perplexity, Dan showed various tools for finding and saving things from the web and the world. These tools included an RSS reader for following blogs and news sites, a tool for downloading and saving YouTube videos, a note-taking application, a tool for capturing audio memos, and the camera on your phone. The particular tools here don't matter as much as knowing why to use them — they key is finding the tools that work well for you.

For sharing perplexity, Dan included technology like a computer with speakers and a projector, a document camera for showing student work, slideshow software, editors for photos and video, and a personal blog to "share the best stuff you do publicly."

For resolving perplexity, Dan made some connections to the Common Core State Standards. Standards aren't technology like computers and smartphones, but the CCSSM — particularly the Standards of Mathematical Practice — can be seen as tools for mathematical task design. There's a lot in the world that could be mathematized, but having a set of standards can help make sure it's done with the right content and practices in mind.

You can access Dan's shared resources for the session at nctm13.mrmeyer.com.

Hart and Hart's Viral Math Videos: A Hart-to-Hart Conversation

Annual Meeting - Saturday, April 20, 12:30 pm

Vi Hart - Khan Academy
George Hart - georgehart.com

I think Christopher Danielson said most of what I was thinking during this somewhat odd father-daughter session. It's difficult to describe the vibe that was in the room, with the presenters casually and sometimes clumsily taking turns describing then showing their videos. Near the end Vi grabbed a guitar for a rather brave musical performance that filled me with some kind of vicarious embarrassment, as if Fiona Apple had gone on stage thinking she was singing for lovelorn teens when in fact it was just those teens' math teachers. Then again, I feel embarrassed for others quite easily.

George Hart and Vi Hart

Perhaps I shouldn't be too critical. Some of the videos were pretty cool and who among us hasn't had at least one "Hey guys, check out this thing on YouTube" kind of moment?


Having a big conference in your backyard is very nice, although I spent far more time on the bus or waiting at bus stations than I would have ever imagined. I take conferences seriously and believe in attending as many sessions as possible. Just as I never skipped a class in college -- and felt guilty about missing anything even when it was absolutely necessary — I'm not one to turn a conference visit into my personal vacation. So my NCTM experience turned into an 80+ hour grind investment not only in my own education, but as a proxy for the many who couldn't attend.

I tried to seek out a balance of sessions that were personally beneficial, high quality, and of wide interest. In a conference of this size there is plenty to choose from, but the downside of that is that session proposals are almost comically short and descriptions in the conference program don't provide much detail. The sessions are also of varying length and they overlap, which I think adds to the variety of sessions a person can attend. This year a new 30-minute session called a "burst" was introduced into the schedule, but I didn't attend one. My colleague +Ryan Grover attended a burst session, but was disappointed that many bursts happened at the same time. That made it difficult to schedule several in a row, and attending a 30-minute burst meant not attending a longer session offered at the same time unless you didn't mind sneaking in halfway through. I don't know what kind of feedback the program committee has gotten, but I hope they find a better approach for the bursts, perhaps something modeled like the paper sessions at the research conference. There, three authors briefly introduce their papers, and then session attendees have the option of sitting at a roundtable for 20 minutes with their choice of two of the authors. Perhaps in the future the bursts could be grouped in a similar way.

It's tricky to consistently find good sessions, and session titles like iPad Games for the Flipped Classroom seem far more likely to attract a standing-room only crowd than something based solidly in both research and practice. Then again, I attended some sessions because the presenter was well-established in the field of mathematics education, and frankly, that didn't always translate into a session that was engaging or helpful to me.

Some people used Twitter to try to improve their chances of finding the best the conference had to offer:

Shaunda McQueeney addressed a particular pet peeve of mine: Those who would rather spend time in the exhibit hall instead of attending sessions:

Over the past year or so I've become more and more aware and annoyed by how Twitter's limitations constrains our ability to communicate complex ideas or have fluent conversations. Unfortunately, the Twitter use at this conference didn't do much to change my mind. As I've written about elsewhere, Twitter is very good at covering events with short summaries of something that is happening or just happened, such as:

But when we try to use Twitter to share and engage in ideas, it's harder to scratch the surface. For example, this Tweet was far and above the most retweeted of any of my Tweets during the conference:

To me, the above statement doesn't really mean much of anything. By itself, I can't imagine it having an impact on a teacher's practice at all, and even if it did have an impact, there's nothing in the Tweet that describes how this is done. This is a platitude and little else, and I knew it when I tweeted it. I have a theory that these things are retweet bait, and I was testing out the theory. Many of the most retweeted Tweets appear as platitudes to me. That doesn't make them all bad, and it's a phenomena certainly not limited to Twitter, but there's a tempting superficiality there that I'd like to think people are aware of. That's why I'm thankful for efforts like MathRecap that at least offer an opportunity to sink some conceptual roots into solid ground.

I certainly could have tweeted Leinwand's talk — he may have been the most tweetable speaker at the conference — but I thought that recording his talk and taking notes would be the better approach in the long run. Conferences reach a limited audience for a limited amount of time. Twitter widens the audience, but is minimally helpful to the person wanting to revisit the event a day, week, or month later. Blogging helps remove limitations of both geographic and temporal limitations, and including audio and video is even better.

I've submitted a proposal to present next year, but I'm concerned about conference and travel expenses. As much as I enjoy conferences, it's difficult on a grad student salary to justify spending hundreds of dollars to present to 25 people, when I could reach many more staying home and assembling the presentation for the web for nothing. I'll wait to see if my proposal is accepted first and then decide from there.