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.

Preliminaries

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!).

Activities

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.

Overall

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).

Conclusion

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:

Positive:

• 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.

Negative:

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

Fortunate:

• 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.

References

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.

References

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.