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.

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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.

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.

References

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

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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.

References

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.

References

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.

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.

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.

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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. ↩