RYSK: Gutiérrez's Political Conocimiento for Teaching Mathematics: Why Teachers Need It and How to Develop It (2018)

Rochelle Gutiérrez keynoting the 2016 CCTM Conference

I haven't used the "RYSK" tag for a blog post in almost four years, but only because I've taken to summarizing research over on the MathEd.net Wiki. That wiki turns five years old this month while this blog turns eight! I think my best strategy is to summarize on the wiki and editorialize here on the blog, and the events of this week demanded that I break my blogging silence and deal with an issue of the moment.

Last Monday I was riding the bus home when Google stuck an article from an anti-liberal education site called Campus Reform into my news feed. It was about a math education professor and white privilege, so I checked it out (in incognito mode — I try not to give Google the wrong ideas about the sites I want more news from). The article was about Rochelle Gutiérrez and honestly, it didn't say all that much except to highlight connections Rochelle was making between math and white privilege. The comments below the article were...what you'd probably expect. I closed the story and didn't think much about it, other than, "I wonder if this story will go anywhere?"

Go somewhere, it did. On Wednesday Google showed me that Fox News had picked up the story. Predictably in this era of internet news, it wasn't original reporting on the content of Rochelle's work. It was just a rehash of the Campus Reform article and it was getting a lot of comments. Judging by what I was seeing, the Fox News patrons didn't seem to have read Rochelle's work either. I searched Twitter for use of Rochelle's handle and saw she was getting a lot of negative comments with some blatant harassment thrown in (I reported one person whose account was subsequently found in violation of Twitter's rules). Those people didn't appear to have read Rochelle's chapter, either. (A notable exception: Jason Miller's post and conversation on Google+, which took the rational approach of asking "Does anyone know more about this?" and got replies like, "Here's more info, but not enough to draw conclusions." Score +1 for Google+.)

If I've learned anything in 2017, it's that I need to be upset/outraged on my own schedule and on my own terms. That usually means doing more listening and learning and not jumping into a soon-forgotten online fray. So I ordered the book Building Support for Scholarly Practices in Mathematics Methods, in which Rochelle's chapter appears, and waited a few days for it to arrive so I could actually read it before commenting.

I've now read and summarized the chapter on the MathEd.net Wiki. Did Rochelle link the privilege of mathematics to the privilege of being White? Did she say we perpetuate that privilege when we focus on Greek mathematical history and not that of other peoples? Did she say we should see mathematical knowledge is relational, and not objective? Yes, she did say all those things, and in that way the original Campus Reform article was mostly accurate. Where it wasn't accurate — and led many other sites and their audiences astray — was representing Rochelle's chapter as mostly about those things. Rochelle made most of those statements in a page or two, then spent the rest of her 27 pages laying out a framework of teacher knowledge meant to help prospective teachers deal with the political realities that affect their work.

What strikes me after reading the chapter is that Rochelle names many political influences on teaching and education that are also common targets of the right: Common Core, Pearson, big philanthropic foundations, bureaucratic inefficiency and misdirection, and control of schools that doesn't reflect local needs. There is plenty of common ground to be explored in the chapter if people choose to look for it and discuss it. The news sites could have done that, but they didn't. It wouldn't be sensational enough to generate traffic and ad revenue, and their typical narrative doesn't leave room for discussing the development of political knowledge meant to benefit traditionally underserved students.

Now that things have (probably) quieted down, we can look at Rochelle's chapter for the reasons she wrote it: to inform math teacher educators who want to help prospective teachers deal with the political pressures and distractions that can interfere with giving students the help they need. If you are a math teacher educator, this looks like a book you should have. I've put the table of contents on the wiki along with the summary of Rochelle's chapter.

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). 

RYSK: Gutiérrez's The Sociopolitical Turn in Mathematics Education (2013)

This is the 18th in a series describing "Research You Should Know" (RYSK).

"Regardless of the focus of a research project, the fact that mathematics is a human practice means it is inherently political, rife with issues of domination and power, just like any other human practice." (Gutiérrez, p. 40)

This quote from Rochelle Gutiérrez is not significant because it represents a cutting-edge perspective in mathematics education research. Instead, the quote is significant because the "sociopolitical turn" has taken the field of mathematics education research to a place where the above -- directly addressed or not -- is accepted by most math ed researchers. Insisting that mathematics education is somehow politically and culturally neutral is now the marginalized view. We didn't reach this perspective overnight, and we will struggle with how this sociopolitical perspective affects mathematics education. But in return for that struggle, we give ourselves a perspective from which to better understand why some students and some reforms succeed while others do not.

I'd seen a pre-print version of this article posted on the NCTM website leading up to the publication of this year's Special Equity Issue. NCTM has posted the article as a "free preview," which is where Bryan Meyer (@doingmath) found it and asked if anybody would want to discuss it with him. A few weeks later, Bryan and I met via Google+ Hangout and talked about the article.

It's been a few weeks since Bryan and I talked, but my main recollections are (a) my explanation of the socio+political was a bit long, but okay, (b) Bryan's pretty dialed in to this, as evidenced by the quality of the questions he asked, and (c) my speculation of what all this means for day-to-day classrooms gets pretty shaky. On that last part, I stand by my statement that I don't think this means there's something wrong with the sociopolitical perspective. Instead, I think it means I'm still slowly coming to understand it and consider all of its implications. Bryan and I are interested in having more of these talks with more people, and recently on Twitter we threw out a few links for possible articles to read. I'd like to have these Hangouts with more people, so we'll be sure to plan ahead and even seek out a regular time (once a month?) to discuss some recent piece of mathematics education research or commentary.

Feel free to comment to this post, the Google+ event, or the YouTube video. (Here would be nice.)

References

Gutiérrez, R. (2013). The sociopolitical turn in mathematics education. Journal for Research in Mathematics Education, 44(1), 37–68. Retrieved from http://www.nctm.org/uploadedFiles/Journals_and_Books/JRME/articles/JRME_Special_Equity_Issue/jrme2010-08-5a.pdf

RYSK: Gutiérrez's (Re)Defining Equity: The Importance of a Critical Perspective (2007)

This is the eighth in a series of posts describing "Research You Should Know" (RYSK).

Do you ever find yourself talking about something, defending something, or promoting something when you suddenly realize you don't have a good definition of that thing?

In one way or another, I've been thinking about equity in math education ever since I was an undergraduate. I remember debating the value of "equality of opportunity" versus "equality of outcomes," and getting a sense for how the NCTM Standards prescribed a type of school mathematics for all students. Here at CU-Boulder, issues of equity and social justice are never far away. But what, exactly, do we mean by equity in math education? And why is it important?

Rochelle Gutiérrez focuses on issues of equity as an associate professor of mathematics education at the University of Illinois at Urbana-Champaign. Even though she's been publishing on issues of equity for well over a decade, in 2007 she wrote a book chapter titled, (Re)Defining Equity: The Importance of a Critical Perspective. In that chapter, she argues why we need a definition of equity that gives teachers and researchers a clear sense of purpose.

When equity is loosely defined, it comes under attack from several directions. First is a belief that not all students can learn, and that mathematical proficiency has more to do with natural ability than with effort. The second threat to equity is a "deficit theory" towards groups of students that haven't had much historical success in mathematics, whether that deficit is seen as biological or cultural. The third threat to equity, says Gutiérrez, comes from within the research community itself: so many issues get covered under the umbrella of "equity" that few of them get the kind of focused attention they need, even while many agree equity is important. As Gutiérrez puts it:

Perhaps the lack of a clear definition is what contributes to a general consensus that equity is worth striving for, everyone having his or her own vision of what it means. However, having a poorly defined target means we are only sure we are moving toward it when, in fact, we are very far away. (p. 38)

Gutiérrez argues that we should leave behind the traditional "excellence versus equity" and "traditional versus reform" debates in favor of a new perspective: dominant versus critical. Instead of teaching mathematics that "reflects the status quo in society, that gets valued in high-stakes testing and credentialing, that privileges a static formalism in mathematics," (p. 39), we should be favoring critical mathematics, that which "squarely acknowledges the positioning of students as members of a society rife with issues of power and domination" (p. 40). This includes using math to examine social and political issues, to highlight perspectives of different cultures, and to challenge the view that mathematics is a static entity. Gutiérrez does not wish to create a dichotomy here -- in fact, she argues the importance of learning dominant mathematics because it can help students better understand and criticize the world.

With that perspective in mind, Gutiérrez defines equity. First, she warns not to confuse it with equality; whereas equity implies "justice" or "fairness," equality implies "sameness." Gutiérrez is *not* arguing that all students should experience the same instruction using the same materials, or that we should expect all students to have the same outcomes. Gutiérrez fully recognizes that, within any group, experiences and outcomes will vary, and that some students will have interests that lead them away from mathematics. That's okay. Instead, she says equity in mathematics should consist of three main parts:

1. "Being unable to predict students' mathematics achievement and participation based solely upon characteristics such as race, class, ethnicity, gender, beliefs, and proficiency in the dominant language" (p. 41, emphasis original). To clarify, Gutiérrez says, "I contend that only when there is sufficient variation within groups and no clear patterns associated with power or status in society between groups can we conclude that this aspect of equity is being addressed" (p. 42, emphasis original). As for measuring achievement, Gutiérrez says we should use standardized tests (but not exclusively), because those are often the tools we use to grant power to individuals.
2. "Being unable to predict students' ability to analyze, reason about, and especially critique knowledge and events in the world as a result of mathematical practice, based solely upon characteristics such as race, class, ethnicity, gender, beliefs, and proficiency in the dominant language" (p. 45, emphasis original). It's this aspect of equity that Gutiérrez uses to stress the critical aspects described above.
3. "An erasure of inequities between people, mathematics, and the globe" (p. 48, emphasis original). Gutiérrez claims "This aspect of equity addresses the fact that having equal access to cultural capital and critical stances to society are necessary but insufficient conditions for change" (p. 48). While this aspect of equity is by far the most difficult to measure, and may not happen in our lifetimes, it should be the key goal of any long-term reform in mathematics education.

Gutiérrez closes her paper with this paragraph:

It might be the case that the first two aspects of equity must be addressed before we would see any changes in the third aspect. That is, students who gain both (1) dominant and (2) critical mathematics identities will lead to different kinds of mathematicians in the academy, thereby changing what counts as mathematics as well as how it is evaluated. The important thing to consider in this (admittedly simplistic) model is that neither the first nor the second aspects of equity are sufficient to redress injustices in the world. Students need to be able to do both -- be able to play the game of mathematics that is currently associated with power and intellectual potential, and be able to change the game of mathematics to serve a better society. (p. 49)

References



Gutiérrez, R. (2007). (Re)defining equity: The importance of a critical perspective. In N. S. Nasir & P. Cobb (Eds.), Improving access to mathematics: Diversity and equity in the classroom (pp. 37-50). New York, NY: Teachers College Press.