Bonnie H. Litwiller, 1937-2012

I got word tonight that my undergraduate advisor, Bonnie Litwiller, passed away a couple days ago at the age of 74.

As a freshman at UNI, I had a temporary advisor until my program became more certain. After declaring as a math education major, Bonnie Litwiller was assigned as my advisor. I knew nothing about her. I remember asking Ed Rathmell, whom I had gotten to know while applying for a scholarship, what to expect from Litwiller as an advisor. I remember his response: "If you listen to her and do what she asks, she's great. She'll have your back when you need something. But don't cross her."

That's an uneasy way to know someone before you even get a chance to meet them. It felt like a description more fitting of mafia boss than a professor. But Rathmell's advice, as usual, was solid. Litwiller proved to be tough, and she made it clear to us that being a good math teacher was hard work. She set a good example: she and her research partner, David Duncan, would set aside a day a week where they'd lock themselves away in the library and write. As UNI isn't a top-level research university, the research activities of professors aren't always visible to the students. But Litwiller's dedication to research was clear, and there was no topic too small or journal too obscure. If she thought she had knowledge that would improve the teaching and learning of mathematics somewhere -- anywhere! -- she would write and submit for publication. She continued to write and publish even after her retirement from UNI in 2000, eventually passing the almost unfathomable mark of 1000 scholarly publications.

I took two classes with Litwiller, Teaching Middle School Mathematics and Teaching High School Mathematics. The classes were tough due to Litwiller being both picky about the quality of our work and her lack of clarity in describing what she wanted us to do. Some of us thought she was just being careless with her assignments, but I always wondered if this wasn't somehow purposeful. Either way, it was clear that she didn't want to do a lot of hand-holding. Some of us, ever so quietly yet respectfully, referred to her as the bulldog. A trusty companion that might just bite if you got out of line. If you didn't have the initiative and sense of responsibility to do quality work, I think she wanted a way for you to sort yourself out of the program. It happened, too; every semester some classmate would go missing and we'd try to find out what happened. Inevitably, someone would say, "They couldn't cut it. Litwiller dropped them from the program." You hear a lot today about colleges adopting GPA or test score requirements to improve the quality of their education majors. We didn't have those -- we had Litwiller. And just like letting a GPA decide who can be a teacher, I'm sure her judgement wasn't perfect and mistakes were made. (An acquaintance of mine, who shall remain nameless but now holds a PhD in math education, told me about a narrow escape from Litwiller's axe after a dispute over access to a local school.) But I think Litwiller had a sense for the quality that people expected from a UNI-prepared teacher, and a sense for giving us some survival skills that would get us through our first few years of teaching. There must have been far more successes than failures, too -- by the time I graduated in 1999, someone had estimated that a quarter of all the math teachers in the State of Iowa had been taught by Bonnie Litwiller.

My appreciation for Litwiller and her work has grown through my years first as a teacher and now as a graduate student in mathematics education. It was she who first introduced me to the NCTM Standards, and her direction of the NCTM Addenda Series was and still is an enormous contribution to the field of math education. What I believe was originally intended to be a six-book series to support the Standards grew into 22 total books, each designed to take the research behind the Standards and turn it into something teachers could use. Litwiller might have been the director and not the author of the Addenda Series, but it carried her trademark: getting as much useful information into the hands of teachers as possible. She gave me two books from the series, the middle school and high school books about statistics and data analysis. It was the first time I really thought about statistics education, and it's since become the area of school mathematics I find most interesting.

The world will miss Bonnie Litwiller, but she didn't leave without making a mark, both on the field of mathematics education and on me. Teacher education is a challenging business, and it's probably best to judge it with a certain amount of hindsight. For all of her toughness, she did have my back when I needed it, just as Ed Rathmell said she would. I may not have learned all that she tried to teach me, but maybe her most important lessons -- a sense of dedication and rejection of "good enough" -- have been most helpful in getting me to where I am today.

The Research Works Act and the White House OSTP

Imagine Company X proposed a law that said if they added value to a public highway -- such as by organizing volunteers to pick up trash on the side of the road -- then that gave Company X ownership of the road and the rights to charge the public tolls to use them. Sounds crazy, right? Well, replace "Company X," "public highway," and "pick up trash" with "Reed Elsevier," "publicly-funded research," and "peer review," respectively, and you've basically got the Research Works Act, a bill currently in the U.S. House of Representatives. If passed, the Research Works Act would prohibit federal funding agencies (such as the National Institutes of Health) from requiring that the research they fund (with your tax dollars) be available to the public. Instead, publishers could restrict access to any research they add value to (such as coordinating volunteers for peer review) for profit. Where does that profit come from? Usually from the high subscription fees paid by research universities, money often obtained from public funds and tuition dollars. The effect is that taxpayers are paying twice for research that, in many cases, they still don't have access to.

Fortunately, people are paying attention. Michael Eisen's op-ed in the New York Times explains the Research Works Act and its potential harm to research and scholarship, and plenty more articles on the subject are easily found. Somewhat coincidentally, we are also at the end of a feedback period for the White House Office of Science and Technology Policy (OSTP), where they have made a formal Request for Information (RFI) about open access to scientific publications. Yes, the Research Works Act should be stopped and seen as little more than a request by for-profit publishers to continue having their work (along with their alarming profits) subsidized by tax dollars. But I don't think stopping one bill is enough. Instead, I hope to see all federal funding agencies adopt policies similar to those of the NIH. I expressed these hopes in an email today to the White House OSTP, the text of which I've copied below.

---

University of Colorado at Boulder
School of Education
249 UCB
Boulder, CO 80309-0249

January 12, 2012

To: Office of Science and Technology Policy
Executive Office of the President
725 17th Street Room 5228
Washington, DC 2050

From: Raymond C. Johnson, Doctoral Student in Mathematics Education
School of Education, University of Colorado at Boulder

Re: Response to the White House RFI on OA publications

I am a researcher, concerned citizen, and a supporter of open, public access to publicly-funded research. I speak for myself and not on behalf of my colleagues or my institution, although I believe I express ideas and opinions shared by many researchers and educators. In response to the White House Office of Science and Technology Policy request for information on “Public Access to Peer-Reviewed Scholarly Publications Resulting From Federally Funded Research,” I urge you to preserve policies that require public access (such as from the National Institutes of Health) and expand similar policies to other federal funding agencies such as the National Science Foundation, a key source of funding for education research in mathematics, science, and technology. Currently it is with great jealousy I see the growth of open access publishing in areas such as health and medicine; as an education researcher I wish I had the ability to share the latest research with teachers and administrators, most of whom cannot afford the high fees charged by publishers of education research. Unfortunately, open access journals in education are relatively rare and undervalued. A change in policy, one that would require public access to federally-funded research, would quickly change the perceived valuation of open access publishing outlets and bring much-needed information to educators everywhere.

Prior to my becoming a researcher I was a high school mathematics teacher for six years in high poverty, rural Colorado school districts. I did not have the benefit of a nearby university or a district support staff with access to recent or prominent research. My main link to information was a powerful one: the internet. However, it seemed that my searches for research about teaching methods, curriculum, education policy implementation, etc., all eventually led me to paywalls put up by publishers to “protect” their work, requesting fees I could not afford to pay. Now, as a researcher, I realize that the authors of education research -- much of it funded with federal dollars -- are asked to give their copyrights to publishers in exchange for so-called “widest possible dissemination” of that research. Researchers neither receive nor expect any pay or rewards for giving away their work, other than some scholarly esteem and the hope their research somehow reaches and benefits students and educators. While that publishing model might have made sense twenty years ago, it does not any more. Any claim of “widest possible dissemination” that currently does not include searchable, full-text publication on the public internet is false, at best, and fraudulent, at worst.

In response to the eight questions in the RFI, I encourage you to consider the arguments and recommendations made by Harvard University in their response (http://osc.hul.harvard.edu/stp-rfi-response-january-2012). Their expertise in these matters far exceeds mine. However, I do wish to make the following amendments to their responses for questions (2) and (7):

(2) What specific steps can be taken to protect the intellectual property interests of publishers, scientists, Federal agencies, and other stakeholders involved with the publication and dissemination of peer-reviewed scholarly publications resulting from federally funded scientific research? Conversely, are there policies that should not be adopted with respect to public access to peer-reviewed scholarly publications so as not to undermine any intellectual property rights of publishers, scientists, Federal agencies, and other stakeholders?

Harvard’s response refers to a need to divide and share rights between researchers and publishers. My recommendation beyond their statement is that any discussion of copyright include Creative Commons (http://creativecommons.org/), an organization dedicated to creating and defending content licenses that allow creators to reserve some, but not all, of their copyrights. Their expertise should be invaluable in any discussion about the sharing of intellectual property rights. The Harvard response includes a recommendation of a Creative Commons license at the end of their response to question 1. I also urge you to consider the expertise of SPARC (http://www.arl.org/sparc/), the Scholarly Publishing & Academic Resources Coalition.

(7) Besides scholarly journal articles, should other types of peer-reviewed publications resulting from federally funded research, such as book chapters and conference proceedings, be covered by these public access policies?

In Harvard’s response, they say they “could support mandatory public access” for non-journal works, but consider these to be “secondary issues” and are “not prepared to list all the types of content to which a federal public-access policy ought to apply.” I worry that this position is short-sighted and leaves too much room to abuse public access policies. Often the events that lead to research becoming a book chapter instead of a journal article are entirely matters of circumstance, and not a basis of quality or public importance. In fact, the entire distinction between article and chapter relates to a paper-based publishing economy, one that is increasingly irrelevant in a digital age. After all, if we were still limited to publishing on paper it is unlikely that this kind of public access policy discussion would even exist. If the spirit of these policies is to give the public access to research they have funded through federal tax dollars, there is no need to worry about “types of content” other than to say the research will consist of bytes and files traveling the internet. Furthermore, if the policy only requires “journal articles” to be published openly, what is to keep publishers from re-branding themselves as something other than a journal? By relabeling their products as books, magazines, or something entirely new, unwanted loopholes around public access are sure to emerge.

Reflections of Multicultural Education

It’s the day after the last day of what has been a very busy semester. Being busy is good, and being awash in new information every day is something I relish. But there comes a time when we must pause and reflect, and too often this semester I have not given myself that time. Admittedly, just keeping up with the flood of new information proved to be too much, and the student-to-student whispers of “You can’t read everything, you know” proved too regularly to be true. But finally, now, I can take a few hours and think about the last core course of my doctoral program: Multicultural Education (MCED), taught by Linda Mizell.

Assessing the value of this class has been difficult, as there were plenty of moments during the semester when I felt I wasn’t making much scholarly progress. One reason for that feeling – and a reason I appreciate – is that prior coursework had left me better prepared for MCED than I expected. (Or so I thought.) Rarely were the issues we explored in MCED not ones I’d considered in prior courses like Culture and Ethnography, Ethics in Education, Policy Issues, Education Research and Policy, and Perspectives on Classrooms, Teaching, and Learning. It is a credit to my institution that attention to multiculturalism and equity permeates into most corners of the school, although I admit there are times where I still sense it as artificially layered on to a lesson or, even worse, uncomfortably absent. A second reason for that lack-of-progress feeling stemmed from not being able to keep up with all the reading and assignments for the semester. As I finished the last of my papers last night, I thought back to what remained unfinished and one reading in particular stood out: Eduardo Bonilla-Silva’s Racism Without Racists.

So after submitting my last final paper, I pulled Bonilla-Silva back off the shelf and picked up where I’d left off. I had read all but the last two chapters, but it was in those last two chapters where things appeared to get most interesting. In this, the third edition of Racism Without Racists, Bonilla-Silva added a new chapter at the end addressing the “Obama Phenomenon.” I started reading and almost immediately I was taken back to what I thought made this book so interesting, engaging, and challenging to begin with: Bonilla-Silva’s outspoken criticism of a system that perpetuates racism and inequality. In general, I do not disagree with Bonilla-Silva’s message. But the style with which the message was delivered came as a bit of an uncomfortable shock.

In his detailed analysis of interviews with both white and minority students, Bonilla-Silva exposed the racism found in peoples’ language. For example, in an interview with a white girl named Jill who claimed, “One of my best friends is black” (p. 58), Bonilla-Silva asks her to go into more detail. Jill then describes her friend as “bright” but with “terrible GMAT scores,” and then says, “What he lacks in intellect he makes up for in…he works so hard and he’s always trying to improve himself.” In his analysis, Bonilla-Silva addresses the contradiction about intelligence and points out that Jill never mentions this friend by name. This example by itself might seem lacking in evidence, but it is far from an isolated incident in the text. The dissection of racism in peoples’ speech happens on page after page. Sometimes it’s subtle, sometimes less so, and I remember feeling during my first reading that I’m glad Bonilla-Silva wasn’t interviewing me, because he seemed to make everybody sound racist!

Now, reflecting exactly on that thought, I see how that thinking exposes how I largely missed Bonilla-Silva’s greater point (even though it’s the title of the book): the kind of racism we’re dealing with now is less about the individual and more about a system. Bonilla-Silva wasn’t after Jill to make her sound like a racist – at least not the kind of racist most people imagine when they hear that label. Bonilla-Silva was instead exposing how Jill, along with most of the other interviewees in the book, demonstrates the systems and structures of racism and how they exist in what we all say, do, and believe. In other words, it’s not about Jill. For the same reason, I shouldn’t have worried about Bonilla-Silva interviewing me, as the interview would have only helped me understand how my actions, behaviors, and attitudes are being affected by the subtle yet significant culture of racism that still exists in our society. And until we are forced to recognize it, there is very little we can or will do about it.

It’s also this same system that allowed much of the country to endorse President Obama, and how that endorsement gives us a false sense of accomplishment that we’ve somehow reached a “post-racial” society. (We haven’t.) As an educator I wonder how we can have policies like NCLB which are so bold to declare a school a failure when achievement gaps persist, yet our greater society and government doesn’t always extend that same failure judgment to the enormous gaps in achievement, income, wealth, health, etc. that we see in our society. Sure, the #Occupy protesters have their message, but it’s unfortunate that so few were shouting until the perils of inequity reached beyond minorities.

The system that Bonilla-Silva describes should not have been an “uncomfortable shock” to me. From where I now stand, I can see how other readings described much of the same system, yet somehow by using more academic or less forceful language I was led to think I understood when I didn’t. Perhaps the best example of this is Beverly Daniel Tatum’s book “Why Are All the Black Kids Sitting Together in the Cafeteria?” I remember thinking as I read it, “I really like Beverly Daniel Tatum because she’s making me feel comfortable about a difficult topic.” Where I feared an interview with Bonilla-Silva, I would have welcomed the opportunity to speak with Beverly Daniel Tatum.

But somehow, disguised by my initial affection for the authors, I didn’t immediately see how in many ways Bonilla-Silva and Tatum were largely describing the same system of racism. I’m glad I read Tatum first and then Bonilla-Silva, because now as I reflect I can see how Tatum’s message didn’t really sink in for me; if it had, I wouldn’t have been so challenged by Bonilla-Silva. The lesson for me is not that I need to keep reading more critical work (although that would certainly help), but that it’s going to take more effort to make myself feel uncomfortable about issues of culture, race, class, power, etc., before somebody else gets the chance to do it for me.

For me, the simple title to this post has a double meaning. First is the more obvious, that I’m finally taking some time to think about a class I experienced over the past semester. Second, and more importantly, is the idea that multicultural education has a reflective property like a mirror bouncing light around a corner. As an educator who had a relatively monocultural upbringing in the rural Midwest, and who apparently can still be surprised by the injustices in the world around me, I need to use what I’ve learned about multicultural education to shine some light not only around corners, but back on myself. There’s so much more for me to see, most of which is hidden by its largeness, not its smallness. As an educator this is what we do: we help students explore and understand the world around them, and our reward for doing so comes both in our students’ growth and our own.

Sorting Out the Summative: When Standards-Based Grading Meets the End of the Semester

Source: Wikipedia

Many teachers who choose to use standards-based grading eventually find themselves facing the reality of their school's grading policies and tradition: the expectation of final, summative grades that are reported as percentages and letters. So regardless how hard you try to focus on quality feedback instead of grades all semester long (for good reason), there comes a time when, for reasons probably beyond your control, you have to turn levels and descriptions of student understanding into numbers. This is SBG's "Monday Morning Problem" that doesn't always get addressed in theory. But this week is finals week for my basic statistics students, so for me the time has come to convert standards-based formative grades into a summative grade, including calculating final exam grades. Here I'll try to describe the two steps I'll take to calculate my students' grades: (a) conversion of their formative scores into a summative score and (b) scoring and inclusion of the final exam into their semester grades.

Formative to Summative
Besides giving students a lot of written and verbal feedback about where they should try to improve, I've been using the simplest of measures to record their performance on class objectives: either students (a) "get it," (b) "sort of get it," or (c) "dont' get it/haven't demonstrated it." You could think of these as "green light," "yellow light," and "red light," respectively. I've tried discerning more levels of understanding in a gradebook and it only seems to lead to confusion and indecision (both for me and students), so I'm sticking to three levels, as suggested in Her & Webb (2004). If I need more detail, I can always go back to the copies of the work students have submitted and the comments I've made.

The gradebook we have for class is pretty primitive and as far as I can tell it only accepts numbers, so I mark my three levels as either a 2, a 1, or a 0. It doesn't take much explaining to students that a 1 shouldn't be viewed as "out of two" and therefore worth 50%. I do tell them, though, that in order to receive credit for the course they should average a 1 across all objectives. In other words, you can't pass the class without an average of at least some understanding of every objective.

Around here and in many other places, 70% seems to be the low end of passing grades. (We're not messing with Ds.) So if a student with all 1s should get at least a 70%, and a student with all 2s maxes out at 100, and we choose a linear function between the two, the "conversion formula" to percentages is simply:

percentage = 30 * objective score average + 40

If you feel a little dirty at this point because you know you just reduced all the various skills, knowledge, and abilities of your students into a single number, I say join the club. If you didn't feel that way I wouldn't have expected you to be using standards-based grading to begin with.

A "No Surprises" Approach to Final Exam Grades
Designing a final exam is often tricky business. It can't possibly assess everything in the course, but we generally want it to include the major topics and themes for the class and be possible to complete in the time allowed. We also have to think about difficulty. Trust me, your students are!

Teachers want their finals to be challenging, but they don't want to have that sinking feeling as they grade the exams that maybe the test was too hard. For whatever reason, sometimes students perform poorly and averaging the final exam grade into their other grades will look like a disaster. But ask yourself: What am I more confident in, my careful judgments of students' ability as demonstrated over an entire semester, or a fleeting, one-time judgement of students' ability on a single assessment during the most stressful time of the year? If you're using standards-based grading, I already know how you'll answer that question. If not, consider this example: I have a student who I know can do stats. She's turned in good work. She's asked quality questions. We've had good discussions. But I also know she has seven final exams this week. I still think she'll do fine, but I'll understand if she's not at her best. And I need a grading system that reflects that understanding.

In order to free myself to still give challenging, yet reasonable, assessments, without risking any huge surprises when grades are calculated, I perform a little statistical magic that ensures that the distribution of final grades has the same center and spread of class grades before the final. I'm sure many of you try "curving" your exam scores some other way, such as letting the top score count as the total possible, or even having a pre-set distribution in mind of how many As, Bs, Cs, etc. you'll allow (which is not a good idea, generally, for reasons described by Krumboltz & Yeh, 1996). I prefer my method because it accounts for the distribution of grades, not just the top score, and the distribution is determined by the students, not arbitrarily by me. Allow me to demonstrate with a couple examples.

Suppose before the final the average percentage grade is 85 and the standard deviation of those grades is 10. Then I grade my final exams and find that the average final exam grade is 60 with a standard deviation of 18. Ouch. But don't worry -- statistics will come to our rescue.

Provided you know a little basic descriptive statistics, the conversion is simple. For each student's final exam score, find out how many standard deviations above or below the mean they scored on the final (their final exam z-score), and match that with the same number of standard deviations above or below the mean they'd fall on the pre-final grade distribution (their pre-final z-score). Consider the following students and the class and exam statistics above:

• Suppose Student A scores a 51 on the final exam. That's 0.5 standard deviations below the mean. (51 - 60 = -9, and -9/18 = -0.5.) So where is 0.5 standard deviations below the mean on the pre-final distribution? If that mean is 85 and the SD is 10, then 0.5 standard deviations below the mean is 80. So I record an 80 for that student instead of a 51.
• Suppose Student B scores a 75 on the final exam. That's about 0.83 standard deviations above the mean. (75 - 60 = 15, and 15/18 = 0.83.) So where is 0.83 standard deviations above the mean on the pre-final distribution? About 8.3% above an 85, so I record their exam grade as a 93.3.
• Suppose Student C scores a 60 on the final exam. That's the same as the mean, so zero standard deviations above or below. That conversion is super-easy: their final exam grade is the mean of the pre-final mean, an 85.

For an example of how to set up a spreadsheet to do this, see https://docs.google.com/spreadsheet/ccc?key=0Anne5Z-jCkqhdDVtemkyaGhnRWFfclJoa0dIUVQ5RVE. I recommend making a copy of it for yourself and seeing what happens as you change values.

This is not a perfect system (and comments about its imperfections are welcome in the comments), but it does take away the element of surprise if the final exam happens to be way too easy or too difficult, or if other circumstances prevent grades from working out the way you'd expect. Yes, this is a norm-referenced system instead of a criterion-referenced system, meaning that the grades students earn on the final is measured largely as how they compare to their classmates and the class average. The good news is this: both the teacher and the students have an incentive before the final to master as many objectives as possible, and that is criterion-referenced. A high pre-final average helps everyone get a high final exam average, and a small pre-final standard deviation minimizes variability in final exam scores.

References

Her, T., & Webb, D. C. (2004). Retracing a path to assessing for understanding. In T. A. Romberg (Ed.), Standards-based mathematics assessment in middle school: Rethinking classroom practice (pp. 200-220). New York, NY: Teachers College Press.

Krumboltz, J. D., & Yeh, C. J. (1996). Competitive grading sabotages good teaching. Phi Delta Kappan, 78(4), 324-326. Retrieved from http://www.jstor.org/stable/20405782

Designing a School

During my first fall of teaching in 2003, the school district I worked for passed a bond issue to build a new high school. The following spring the architects and facility committee (which I would later join) asked for staff input. So I ask you: What would your ideal school look like? What features would you prioritize? How would you maximize utility within a budget?

I was reminded of this activity by a recent post by Zac Chase. In that post, he discusses a class activity where he and other students plan the layout of a school in order to think about the environments that best support teaching and learning. In 2004, when I was faced with a similar task, I set to work sketching on paper. When sketching wasn't good enough, I went with graph paper and scale drawings. When graph paper wasn't good enough, I downloaded a free CAD program, taught myself how to use it, and set out to design an entire school. I was a bit obsessed. I had the following goals and guidelines to consider:

1. The design needed to accommodate 750 students in classrooms and have "common spaces" (gym, locker room, cafeteria, library, etc.) to handle an expansion up to 1500 students.
2. The school budget allowed for approximately 115,000 square feet.
3. Hallways are an expensive use of little-used space. I wanted to minimize them.
4. Departments would have common computer lab space and office space for teachers.

After a lot of editing and calculating, this is what I came up with on the first floor (open link in new tab and zoom for maximum detail):

First floor

And here was the plan for the second floor:

Second floor

I was (and still am) pretty proud of this creation. In fact, I still believe this school offers a better use of space than the school that was eventually built. However, with 7+ years of hindsight, I think this plan could have used the following improvements:

1. Instead of shared "computer lab" space for each department, students would take their technology with them to the classroom.
2. In place of the computer spaces, I'd provide more space for student group collaboration. I was thinking about the office for teacher collaboration space, but at the time I didn't think enough about student collaboration space.
3. I didn't think too much about the cafeteria, and it shows. Dining areas should be more inviting than the rows-of-tables design I designed.

One other lesson I learned after serving on two facility committees is this: Don't just ask teachers what they want in their classroom and school. Ask teachers what they imagine a teacher twenty years from now will want. Otherwise, it's too easy to give teachers the impression that the school is being custom-built for them, something that's not likely to happen. It might not even be desirable. Instead, ask them questions that reflect the school's long-term value to the community.

Those are important, but otherwise I think my floorplans still have something to offer. I don't know why I hadn't shared them until now, but maybe they'll be of some use to somebody looking for school building ideas. Just promise me that if you build this thing, invite me to come see it!