COMET • Vol. 6, No. 21 – 7 September 2005


(1) Free Event at UC Berkeley–A Conversation with the Mathematical Writers of The Simpsons and Futurama

Source: Mathematical Sciences Research Institute (MSRI)

MSRI invites the public to attend a free, hour-long event at 2:00 PM on Sunday, October 16, 2005, with moderator Sarah J. Greenwald and writers from The Simpsons and Futurama: David X. Cohen, Ken Keeler, and Jeff Westbrook. All of these writers have backgrounds and advanced degrees in either mathematics or computer science. The conversation will take place in the Chan Shun Auditorium (Rm. 2050) of the Valley Life Sciences Building at UC Berkeley.

For more information about mathematics in episodes of The Simpsons and Futurama, as well as the mathematics backgrounds of many of the writers of these shows, visit

(2) Mathematics Subject Matter Committee Telephone Conference

Source: Tracie Yee, Curriculum Frameworks and Instructional Resources Division, California Department of Education

The Mathematics Subject Matter Committee of the Curriculum Commission will hold a teleconference on Wednesday, September 14, from 3:30-5:00 p.m. (see above Web site for information regarding locations). The purpose of the conference call is to discuss the agenda for the publishers’ briefing to be held on Friday, September 30, 1:00-3:00 p.m., following the Curriculum Commission meeting. All publishers interested in submitting mathematics materials for consideration in the 2007 primary adoption are encouraged to attend the September 30 meeting.

A schedule for curriculum framework development and the adoption of K-8 instructional materials is available for download from

(3) Follow-up Report:  MSRI Workshop–Mathematical Knowledge for Teaching (K-8): Why, What and How?

Source: Mathematical Sciences Research Institute (MSRI)

On 25-28 May 2005, MSRI held the second conference in its series, “Critical Issues in Mathematics Education,” on the Asilomar Conference Grounds.

One of the major goals of the workshop was to foster productive partnerships among research mathematicians, mathematics educators, educational researchers, teachers of school mathematics, and policymakers that will support them in their efforts.

To access dozens of high quality streaming videos of workshop sessions, visit   Available streaming videos (topics, speakers) include the following (see above Web site for a complete listing and links to the videos):

Must Knowing How to Teach Be Limited by Teaching What One Knows? (Lee Shulman, Richard Schaar)

Teacher’s Knowledge of Mathematics (Deborah Ball)

What Evidence Exists About the Relationship Between Teachers’ Knowledge of Mathematics and Student Achievement? (Jim Hiebert, David Monk, Heather Hill, Dan Fallon)

What Mathematical Knowledge, Skills, and Habits Do Teachers Need in Order to Teach Effectively? (Deborah Ball, Roger Howe, Liping Ma, Randy Philipp, Hyman Bass, Pam Grossman, Zal Usiskin, Robert Moses, Jill Adler, Lena Khisty, Marta Civil, William Velez, Ruth Cossey, Carlos Cabana)

What Can Mathematics Departments and Schools of Education Do to Help Teachers Develop Such Knowledge? (Jim Lewis, Sybilla Beckmann, James Milgram, Ira Papick)

What are the Critical Next Steps with Respect to Policy? What are Directions for Research? Come Back to Evidence (Jim Lewis, Diane Spresser, Dan Fallon, Linda Curtis-Bey, Tom Fortmann, Cathy Seeley, Deborah Ball, Ruth Cossey, Jeremy Kilpatrick, David Eisenbud)


(1) Examining Effective Mathematics Instruction

Source: American Educator – Fall 2005

[Overview from the “PEN Weekly NewsBlast” for September 2, 2005] The cornerstone of effective mathematics instruction is, not surprisingly, teachers’ knowledge of math. If you are going to teach multiplication, for example, you need to know how to multiply correctly. But is that all you need to know? Must you also be able to identify students’ errors and analyze the merits of the algorithms they invent? The Fall 2005 issue of American Educator tackles these issues with articles by mathematicians and researchers that explore what it means to teach mathematics effectively…

[From “Helping Children Learn Mathematics” by the Editor of American Educator]

…Thanks to the work of Harold Stevenson, James Stigler, and others, we know that the culture of schooling is an important factor in how mathematics is taught and learned. The data on some 50 countries, collected and analyzed as a part of the Third International Mathematics and Science Study, reveal the central importance of a mathematics curriculum that is focused, logical, and coherent–characteristics that are sorely lacking in U.S. curricula. And, perhaps most important, we know that teachers’ knowledge of the mathematical content to be taught is absolutely crucial.

But what else do mathematics teachers need to know? To teach multiplication to third-graders, for example, is it enough to know how to multiply reliably oneself, or does the teacher also need to know how to quickly diagnose and correct students’ mistakes? What about knowing how to react if a student gets the right answer by making up a new algorithm? Broadly speaking, is there a deeper knowledge of elementary mathematics that is needed “just” to teach multiplication to third-graders?

Fortunately, Deborah Loewenberg Ball and her colleagues have been asking questions like these for over a decade. They don’t yet have definitive answers–but they do have an exciting program of research that has already tied teachers’ mathematical content knowledge to student achievement and, in the years to come, promises to identify…what knowledge successful mathematics teachers need to have. Deborah Ball, Heather Hill, and Hyman Bass explain their work and findings to date in this issue.

While Ball and her colleagues have been working on large-scale assessments of teachers’ mathematical knowledge and its connection to student achievement, Ron Aharoni has been in the classroom discovering, through many less-than-perfect lessons and the occasional home run, what elementary mathematics teachers need to know. A professional mathematician, Aharoni accepted the challenge of working in elementary math classrooms several years ago. This special section on teaching mathematics opens with his personal reflections and insights:

(a) “What I Learned in Elementary School” by Ron Ahaoni

(b) “The Role of Curriculum” by William H. Schmidt

(c) “Knowing Mathematics for Teaching: Who Knows Mathematics Well Enough to Teach Third Grade, and How Can We Decide?” by Deborah Loewenberg Ball, Heather C. Hill, and Hyman Bass

(d) Mathematical Knowledge for Teaching: A Research Review” (excerpt from Adding It Up, published by the National Research Council)

(e) “Mathematics for Teaching, Then and Now” (problems from the State of California’s teacher certification exam given in December 1874)

(2) Finding Common Ground in K-12 Mathematics Education

Source: Mathematical Association of America

The MAA hopes to help encourage and facilitate constructive discourse between mathematicians and mathematics educators in order to seek common ground in their mutual efforts to improve K-12 mathematics teaching and learning. The success of two pilot meetings (one at NSF in December 2004 and a second at the MAA offices in June 2005) with two mathematicians (R. James Milgram and Wilfried Schmid), three mathematics educators (Deborah Loewenberg Ball, Joan Ferrini-Mundy and Jeremy Kilpatrick) and a moderator from the business community (Richard Schaar) demonstrated that such common ground does exist among individuals who are thought to be strongly aligned with different sides in what has come to be known as the “Math Wars.”

These meetings resulted in a document designed to serve as a starting point for future conversations. Agreeing that “All students must have a solid grounding in mathematics to function effectively in today’s world,” the group started with three fundamental premises:

1. Basic skills with numbers continue to be vitally important for a variety of everyday uses.

2. Mathematics requires careful reasoning about precisely defined objects and concepts.

3. Students must be able to formulate and solve problems.

From there, the group explored a number of topics, including the importance of automatic recall of basic facts, the use of calculators in lower grades, instructional methods and teacher knowledge, and found significant points of agreement. The full text of the report is available as an HTML file at and as a PDF file at

Other groups have met with similar intentions of focusing serious effort on what is essential in the K-12 mathematics curriculum and how best to achieve some level of consensus between various constituencies. We expect further articles and reports will become available that help the mathematical community participate more effectively in guiding our schools towards providing students with the skills they need to succeed, both in higher education and the workplace.

This site ( will serve as a repository for documents resulting from this and related efforts.


“Reaching for Common Ground in K-12 Mathematics Education” by

Deborah Loewenberg Ball, Joan Ferrini-Mundy, Jeremy Kilpatrick, R. James Milgram, Wilfried Schmid, and Richard Schaar

[Excerpt] Over the past decade, much debate has arisen between mathematicians and mathematics educators. These debates have significantly distracted the attention of key players at all levels, and have impeded efforts to improve mathematics learning in this country. This document represents an attempt to identify a preliminary list of positions on which many may be able to agree.

Our effort arose out of discussions between Richard Schaar and major players in both communities. He suspected that some of these disagreements might be more matters of language and lack of communication than representative of fundamental differences of view. To test this idea, he convened a small group of mathematicians and mathematics educators.

We tried to bring clarity to key perspectives on K-12 mathematics education. We began by exploring typical “flashpoint” topics and probed our own positions on each of these to determine whether and where we agreed or disagreed. For the first meeting, held in December 2004, we began with summary statements drawn from prior exchanges among the members of our group. We affirmed some agreements in this meeting, and “discovered” others. We listened closely to one another, frequently asking for clarification, or for examples. We tested our understanding of others’ points of view by proposing statements that we then examined collectively. We drafted this document as a group, composing actual text as we worked. One of us typed, and our emerging draft was projected onto a screen in the meeting room. The process enabled us to take issue with particular words and terms, and then reshape them until all of us were satisfied. We were forced to look closely at our own language and to seek common ground, not only in the terms we used, but even in their nuanced meaning.

This document was completed at our second meeting, in June 2005. All of us are encouraged by the extent of our agreements. The document treats only a subset of the controversial issues, many of which arise in K-8 mathematics. We expect to continue the process by examining a wider range of major issues in mathematics education. We have necessarily limited ourselves to questions depending primarily on disciplinary judgment, as opposed to those requiring empirical evidence.

We begin with three fundamental assertions and continue with a list of areas in which we found common ground. For each, we have written a short paragraph that captures the fundamental points of our agreement. Our next step is to explore how others respond to the document, and to use their responses to decide how best to make progress on the aims of this project. Our goal is to forge new alliances, across communities, necessary to develop effective solutions to the serious problems that plague mathematics education in this country…

(3) “Classroom Gestures Studied for Effects on Learning: Hand Motions Seen as Teaching Tools and Clues to Comprehension” by Debra Viadero

Source: Education Week – 7 September 2005

“When students are learning, they gesture extensively, and their gestures reveal things they understand or are trying to grapple with,” said Martha W. Alibali, a professor of psychology and educational psychology at the University of Wisconsin-Madison.

Dr. Alibali is among a small but growing cadre of researchers who are taking a close look at the gestures people make and the role that they play in the classroom. When the pupil cups her hand, or the teacher points to the blackboard, thoughts and ideas are being communicated, often unconsciously, those experts contend, and those silent movements can enhance or hinder learning.

The new research follows decades of studies in linguistics, anthropology, psychology, and other fields examining how gestures function in other contexts, such as everyday conversations. In the late 1980s and the 1990s, a few scholars began to zero in on gestures that occur in the learning process.

Such studies have shown, for instance, that teachers gesture all the time in different ways, and that sometimes those gestures convey erroneous information…

Wolff-Michael Roth, a professor of applied cognitive science at the University of Victoria in British Columbia, [said] “But what sticks in our minds, often better than words, are images. If teachers use gestures that are inappropriate, then they put ideas into kids’ minds that they don’t really want there”…

Investigators found that students learned more, in the sense that they scored higher on a test of symmetry than they had before, from videotapes incorporating both speech and gesture…

Alibali and [psychologist] Susan Goldin-Meadow contend that “mismatches” between students’ verbal responses and their gestures signal that they are “ready to learn” a concept.

Their studies have shown that children who make such mismatched gestures, with a little more instruction, more easily master the concepts being taught than students who don’t gesture at all when they give a wrong answer, or those whose gestures and verbal responses are both incorrect…

As students master a concept, researchers say, they replace their gestures with appropriate language.

Teachers who pick up on these subtle cues can tailor their instruction accordingly, say Goldin-Meadow and Alibali. Similarly, some experts also believe that teachers who are conscious of their own gestures and those motions’ effect on students could use them more deliberately to promote learning.

To a degree, some teachers may already do that, consciously or unconsciously.  Alibali, for instance, videotaped a 6th grade math teacher introducing her students to algebra concepts. Watching the tapes later, the researchers noticed that the teacher gestured more frequently when discussing more abstract ideas or when students asked questions…

Experts agree that the studies are opening a new window on learning. “We’ve had this almost exclusive look in education at language,” said Roth, the Canadian researcher. “I think that’s been to the detriment of some of these other ways we’ve learned to communicate.”