School of Education, Room 320-B

University of Colorado Boulder

249 UCB

Boulder, CO 80309

**David Webb** is Associate Professor of Mathematics Education and the Executive Director of Freudenthal Institute USA, an international research collaborative for mathematics education. Dr. Webb's research interests are in the areas of the preparation of mathematics teachers, classroom assessment, and the design of professional development activities. Recent research projects have focused on studies of teacher change in classroom assessment, the impact of reform curricula on student learning and achievement, and teacher design and use of formative assessment tools. Dr. Webb taught mathematics and computer applications courses at both the middle school and high school levels in Southern California. He currently teaches methods courses for prospective middle and high school mathematics teachers, and graduate level seminars that focus on the nature of mathematics and mathematics education.

Dr. Webb is a member of the American Educational Research Association, the National Council of Teachers of Mathematics, the National Council for Supervisors of Mathematics, and the National Society for the Study of Education.

### Education

PhD Curriculum and Instruction (Mathematics Education), University of Wisconsin, 2001

MA Education, University of California, Santa Barbara, 1994

BS Applied Mathematics, UCLA, 1988

My research interests have focused on the study of teachers’ classroom assessment practices, to better understand and model the relationship between teachers’ instructional goals, curricular decisions, and interpretation of student verbal and written work. I have focused on teachers’ instructionally embedded assessment practices: how teachers elicit, regard, and act upon students’ verbal and written responses during instruction. Unresolved questions that emerged during my experience as a mathematics teacher motivated this line of inquiry at a time when teaching and learning of mathematics was being redefined in terms of mathematical processes such as communication, problem solving and students’ representations.

I have complemented my research with extensive experience in curriculum and assessment development during my work at UC Santa Barbara in the “Preparing Latino Students for Algebra” project, as co-author of *Balanced Unit Assessments* for middle grades, as site coordinator for the “Classroom Assessment as a Basis for Teacher Change” project, and as co-PI of the “Revision of the Mathematics in Context Materials” project. Unique to the three latter projects was the theory-driven approach to material development I engaged in through ongoing collaboration with education researchers from the Freudenthal Institute, at the University of Utrecht, the Netherlands. The theory of Realistic Mathematics Education (RME) and the approach to classroom-based developmental research espoused by Hans Freudenthal and other Dutch educators was used to inform the design and identification of problem contexts that offered greater “mathematical lift” and access to students’ mathematical representations.

Given the limited assessment materials available to support teachers’ formative assessment practices, I have found the simultaneous work in material development and research of teachers’ classroom practices to be mutually informative. Teacher use of curriculum and assessment materials often reveals fruitful learning lines (or developmental trajectories) essential for formative assessment. This research program is theory-driven and classroom-based. It can inform research in teaching and learning. And it can be applied in a manner relevant to the needs of teachers. My future research objectives involve further development of domain-specific design principles for formative assessment that can be used to advance teachers’ ability to elicit and make sense of students’ informal and pre-formal representations of mathematics, teacher knowledge of mathematics, and principled use of problem solving contexts. This line of research would be particularly relevant for addressing the instructional needs of students who typically struggle with formal, procedure-driven mathematics but who can often appropriate less formal procedures when they are anchored in meaningful contexts.

My teaching interests are in the areas of curriculum, instruction and assessment in mathematics education, and the intersection between state and national education policies and mathematics reform. I teach courses designed to prepare mathematics teachers for secondary school classrooms. As a former middle and high school mathematics teacher in Southern California in the early 1990s, I had the opportunity to experience first-hand the challenge of interpreting and applying national and state policies designed reform mathematics education. In the courses I teach, therefore, I seek to create opportunities in which teachers and graduate students can critically examine their beliefs about mathematics as a discipline as well as related conceptions regarding the teaching and learning of mathematics. The courses I typically teach include the following:

### Courses frequently taught

**EDUC 5375: Materials and Methods in Secondary Mathematics **

This course is designed for students who are planning to obtain teacher licensure to teach mathematics at the middle and/or secondary school level in Colorado and practicing mathematics teachers pursuing a graduate degree at CU-Boulder who are interested in contemporary methods for teaching mathematics. The purpose of this course is to promote the skills, habits, and knowledge of effective teaching, learning, and assessment. This will be accomplished through examination of readings, instructional materials, and instruction. In this course, we will revisit and explore the mathematics of middle and high school curricula and examine the mathematics in these materials from a pedagogical point of view. Students will utilize the methods and strategies under investigation by applying them in actual classroom settings, through current classroom assignments (practicum or current professional experiences).

**EDUC 6804: Nature of Mathematics and Mathematics Education**

This graduate course explores mathematics from both philosophical and practical points of view. Using a survey of philosophical perspectives about mathematics as a backdrop (What is mathematics? Is it a human creation, or universal truth? Is it fallible?), the second part of the course turns toward contemporary issues in debates about mathematics teaching and learning and addresses topics such as: school mathematics and reform-based initiatives, proposals and methods for improving equity and student access to mathematics, and the design of mathematics curriculum and assessment in grades K to 12. The structure of this class should offer practicing teachers and graduate students an opportunity to examine and deepen their content knowledge and reflect on how they communicate mathematics to students through their classroom practices. Therefore, one of the underlying goals of the course is to motivate reflection on current classroom practices and support further exploration of ways educators might apply new knowledge to ensure, enrich, and extend future students’ learning and experience of mathematics.

*Reviewer for Journal for Research in Mathematics Education, American Education Research Journal, Journal for Teacher Education*, and many professional conferences- Co-chair, Division C, Section 2 (Learning and Instruction, Mathematics), AERA Annual Convention, 1998
- Mathematics Content Review Panel for “Studies of Enacted Curriculum” project, Cyberchase television series, and the Annenburg professional development video series for algebra
- U.S. Item Selection, OECD Programme for International Student Assessment
- Chair of the Realistic Mathematics Education Conferences in Madison, WI (November 14-15, 2005) and Boulder, CO (November 16, 2005)

(For complete list of publications, please see the faculty member's curriculum vitae.)

### Selected Articles

Webb, D. C., Romberg, T. A., Burrill, J., & Ford, M. J. (2005). Teacher Collaboration: Focusing on Problems of Practice. In T. A. Romberg & T. P. Carpenter (Eds.),*Understanding Math and Science Matters* (pp. 231-251). Mahwah. NJ: Lawrence Erlbaum Associates.

Webb, D. C. (2004). Enriching Assessment Opportunities Through Classroom Discourse. In T. A. Romberg (Ed.), *Standards-Based Mathematics Assessment in Middle School: Rethinking Classroom Practice* (pp. 169-187). New York: Teachers College Press.

Webb, D. C., Romberg, T. A., Dekker, T., de Lange, J., &Abels, M. (2004). Classroom Assessment as a Basis for Teacher Change. In T. A. Romberg (Ed.),*Standards-Based Mathematics Assessment in Middle School: Rethinking Classroom Practice* (pp. 223-235). New York: Teachers College Press.

Brenner, M.E., Mayer, R. E., Moseley, B., Duran, R., Brar, T., Smith, B. R., & Webb, D. (1997). The Role of Multiple Representations in Learning Algebra. American Educational Research Journal,

34(4), 663-689.

### Book Chapters

Webb, D. C., Romberg, T. A., Ford, M. J., & Burrill, J. (2005). Teacher collaboration: Focusing on problems of practice. In T. A. Romberg & T. P. Carpenter (Eds.),*Understanding mathematics and science matters *(pp. 231-251). Mahwah, NJ: Lawrence Erlbaum Associates.

Webb, D. C. (2004). Enriching Assessment Opportunities Through Classroom Discourse. In T. A. Romberg (Ed.), *Standards-Based Mathematics Assessment in Middle School: Rethinking Classroom Practice* (pp. 169-187). New York: Teachers College Press.

Webb, D. C., Romberg, T. A., Dekker, T., de Lange, J., & Abels, M. (2004). Classroom Assessment as a Basis for Teacher Change. In T. A. Romberg (Ed.),*Standards-Based Mathematics Assessment in Middle School: Rethinking Classroom Practice* (pp. 223-235). New York: Teachers College Press.

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: Teachers College Press.