Math

Working with Teachers and Leveraging Technology to Scale Opportunities to Learn More Complex and Conceptually Difficult Middle School Mathematics

Principal Investigator:

Co-Investigator:

Project Overview

Background & Purpose:

Ambitious combinations of technology and curriculum can be difficult for teachers to implement, an important challenge to overcome in bringing proven technology-based innovations to larger numbers of schools, classrooms, and students. This project is investigating the impacts of a mature innovation that integrates technology, curriculum, and teacher professional development when used in the geographically and demographically diverse classrooms of a sample of 7^th and 8^th grade teachers in Texas.

Using a randomized experimental design complemented by case studies, the project addresses the question: "Can a wide variety of teachers use innovative technology and curriculum so that their students learn complex and conceptually difficult mathematics?" Investigators are studying the impacts of two interventions (one for 7^th grade teachers and their students, another for 8^th grade teachers and their students); why these interventions may have had the impacts they have; exploring the generalizability of the findings; identifying new insights and questions to inform new research and development; and generating findings that will help to establish future research and development agendas.

Setting:

This study takes place in the geographically and demographically state of Texas. The Texas Education Authority divides the state into 20 regions. Teachers participating in this study work in schools spread across seven of these regions: Region 1/ Edinburg, Region 6/ Corpus Christi, Region 9/ Wichita Falls, Region 10/ Dallas, Region 11/ Ft. Worth, Region 13/ Austin, Region 17/ Lubbock and Region 18/ Midland. These regions represent areas that are urban, rural, and suburban, and student populations diverse with respect to ethnicity and socioeconomic status.

Research Design:

This project combines a number of studies and sub-studies, employing multiple methodologies. The core design entailed two randomized experiments, one focusing on 7^th grade teachers and their students, and one focusing on 8^th grade teachers and their students. Embedded within these studies were a quasi-experiment, several in-depth case studies, and a study of innovation spread.. Members of the project have used a variety of quantitative methods (e.g., hierarchical linear modeling) and qualitative methods (e.g., thematic analysis) to analyze project data.Multiple sources of original data were collected and multiple instruments were developed, including assessments of students’ knowledge of key mathematical concepts (i.e., rate and proportionality, linear function); assessments of teacher mathematical knowledge for teaching; a questionnaire about teacher background, attitudes, and beliefs; a teacher log about their class and unit implementation; an interview protocol about teachers’ experiences in the program; a survey about continued use and spread of use to other colleagues; classroom observation protocols for case studies; and a clinical interview protocol for case studies.

Two interventions were evaluated, one for the 7^th grade experiment, and one for 8^th grade experiment. Both interventions have three integrated components: (1) SimCalc Mathworlds software; (2) a three-week replacement unit for key middle school math content; and (3) teacher professional development. The content of the 7^th grade intervention is rate & proportionality; the content of the 8^th grade intervention is linear function. In the comparison condition for the 7^th grade experiment, teacher professional development focused on rate & proportionality, and teachers used their regular textbooks/ classroom materials for teaching rate & proportionality. In the comparison condition for the 8^th grade experiment, teacher professional development focused on statistics, and teachers taught with their regular textbooks/ classroom materials for teaching linear function.

Findings:

Briefly, across two large-scale experiments, the investigators have replicated a strong main effect demonstrating that SimCalc is effective in enabling a wide variety of teachers in a diversity of settings to extend students’ learning to more advanced mathematics. The main effects were statistically significant and showed that students in the treatment group learned more than students in the control group. In the 7^th and 8^th grade experiments, hierarchical linear modeling revealed main effects with effect sizes of 0.84 and 0.79 respectively. These student learning effects, particularly on the advanced portions of the tests, were robust across demographic group, despite marked group differences at pretest. Results of this project are currently available and applicable to education researchers, education policymakers, school administrators, school teachers, university and college instructors, teacher-educators or professional development providers, and assessment experts/organizations.

Publications & Presentations:

Beaton, D., & Hegedus, S. (2006). Constructing an architecture for an interactive educational research database: Issues of design and implementation. In N-S. Chen & P. Isaías (Eds.), Proceedings of the Multi 2006: IADIS Virtual Multi Conference on Computer Science and Information Systems (pp. 121-128). Lisbon, Portugal: IADIS Press.

Chao, T. P., Empson, S. B., & Shechtman, N. (2007, July). Using principal components analysis to model student understanding of multiple representations of rate and proportionality with SimCalc MathWorlds. Paper presented at the Thirteenth International Conference on the Teaching of Mathematical Modeling and Applications, Bloomington, IN.

Dickey-Kurdziolek, M. (2007). Teacher choice and effects of classroom resource utilization in a technological intervention on rate and change. Presentation at the GROUP Doctoral Colloquium, November 3-8, Sanibel, FL.

Dickey-Kurdziolek, M. (2008). Teacher decisions and student access to resources. Presentation at the ICLS Doctoral Consortium, June 23-24, Utrecht, Netherlands.

Dickey-Kurdziolek, & M., McLeese, M. (2008). Scaling Up SimCalc: Qualitative Inquiry. Presentation at the CHCI@VT Seminar Series, February 29, Blacksburg, VA.

Dunn, M., Roschelle, J., Knudsen, J., Hegedus, S., Schorr, R., & Hemphill, S. (2007, March). Scaling up a technology-rich innovation using a mutli-tiered trainers model. Presentation at the Research Presession of the National Council of Supervisors of Mathematics, Atlanta, GA.

Dunn, M., Schorr, R., Hegedus, S., & Roschelle, J. (2007, October). Investigating the scale-up of a technology-rich innovation. Paper presented at the 29th Annual Conference of the North American Chapter of the International Group for the Psychology of Mathematics Education, Lake Tahoe, NV.

Empson, S. B., Greenstein, S., Maldonado, L., & Chao, T. (2008, March). A discourse-analytic perspective on relationships between students’ opportunities to engage with mathematics and achievement gains.Paper presented at the annual meeting of AERA as part of the symposium, Enhancing Mathematics Learning with Technology: Civic, Teacher, Student, and Content Perspectives on Scaling Up SimCalc, New York, NY.

Empson, S. B., & Knudsen, J. (2006). What can we understand about achievement gaps in mathematics by studying classroom processes? In S. Alatorre, J. L. Cortina, M. Sáiz, & A. Méndez (Eds.), Proceedings of the 28th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, (Vol. 2, pp. 196-8). Mérida, Mexico: Universidad Pedagógica Nacional.

Estrella, G. (2007, June). Algebra comes alive through SimCalc. Presentation at Conference for the Advancement of Mathematics Teaching, San Antonio, TX.

Hegedus, S. (2005, September). Dynamic representations: A new perspective on instrumental genesis. Proceedings of the Fourth Congress of the European Society for Research in Mathematics Education (pp. 1031-1039). Saint Feliu de Guixols, Spain: Authors.

Hegedus, S. (2006). Jim Kaput–1942-2005: A mentor, a colleague, a friend. For the Learning of Mathematics, 26(1), 31-33.

Hegedus, S. (2007). Classroom connectivity. Educational Technology, XLVII(3), 21-25. (Special Issue on Mobile Computing).

Hegedus, S., & Dalton, S. (2006, April). Engaging students’ minds by bringing trigonometry to life! Presentation at the Annual Meeting of the National Council for Teachers of Mathematics, St. Louis, MO.

Hegedus, S., & Dalton, S. (2007, April). Faster and faster: Introducing quadratic functions via linearly varying speed. Workshop presented at the Association of Teachers of Mathematics in Massachusetts 2007 Spring Conference, Marlborough, MA.

Hegedus, S., Dalton, S., & Davis, G. (2006, July). Modeling teachers’ questions in high school mathematics classes. Poster session presented at the 30th Annual Meeting of the International Group for the Psychology of Mathematics Education, Prague, Czech Republic.

Hegedus, S., Kaput, J., & Lesh, R. (2007). Technology becoming infrastructural in mathematics education. In R. Lesh, E. Hamilton, & J. Kaput (Eds.), Foundations for the future in mathematics and science (pp. 173-192). Mahwah, NJ: Lawrence Erlbaum.

Hegedus, S. & Lesh, R. (Eds.) (2008). Democratizing access to mathematics through technology: Issues of design and implementation (Special Issue). Educational Studies in Mathematics, 68(2), 81-93.

Hegedus, S., & Moreno-Armella, L. (in press). Analyzing the impact of dynamic representations and classroom connectivity on participation, speech and learning. To appear in L. Radford, G. Schubring, & F. Seeger (Eds.), Semiotics education: Epistemology, historicity and culture. Rotterdam, the Netherlands: Sense Publishers.

Hegedus, S., Moreno-Armella, L., & Dalton, S. (2007, February). Technology that mediates and participation in mathematical cognition. Paper presented of the 5th Congress of the European Society for Research in Mathematics Education Conference, Larnaca, Cyprus.

Hegedus, S., Moreno-Armella, L., & Roschelle, J. (2008). Mathematical foundations in middle school. For Journal of Research and Mathematics Education. Manuscript submitted for publication.

Hegedus, S., & Penuel, W. (2008). Studying new forms of participation and classroom identity in mathematics classrooms with integrated communication and representational infrastructures. Educational Studies in Mathematics: Democratizing Access to Mathematics through Technology—Issues of design and Implementation, 68(2), 171-184.

Hegedus, S., Penuel, W., & Blanton, M. (2007, March). Exploring frameworks for capturing students mathematical identities in diverse classroom settings. Presentation at the annual meeting of AERA. New York, NY.

Hegedus, S., Roschelle, J., Lesh, R., Brady, C., & Pea R. (2006, June-July). Representational and connectivity infrastructure: Making a difference with attention to content, technology, and scale. A session honoring the memory of Jim Kaput. Invited symposium at the International Conference for the Learning Sciences, Indiana University, Bloomington, IN.

Hopkins, Bill (2007, September). Results from Scaling Up SimCalc at the Texas Association of Supervisors of Mathematics fall meeting. Presentation at the business meeting of members, Austin, TX.

Kaput, J., Hegedus, S., & Lesh, R. (2007). Technology becoming infrastructural in mathematics education. In R. Lesh, E. Hamilton, & J. Kaput (Eds.), Foundations for the future in mathematics and science (pp. 172-192). Mahwah, NJ: Lawrence Erlbaum Associates.

Knudsen, J., & McNemar, B. (2007, March). Algebra comes alive through technology and simulations: SimCalc replacement units for 7th and 8th grade. Presentation at the annual meeting of the National Council of Supervisors of Mathematics, Atlanta, GA.

Means, B., & Roschelle, J. (2007, May). Rigorous research on the effects of learning technology: Are we learning anything? Presentation at the Future of Learning Series, Stanford Center for Innovations in Learning, Stanford, CA.

Moreno-Armella, L., & Hegedus, S., & Kaput J.(2008). Constitution of symbols and the evolution of the reference field with digital technologies. Special Issue of Educational Studies in Mathematics: Democratizing Access to Mathematics through Technology—Issues of Design and Implementation, 68(2), 99-112.

Pierson, J. (2006). The relationship between teacher follow-up moves and mathematics learning. Unpublished proposal for doctoral dissertation, University of Texas at Austin.

Pierson, J. (2007, April). “She’s the smart one and I’m the dumb one”: How identity, positioning, and power impact the co-construction of mathematical meaning. Paper presented at the annual meeting of AERA, Chicago, IL.

Pierson, J. (2007, October). The impact of moment-to-moment discourse moves on opportunities to learn mathematics. Paper presented at the 29th Annual Conference of the North American Chapter of the International Group for the Psychology of Mathematics Education, Lake Tahoe, NV.

Pierson, J. (2008, March). Identifying differences in patterns of classroom discourse and their relationship to mathematics achievement scores. Paper presented at the annual meeting of AERA, New York, NY.

Roschelle, J. (2005, July). Democratizing access to the mathematics of change. Presentation at the Tablet PCs in Higher Education Conference, Seattle, WA.

Roschelle, J. (2005, August). Implementation fidelity: A tale of two projects. Presentation at the IERI PI Meeting, Washington, DC.

Roschelle, J. (2005, December). Scaling up innovative technology-based mathematics to a wide variety of teachers. Presentation at the International Conference of Computers in Education, Singapore.

Roschelle, J. (2006, April). Getting to scale with innovations that deeply restructure how students come to know mathematics. Presentation at the annual meeting of AERA, San Francisco, CA.

Roschelle, J. (2006, April). Jim Kaput’s legacy and impact on mathematics education, learning technology and educational reform. Presentation at the annual meeting of AERA, San Francisco, CA.

Roschelle, J. (2006, May). Children’s use of media in school: Enabling access to advanced mathematics. Invited presentation at the National Institute of Child Health and Human Development workshop on Effects of Electronic Media on Children, Washington, DC.

Roschelle, J. (2007, January). Can technology-based representations deepen math learning in a wide variety of classrooms? Presentation at the Center for Learning in Informal and Formal Environments, University of Washington, the American Association of Physics Teachers Annual Meeting, and the Bill & Melinda Gates Foundation, Seattle, WA.

Roschelle, J. (2007, March). Can Technology-Based Representations Deepen Math Learning and Close the Gap? Research Findings from a Large Scientific Study Keynote presentation at the NCTM Annual Meeting and Exposition, Atlanta, GA.

Roschelle, J. (2007, March). Can technology-based representations deepen math learning and close the gap? Research findings from a large scientific study. Presentation at the featured speaker session of the annual meeting of the National Council of Teachers of Mathematics, Atlanta, GA.

Roschelle, J. (2007, March). Scientifically-based research studies examining the use of technology in mathematics education. Presentation at the Consortium for School Networking, 12th Annual K-12 School Networking Conference, San Francisco, CA.

Roschelle, J. (2007, July). Can CSCL make a global contribution? Presentation at the Computer Supported Collabortive Learning Conference, Rutgers University, New Brunswick, NJ.

Roschelle, J. (2008, February). Integrating Technology, Curriculum and TPD in 7th and 8th Grade Math: What We Can Learn from a Randomized Experiment. Presentation at the Math and Science Partnerships Regional Conference, San Francisco, CA.

Roschelle, J. (2008, April). Can a Technology-Enhanced Curriculum Improve Student Learning of Important Mathematics? Presentation at NCSM Annual Conference, Salt Lake City, UT.

Roschelle, J., Empson, S., Hegedus, S., Hopkins, B., & Tatar, D. (2008, March). Enhancing mathematics learning with technology: civic, teacher, student and content perspectives on scaling up simcalc. Presentation at the annual meeting of AERA, New York, NY.

Roschelle, J., Shechtman, N. & Tatar, D. (2008, March). Mapping "geography of opportunity" in a large scale randomized experiment on enhancing mathematics with technology. Presentation at the annual meeting of AERA, New York, NY.

Roschelle, J., Tatar, D., Shechtman, N., & Hegedus, S. (2008, March). Using an integration of technology, curriculum, and tpd at scale to improve student learning of important mathematics. Presentation at the Society for Research on Educational Effectiveness-2008 Conference, Crystal City, VA.

Roschelle, J., Tatar, D., & Kaput, J. (in press). Getting to scale with innovations that deeply restructure how students come to know mathematics. In A. Kelly, R. Lesh, & J. Baek (Eds.), Handbook of design research methods in mathematics, science and technology education. Mahwah, NJ: Lawrence Erlbaum.

Roschelle, J., Tatar, D., Shechtman, N., Hegedus, S., Hopkins, B., Knudsen, J., & Dunn, M. (2007). Extending the SimCalc approach to grade 8 mathematics (SimCalc Technical Report 02). Menlo Park, CA: SRI International.

Roschelle, J., Tatar, D., Shechtman, N., Hegedus, S., Hopkins, B., Knudsen, J., & Stroter, A. (2007). Can a technology-enhanced curriculum improve student learning of important mathematics? (SimCalc Technical Report 01). Menlo Park, CA: SRI International.

Roschelle, J., Tatar, D., Shechtman, N., & Knudsen, J. (in press). The role of scaling up research in designing for and evaluating robustness. Educational Studies in Mathematics.

Shechtman, N., Haertel, G., Gallagher, L., & Rafanan, K. (2006, April). Designing and validating assessments for research: A practical road map from conceptual framework to work plan. Daylong workshop at the annual meeting of AERA, San Francisco, CA.

Shechtman, N., Haertel, G., Gallagher, L., & Rafanan, K. (2007, April). Designing and validating assessments for research: A practical road map from conceptual framework to work plan. Workshop at the annual meeting of AERA, Chicago, IL.

Shechtman, N., Knudsen, J., Roschelle, J., Haertel, G., Gallagher, L., Rafanan, K., & Vahey, P. (2006, April). Measuring middle-school teachers’ mathematical knowledge for teaching rate and proportionality. Roundtable discussion at the annual meeting of AERA, San Francisco, CA.

Stroter, A. (2008, May). Teacher-student racial and ethnic congruence: race still matters in the classroom. Paper presented at Human Center For Interaction Workshops, Virginia Polytechnic Institute, Blacksburg, VA.

Stroter, A. (2008, April). Teacher-student racial and ethnic congruence: race still matters in the classroom. Invited talk at the University of Iowa, Iowa City, IS.

Stroter, A., & Tatar, D. (2007). An experimental study on middle school mathematics using simcalc (mathworlds) software. Poster presented at School of Education Student Association Research Symposium annual conference, Blacksburg, VA.

Stroter, A. & Tatar, D. (2008, March). Teacher-student racial and ethnic congruence: race still matters in the classroom. Invited Talk at Center for Naval Analysis (CNA) Corporation, Alexandria, VA.

Stroter, A. & Tatar, D. (April 2008). Teacher-student racial and ethnic congruence: race still matters in the classroom. Paper presented at the annual meeting of AERA, New York, NY.

Tatar, D. & Dickey-Kurdziolek, M. (2008). Beyond simple evaluation: the case of an effective classroom technology and its prospects for impact. Human-Computer Interaction Consortium. January 30-February 3, Snowbird, CO.

Tatar, D., Ravitz, J., & Stroter, A. (2008). Triangulating: using national survey data to inform the interpretation of randomized, controlled experiment with teachers. Paper presented at the annual meeting of AERA, New York, NY.

Tatar, D., Roschelle, J., Knudsen, J., Shechtman, N., Kaput, J., & Hopkins, B. (2008). Scaling Up Innovative Technology-Based Mathematics. Journal of the Learning Sciences, 17 (2), 248-286.

Vahey, P. (2008, April). Can a technology-enhanced curriculum improve student learning of important mathematics? Presentation at the NCSM Annual Conference, Salt Lake City, UT

Vahey, P. (2008, April). Supporting all students in learning advanced math: findings from a technology enhanced curriculum study. 2008 Celebrating Educational Opportunities for Hispanic Students Conference: Meeting the diverse needs of all children---a courageous conversation, San Jose, CA.

Other Products:

• SimCalc MathWorlds® for Calculators v. 5.0
• SimCalc MathWorlds® for Computers v 2.0
• Online Diffusion-Tracking Database (http://www.simcalc.umassd.edu/texas/) No longer available.
• SimCalc Teacher Database (http://simcalcmanager.sri.com/login.aspx) for managing and archiving data collected from teachers/research participants; access restricted to the project team.
• Designing Cell Phone Games, an eighth-grade unit on linear functions, available in student and teacher editions.
• Managing the Soccer Team, a seventh-grade unit on rate and proportionality, available in student and teacher editions.
• SimCalc Leadership Institute, a mathematics professional development seminar for professional development leaders, launched in Dallas, Texas in February 2008.
• Designing and Validating Assessments for Research: A Practical Roadmap from Conceptual Framework to Work Plan, a workshop on the assessment development process for the Scaling up SimCalc project presented at annual meetings of AERA (2006 and 2007) and the Texas Regional Collaborative for Excellence in Science and Mathematics Teaching.