Longitudinal Investigation of the effect of Curriculum on Algebra Learning

An NSF funded project

Publications

Cai, J. & Howson, A. G. (2013).  Toward an international mathematics curriculum.  In M. A. Clements, A. Bishop, C. Keitel, J. Kilpatrick, & K.S. F. Leung (Eds.), Third International Handbook of Mathematics Education Research (pp. xx-xxx).  Springer.

Cai, J. & Hwang, S. (2013).  Characterizing mathematics education in China: A perspective on improving student learning.  In Sriraman, B., Cai, J., Lee, K-H., Fan, F., Shimuzu, Y., Lim C. S., Subramanium, K. (Eds). The First Sourcebook on Asian Research in Mathematics Education: China, Korea, Singapore, Japan, Malaysia and India (pp. xx-xxx). Information Age Publishing, Charlotte, NC.  

Cai, J., Nie, B., Ye, L. (2013).  Mathematical problem solving in Chinese classroom.  In Sriraman, B., Cai, J., Lee, K-H., Fan, F., Shimuzu, Y., Lim C. S., Subramanium, K. (Eds), The First Sourcebook on Asian Research in Mathematics Education: China, Korea, Singapore, Japan, Malaysia and India (pp. xx-xxx). Information Age Publishing, Charlotte, NC. 

Ni, Y., Li, Q., Cai, J. & Hou, K. (2013).  Has curriculum reform made a difference in the classroom? An evaluation of the new mathematics curriculum in Mainland China.  In Sriraman, B., Cai, J., Lee, K-H., Fan, F., Shimuzu, Y., Lim C. S., Subramanium, K. (Eds), The First Sourcebook on Asian Research in Mathematics Education: China, Korea, Singapore, Japan, Malaysia and India (pp. xx-xxx) . Information Age Publishing, Charlotte, NC.   

Suter, L. & Cai, J. (2013).  Charactering Chinese mathematics curriculum: An international comparative perspective.  In Sriraman, B., Cai, J., Lee, K-H., Fan, F., Shimuzu, Y., Lim C. S., Subramanium, K. (Eds), The First Sourcebook on Asian Research in Mathematics Education: China, Korea, Singapore, Japan, Malaysia and India (pp. xx-xxx). Information Age Publishing, Charlotte, NC.

Nie, B., Freedman, T., Hwang, S., Wang, N., Moyer, J. C., & Cai, J. (2013). An investigation of teachers’ intentions and reflections about using standards-based and traditional textbooks in the classroom. Zentralblatt fuer Didaktik der Mathematik (International Journal on Mathematics Education).

Cai, J., Moyer, J. C., Wang, N., Hwang, S., Nie, B., & Garber, T. (2012). Mathematical problem posing as a measure of curricular effect on students' learning. Educational Studies in Mathematics.

Cai, J., & Wong, N. Y. (2012). Effective mathematics teaching: Conceptualisation, research, and reflections. In W. Blum, F. R. Borromeo. & K. Maaß (Eds.), Mathematikunterricht im Kontext von Realität, Kultur und Lehrerprofessionalität (pp. 294-303). Wiesbaden: Springer Spektrum.

Cai, J., Wang, N., Moyer, J. C., Wang, C., & Nie, B. (2011). Longitudinal investigation of the curricular effect: An analysis of student learning outcomes from the LieCal Project in the United State.  International Journal of Educational Research, 50(2), 117-136.

Cai, J. & Ni, Y. (2011). Investigating curricular effect on the teaching and learning of mathematics in a cultural context: Theoretical and methodological considerations. International Journal of Educational Research, 50(2), 65-70.

Moyer, J. C., Cai, J., Nie, B., & Wang, N. (2011). Impact of curriculum reform: Evidence of change in classroom instruction in the United States. International Journal of Educational Research, 50(2), 87-99.

Ni, Y. & Cai, J. (2011). Searching for evidence of curricular effect on the teaching and learning of mathematics: Lessons from the two longitudinal projects. International Journal of Educational Research, 50(2), 137-143.

Cai, J. & Knuth, E. (Eds.). (2011). Early algebraization: A global dialogue from multiple perspectives.  New York, NY: Springer.

Cai, J., Moyer, J. C., Wang, N., & Nie, B. (2011).  Examining students’ algebraic thinking in a curricular context: A longitudinal study. In J. Cai & E. Knuth (Eds.)., Early algebraization: A global dialogue from multiple perspectives (pp. 161-186).  New York, NY: Springer.

Cai, J., Ng, S. F., & Moyer, J. C. (2011).  Developing students’ algebraic thinking in earlier grades: Lessons from China and Singapore.  In J. Cai & Knuth, E., (Eds.), Early algebraization: A global dialogue from multiple perspectives (pp. 25-42).  New York, NY: Springer.

Cai, J. & Knuth, E. (2011).  Introduction: A global dialogue about early algebraization.  In J. Cai & Knuth, E., (Eds.), Early algebraization: A global dialogue from multiple perspectives (pp. vii-xi).  New York, NY: Springer.

Cai, J. & Merlino, F. J. (2011).  Metaphor: A powerful means for assessing students’ mathematical disposition.  In D. J. Brahier & W. Speer (Eds.), Motivation and disposition:  Pathways to learning mathematics (pp.147-156). National Council of Teachers of Mathematics 2011 Yearbook.  Reston, VA: NCTM.

Huang, R. & Cai, J. (2011). Pedagogical representations to teach linear relations in Chinese and U.S. classrooms: Parallel or hierarchical?  Journal of Mathematical Behavior, 30(2), 149-165.

  Cai, J. (2010). Evaluation of mathematics education programs. In E. Baker, B. McGraw, & P. Peterson (Eds.), International encyclopedia of education, Volume 3 (pp. 653-659). Oxford: Elsevier.

Cai, J., Nie, B., & Moyer, J. (2010). The teaching of equation solving: Approaches in Standards-based and traditional curricula in the United States. Pedagogies: An International Journal, 5(3), 170-186.

Cai, J. (2010). Helping students becoming successful problem solvers.  In D. V. Lambdin & F. K. Lester (Eds.), Teaching and learning mathematics: Translating research to the elementary classroom (pp. 9 - 14).  Reston, VA: National Council of Teachers of Mathematics.  

Cai, J., Moyer, J., Nie, B., & Wang, N. (2009). Learning mathematics from classroom Instruction using Standards-based and traditional curricula: An analysis of Instructional tasks. In S. L. Swars, D. W. Stinson, & S .Lemons-Smith (Eds.), Proceedings of the 31st annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (Vol. 5, pp. 692-699 ). Atlanta, GA: Georgia State University.

Moyer, J., Cai, J., Laughlin, C., & Wang, N. (2009). The effect of curriculum type on middle grades instruction. In S. L. Swars, D. W. Stinson, & S .Lemons-Smith (Eds.), Proceedings of the 31st annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (Vol. 5, pp. 201-209 ). Atlanta, GA: Georgia State University.

  Nie, B., Cai, J., & Moyer, J. (2009). How a standards-based mathematics curriculum differs   from a traditional curriculum: with a focus on intended treatments of the ideas of variable. Zentralblatt fuer Didaktik der Mathematik (International Journal on Mathematics Education), 41(6), 777–792.

Cai, J. (2009).  Teaching mathematics through problem solving: A future direction of problem-solving research.  In B. Sriraman & L. English (Eds.), Theories of mathematics education (pp. 275-284). New York: Springer.

Moyer, J. C., Cai, J., & Laughlin, C. (2009). High quality coaching using the LieCal observation instrument. Journal of Mathematics Education Leadership, 11(1), 12-20.

Cai, J., Moyer, J. C., Wang, N., & Nie, B. (2009). Curricular impact on the development of algebraic thinking: A longitudinal study.  In M. Tzekaki, M. Kaldrimidou, & H. Sakonidis (Eds.), Proceedings of the 33rd Conference of the International Group for the Psychology of Mathematics Education, Vol. 2. (pp. 241 – 248).  Thessaloniki, Greece: PME.

Moyer, J. C., Cai, J., Laughlin, C., & Wang, N. (2009).  The effect of curriculum type on middle grades instruction. In Swars, S. L., Stinson, D. W., & Lemons-Smith, S. (Eds.), Proceedings of the 31st annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, Vol. 5. (pp. 201-209). Atlanta, GA: Georgia State University.

Wang, N., Cai, J. & Moyer, J. C. (2009). Scoring student responses to mathematics performance assessment tasks: Does the number of score levels matter? In M. Tzekaki, M. Kaldrimidou, & H. Sakonidis (Eds.),  Proceedings of the 33rd Conference of the International Group for the Psychology of Mathematics Education, Vol. 5. (pp. 321 – 328).  Thessaloniki, Greece: PME.

Cai, J. & Moyer, J. C. (2008). Developing algebraic thinking in earlier grades: Some insights from international comparative studies. In Greene, C. E. & Rubenstein, R. (Eds.), Algebra and algebraic thinking in school mathematics (pp. 169-182). National Council of Teachers of Mathematics 2008 Yearbook. Reston, VA: NCTM.

Cai, J. & Moyer J. C. (2006). A conceptual framework for studying curricular effects on students’ learning: Conceptualization and design in the LieCal Project. Poster presented at the 2006 annual meeting of the International Group of Psychology of Mathematics Education, Prague, Czech Republic: Charles University in Prague.

Wang, N. & Cai, J. (2006). An investigation of factors influencing teachers’ scoring student responses to mathematics constructed-response assessment tasks.  In J., Novotna, H. Moraova, M. Kratka, & N. Stehlikova (Eds.), Proceedings of the Thirtieth Annual Meeting of the International Group for the Psychology of Mathematics Education, Vol. 2, (pp. 313-320).  Prague, Czech Republic: Charles University in Prague.

Cai, J. (2005). Critical features of effective mathematics instruction: Issues and Practice. In Lam, L. (Ed.), Recent advances in mathematics education research and teaching practices (Proceedings of the International Conference on Mathematics Education). Hong Kong, China: The Hong Kong Institute of Education, July 6-8, 2005.

 

 

Presentations

 

Cai, J. (July, 2012). Curriculum reform and mathematics learning: Evidence from two longitudinal studies. Regular lecture at The 12th International Congress on Mathematical Education, Seoul, Korea, July 08~15, 2012.

Cai, J., Nie, B., Moyer, J. C., & Wang, N. (April, 2012). Learning mathematics using Standards-based and traditional curricula: An analysis of homework problems. Paper presented at the annual meeting of American Educational Research Association, Vancouver, British Columbia, Canada, April 13 – 17, 2012.

Cai, J., Wang, N., Moyer, J. C., & Nie, B. (April, 2012). Longitudinal investigation of the effect of curriculum on algebra learning: Beyond grade bands. Paper presented at the annual meeting of American Educational Research Association, Vancouver, British Columbia, Canada, April 13 – 17, 2012.

Cai, J., Robison, V., Moyer, J. C., Wang, N., & Nie, B. (April, 2012). Mathematical dispositions and student learning: A metaphorical analysis. Paper presented at the annual meeting of American Educational Research Association, Vancouver, British Columbia, Canada, April 13 – 17, 2012.

Nie, B., Cai, J., & Moyer, J. C. (April, 2012).  Pedagogical and mathematical analyses of teaching equation solving in Standards-based and traditional curricula. Paper presented at the annual meeting of American Educational Research Association, Vancouver, British Columbia, Canada, April 13 – 17, 2012.

Cai, J., Moyer, J. C., & Nie, B. (April, 2012). Analyses of teaching equation solving in Standards-based and traditional curricula. Poster presented at the Research Pre-session of the National Council of Teachers of Mathematics annual meeting, Philadelphia, PA, April 25-28, 2012.

Mitchell, M., Tarr, J. E., Cai, J., Moyer, J. C., Wang, N., Grouws, D.,  King, K., & McDuffie, A. R. (2012). What matters about student learning: Curriculum implementation from three perspectives. Research Symposium at the Research Pre-session of the National Council of Teachers of Mathematics annual meeting, Philadelphia, PA, April 25-28, 2012.

Cai, J., Moyer, J. C., Shih, J. C., & Wang, N. (April, 2011). Investigating the effects of curricula and classroom emphases on algebra learning: Cross-sectional analyses. Paper presented at the annual meeting of American Educational Research Association, New Orleans, Louisiana, April 08 –12, 2011.

Moyer, J. C., Cai, J., & Nie, B. (April, 2011).  Approaches to developing function sense in three middle school curricula. Poster presented at the Research Pre-session of the National Council of Teachers of Mathematics annual meeting, Indianapolis, Indiana, April 11-13, 2011.

Nie, B., Freedman, T., Wang, N., Moyer, J. C., & Cai, J. (April, 2011).  Teachers' intentions and reflections for classroom instruction in a curricular context. Paper presented at the annual meeting of American Educational Research Association, New Orleans, Louisiana, April 08 –12, 2011.

Cai, J., Wang, N., Moyer, J. C., & Nie, B. (April/May, 2010). Impact of curriculum reform: Evidence of student learning outcomes in the United States.  Paper presented as part of the Symposium on Curricular Impact on Teaching and Learning: Two Longitudinal Studies from the USA and China, organized by Jinfa Cai & Yujing Ni, at the at the annual meeting of American Educational Research Association. April 30 – Tuesday, May 4, Denver, Colorado.

 

Cai, J., Wang, N., Nie, B., Moyer, J. C., & Wang, C. (April/May, 2010). Student learning and classroom instruction using Standards-based and traditional curricula: An analysis of instructional tasks. Paper presented at the annual meeting of American Educational Research Association. April 30 – Tuesday, May 4, Denver, Colorado.

 

Moyer, J. C., Cai, J., & Nie, B. (April/May, 2010). Developing functional sense in middle school: Approaches in Standards-based and traditional curricula.  Paper presented at the annual meeting of American Educational Research Association. April 30 – Tuesday, May 4Denver, Colorado.

 

Moyer, J. C., Cai, J., Wang, N., & Nie, B. (April/May, 2010). Impact of curriculum reform: Evidence of change in classroom practice in the United States. Paper presented as part of the Symposium on Curricular Impact on Teaching and Learning: Two Longitudinal Studies from the USA and China, organized by Jinfa Cai & Yujing Ni, at the annual meeting of American Educational Research Association. April 30 – Tuesday, May 4, Denver, Colorado.

 

Nie, B., Cai, J., & Moyer, J. C. (April/May, 2010).  Does a Standards-based curriculum really differ from a traditional curriculum: A case of variable.  Paper presented at the annual meeting of American Educational Research Association. April 30 – Tuesday, May 4, Denver, Colorado.

 

Cai, J., Moyer, J. C., Wang, N., & Nie, B. (September, 2009).  Learning from classroom instruction in a curricular content: An analysis of instructional tasks. Paper presented at the 31st annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. Atlanta, GA: Georgia State University.

 

Moyer, J. C., Cai, J., Laughlin, C., & Wang, N. (September, 2009).  The effect of curriculum type on middle grades instruction. Paper presented at the 31st annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. Atlanta, GA: Georgia State University.

 

Cai, J., Moyer, J. C., Wang, N., & Nie, B. (July, 2009). Curricular impact on the development of algebraic thinking: A longitudinal study. Paper presented at the 33rd Conference of the International Group for the Psychology of Mathematics Education.  Thessaloniki, Greece.

 

Wang, N., Cai, J. & Moyer, J. C. (July, 2009). Scoring student responses to mathematics performance assessment tasks: Does the number of score levels matter? Paper presented at the 33rd Conference of the International Group for the Psychology of Mathematics Education.  Thessaloniki, Greece.

 

Moyer, J. C. & Cai J. (May, 2009). A world view of algebraic thinking. Presentation at Wisconsin Mathematics Council 41st Annual Conference, Green Lake, WI. May 6-8, 2009.

 

Moyer, J. C., Laughlin, C., & Cai, J. (May, 2009). Using a research-based observation tool to help coach for quality teaching. Presentation at Wisconsin Mathematics Council 41st Annual Conference, Green Lake, WI. May 6-8, 2009.

 

Cai, J., Moyer, J. C., Nie, B. (April, 2009). The development of algebraic thinking: Insights from a longitudinal study.  A Research Into Practice session presented the National Council of Teachers of Mathematics Annual Meeting.  Washington, D.C., April 22-25, 2009.

 

Cai, J., Moyer, J. C., Nie, B., Wang, N. (April, 2009). The Development of middle school students' algebraic thinking: A longitudinal study. Paper presented at the annual meeting of American Educational Research Association.  San Diego, CA. April 13–17, 2009.

 

Cai, J., Moyer, J. C., Wang, N., & Nie, B. (April, 2009). Curricular effect on algebra learning: A 3-year longitudinal study. Symposium (organized by Jinfa Cai) presented at the Research Pre-session of the National Council of Teachers of Mathematics Annual Meeting.  Washington, D.C., April 20-22, 2009.

 

Cai, J., Moyer, J. C., Wang, N., Shih, J., & Nie, B. (April, 2009). A longitudinal investigation of Curricular effect on students’ procedural and conceptual understanding of Algebra. Paper presented at the annual meeting of American Educational Research Association.  San Diego, CA. April 13–17, 2009.

 

Moyer, J., Cai, J., Wang, N., & Nie, B. (April, 2009). Learning from instruction: Profiles of classroom experiences using Standards-based and traditional curricula.  Paper presented at the annual meeting of American Educational Research Association. San Diego, CA. April 13–17, 2009.

 

Cai, J. (January, 2009).  What really works in the current mathematics education reform?  Evidence from a longitudinal study.  Invited seminar at the Faculty of Education, The Chinese University of Hong Kong, Hong Kong, SAR.  January, 12, 2009. 

 

Nie, B., Cai, J., & Moyer, J. C. (November, 2008). How does a Standards-based curriculum differ from a traditional curriculum? Paper presented at the School Science and Mathematics Association 2008 Annual Convention, Raleigh-Durham, NC. November 13-15, 2008.

 

Cai, J. Moyer, J. C., Wang, N., Nie, B., & Shih, J. (April, 2008).  Longitudinal investigation of the effect of curricula on algebra learning:  Initial findings from the first two years.  Symposium (organized by Jinfa Cai) presented at the Research Pre-session of the National Council of Teachers of Mathematics Annual Meeting.  Salt Lake, UT, April 7-9, 2008.

 

Laughlin, C., Moyer, J. C., & Cai, J. (April, 2008).  Helping coaches support quality teaching in daily practice using a research observation tool. Presentation at the 2008 annual meeting of the National Council of Teachers of Mathematics Annual Meeting.  Salt Lake, UT, April 9-12, 2008.

 

Monaghan, S. R., Moyer, J. C., & Cai, J. (April, 2008).  Principals as instructional leaders of middle school mathematics.   Paper presented at the Research Pre-session of the National Council of Teachers of Mathematics Annual Meeting.  Salt Lake, UT, April 7-9, 2008.

 

Ni, Y., Li, Q., Cai, J. Hau, K-T, Liu, H., & Zhang, Z. (April, 2008).  Effects of a reformed curriculum on student learning outcomes in primary mathematics.  Paper presented at the annual meeting of American Educational Research Association.  New York, NY.  March 24-27, 2008.

 

Cai, J. (May, 2007).  Designing empirical research studies in mathematics education: Using the LieCal Project and others as examples.  A two-hour lecture at the Institute of Mathematics, Southwest Normal University.  May 15, 2007.

 

Cai, J. & Moyer, J. C. (April, 2007).  LieCal Project: Conceptualization and design.  Paper presented at the symposium, Designing Longitudinal Studies of Curricula: Insights from Three NSF-Funded Projects, organized by Jinfa Cai, at the 2007 annual meeting of the National Council in Teaching Mathematics, Research Pre-session.  March, 19-24, 2007.  Atlanta, GA.

 

Cai, J. (April, 2007).  Designing longitudinal studies:  Insights from three NSF-funded projects.  Symposium at the 2007 annual meeting of the National Council of Teachers of Mathematics, Research Pre-session.  March, 19-24, 2007.  Atlanta, GA. [Other participants include: Douglas Grouws (Missouri), Paul Kehle (Hobart and William Smith), Diana Lambdin (Indiana), Jack Moyer (Marquette), James Tarr (Missouri), and Jeremy Kilpatrick (Georgia)].

 

Cai, J. (April, 2007).  Discussant for the symposium, Teachers' Use of Reform Materials and Traditional Textbooks, organized by John C. Moyer, at the 2007 annual meeting of the National Council in Teaching Mathematics, Research Pre-session.  March, 19-24, 2007.  Atlanta, GA.  (Other participants include Gwendolyn Lloyd, Virginia Tech, and Beth Herbel-Eisenmann, Iowa State).

 

Moyer, J. C. & Cai, J. (April, 2007). Algebraic thinking around the world.  Presentation at the National Council of Teachers of Mathematics 2007 Annual Meeting.  March 20-24, 2007, Atlanta, GA.

 

Moyer, J. C., Cai, J., Wang, N., Freedman, T., & Nie, B. (April, 2007).  Teachers' use of reform materials and traditional textbooks: evidence from the LieCal project.  Paper presented at the symposium, Teachers' Use of Reform Materials and Traditional Textbooks, organized by John C. Moyer, at the 2007 annual meeting of the National Council in Teaching Mathematics, Research Pre-session.  March, 19-24, 2007.  Atlanta, GA.   

 

Moyer, J. C., Laughlin, C., & Cai, J. (April, 2007). Fostering high quality teaching in daily practice through the lens of a research protocol.  Presentation at the Thirty-Ninth Annual NCSM Conference. March, 18-20, 2007.  Atlanta, GA.

 

Wang, N. & Cai, J. (April, 2007).  What do we know about how teachers’ scoring open-ended mathematics assessment tasks?  Paper presented at the 2007 annual meeting of the American Educational Research Association, April 3-9, 2007.  Chicago, IL.

 

Wang, N. & Cai, J. (July, 2006). An investigation of factors influencing teachers’ scoring student responses to mathematics constructed-response assessment tasks.  Paper presented at the Thirtieth Annual Meeting of the International Group for the Psychology of Mathematics Education.  Prague, Czech Republic: Charles University in Prague.

 

 

 

 

 

 

 

 

 

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