The project team is collecting and studying numerous scholarly publications related to student and teacher statistical learning and understanding, teacher preparation, mathematics and statistics education curriculum, and assessment and evaluation of statistical understanding. The following provides a list of the work that is being reviewed to help guide the research of Project-SET.

**Statistical Learning References**

Bakker, A. (2004). Reasoning about shape as a pattern in variability. *Statistics Education Research Journal*, *3*(2), 64-83.

Batanero, C., Estepa, A., Godino, J.D., & Green, D.R. (1996). Intuitive strategies and preconceptions about association in contingency tables. *Journal for Research in Mathematics Education*, *27*, 151-169.

Batanero, C., Estepa, A., & Godino, J.D. (1997). Evolution of students’understanding of statistical association in a computer-based teaching environment. In J.B. Garfield & G. Burrill (Eds.), *Research on the role of technology in teaching* *and learning statistics: Proceedings of the 1996 IASE Round Table Conference *(pp. 191-205). Voorburg, Netherlands: International Statistical Institute.

Cai, J. (2000). Understanding and representing the arithmetic averaging algorithm: An analysis and comparison of U.S. and Chinese students’ responses. *International Journal of Mathematical Education in Science and Technology*, *31*, 839-855.

Cobb, P., Confrey, J., diSessa, A., Lehrer, R., & Schauble, L. (2003). Design experiments in educational research.* Educational Researcher*, *32*(1), 9–13.

Estepa, A., & Batanero, C. (1996). Judgments of correlation in scatterplots: Students’ intuitive strategies and preconceptions. *Hiroshima Journal of Mathematics* *Education, 4, *25-41.

Estepa, A., & Sanchez-Cobo, F.T. (1998). Correlation and regression in secondary school textbooks. In L. Pereira Mendoza, L. Seu, T. Wee, & W.K. Wong (Eds.), *Proceedings of the Fifth International Conference on the Teaching of * *Statistics *(vol. 2, pp. 671-676). Voorburg, Netherlands: International Statistical Institute.

Estepa, A., & Sanchez-Cobo, F.T. (2003). Evaluacion de la comprension de la correlacion y regression a partir de la resolucion de problemas. *Statistics Education Research Journal, 2*(1), 54-68.

Fischbein, E. & Schnarch, D. (1997). The Evolution with Age of Probabilistic, Intuitively Based Misconceptions. *Journal for Research in Mathematics Education*, *28*, 96-105.

Friel, S.N., Curcio, F.R., & Bright, G.W. (2001). Making sense of graphs: Critical factors influencing comprehension and instructional implications. *Journal for Research in Mathematics Education*, *32*, 124-158.

Garfield, J., & Ahlgren (1988). Difficulties in Learning Basic Concepts in Probability and Statistics: Implications for Research. *Journal for Research in Mathematics Education*, *19*, 44-63.

Garfield, J. & Ben-Zvi, D. (2007). How Students Learn Statistics Revisited: A Current Review of Research on Teaching and Learning Statistics. *International Statistics Review, 75(*3), 372-396.

Garfield, J., & Ben-Zvi, D. (2008). *Developing students’ statistical reasoning: Connecting research and teaching practice*. Springer.

Green, D. R. (1983). A survey of probability concepts in 3000 pupils aged 11-16 years. In D.R. Grey, P. Holmes, V. Barnett, & G.M. Constable (Eds.), *Proceedings of the First International Conference on Teaching Statistics. Sheffield, UK: Teaching Statistics Trust.*

Groth, R.E. (2002). Characterizing secondary students’ understanding of measures of central tendency and variation. In D.S. Mewborn, P. Sztajn, D.Y. White, H.G. Wiegel, R.L. Bryant, & K. Nooney (Eds.), *Proceedings of the twenty-fourth annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education*: *Volume 1* (pp. 247-257). Columbus, OH: ERIC Clearinghouse for Science, Mathematics, and Environmental Education.

Groth,R. (2003). High School Students’ Levels of Thinking in Regard to Statistical Study Design. *Mathematics Education Research Journal, 15*(3), 252-269.

Groth, R.E. (2006). An exploration of students’ statistical thinking. *Teaching Statistics*, *28*(1), 17-21.

Groth, R.E., & Powell, N.N. (2004). Using research projects to help develop high school students’ statistical thinking. *Mathematics Teacher*, *97*, 106-109.

Jacobs, V.R. (1999). How do students think about statistical sampling before instruction? *Mathematics Teaching in the Middle School*, *5*, 240-246, 263.

Jones, G.A., Langrall, C.W., & Mooney, E.S. (2007). Research in probability: Responding to classroom realities. In F.K. Lester, Jr. (Ed.), *Second handbook of research on mathematics teaching and learning* (pp. 909-955). Charlotte, NC: Information Age Publishing.

Konold, C. (1995). Issues in assessing conceptual understanding in probability and statistics. *Journal of Statistics Education*, *3* (1).

Konold, C. & Higgings, T., (2003). Reasoning about data. In J. Kilpatrick, W.G. Martin, & D. Schifter (Eds.). *A Research Companion to Principles & Standards for School Mathematics *(chapter 13). National Council of Teachers of Mathematics (NCTM), Reston VA, 2003.

Konold, C., & Pollatsek, A. (2002). Data analysis as the search for signals in noisy processes. *Journal for Research in Mathematics Education*, *33*, 259-289.

Konold, C., Pollatsek, A., Well, A., & Gagnon, A. (1997). Students analyzing data: Research of critical barriers. In J.B. Garfield & G. Burrill (Eds.), *Research on the role of technology in teaching and learning statistics: Proceedings of the 1996 IASE Roundtable Conference* (pp. 151-167). Voorburg, The Netherlands: International Statistical Institute.

McClain, K., McGatha, M., & Hodge, L.L. (2000). Improving data analysis through discourse. *Mathematics Teaching in the Middle School*, *5*, 548-553.

Mokros, J., & Russell, S.J. (1995). Children’s concepts of average and representativeness. *Journal for Research in Mathematics Education*, *26*, 20-39.

Mooney, E.S. (2002). A framework for characterizing middle school students’ statistical thinking. *Mathematical Thinking and Learning*, *4*, 23-63.

Piaget & Inhelder (1975). *The origin of the idea of chance in children*. London: Routledge & Kegan Paul.

Pfannkuch, M. (2005). Probability and statistical inference: How can teachers enable learners to make the connection? In G.A. Jones (Ed.), *Exploring probability in school*: *Challenges for teaching and learning *(pp. 267-294). New York: Springer.

Roth, W.-M., & McGinn, M. (1997). Graphing: Cognitive ability or practice? *Science Education*, *81*, 91-106.

Schwartz, D.L., Goldman, S.R., Vye, N.J., & Barron, B.J. (1998). Aligning everyday and mathematical reasoning: The case of sampling assumptions. In S.P. Lajoie (Ed.), *Reflections on statistics*: *Learning*, *teaching*, *and assessment in grades K-12* (pp. 233-273). Mahwah, NJ: Erlbaum.

Shaughnessy, J.M. (2007). Research on statistics learning and reasoning. In F.K. Lester (Ed.), *Second handbook of research on mathematics teaching and learning *(pp. 957-1009). Charlotte, NC: Information Age Publishing.

Shaughnessy, J.M. (2003). Research of Student’s Understanding of Probability. In J. Kilpatrick, W.G. Martin, & D. Schifter (Eds.). *A Research Companion to Principles & Standards for School Mathematics *(chapter 14). National Council of Teachers of Mathematics (NCTM), Reston VA, 2003.

Shaughnessy, J.M., Ciancetta, M., & Canada, D. (2004). Types of student reasoning on sampling tasks. In M. Johnsen Hoines & A. Berit Fuglestead (Eds.), *Proceedings of the 28 ^{th} meeting of the International Group for the Psychology of Mathematics Education* (Vol. 4, pp. 177-184). Bergen, Norway: Bergen University College Press.

Stroup, (1984). The statistician and the pedagogical monster: Characteristics of effective instructors of large statistics classes. In *Proceedings of the Section on Statistical Education*. Washington, DC: American Statistical Association.

Tarr, J.E., & Shaughnessy, J.M. (2007). Student performance in data analysis, statistics, and probability. In P. Kloosterman & F.K. Lester, Jr. (Eds.), *Results and interpretations of the 2003 mathematics assessment of the National Assessment of Educational Progress* (pp. 139-168). Reston, VA: National Council of Teachers of Mathematics.

Utts, J. (2003). What educated citizens should know about statistics and probability? *The American Statistician*, *57*(2), 74–79.

Watson, J.M., & Moritz, J.B. (1999). The beginning of statistical inference: Comparing two data sets. *Educational Studies in Mathematics*, *37*, 145-168.

Zawojewski, J.S., & Shaughnessy, J.M. (2000). Data and chance. In E.A. Silver & P.A. Kenney (Eds.), *Results from the Seventh Mathematics Assessment of the National Assessment of Educational Progress* (pp. 235-268). Reston, VA: National Council of Teachers of Mathematics.

Zimmerman, G., & Jones, G.A. (2002). Probability simulation: What meaning does it have for high school students? *Canadian Journal of Mathematics, Science, and Technology Education*, *2*, 221-236.

**Teacher Preparation References**

Ball, D. (1991). Research on teaching mathematics: Making subject matter knowledge part of the equation. In J. Brophy (Ed.), *Advances in research on teaching:* *Teachers’ subject matter knowledge and classroom instruction* (Vol. 2, pp. 1–48). Greenwich, CT: JAI Press.

Ball, D. L., & Bass, H. (2000). Interweaving content and pedagogy in teaching and learning to teach: Knowing and using mathematics. In J. Boaler (Ed.), *Multiple perspectives on* *the teaching and learning of mathematics *(pp. 83–104). Westport: Ablex.

Ball, D. L., Hill, H. H., & Bass, H. (2005). Knowing mathematics for teaching: Who knows mathematics well enough to teach third grade, and how can we decide? *American Mathematical Educator*, Fall, 14–46.

Conference Board of the Mathematical Sciences. (2001). *The mathematical education of teachers*. Providence, RI: American Mathematical Society.

Franke, M., Webb, N., Chan, A., Ing, M., Freund, D., & Battey, D. (2009). Teacher questioning to elicit students’ mathematical thinking in elementary school. *Journal of Teacher Education*, *60*(4), 380–392.

Garfield, J., & Everson, M. (2009). Preparing teachers of statistics: A graduate course for future teachers. *Journal of Statistics Education*, *17*.

Gould, R., & Peck, R. (2004). Preparing teachers to teach statistics. *Proceedings of the International Congress on Mathematics Education, Proceedings*.

Groth, R. E. (2008). Assessing teachers’ discourse about the Pre-k-12 Guidelines for Assessment and Instruction in Statistics Education (GAISE). *Statistics Education Research Journal*, *7*(1), 16–39.

Groth, R. E. (2007). Toward a conceptualization of statistical knowledge for teaching. *Journal for Research in Mathematics Education*, *38*, 427–437.

Hill, H. C., & Ball, D. L. (2004), Learning mathematics for teaching: Results from California’s Mathematics Professional Development Institutes. *Journal of Research in Mathematics Education*, *35*, 330–351.

Krainer, K. (1993). Understanding students’ understanding: On the importance of cooperation between teachers and researchers. In P. Boero, (Ed.), *Proceedings of the 3 ^{rd} Bratislava International Symposium on Mathematical Teacher Education*, Comenius University Bratislava.

Makar, K., & Confrey, J. (2004). Secondary teachers’ statistical reasoning in comparing two groups. In D. Ben-Zvi & J. Garfield (Eds.), *The challenge of developing statistical literacy, reasoning and thinking *(pp. 353–374). Boston: Kluwer Academic Publishers.

Metz (2010). Using GAISE and NCTM Standards as Frameworks for Teaching Probability and Statistics to Pre-Service Elementary and Middle School Mathematics Teachers. *Journal of Statistical Education*, *18*, 3.

Santagata, R. (2009). Designing video-based professional development for mathematics teachers in low-performing schools. *Journal of Teacher Education, 60(*1), 38-51.

Shulman, D. (1986). Those who understand: Knowledge growth in teaching. *Educational Researcher*, *15*, 4–14.

Yadav, A. (2008). What works for them? Preservice teachers’ perceptions of their learning from video cases. *Action in Teacher Education*, *29*(4), 27–38.

**Curriculum References**

Burrill, G. (2005). *Curriculum issues in statistics education*. Universiti Teknologi Malaysia.

Cobb, G. W. (1992). Teaching statistics. In L. A. Steen (Ed.), *Heeding the call for change: Suggestions for curricular action* (MAA Notes No. 22, pp. 3–43). Washington, DC: Mathematical Association of America.

Cobb, G. W. (1993). Reconsidering statistics education: A National Science Foundation Conference. *Journal of Statistics Education*, *1*(1).

Cobb, G. W., & Moore, D. S. (1997). Mathematics, statistics, and teaching. *American Mathematical* *Monthly*, *104*, 801–823.

delMas, R.C. (2004). A comparison of mathematical and statistical reasoning. In J. Garfield & D. Ben-Zvi (Eds.), *The challenge of developing statistical literacy, reasoning, and thinking* (pp. 79-95). Dordrecht, The Netherlands: Kluwer.

Daro, Mosher & Corcoran (2011). *A Foundation for Standards, Curriculum, Assessment, and Instruction. CPRE Research Report # RR-68*. Consortium for Policy Research in Education, Philadelphia, PA.

Franklin, C., Kader, G., Mewborn, D., Moreno, J., Peck, R., Perry, M., & Scheaffer, R. (2007). *Guidelines for assessment and instruction in statistics education (GAISE) report: A preK–12* *curriculum framework*. Alexandria, VA: American Statistical Association. (Also available at www.amstat.org.)

Garfield et al. (2005). *Guidelines for assessment and instruction in statistics education (GAISE) college report*. Alexandria, VA: American Statistical Association. (Also available at www.amstat.org.)

Gravemeijer, K. (1999) How emergent models may foster the constitution of formal mathematics. *Mathematical Thinking and Learning 1* (2), 155–177.

Greeno, J. G. (2003). Situative research relevant to standards for school mathematics. In J. Kilpatrick, W. G. Martin, & D. Schifter (Eds.), *A research companion to Principles* *and Standards for School Mathematics *(pp. 304–332). Reston, VA: NCTM.

Lappan & Briars (1995 )How should mathematics be taught? In I.M. Carl (Eds.) *Seventy-five years of progress: Prospects for school mathematics* (pp 115-156). Reston VA, NCTM.

Newton, J., Dietiker, L., & Horvath, A. (2008). Statistics: A look across K-8 state standards. In C. Batanero, G. Burrill, C. Reading, & A. Rossman (Eds.), *Joint ICMI/IASE Study: Teaching Statistics in School Mathematics. Challenges for Teaching and Teacher Education. Proceedings of the ICMI Study 18 and 2008 IASE Round Table Conference.*

Petrosino A.J, Lehrer, R., & Schauble, L. (2003) Structuring error and experimental variation as distribution in the fourth grade. *Mathematical Thinking and Learning, 5*(2&3), 131-156.

**Assessment and Evaluation of Statistical Reasoning References**

Chervany, N.L., Collier, R.D., Fienberg, S., & Johnson, P. (1977). A framework for the development of measurement instruments for evaluating the introductory statistics course. *The American Statistician*, *31*(1), 17-23.

delMas, R., Garfield, J., Ooms, A., & Chance, B. (2007). Assessing students’ conceptual understanding after a first course in statistics. *Statistics Education Research Journal*, *6*(2), 28–58.

Garfield , J. (2000). *Evaluating the statistics education reform*. Final report to the National Science Foundation. http://education.umn.edu/EdPsych/Projects/Impact.html.

**Learning Progressions/Learning Trajectory References**

Clements, D. H. (2010). Tools, technologies, and trajectories. In Z. Usiskin, K. Andersen & N. Zotto (Eds.), *Future curricular trends in school algebra and geometry* (pp. 259-266). Charlotte, NC: Information Age Publishing, Inc.

Clements, D. H., & Sarama, J. (2004). Learning trajectories in mathematics education. *Mathematical Thinking and Learning, 6(2),* 81-89.

Clements, D. H., & Sarama, J. (2011). Standards, curriculum, and learning trajectories in mathematics education. In Susan Pettit-Riley (Eds.), *Research in mathematics education: Where do we go from here? (*pp. 7-29). Institute for Research on Mathematics and Science Education, Michigan State University, East Lansing, MI.

Duschl, R.A., Schweingruber, H.A., & Shouse, A. (Eds.). (2007). *Taking science to school: Learning and teaching science in grades K-8.* Washington, DC: National Academy Press.

Krajcik, J., Shin, N., Stevens, S. & Short, H. (2009). *Using learning progressions to inform the design of coherent science curriculum materials.* Paper presented at the American Educational Research Association annual meeting, San Diego, CA.

Mohan, L., Chen, J., and Anderson, C. W. (2009). Developing a multi-year learning progression for carbon cycling in socio-ecological systems. *Journal of Research in Science Teaching, 46*(6), 675-698.

Sarama, J., & Clements, D. H. (2009). Teaching math in the primary grades: The learning trajectories approach. *Young Children, 64*(2), 63-65.

Sarama, J., Clements, D. H., Barrett, J. E., Van Dine, D. W., & McDonel, J. S. (2011). Evaluation of a learning trajectory for length in the early years. *ZDM-The International Journal on Mathematics Education, 43*, 667-680.

Schwarz, C.V., Reiser, B. J., Davis, E. A., Kenyon, L., Acher, A., Fortus, D., Shwartz, Y., Hug, B., & Krajcik, J. (2009). Developing a learning progression for scientific modeling: Making scientific modeling accessible and meaningful for learners. *Journal of Research in Science Teaching*: 632-654.

Simon, M. A. (1995) Reconstructing mathematics pedagogy from a constructivist perspective. *Journal for Research in Mathematics Education, 26*(2), 114-145.

Simon & Tzur (2004) Explicating the role of mathematical tasks in conceptual learning: An elaboration of hypothetical learning trajectory. *Mathematical Thinking and Learning, 6*(2), 91-104.

Songer, N.B. and Gotwals, A. (2012) Guiding explanation construction by children at the entry points of learning progressions. *Journal of Research in Science Teaching,* *49(*2), 141-165.

Stevens, S., Delgado, C. & Krajcik, J., (2010). Developing a Hypothetical Multi-Dimensional Learning Progression for the Nature of Matter. *Journal of Research in Science Teaching, 47(*6), 687-725.