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Design of Statistics Learning Environments

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International Handbook of Research in Statistics Education

Abstract

The goal of this chapter is to draw attention to the need to think about learning environments and their design as a way of considering how sustainable change in the learning and teaching of statistics can be supported. The goal is not to advocate one particular approach to the design of learning environments but rather to raise awareness of the need to consider this lens in statistics education. We first present the rationale for the importance of a focus on learning environments for statistics education. We provide several examples of learning environments that operationalize and integrate various design perspectives and are informed by two theoretical frameworks: social constructivist theory of learning and realistic mathematics education theory. We discuss these examples in a critical way by comparing and evaluating their designs, looking for common threads among them, and develop from them six design considerations for statistics learning environments. Finally, we discuss implications and emerging directions and goals for further implementation and research.

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Notes

  1. 1.

    Learning occurs in a wide continuum of settings from the “designed” to the “ambient” (Kali, Tabak, Ben-Zvi, et al., 2015). On this continuum, this chapter focuses on designed learning environments rather than informal and ambient ways of learning.

  2. 2.

    Others use the term learning ecology instead of learning environment to emphasize that the educational system is always dynamic and emerging rather than a static entity (Cobb, Confrey, diSessa, Lehrer, & Schauble, 2003; Lehrer & Pfaff, 2011).

  3. 3.

    In practice, “the model” in the emergent modeling heuristic is actually shaped as a series of consecutive sub-models that can be described as a cascade of inscriptions or a chain of signification.

  4. 4.

    Note, however, that the students have to be made aware that not all distributions are unimodal.

  5. 5.

    Advanced placement is a US academic program with more than 30 courses in a wide variety of subject areas that provides secondary school students with the opportunity to study and learn at the college level.

References

  • Ainley, J., Gould, R., & Pratt, D. (2015). Learning to reason from samples: commentary from the perspectives of task design and the emergence of “big data”. Educational Studies in Mathematics, 88(3), 405–412.

    Article  Google Scholar 

  • Ainley, J., & Pratt, D. (2014a). Chance re-encounters: ‘computers in probability education’ revisited. In D. Frischemeier, P. Fischer, R. Hochmuth, T. Wassong, & P. Bender (Eds.), Using tools for learning mathematics and statistics (pp. 165–177). New York: Springer.

    Google Scholar 

  • Ainley, J., & Pratt, D. (2014b). Expressions of uncertainty when variation is partially determined. In K. Makar, B. de Sousa, & R. Gould (Eds.), Sustainability in statistics education. Proceedings of the 9th International Conference on Teaching Statistics (ICOTS9, July, 2014), Flagstaff, AZ, USA. Voorburg, Netherlands: International Statistical Institute.

    Google Scholar 

  • Ainley, J., Pratt, D., & Hansen, A. (2006). Connecting engagement and focus in pedagogic task design. British Educational Research Journal, 32(1), 23–38.

    Article  Google Scholar 

  • Aridor, K., & Ben-Zvi, D. (2017). The co-emergence of aggregate and modelling reasoning. Statistics Education Research Journal, 16(2).

    Google Scholar 

  • Arnold, P. (2014). Statistical investigative questions: An enquiry into posing and answering investigative questions from existing data. Unpublished doctoral thesis, University of Auckland, New Zealand.

    Google Scholar 

  • Baeten, M., Kyndt, E., Struyven, K., & Dochy, F. (2010). Using student-centred learning environments to stimulate deep approaches to learning: Factors encouraging or discouraging their effectiveness. Educational Research Review, 5(3), 243–260.

    Article  Google Scholar 

  • Baglin, J. (2013). Evaluating learning theory-based methods for improving the learning outcomes of introductory statistics courses (unpublished doctoral dissertation). RMIT University.

    Google Scholar 

  • Bakker, A. (2004). Design research in statistics education: On symbolizing and computer tools. Utrecht, The Netherlands: CD Beta Press.

    Google Scholar 

  • Bakker, A., & Gravemeijer, K. (2004). Learning to reason about distribution. In D. Ben-Zvi & J. Garfield (Eds.), The challenging of developing statistical literacy, reasoning, and thinking (pp. 147–168). Dordrecht, Netherlands: Kluwer Academic Publishers.

    Chapter  Google Scholar 

  • Bakker, A., & Gravemeijer, K. (2006). An historical phenomenology of mean and median. Educational Studies in Mathematics, 62(2), 149–168.

    Article  Google Scholar 

  • Barron, B. J. S., Schwartz, D. L., Vye, N. J., Moore, A., Petrosino, A., Zech, L., et al. (1998). Doing with understanding: Lessons from research on problem- and project-based learning. The Journal of the Learning Sciences, 7(3-4), 271–311.

    Article  Google Scholar 

  • Barry, J. (2007). Acculturation. In J. Grusec & P. Hastings (Eds.), Handbook of socialization: Theory and research (pp. 543–560). New York: Guilford Press.

    Google Scholar 

  • Ben-Zvi, D. (2000). Toward understanding the role of technological tools in statistical learning. Mathematical Thinking and Learning, 2(1-2), 127–155.

    Article  Google Scholar 

  • Ben-Zvi, D. (2006). Scaffolding students’ informal inference and argumentation. In A. Rossman & B. Chance (Eds.), Proceedings of the 7th International Conference on Teaching Statistics (CD-ROM). International Statistical Institute: Voorburg, Netherlands.

    Google Scholar 

  • Ben-Zvi, D. (2007). Using wiki to promote collaborative learning in statistics education. Technology Innovations in Statistics Education, 1(1).

    Google Scholar 

  • Ben-Zvi, D., & Aridor, K. (2016). Children’s wonder how to wander between data and context. In D. Ben-Zvi & K. Makar (Eds.), The teaching and learning of statistics: International perspectives (pp. 25–36). Switzerland: Springer International Publishing.

    Chapter  Google Scholar 

  • Ben-Zvi, D., Aridor, K., Makar, K., & Bakker, A. (2012). Students’ emergent articulations of uncertainty while making informal statistical inferences. ZDM, 44(7), 913–925.

    Article  Google Scholar 

  • Ben-Zvi, D., & Ben-Arush, T. (2014). Exploratory data analysis instrumented learning with TinkerPlots. In D. Frischemeier, P. Fischer, R. Hochmuth, T. Wassong, & P. Bender (Eds.), Using tools for learning mathematics and statistics (pp. 193–208). New York: Springer.

    Google Scholar 

  • Ben-Zvi, D., Gil, E., & Apel, N. (2007). What is hidden beyond the data? Helping young students to reason and argue about some wider universe. In D. Pratt & J. Ainley (Eds.), Reasoning about informal inferential statistical reasoning. Proceedings of the 5th International Research Forum on Statistical Reasoning, Thinking, And Literacy. Warwick, UK: University of Warwick.

    Google Scholar 

  • Bereiter, C. (1985). Towards a solution of the learning paradox. Review of Educational Research, 55(2), 201–226.

    Google Scholar 

  • Bidgood, P., Hunt, N., & Jolliffe, F. (Eds.). (2010). Assessment methods in statistical education: An international perspective. West Sussex, UK: Wiley.

    Google Scholar 

  • Biehler, R. (2003). Interrelated learning and working environments for supporting the use of computer tools in introductory classes. In International Statistical Institute (Ed.): CD-ROM Proceedings of the IASE Satellite Conference on Statistics Education and the Internet, Max-Planck-Institute for Human Development, Berlin, 11-12 August 2003, Voorburg, Netherlands.

    Google Scholar 

  • Biehler, R., Ben-Zvi, D., Bakker, A., & Makar, K. (2013). Technology for enhancing statistical reasoning at the school level. In M. A. Clements, A. Bishop, C. Keitel, J. Kilpatrick, & F. Leung (Eds.), Third international handbook of mathematics education (pp. 643–690). Springer.

    Google Scholar 

  • Bielaczyc, K. (2006). Designing social infrastructure: Critical issues in creating learning environments with technology. The Journal of the Learning Sciences, 15(3), 301–329.

    Article  Google Scholar 

  • Bielaczyc, K., & Collins, A. (1999). Learning communities in classrooms: A reconceptualization of educational practice. In C. M. Reigeluth (Ed.), Instructional-design theories and models: A new paradigm of instructional theories (Vol. II, pp. 269–292). Mahwah, NJ: Lawrence Erlbaum Associates, Publishers.

    Google Scholar 

  • Boud, D., Keogh, R., & Walker, D. (1985). Promoting reflection in learning: A model. In D. Boud, R. Keogh, & D. Walker (Eds.), Reflection: Turning experience into learning (pp. 18–39). East Brunswick, NJ: Nichols.

    Google Scholar 

  • Bransford, J., Brown, A. L., & Cocking, R. R. (Eds.). (2000). How people learn: Brain, mind, experience, and school. Washington, DC: National Academy Press.

    Google Scholar 

  • Brown, A. L., & Campione, J. C. (1994). Guided discovery in a community of learners. In K. McGilly (Ed.), Classroom lessons: Integrating cognitive theory and classroom practice (pp. 229–272). Cambridge: The MIT Press.

    Google Scholar 

  • Burgess, T. (2007). Investigating the nature of teacher knowledge needed and used in teaching statistics. Unpublished doctoral thesis, Massey University, New Zealand.

    Google Scholar 

  • Burrill, G., & Biehler, R. (2011). Fundamental statistical ideas in the school curriculum and in training teachers. In C. Batanero, G. Burrill, & C. Reading (Eds.), Teaching statistics in school mathematics-challenges for teaching and teacher education - a Joint ICMI/IASE Study: The 18th ICMI Study (pp. 57–69). Dordrecht: Springer.

    Chapter  Google Scholar 

  • Chance, B., Ben-Zvi, D., Garfield, J., & Medina, E. (2007). The role of technology in improving student learning of statistics. Technology Innovations in Statistics Education Journal, 1(1).

    Google Scholar 

  • Cialdini, R. B., & Trost, M. R. (1998). Social influence: Social norms, conformity, and compliance. In D. Gilbert, S. Fiske, & G. Lindzey (Eds.), The handbook of social psychology (Vol. 2, 4th ed., pp. 151–192). New York: McGraw-Hill.

    Google Scholar 

  • Clark, I. (2012). Formative assessment: Assessment is for self-regulated learning. Educational Psychology Review, 24(2), 205–249.

    Article  Google Scholar 

  • Cobb, G. W. (1992). Report of the joint ASA/MAA committee on undergraduate statistics. In In the American Statistical Association 1992 Proceedings of the Section on Statistical Education (pp. 281–283). Alexandria, VA: American Statistical Association.

    Google Scholar 

  • Cobb, G. W. (1993). Reconsidering statistics education: A national science foundation conference. Journal of Statistics Education, 1(1), 1–28.

    Article  Google Scholar 

  • Cobb, P. (1994a). Constructivism in mathematics and science education. Educational Researcher, 23(7), 4–4.

    Google Scholar 

  • Cobb, P. (1994b). Where is the mind? Constructivist and sociocultural perspectives on mathematical development. Educational Researcher, 23(7), 13–20.

    Article  Google Scholar 

  • Cobb, P., & McClain, K. (2004). Principles of instructional design for supporting the development of students’ statistical reasoning. In D. Ben-Zvi & J. Garfield (Eds.), The challenge of developing statistical literacy, reasoning, and thinking (pp. 375–396). Dordrecht, Netherlands: Kluwer Academic Publishers.

    Chapter  Google Scholar 

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

    Article  Google Scholar 

  • Cobb, P., Gravemeijer, K., & Yackel, E. (2011). Introduction. In E. Yackel, K. Gravemeijer, & A. Sfard (Eds.), A journey in mathematics education research, insights from the work of Paul Cobb (pp. 109–115). Dordrecht: Springer.

    Google Scholar 

  • Cobb, P., McClain, K., & Gravemeijer, K. (2003). Learning about statistical covariation. Cognition and Instruction, 21(1), 1–78.

    Article  Google Scholar 

  • Cognition and Technology Group at Vanderbilt. (1998). Designing environments to reveal, support, and expand our children’s potentials. In S. A. Soraci & W. McIlvane (Eds.), Perspectives on fundamental processes in intellectual functioning: A survey of research approaches (Vol. 1, pp. 313–350). Stamford, CT: Ablex.

    Google Scholar 

  • Collins, A. (1999). Design issues for learning environments. In S. Vosniadou, E. De Corte, R. Glaser, & H. Mandl (Eds.), International perspectives on the psychological foundations of technology-based learning environments (pp. 347–361). Hillsdale, NJ: Lawrence Erlbaum Associates.

    Google Scholar 

  • Connor, D. (2002). CensusAtSchool 2000: Creation to collation to classroom. Paper presented at the 6th International Conference on Teaching Statistics (ICOTS-6) at Cap Town, South Africa. http://iase-web.org/documents/papers/icots6/2d1_conn.pdf.

  • Conway IV, B. M. (2015). A comparison of high school students’ development of statistical reasoning outcomes in high and low statistical reasoning learning environments. Doctoral dissertation, Auburn University, USA.

    Google Scholar 

  • Cuban, L. (2003). Why is it so hard to get good schools? New York: Teachers College, Columbia University.

    Google Scholar 

  • Darling-Hammond, L. (1997). The right to learn: A blueprint for creating schools that work. Jossey-Bass.

    Google Scholar 

  • De Corte, E., Verschaffel, L., Entwistle, N., & van Merrienboer, J. (2003). Powerful learning environments (Unravelling basic components and dimensions). UK: Emerald.

    Google Scholar 

  • Edelson, D., & Reiser, B. (2006). Making authentic practices accessible to learning: Design challenges and strategies. In R. K. Sawyer (Ed.), The Cambridge handbook of the learning sciences (pp. 335–354). New York, NY: Cambridge University Press.

    Google Scholar 

  • Everson, M., Zieffler, A., & Garfield, J. (2008). Implementing new reform guidelines in teaching introductory college statistics courses. Teaching Statistics, 30(3), 66–70.

    Article  Google Scholar 

  • Franklin, C., & Garfield, J. (2006). The guidelines for assessment and instruction in statistics education (GAISE) project: Developing statistics education guidelines for pre K-12 and college courses. In G. F. Burrill (Ed.), Thinking and reasoning about data and chance: Sixty-eighth NCTM yearbook (pp. 345–375). Reston, VA: National Council of Teachers of Mathematics.

    Google Scholar 

  • Freudenthal, H. (1973). Mathematics as an educational task. Dordrecht, the Netherlands: Reidel.

    Google Scholar 

  • Freudenthal, H. (1983). Didactical phenomenology of mathematical structures. Dordrecht, the Netherlands: Reidel.

    Google Scholar 

  • Gal, I., & Garfield, J. (Eds.). (1997). The assessment challenge in statistics education. Amsterdam: IOS Press.

    Google Scholar 

  • Garfield, J., & Ben-Zvi, D. (2007). How students learn statistics revisited: A current review of research on teaching and learning statistics. International Statistical Review, 75(3), 372–396.

    Article  Google Scholar 

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

    Google Scholar 

  • Garfield, J., & Ben-Zvi, D. (2009). Helping students develop statistical reasoning: Implementing a statistical reasoning learning environment. Teaching Statistics, 31(3), 72–77.

    Article  Google Scholar 

  • Garfield, J., Hogg, B., Schau, C., & Whittinghill, D. (2002). First courses in statistical science: The status of educational reform efforts. Journal of Statistics Education [Online], 10(2).

    Google Scholar 

  • Gil, E., & Ben-Zvi, D. (2011). Explanations and context in the emergence of students’ informal inferential reasoning. Mathematical Thinking and Learning, 13(1-2), 87–108.

    Google Scholar 

  • Gil, E., & Ben-Zvi, D. (2014). Long term impact of the connections program on students’ informal inferential reasoning. In K. Makar, B. de Sousa and R. Gould (Eds.), Sustainability in statistics education (Proceedings of the Ninth International Conference on Teaching Statistics, ICOTS9, July 2014). Voorburg, The Netherlands: International Association for Statistical Education and International Statistical Institute.

    Google Scholar 

  • Gravemeijer, K. (2002a). Developing research, a course in elementary data analysis as an example. In F. Lin (Ed.), Common sense in mathematics education (pp. 43–68). Taipei, Taiwan: National Taiwan Normal University.

    Google Scholar 

  • Gravemeijer, K. (2002b). Emergent modeling as the basis for an instructional sequence on data analysis. Paper presented at the 6th International Conference on Teaching Statistics (ICOTS-6) at Cape Town, South Africa.

    Google Scholar 

  • Gravemeijer, K. (2004). Learning trajectories and local instruction theories as means of support for teachers in reform mathematics education. Mathematical Thinking and Learning, 6(2), 105–128.

    Article  Google Scholar 

  • Gravemeijer, K., & Cobb, P. (2013). Design research from the learning design perspective. In T. Plomp & N. Nieveen (Eds.), Educational design research: An introduction (part A) (pp. 72–113). Enschede: SLO (Netherlands Institute for curriculum development). Retrieved from http://downloads.slo.nl/Documenten/educational-design-research-part-a.pdf.

    Google Scholar 

  • Heyd-Metzuyanim, E. (2013). The co-construction of learning difficulties in mathematics—teacher–student interactions and their role in the development of a disabled mathematical identity. Educational Studies in Mathematics, 83(3), 341–368.

    Article  Google Scholar 

  • Hickey, D. T., Kindfield, A. C., Horwitz, P., & Christie, M. A. (2003). Integrating curriculum, instruction, assessment and evaluation in a technology-supported genetics learning environment. American Educational Research Journal, 40(2), 495–538.

    Article  Google Scholar 

  • Hod, Y., & Ben-Zvi, D. (2015). Students negotiating and designing their collaborative learning norms: A group developmental perspective in learning communities. Interactive Learning Environments, 23(5), 578–594.

    Article  Google Scholar 

  • Jacobson, M., & Reimann, P. (Eds.). (2010). Designs for learning environments of the future (international perspectives from the learning sciences). New York, NY: Springer Science+Business Media.

    Google Scholar 

  • Jonassen, D., & Land, S. (Eds.). (2012). Theoretical foundations of learning environments (2nd ed.). New York, NY: Routledge.

    Google Scholar 

  • Kali, Y., Tabak, I., Ben-Zvi, D., et al. (2015). Technology-enhanced learning communities on a continuum between ambient to designed: What can we learn by synthesizing multiple research perspectives? In O. Lindwall, P. Koschman, T. Tchounikine, & S. Ludvigsen (Eds.), Exploring the material conditions of learning: The computer supported collaborative learning conference (Vol. II, pp. 615–622). Gothenburg, Sweden: The International Society of the Learning Sciences.

    Google Scholar 

  • Kapur, M., & Bielaczyc, K. (2012). Designing for productive failure. The Journal of the Learning Sciences, 21(1), 45–83.

    Article  Google Scholar 

  • Kingston, N., & Nash, B. (2011). Formative assessment: A meta-analysis and a call for research. Educational Measurement: Issues and Practice, 30(4), 28–37.

    Article  Google Scholar 

  • Kohn, A. (1999). The schools our children deserve: Moving beyond traditional classrooms and ‘tougher standards’. Boston: Houghton Mifflin.

    Google Scholar 

  • Konold, C., & Miller, C. D. (2011). TinkerPlots: Dynamic Data Exploration (Version v2.0) [Computer software]. Available: https://www.tinkerplots.com/

  • Konold, C. & Pollatsek, A. (2002). Data analysis as the search for signals in noisy processes. Journal for Research in Mathematics Education, 33(4), 259–289.

    Google Scholar 

  • Lehrer, R. (2009). Designing to develop disciplinary knowledge: Modeling natural systems. American Psychologist, 64(8), 759–771.

    Article  Google Scholar 

  • Lehrer, R., & Pfaff, E. (2011). Designing a learning ecology to support the development of rational number: Blending motion and unit partitioning of length measures. In D. Y. Dai (Ed.), Design research on learning and thinking in educational settings: Enhancing intellectual growth and functioning (pp. 131–160). New York: Routledge.

    Google Scholar 

  • MacGillivray, H., & Pereira-Mendoza, L. (2011). Teaching statistical thinking through investigative projects. In C. Batanero, G. Burrill, & C. Reading (Eds.), Teaching statistics in school mathematics-challenges for teaching and teacher education (pp. 109–120). New York: Springer.

    Chapter  Google Scholar 

  • Makar, K., & Ben-Zvi, D. (2011). The role of context in developing reasoning about informal statistical inference. Mathematical Thinking and Learning, 13(1-2), 1–4.

    Article  Google Scholar 

  • Makar, K., Bakker, A., & Ben-Zvi, D. (2011). The reasoning behind informal statistical inference. Mathematical Thinking and Learning, 13(1-2), 152–173.

    Article  Google Scholar 

  • Makar, K., Bakker, A., & Ben-Zvi, D. (2015). Scaffolding norms of argumentation-based inquiry in a primary mathematics classroom. ZDM, 47(7), 1107–1120.

    Article  Google Scholar 

  • Manor, H., & Ben-Zvi, D. (2017). Students’ emergent articulations of statistical models and modelling in making informal statistical inferences. Statistics Education Research Journal, 16(2).

    Google Scholar 

  • Moore, D. S. (1997). New pedagogy and new content: The case of statistics. International Statistical Review, 65(2), 123–137.

    Article  Google Scholar 

  • Moore, D. S. (1998). Statistics among the liberal arts. Journal of the American Statistical Association, 93(444), 1253–1259.

    Article  Google Scholar 

  • Neumann, D. L., Hood, M., & Neumann, M. M. (2013). Using real-life data when teaching statistics: Student perceptions of this strategy in an introductory statistics course. Statistics Education Research Journal, 12(2), 59–70.

    Google Scholar 

  • Loveland, J. L. (2014). Traditional lecture versus an activity approach for teaching statistics: A comparison of outcomes (unpublished doctoral dissertation). Utah State University.

    Google Scholar 

  • Pfannkuch, M., & Ben-Zvi, D. (2011). Developing teachers’ statistical thinking. In C. Batanero, G. Burrill, & C. Reading (Eds.), Teaching statistics in school mathematics-challenges for teaching and teacher education (a Joint ICMI/IASE Study, the 18th ICMI Study) (pp. 323–333). New York: Springer.

    Chapter  Google Scholar 

  • Pfannkuch, M., & Rubick, A. (2002). An exploration of students’ statistical thinking with given data. Statistics Education Research Journal, 1(2), 4–21.

    Google Scholar 

  • Piaget, J. (1978). Success and understanding. Cambridge, MA: Harvard University Press.

    Google Scholar 

  • Pratt, D., Griffiths, G., Jennings, D. & Schmoller, S. (2016). Tensions and compromises in the design of a MOOC for adult learners of mathematics and statistics. Presented at the 13th International Congress on Mathematical Education, Hamburg.

    Google Scholar 

  • Prediger, S., Gravemeijer, K., & Confrey, J. (2015). Design research with a focus on learning processes: An overview on achievements and challenges. ZDM Mathematics Education, 47(6), 877–891.

    Article  Google Scholar 

  • Reston, E., & Bersales, L. G. (2008). Reform efforts in training statistics teachers in the Philippines: Challenges and prospects. In C. Batanero, G. Burrill, C. Reading, & A. Rossman (Eds.), Teaching statistics in school mathematics: Challenges for teaching and teacher education. Proceedings of the ICMI Study 18 and 2008 IASE Round Table Conference.

    Google Scholar 

  • Rogoff, B. (1994). Developing understanding of the idea of communities of learners. Mind, Culture, and Activity, 1(4), 209–229.

    Google Scholar 

  • Rogoff, B., Turkanis, C. G., & Bartlett, L. (2001). Learning together children and adults in a school community. London, UK: Oxford University Press.

    Google Scholar 

  • Roseth, C. J., Garfield, J. B., & Ben-Zvi, D. (2008). Collaboration in learning and teaching statistics. Journal of Statistics Education, 16(1), 1–15.

    Article  Google Scholar 

  • Savelsbergh, E. R., Prins, G. T., Rietbergen, C., Fechner, S., Vaessen, B. E., Draijer, J. M., et al. (2016). Effects of innovative science and mathematics teaching on student attitudes and achievement: A meta-analytic study. Educational Research Review, 19, 158–172.

    Article  Google Scholar 

  • Sawyer, R. K. (2014). Introduction. In R. K. Sawyer (Ed.), The Cambridge handbook of the learning sciences (pp. 1–18). Cambridge, UK: Cambridge University Press.

    Chapter  Google Scholar 

  • Scardamalia, M., & Bereiter, C. (2014). Knowledge building and knowledge creation: Theory, pedagogy, and technology. In K. Sawyer (Ed.), The Cambridge handbook of the learning sciences (2nd ed., pp. 397–417). New York: Cambridge University Press.

    Chapter  Google Scholar 

  • Sfard, A., & Cobb, P. (2014). Research in mathematics education: What can it teach us about human learning. In R. K. Sawyer (Ed.), The Cambridge handbook of the learning sciences (pp. 545–564). Cambridge, UK: Cambridge University Press.

    Chapter  Google Scholar 

  • Sfard, A., & Linchevski, L. (1994). The gains and the pitfalls of reification - the case of algebra. Educational Studies in Mathematics, 26(2), 191–228.

    Article  Google Scholar 

  • Shaughnessy, J. M., Garfield, J., & Greer, B. (1996). Data handling. In A. J. Bishop, K. Clements, C. Keitel, J. Kilpatrick, & C. Laborde (Eds.), International handbook of mathematics education (part 1) (pp. 205–238). Dordrecht, Netherlands: Kluwer.

    Google Scholar 

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

    Article  Google Scholar 

  • Slootmaeckers, K., Kerremans, B., & Adriaensen, J. (2014). Too afraid to learn: Attitudes towards statistics as a barrier to learning statistics and to acquiring quantitative skills. Politics, 34(2), 191–200.

    Article  Google Scholar 

  • Streefland, L. (1991). Fractions in realistic mathematics education: A paradigm of developmental research. Dordrecht: Kluwer Academic Publishers.

    Book  Google Scholar 

  • Treffers, A. (1987). Three dimensions: A model of goal and theory description in mathematics education - the Wiskobas Project. Dordrecht: Reidel.

    Book  Google Scholar 

  • van Hiele, P. M. (1986). Structure and insight: A theory of mathematics education. Orlando, FL: Academic Press.

    Google Scholar 

  • Vosniadou, S., & Vamvakoussi, X. (2006). Examining mathematics learning from a conceptual change point of view: Implications for the design of learning environments. In L. Verschaffel, F. Dochy, M. Boekaerts, & S. Vosniadou (Eds.), Instructional psychology: Past, present and future trends. Sixteen essays in honour of Erik De Corte (pp. 55–70). Oxford, UK: Elsevier.

    Google Scholar 

  • Vosniadou, S., Ioannides, C., Dimitrakopoulou, A., & Papademetriou, E. (2001). Designing learning environments to promote conceptual change in science. Learning and Instruction, 11(4), 381–419.

    Article  Google Scholar 

  • Vygotsky, L. (1978). Mind in society. Cambridge, MA: Harvard University Press.

    Google Scholar 

  • Watson, A., & Ohtani, M. (Eds.). (2015). Task design in mathematics education: An ICMI study 22. Cham: Springer.

    Google Scholar 

  • Wenger, E. (1998). Communities of practice: Learning, meaning, and identity. Cambridge: Cambridge University Press.

    Book  Google Scholar 

  • Wild, C. (2007). Virtual environments and the acceleration of experiential learning. International Statistical Review, 75(3), 322–335.

    Article  Google Scholar 

  • Yackel, E., & Cobb, P. (1996). Sociomathematical norms, argumentation, and autonomy in mathematics. Journal for Research in Mathematics Education, 27(4), 458–477.

    Article  Google Scholar 

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Ben-Zvi, D., Gravemeijer, K., Ainley, J. (2018). Design of Statistics Learning Environments. In: Ben-Zvi, D., Makar, K., Garfield, J. (eds) International Handbook of Research in Statistics Education. Springer International Handbooks of Education. Springer, Cham. https://doi.org/10.1007/978-3-319-66195-7_16

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