Abstract
In this overview and critique of perspective II, we briefly focus on several ways that Models & Modeling Perspectives (MMP) can be used to provide a unifying theoretical framework for developing both: (a) a coherent summary of the kind of research reported in this book, and (b) a useful list of testable claims that appear to be priorities to investigate in future research emanating from the kind of studies reported here. In particular, MMP was developed to identify: (a) emerging new types of mathematical thinking that appear to be needed beyond mathematics classrooms—including in situations involving new sciences (e.g., social sciences, engineering) not traditionally emphasized in K-12 curriculum materials, (b) new ways to operationally define important achievements currently being ignored in both school testing programs and documents specifying standards for teaching and learning, and (c) new teaching and learning opportunities made possible by new model-development tools for students (Lesh and Doerr, Beyond constructivist: a models & modeling perspective on mathematics teaching, learning, and problems solving, Erlbaum, Hillsdale, 2003; Lesh, Models & Modeling in Mathematics Education, Monograph for International Journal for Mathematical Thinking & Learning, Erlbaum, Hillsdale, 2003b).
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Borromeo-Ferri, R., & Lesh, R. (2011). Should interpretation systems be considered to be models if they only function implicitly? In G. Kaiser, W. Blum, & K. Maass (Eds.), Teaching mathematical modeling & applications. Berlin: Springer.
Common Core State Standards Initiative (2010). Common Core State Standards for mathematics. Retrieved from http://www.corestandards.org/assets/CCSSI_Math%20Standards.pdf.
Doerr, H., & Lesh, R. (2010). Model-eliciting activities: do they work in the education of students, teams, or teachers? In G. Kaiser, W. Blum, & K. Maass (Eds.), Teaching mathematical modeling & applications. Berlin: Springer.
Hamilton, E., Lesh, R., Lester, F., & Yoon, C. (2007). The use of reflection tools in building personal models of problem solving. In R. Lesh, E. Hamilton, & J. Kaput (Eds.), Foundations for the future in mathematics education (pp. 349–366). Mahwah: Erlbaum.
Kelly, A., & Lesh, R. (Eds.) (2000). The handbook of research design in mathematics and science education. Hillsdale: Erlbaum.
Kelly, A. E., Lesh, R. A., & Baek, J. (2009). Handbook of design research methods in education. New York: Routledge.
Lesh, R. (2002). Research design in mathematics education: focusing on design experiments. In L. English (Ed.), International handbook of research design in mathematics education. Hillsdale: Erlbaum.
Lesh, R. (2003a). Multi-tier design research. In L. English, M. Bartolini Bussi, G. Jones, R. Lesh, B. Sriraman, & D. Tirosh (Eds.), Handbook of international research in mathematics education. New York: Routledge.
Lesh, R. (2003b). Monograph for international journal for mathematical thinking & learning. Models & modeling in mathematics education. Hillsdale: Erlbaum.
Lesh, R., & Caylor, E. (2007). Modeling as application vs modeling as a way to create mathematics. International Journal of Computers for Mathematical Learning, 12, 173–194.
Lesh, R., & Doerr, H. (2003). Beyond constructivist: a models & modeling perspective on mathematics teaching, learning, and problems solving. Hillsdale: Erlbaum.
Lesh, R., & Doerr, H. (2011). Alternatives to trajectories and pathways to describe development in modeling and problem solving. In R. Borromeo-Ferri (Ed.), Teaching mathematical modeling & applications. Berlin: Springer.
Lesh, R., & Lamon, S. (1992). Assessing authentic mathematical performance. Washington: American Association for the Advancement of Sciences Press.
Lesh, R., & Sriraman, B. (2005). Mathematics education as a design science. International Reviews on Mathematical Education, 37(6), 490–505.
Lesh, R., & Sriraman, B. (2010). Mathematics education as a design science. In B. Sriraman & L. English (Eds.) Advances in mathematics education: Vol. 1. Theories of mathematics education: seeking new frontiers Berlin: Springer.
Lesh, R., & Yoon, C. (2004). Evolving communities of mind—in which development involves several interacting and simultaneously developing strands. Mathematical Thinking and Learning, 6(2), 205–226.
Lesh, R., & Zawojewski, J. (2007). Problem solving and modeling. In F. K. Lester Jr. (Ed.), Second handbook of research on mathematics teaching and learning (pp. 763–804). Charlotte: Information Age Publishing.
Lesh, R., Hamilton, E., & Kaput, J. (Eds.) (2007). Models & modeling as foundations for the future in mathematics education. Hillsdale: Erlbaum.
Lesh, R., Carmona, G., & Moore, T. (2010a). Six sigma learning gains and long term retention of understanding and attitudes related to models & modeling. Mediterranean Journal for Research in Mathematics Education, 9(1), 19–54.
Lesh, R., Haines, C., Galbraith, P., & Hurford, A. (2010b). Modeling students’ mathematical modeling competencies. Berlin: Springer.
Piaget, J. (1970). Genetic epistemology. New York: Norton.
Sriraman, B., & Lesh, R. (2007). Leaders in mathematical thinking & learning—a conversation with Zoltan P. Dienes. Mathematical Thinking and Learning: An International Journal, 9(1), 59–75.
Vygotsky, L. S. (1962). Thought and language. Cambridge: Massachusetts Institute of Technology Press.
Zawojewski, J., Diefes-Dux, H., & Bowman, K. (Eds.) (2009). Models and modeling in engineering education: designing experiences for all students. Rotterdam: Sense Publications.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Lesh, R., Sriraman, B. (2014). A Brief Overview and Critique of Perspective II on Probabilistic and Statistical Reasoning. In: Chernoff, E., Sriraman, B. (eds) Probabilistic Thinking. Advances in Mathematics Education. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-7155-0_17
Download citation
DOI: https://doi.org/10.1007/978-94-007-7155-0_17
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-007-7154-3
Online ISBN: 978-94-007-7155-0
eBook Packages: Humanities, Social Sciences and LawEducation (R0)