Examining the design features of a communication-rich, problem-centred mathematics professional development

References

• Banilower ER, Heck DJ, Weiss IR. Can professional development make the vision of the standards a reality? The impact of the national science foundation's local systemic change through teacher enhancement initiative. J Res Sci Teach. 2007;44:375–395.
   Web of Science ®Google Scholar
• Desimone LM. Improving impact studies of teachers’ professional development: toward better conceptualizations and measures. Educ Res. 2009;38:181–199.
   Web of Science ®Google Scholar
• Desimone LM, Porter AC, Garet MS, et al. Effects of professional development on teachers’ instruction: results from a three-year longitudinal study. Educ Eval Policy Anal. 2002;24:81–112.
   Web of Science ®Google Scholar
• Elmore RF. Bridging the gap between standards and achievement: the imperative for professional development in education. Washington (DC): Albert Shanker Institute; 2002. Available from: http://www.shankerinstitute.org/sites/shanker/files/Bridging_Gap.pdf
   Google Scholar
• Garet MS, Porter AC, Desimone L, et al. What makes professional development effective? Results from a national sample of teachers. Am Educ Res J. 2001;38:915–945.
   Web of Science ®Google Scholar
• Hawley WD, Valli L. The essentials of effective professional development: A new consensus. In: Darling Hammond L, Sykes G, editors. Teaching as the learning profession: handbook of policy and practice. San Francisco (CA): Jossey-Bass; 1999. p. 127–150.
   Google Scholar
• Borko H, Putnam RT. Professional development and reform-based teaching: Introduction to the theme issue. Teach Teach Educ. 1998;14:1–3.
   Web of Science ®Google Scholar
• Doerr HM, Goldsmith LT, Lewis CC. Professional development research brief: mathematics professional development. Reston (VA): National Council of Teachers of Mathematics; 2010.
   Google Scholar
• Heck DJ, Banilower ER, Weiss IR, et al. Studying the effects of professional development: the case of the NSF's local systemic change through teacher enhancement initiative. J Res Math Educ. 2008;39:113–152.
   Web of Science ®Google Scholar
• Izsák A, Jacobson E, de Araujo Z, et al. Measuring mathematical knowledge for teaching fractions with drawn quantities. J Res Math Educ. 2012;43:391–427.
   Web of Science ®Google Scholar
• Orrill CH, Cohen AS. Why defining the construct matters: an examination of teacher knowledge using different lenses on one assessment. The Math Enthusiast. 2016;13:93–110.
   Web of Science ®Google Scholar
• Harris G, Stevens T, Higgins R. A professional development model for middle school teachers of mathematics. Int J Math Educ Sci Technol. 2011;42:951–961.
   Google Scholar
• National Governors Association Center for Best Practices, Council of Chief State School Officers, Officers NGAC for BP& C of CSS. Common core standards for mathematics. [Internet]. Washington (DC): National Governors Association Center for Best Practices, Council of Chief State School Officers, Officers NGAC for BP& C of CSS; 2010. Available from: http://www.corestandards.org/the-standards/mathematics.
   Google Scholar
• Schmidt WH, Houang RT. Curricular coherence and the common core state standards for mathematics. Educ Res. 2012;41:294–308.
   Web of Science ®Google Scholar
• Orrill CH, The InterMath Team. What learner-centered professional development looks like: the pilot studies of the InterMath professional development project. The Math Educ. 2006;16:4–13.
   Google Scholar
• Jonassen DH, Hung W. All problems are not equal: Implications for problem-based learning. Interdiscip J Probl Learn. 2008;2:10–13.
   Google Scholar
• National Council of Teachers of Mathematics. Principles and standards for school mathematics. Reston (VA): National Council of Teachers of Mathematics; 2000.
   Google Scholar
• Savery JR. Overview of PBL: definitions and distinctions. Interdiscip J Probl Learn. 2006;1:9–20.
   Google Scholar
• Savery JR, Duffy TM. Problem-based learning: An instructional model and its constructivist framework. In: Wilson B, editor. Constructivist learning environments: case studies in instructional design. Cliffs (NJ): Educational Technology Publications; 1995. p. 135–148.
   Google Scholar
• Hall R. Videorecording as theory. In: Kelly AE, Lesh RA, editors. Handbook of research design in mathematics and science education. Mahwah (NJ): Lawrence Erlbaum; 2000. p. 647–664.
   Google Scholar
• Izsák A, Orrill CH, Cohen A, et al. Measuring middle grades teachers' understanding of rational numbers with the mixture Rasch model. Elem School J. 2010;110:279–300.
   Web of Science ®Google Scholar
• Wilson M. Constructing measures: an item response modelling approach. Mahwah (NJ): Erlbaum; 2005.
   Google Scholar
• Izsák A. Mathematical knowledge for teaching fraction multiplication. Cogn Instr. 2008;26:95–143.
   Web of Science ®Google Scholar
• Charmaz K. Constructing grounded theory. 2nd ed. Los Angeles (CA): Sage; 2014.
   Google Scholar
• Brown RE. Community building in mathematics professional development. Athens (GA): University of Georgia; 2009.
   Google Scholar
• Wenger E. Communities of practice: learning, meaning, and identity. Cambridge: Cambridge University Press; 1998.
   Google Scholar
• Stein MK, Engle RA, Smith MS, et al. Orchestrating productive mathematical discussions: five practices for helping teachers move beyond show and tell. Math Think Learn. 2008;10:313–340.
   Google Scholar
• Henning JE, McKeny T, Foley GD, et al. Mathematics discussions by design: creating opportunities for purposeful participation. J Math Teach Educ. 2012;15:453–479.
   Google Scholar
• National Council of Teachers of Mathematics. Principles to actions: Ensuring mathematical success for all. Reston (VA): National Council of Teachers of Mathematics; 2014.
   Google Scholar
• National Council of Teachers of Mathematics. Mathematics teaching today: Improving practice, improving student learning. 2nd ed. Reston (VA): National Council of Teachers of Mathematics; 2007.
   Google Scholar
• Ball DL, Thames MH, Phelps G, et al. Content knowledge for teaching: what makes it special? J Teach Educ. 2008;59:389–407.
   Web of Science ®Google Scholar
• ConferenceBoard of the Mathematical Sciences. The mathematical education of teachers II. ( Issues in Mathematics Education, Vol. 17). Providence (RI): American Mathematical Society; and Washington, DC: Mathematical Association of America; 2012. Available from: http://www.ams.org/books/cbmath/017/cbmath017-endmatter.pdf
   Google Scholar
• Shulman LS. Those who understand: knowledge growth in teaching. Educ Res. 1986;15:4–14.
   Google Scholar
• Jonassen DH. Toward a design theory of problem solving. Educ Technol Res Dev. 2000;48:63–85.
   Web of Science ®Google Scholar
• Bleier SK, Baxter WA, Stephens CD, et al. Constructing meaning: standards for mathematical practice. Teach Child Math. 2015;21:336–344.
   Google Scholar
• Lamon SJ. Rational numbers and proportional reasoning. In: Lester FK, editor. Second handbook for research on mathematics teaching and learning. Charlotte (NC): Information Age Publishing; 2007. p. 629–667.
   Google Scholar
• Lee SJ, Brown RE, Orrill CH. Mathematics teachers' reasoning about fractions and decimals using drawn representations. Math Think and Learn. 2011;13:198–220.
   Web of Science ®Google Scholar
• Post T, Harel G, Behr M, et al. Intermediate teachers’ knowledge of rational number concepts. In: Fennema E, Carpenter TP, Lamon SJ. editors. Papers from first Wisconsin symposium for research on teaching and learning mathematics. Madison (WI): Wisconsin Centre for Education Research; 1998. p. 194–219.
   Google Scholar
• Lesh RA, Post T, Behr MJ. Representations and translations among representations in mathematics learning and problem solving. In: Janvier C, editor. Problems of representations in the teaching and learning of mathematics. Hillsdale (NJ): Lawrence Erlbaum; 1987. p. 33–40.
   Google Scholar
• Dreyfus T, Eisenber T. On different facets of mathematical thinking. In: Sternberg RJ, Ben-Zeev T, editors. The nature of mathematical thinking. Mahwah (NJ): Erlbaum; 1996. p. 253–284.
   Google Scholar
• Van de Walle JA. Elementary and middle school mathematics: Teaching developmentally. 6th ed. Boston (MA): Pearson Education; 2007.
   Google Scholar
• Orrill CH, Polly D. Supporting mathematical communication through technology. In: Polly D, editor. Common core mathematics standards and implementing digital technologies. Hershey (PA): IGI Global; 2013. p. 22–36.
   Google Scholar
• Burke J, Orill J. Fraction bars. [web software]. Dartmouth (MA): University of Massachusetts Dartmouth; 2013.
   Google Scholar
• Franke ML, Kazemi E, Battey D. Mathematics teaching and classroom practice. In: Lester FK, editor. Second handbook of research on mathematics teaching and learning. Charlotte (NC): Information Age Publishing; 2007. p. 225–256.
   Google Scholar
• Boaler J, Staples M. Creating mathematical futures through an equitable teaching approach: the case of Railside School. Teach Coll Rec. 2008;110:608–645.
   Web of Science ®Google Scholar
• Sherin MG. A balancing act: developing a discourse community in a mathematics classroom. J Math Teach Educ. 2002;5:205–233.
   Google Scholar
• Wood T, Williams G, McNeal B. Children's mathematical thinking in different classroom cultures. J Res Math Educ. 2006;37:222–255.
   Web of Science ®Google Scholar
• Hill HC. Professional development standards and practices in elementary school mathematics. Elem Sch J. 2004;104:215–231.
   Web of Science ®Google Scholar
• Burkhardt H, Fraser R, Ridgway J. The dynamics of curriculum change. In: Wirszup I, Streit R, editors. Developments in school mathematics education around the World. Reston (VA): National Council of Teachers of Mathematics; 1990. p. 3–30.
   Google Scholar
• Foley GD, Khoshaim HB, Alsaeed M, et al. Professional development in statistics, technology, and cognitively demanding tasks: classroom implementation and obstacles. Int J Math Educ Sci Technol. 2012;43:177–196.
   Google Scholar