Mathematics teachers’ views about the limited utility of real analysis: A transport model hypothesis

Alcock, 2015, Investigating and improving undergraduate proof comprehension, Notices of the American Mathematical Society, 62, 742, 10.1090/noti1263 Ball, 2008, Content knowledge for teaching what makes it special?, Journal of Teacher Education, 59, 389, 10.1177/0022487108324554 Barnett, 2002, When and where do we apply what we learn?: A taxonomy for far transfer, Psychological Bulletin, 128, 612, 10.1037/0033-2909.128.4.612 Bieda, 2010, Enacting proof-related tasks in middle school mathematics: Challenges and opportunities, Journal for Research in Mathematics Education, 41, 351, 10.5951/jresematheduc.41.4.0351 Bremigan, 2011 Bryan, 1999, The conceptual knowledge of preservice secondary mathematics teachers: How well do they know the subject matter they will teach?, Issues in the Undergraduate Mathematics Preparation of School Teachers: The Journal, 1, 1 Conference Board of the Mathematical Sciences, 2001 Conference Board of the Mathematical Sciences, 2012 Common Core State Standards in Mathematics (CCSSM), 2010 Cankoy, 2010, Mathematics teachers’ topic-specific pedagogical content knowledge in the context of teaching a^0, 0! and a/0, Educational Sciences: Theory & Practice, 10, 749 Cornu, 1991, Limits, 153 Darling-Hammond, 2000, Teacher quality and student achievement: A review of state policy evidence, Educational Policy Analysis Archives, 8 Davis, 1986, The notion of limit: Some seemingly unavoidable misconception stages, The Journal of Mathematical Behavior, 5, 281 Deng, 2007, Knowing the subject matter of a secondary-school science subject, Journal of Curriculum Studies, 39, 503, 10.1080/00220270701305362 Even, 1990, Subject matter knowledge for teaching and the case of functions, Educational Studies in Mathematics, 21, 521, 10.1007/BF00315943 Even, 2011, The relevance of advanced mathematics studies to expertise in secondary school mathematics teaching: Practitioners’ views, ZDM, 43, 941, 10.1007/s11858-011-0346-1 Ferrini-Mundy, 2010, The mathematical education of prospective teachers of secondary school mathematics: Old assumptions, new challenges, 31 Fitzpatrick, 2006 Gaughan, 1998 Goulding, 2003, Undergraduate mathematics experience: Its significance in secondary mathematics teacher preparation, Journal of Mathematics Teacher Education, 6, 361, 10.1023/A:1026362813351 Heinze, 2015, Teachers’ mathematical content knowledge in the field of tension between academic and school mathematics, Paper presented at didactics of mathematics in higher education as a scientific discipline Klein, 1932 Lobato, 2012, The actor-oriented transfer perspective and its contributions to educational research and practice, Educational Psychologist, 47, 232, 10.1080/00461520.2012.693353 Monk, 1994, Subject area preparation of secondary mathematics and science teachers and student achievement, Economics of Education Review, 13, 125, 10.1016/0272-7757(94)90003-5 Moreira, 2008, Academic mathematics and mathematical knowledge needed in school teaching practice: Some conflicting elements, Journal of Mathematics Teacher Education, 11, 23, 10.1007/s10857-007-9057-5 Murray, 2013, What do secondary preservice mathematics teachers need to know?, Notices of the American Mathematical Society, 60, 1297, 10.1090/noti1048 National Council of Teachers of Mathematics (NCTM), 2000 Pinto, 1999, Student constructions of formal theory: Giving and extracting meaning, Vol. 4, 65 Rhoads, 2014 Roh, 2008, Students’ images and their understanding of definitions of the limit of a sequence, Educational Studies in Mathematics, 69, 217, 10.1007/s10649-008-9128-2 Rowland, 2005, Elementary teachers’ mathematics subject knowledge: The knowledge quartet and the case of Naomi, Journal of Mathematics Teacher Education, 8, 255, 10.1007/s10857-005-0853-5 Sánchez, 2003, Four student teachers’ pedagogical reasoning on functions, Journal of Mathematics Teacher Education, 6, 5, 10.1023/A:1022123615355 Shulman, 1986, Those who understand: Knowledge growth in teaching, Educational Researcher, 15, 4, 10.3102/0013189X015002004 Sierpińska, 1987, Humanities students and epistemological obstacles related to limits, Educational Studies in Mathematics, 18, 371, 10.1007/BF00240986 Strauss, 1990 Sultan, 2011 Ticknor, 2012, Situated learning in an abstract algebra classroom, Educational Studies in Mathematics, 81, 307, 10.1007/s10649-012-9405-y Usiskin, 2003 Weber, 2004, Traditional instruction in advanced mathematics courses: A case study of one professor’s lectures and proofs in an introductory real analysis course, Journal of Mathematical Behavior, 23, 115, 10.1016/j.jmathb.2004.03.001 Weber, 2008, The role of affect in learning real analysis: A case study, Research in Mathematics Education, 10, 71, 10.1080/14794800801916598 Wasserman, 2013, Beginning teachers’ perspectives on attributes for teaching secondary mathematics: Reflections on teacher education, Mathematics Teacher Education and Development, 15, 70 Wasserman, 2016, Abstract algebra for algebra teaching: Influencing school mathematics instruction, Canadian Journal of Science Mathematics and Technology Education, 16, 28, 10.1080/14926156.2015.1093200 Wasserman, 2017, Nonlocal mathematical knowledge for teaching, Journal of Mathematical Behavior Wasserman, 2017, Pedagogical applications from real analysis for secondary mathematics teachers, For the Learning of Mathematics, 37, 14 Wasserman, 2017, Making real analysis relevant to secondary teachers: Building up from and stepping down to practice, PRIMUS, 7, 559, 10.1080/10511970.2016.1225874 Wasserman, 2017, Leveraging real analysis to foster pedagogical practices, 1 Winsløw, 2014, Klein’s double discontinuity revisited: Contemporary challenges for universities preparing teachers to teach calculus, Recherches en Didctique des Matematiques, 34, 59 Yopp, 2011, Why it is important for in-service elementary mathematics teachers to understand the equality. 999… = 1, The Journal of Mathematical Behavior, 30, 304, 10.1016/j.jmathb.2011.07.007 Zazkis, 2010, Advanced mathematical knowledge in teaching practice: Perceptions of secondary mathematics teachers, Mathematical Thinking and Learning, 12, 263, 10.1080/10986061003786349