Skip to main content

2018 | OriginalPaper | Buchkapitel

Research in Collegiate Mathematics Education

verfasst von : Shandy Hauk, Chris Rasmussen, Nicole Engelke Infante, Elise Lockwood, Michelle Zandieh, Stacy Brown, Yvonne Lai, Pao-sheng Hsu

Erschienen in: Advances in the Mathematical Sciences

Verlag: Springer International Publishing

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

The chapter sketches some of the landscape of current research in undergraduate mathematics education and offers useful information for present and future faculty members. Six research projects related to the teaching and learning of post-secondary mathematics are summarized. Approaches in the research reported here include individual interviews, classroom observations, national survey, and in-depth study of a particular instance or case of learning. The collegiate mathematics topics at the heart of the respective studies range from calculus, combinatorics, linear algebra, and foundations of proof to the application of mathematics to teaching in the development of future teachers.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Literatur
5.
Zurück zum Zitat S.A. Annin, K.S. Lai. Common errors in counting problems. Math. Teach. 103(6), 402–409 (2010) S.A. Annin, K.S. Lai. Common errors in counting problems. Math. Teach. 103(6), 402–409 (2010)
6.
Zurück zum Zitat S. Antonini, M.A. Mariotti, Reasoning in an absurd world: difficulties with proof by contradiction, in Proceedings of the 30th PME Conference, Prague, vol. 2 (2006), pp. 65–72 S. Antonini, M.A. Mariotti, Reasoning in an absurd world: difficulties with proof by contradiction, in Proceedings of the 30th PME Conference, Prague, vol. 2 (2006), pp. 65–72
7.
Zurück zum Zitat S. Antonini, M.A. Mariotti, Indirect proof: what is specific to this way of proving? ZDM Math. Educ. 40, 401–412 (2008)CrossRef S. Antonini, M.A. Mariotti, Indirect proof: what is specific to this way of proving? ZDM Math. Educ. 40, 401–412 (2008)CrossRef
9.
Zurück zum Zitat H. Bass, Mathematics, mathematicians, and mathematics education. Bull. Am. Math. Soc. 42(4), 417–430 (2005)CrossRef H. Bass, Mathematics, mathematicians, and mathematics education. Bull. Am. Math. Soc. 42(4), 417–430 (2005)CrossRef
10.
Zurück zum Zitat R. Blair, E.E. Kirkman, J.W. Maxwell, Statistical Abstract of Undergraduate Programs in the Mathematical Sciences in the United States. Conference Board of the Mathematical Sciences (American Mathematical Society, Providence, 2012) R. Blair, E.E. Kirkman, J.W. Maxwell, Statistical Abstract of Undergraduate Programs in the Mathematical Sciences in the United States. Conference Board of the Mathematical Sciences (American Mathematical Society, Providence, 2012)
11.
Zurück zum Zitat M. Bona, Introduction to Enumerative Combinatorics (McGraw Hill, New York, 2007)MATH M. Bona, Introduction to Enumerative Combinatorics (McGraw Hill, New York, 2007)MATH
12.
Zurück zum Zitat V. Braun, V. Clarke, Using thematic analysis in psychology. Qual. Res. Psychol. 3(2), 77–101 (2006)CrossRef V. Braun, V. Clarke, Using thematic analysis in psychology. Qual. Res. Psychol. 3(2), 77–101 (2006)CrossRef
13.
Zurück zum Zitat D. Bressoud, V. Mesa, C. Rasmussen (eds.), Insights and Recommendations from the MAA National Study of College Calculus (Mathematical Association of America, Washington, DC, 2015) D. Bressoud, V. Mesa, C. Rasmussen (eds.), Insights and Recommendations from the MAA National Study of College Calculus (Mathematical Association of America, Washington, DC, 2015)
14.
Zurück zum Zitat L. Cohen, L. Manion, K. Morrison, Research Methods in Education (Routledge, London, 2011) L. Cohen, L. Manion, K. Morrison, Research Methods in Education (Routledge, London, 2011)
18.
Zurück zum Zitat M.M. Eizenberg, O. Zaslavsky, Students’ verification strategies for combinatorial problems. Math. Think. Learn. 6(1), 15–36 (2004)CrossRef M.M. Eizenberg, O. Zaslavsky, Students’ verification strategies for combinatorial problems. Math. Think. Learn. 6(1), 15–36 (2004)CrossRef
21.
Zurück zum Zitat N. Engelke Infante, The second derivative test: a case study of instructor gesture use. Paper presented at the 38th annual conference of the North American chapter of the international group for the psychology of mathematics education, Tucson, AZ, 2016 N. Engelke Infante, The second derivative test: a case study of instructor gesture use. Paper presented at the 38th annual conference of the North American chapter of the international group for the psychology of mathematics education, Tucson, AZ, 2016
22.
Zurück zum Zitat S. Freeman, S.L. Eddy, M. McDonough, M.K. Smith, N. Okoroafor, H. Jordt, M.P. Wenderoth, Active learning increases student performance in science, engineering, and mathematics.Proc. Natl. Acad. Sci. 111(23), 8410–8415 (2014)CrossRef S. Freeman, S.L. Eddy, M. McDonough, M.K. Smith, N. Okoroafor, H. Jordt, M.P. Wenderoth, Active learning increases student performance in science, engineering, and mathematics.Proc. Natl. Acad. Sci. 111(23), 8410–8415 (2014)CrossRef
23.
Zurück zum Zitat M. Goetting, The college students’ understanding of mathematical proof, Doctoral dissertation, University of Maryland (1995) M. Goetting, The college students’ understanding of mathematical proof, Doctoral dissertation, University of Maryland (1995)
24.
Zurück zum Zitat S. Goldin-Meadow, Beyond words: the importance of gesture to researchers and learners. Child Dev. 71(1), 231–239 (2000)CrossRef S. Goldin-Meadow, Beyond words: the importance of gesture to researchers and learners. Child Dev. 71(1), 231–239 (2000)CrossRef
25.
Zurück zum Zitat M. Goulding, G. Hatch, M. Rodd, Undergraduate mathematics experience: its significance in secondary mathematics teacher preparation. J. Math. Teach. Educ. 6(4), 361–393 (2003)CrossRef M. Goulding, G. Hatch, M. Rodd, Undergraduate mathematics experience: its significance in secondary mathematics teacher preparation. J. Math. Teach. Educ. 6(4), 361–393 (2003)CrossRef
26.
Zurück zum Zitat G. Harel, L. Sowder, Students’ proof schemes: results from exploratory studies, in Research on Collegiate Mathematics Education. III, ed. by A. Schoenfeld, J. Kaput, E. Dubinsky (American Mathematical Society, Providence, 1998), pp. 234–283CrossRef G. Harel, L. Sowder, Students’ proof schemes: results from exploratory studies, in Research on Collegiate Mathematics Education. III, ed. by A. Schoenfeld, J. Kaput, E. Dubinsky (American Mathematical Society, Providence, 1998), pp. 234–283CrossRef
27.
Zurück zum Zitat A.B. Hostetter, K. Bieda, M.W. Alibali, M.J. Nathan, E. Knuth, Don’t just tell them, show them! Teachers can intentionally alter their instructional gestures. Paper presented at the 28th annual conference of the cognitive science society, Vancouver, BC, 2006 A.B. Hostetter, K. Bieda, M.W. Alibali, M.J. Nathan, E. Knuth, Don’t just tell them, show them! Teachers can intentionally alter their instructional gestures. Paper presented at the 28th annual conference of the cognitive science society, Vancouver, BC, 2006
28.
Zurück zum Zitat H. Howell, Y. Lai, G. Phelps, Assessing mathematical knowledge for teaching beyond conventional content knowledge: do elementary models extend? Paper presented at the annual meeting of the american educational research association, Washington, DC, 2016 H. Howell, Y. Lai, G. Phelps, Assessing mathematical knowledge for teaching beyond conventional content knowledge: do elementary models extend? Paper presented at the annual meeting of the american educational research association, Washington, DC, 2016
29.
Zurück zum Zitat M. Kogan, S.L. Laursen, Assessing long-term effects of inquiry-based learning: a case study from college mathematics. Innov. High. Educ. 39(3), 183–199 (2014)CrossRef M. Kogan, S.L. Laursen, Assessing long-term effects of inquiry-based learning: a case study from college mathematics. Innov. High. Educ. 39(3), 183–199 (2014)CrossRef
30.
Zurück zum Zitat B. Koichu, R. Zazkis, Decoding a proof of Fermat’s Little Theorem via script writing. J. Math. Behav. 32, 364–376 (2013)CrossRef B. Koichu, R. Zazkis, Decoding a proof of Fermat’s Little Theorem via script writing. J. Math. Behav. 32, 364–376 (2013)CrossRef
31.
Zurück zum Zitat G. Kuh, T. Cruce, R. Shoup, J. Kinzie, R. Gonyea, Unmasking the effects of student engagement on first-year college grades and persistence. J. High. Educ. 79(5), 540–563 (2008)CrossRef G. Kuh, T. Cruce, R. Shoup, J. Kinzie, R. Gonyea, Unmasking the effects of student engagement on first-year college grades and persistence. J. High. Educ. 79(5), 540–563 (2008)CrossRef
32.
Zurück zum Zitat G. Lakoff, R. Nunez, Where Mathematics Comes From: How the Embodied Mind Brings Mathematics into Being (Basic Books, New York, 2000)MATH G. Lakoff, R. Nunez, Where Mathematics Comes From: How the Embodied Mind Brings Mathematics into Being (Basic Books, New York, 2000)MATH
33.
Zurück zum Zitat U. Leron, A direct approach to indirect proofs. Educ. Stud. Math. 16(3), 321–325 (1985)CrossRef U. Leron, A direct approach to indirect proofs. Educ. Stud. Math. 16(3), 321–325 (1985)CrossRef
35.
Zurück zum Zitat E. Lockwood, B. Schaub, An unexpected outcome: students’ focus on order in the multiplication principle, in Proceedings of the 20th Conference on Research on Undergraduate Mathematics Education, San Diego, CA (2017) E. Lockwood, B. Schaub, An unexpected outcome: students’ focus on order in the multiplication principle, in Proceedings of the 20th Conference on Research on Undergraduate Mathematics Education, San Diego, CA (2017)
37.
Zurück zum Zitat M.J. Nathan, K.R. Koedinger, M.W. Alibali, Expert blind spot: when content knowledge eclipses pedagogical content knowledge, in Proceedings of the Third International Conference on Cognitive Science, ed. by L. Chen et al. (USTC Press, Beijing, 2001), pp. 644–648 M.J. Nathan, K.R. Koedinger, M.W. Alibali, Expert blind spot: when content knowledge eclipses pedagogical content knowledge, in Proceedings of the Third International Conference on Cognitive Science, ed. by L. Chen et al. (USTC Press, Beijing, 2001), pp. 644–648
39.
Zurück zum Zitat D. Plaxco, M. Zandieh, M. Wawro, Stretch Directions and Stretch Factors: A Sequence Intended to Support Guided Reinvention of Eigenvector and Eigenvalue. Challenges and Strategies in Teaching Linear Algebra, ed. by S. Stewart, C. Andrews-Larson, A. Berman, M. Zandieh (Berlin: Springer, 2018), pp. 172–192.CrossRef D. Plaxco, M. Zandieh, M. Wawro, Stretch Directions and Stretch Factors: A Sequence Intended to Support Guided Reinvention of Eigenvector and Eigenvalue. Challenges and Strategies in Teaching Linear Algebra, ed. by S. Stewart, C. Andrews-Larson, A. Berman, M. Zandieh (Berlin: Springer, 2018), pp. 172–192.CrossRef
40.
Zurück zum Zitat President’s Council of Advisors on Science and Technology (PCAST), Engage to Excel: Producing One Million Additional College Graduates with Degrees in Science, Technology, Engineering, and Mathematics (The White House, Washington, DC, 2012) President’s Council of Advisors on Science and Technology (PCAST), Engage to Excel: Producing One Million Additional College Graduates with Degrees in Science, Technology, Engineering, and Mathematics (The White House, Washington, DC, 2012)
41.
Zurück zum Zitat C. Rasmussen, O.N. Kwon, An inquiry-oriented approach to undergraduate mathematics. J. Math. Behav. 26, 189–194 (2007)CrossRef C. Rasmussen, O.N. Kwon, An inquiry-oriented approach to undergraduate mathematics. J. Math. Behav. 26, 189–194 (2007)CrossRef
42.
Zurück zum Zitat C. Rasmussen, M. Zandieh, M. Wawro, How do you know which way the arrows go? The emergence and brokering of a classroom mathematics practice, in Mathematical Representations at the Interface of the Body and Culture, ed. by W.-M. Roth (Information Age, Charlotte, 2009), pp. 171–218 C. Rasmussen, M. Zandieh, M. Wawro, How do you know which way the arrows go? The emergence and brokering of a classroom mathematics practice, in Mathematical Representations at the Interface of the Body and Culture, ed. by W.-M. Roth (Information Age, Charlotte, 2009), pp. 171–218
43.
Zurück zum Zitat B. Richmond, T. Richmond, A Discrete Transition to Advanced Mathematics (American Mathematical Society, Providence, 2009)MATH B. Richmond, T. Richmond, A Discrete Transition to Advanced Mathematics (American Mathematical Society, Providence, 2009)MATH
44.
Zurück zum Zitat K.H. Rosen, Discrete Mathematics and Its Applications, 6th edn. (McGraw Hill, New York, 2007) K.H. Rosen, Discrete Mathematics and Its Applications, 6th edn. (McGraw Hill, New York, 2007)
45.
Zurück zum Zitat W.M. Roth, Gestures: their role in teaching and learning. Rev. Educ. Res. 71(3), 365–392 (2001)CrossRef W.M. Roth, Gestures: their role in teaching and learning. Rev. Educ. Res. 71(3), 365–392 (2001)CrossRef
46.
Zurück zum Zitat W.M. Roth, D. Lawless, Scientific investigations, metaphorical gestures, and the emergence of abstract scientific concepts. Learn. Instr. 12, 285–304 (2002)CrossRef W.M. Roth, D. Lawless, Scientific investigations, metaphorical gestures, and the emergence of abstract scientific concepts. Learn. Instr. 12, 285–304 (2002)CrossRef
47.
Zurück zum Zitat E. Seymour, N.M. Hewitt, Talking About Leaving: Why Undergraduates Leave the Sciences (Westview, Boulder, 1997) E. Seymour, N.M. Hewitt, Talking About Leaving: Why Undergraduates Leave the Sciences (Westview, Boulder, 1997)
48.
Zurück zum Zitat A. Sfard, When the rules of discourse change, but nobody tells you: making sense of mathematics learning from a commognitive standpoint. J. Learn. Sci. 16(4), 567–615 (2007)CrossRef A. Sfard, When the rules of discourse change, but nobody tells you: making sense of mathematics learning from a commognitive standpoint. J. Learn. Sci. 16(4), 567–615 (2007)CrossRef
49.
Zurück zum Zitat C.S. Ticknor, Situated learning in an abstract algebra classroom. Educ. Stud. Math. 81(3), 307–323 (2012)CrossRef C.S. Ticknor, Situated learning in an abstract algebra classroom. Educ. Stud. Math. 81(3), 307–323 (2012)CrossRef
50.
Zurück zum Zitat V. Tinto, Linking learning and leaving, in Reworking the Student Departure Puzzle, ed. by J.M. Braxton (Vanderbilt University, Nashville, 2004) V. Tinto, Linking learning and leaving, in Reworking the Student Departure Puzzle, ed. by J.M. Braxton (Vanderbilt University, Nashville, 2004)
51.
Zurück zum Zitat A. Tucker, Applied Combinatorics, 4th edn. (Wiley, New York, 2002)MATH A. Tucker, Applied Combinatorics, 4th edn. (Wiley, New York, 2002)MATH
52.
Zurück zum Zitat N. Wasserman, M. Villanueva, J.-P. Mejia-Ramos, K. Weber, Secondary mathematics teachers’ perceptions of real analysis in relation to their teaching practice, in Proceedings of the 18th Conference on Research in Undergraduate Mathematics Education, Pittsburgh, PA (2015) N. Wasserman, M. Villanueva, J.-P. Mejia-Ramos, K. Weber, Secondary mathematics teachers’ perceptions of real analysis in relation to their teaching practice, in Proceedings of the 18th Conference on Research in Undergraduate Mathematics Education, Pittsburgh, PA (2015)
53.
Zurück zum Zitat M. Wawro, C. Rasmussen, M. Zandieh, C. Larson, Design research within undergraduate mathematics education: an example from introductory linear algebra, in Educational Design Research-Part B: Illustrative Cases, ed. by T. Plomp, N. Nieveen (SLO, Enschede, 2013), pp. 905–925 M. Wawro, C. Rasmussen, M. Zandieh, C. Larson, Design research within undergraduate mathematics education: an example from introductory linear algebra, in Educational Design Research-Part B: Illustrative Cases, ed. by T. Plomp, N. Nieveen (SLO, Enschede, 2013), pp. 905–925
54.
Zurück zum Zitat H. Wu, The mis-education of mathematics teachers. Not. Am. Math. Soc. 58(3), 372–384 (2011)MATH H. Wu, The mis-education of mathematics teachers. Not. Am. Math. Soc. 58(3), 372–384 (2011)MATH
57.
Zurück zum Zitat R. Zazkis, D. Zazkis, Script writing in the mathematics classroom: imaginary conversations on the structure of numbers. J. Res. Math. Educ. 16(1), 54–70 (2014) R. Zazkis, D. Zazkis, Script writing in the mathematics classroom: imaginary conversations on the structure of numbers. J. Res. Math. Educ. 16(1), 54–70 (2014)
Metadaten
Titel
Research in Collegiate Mathematics Education
verfasst von
Shandy Hauk
Chris Rasmussen
Nicole Engelke Infante
Elise Lockwood
Michelle Zandieh
Stacy Brown
Yvonne Lai
Pao-sheng Hsu
Copyright-Jahr
2018
DOI
https://doi.org/10.1007/978-3-319-98684-5_14