Future mathematics teachers’ professional knowledge of elementary mathematics from an advanced standpoint

This paper reports a joint research project by researchers from three countries on an international comparative study that examines the professional knowledge of prospective mathematics teachers in elementary mathematics from an advanced standpoint. For this study, mathematical problems on various topics of elementary mathematical content were developed. Using this instrument, the mathematical knowledge of future teachers from Germany, Hong Kong, China (Hangzhou) and South Korea was measured empirically. The paper presents the design of the study, and also results are discussed. The results show that there are systematic differences among the participating countries; for example, the Korean future teachers outperform their counterparts in other countries. A more detailed analysis of the results suggests that the future teachers often do not seem to be able to link school and university knowledge systematically and cannot achieve the crucial “advanced standpoint” from the teacher training programme.

[1]  John A. Dossey,et al.  Mathematics, Pedagogy, and Secondary Teacher Education , 1999 .

[2]  T. A. Warm.  Weighted likelihood estimation of ability in item response theory , 1989 .

[3]  W. Blum,et al.  Didaktik der analysis , 1983 .

[4]  Michael O. Martin,et al.  TIMSS 2003 Technical Report: Findings from IEA's Trends in International Mathematics and Science Study at the Fourth and Eighth Grades. , 2004 .

[5]  Ruhama Even.  Subject-Matter Knowledge and Pedagogical Content Knowledge: Prospective Secondary Teachers and the Function Concept. , 1993 .

[6]  Tommy Dreyfus,et al.  IMAGES AND DEFINITIONS FOR THE CONCEPT OF FUNCTION , 1989 .

[7]  J. Baumert,et al.  Konzeptualisierung und Testkonstruktion zum fachbezogenen Professionswissen von Mathematiklehrkräften , 2011 .

[8]  Anthony Ralston,et al.  Knowing and teaching elementary mathematics , 1999 .

[9]  Margaret Wu,et al.  APPLYING THE RASCH MODEL TO PSYCHO-SOCIAL MEASUREMENT A PRACTICAL APPROACH , 2007 .

[10]  J. Baumert,et al.  Professionelle Kompetenz von Lehrkräften , 2013 .

[11]  O. Kwon,et al.  Standards for professionalization of mathematics teachers: policy, curricula, and national teacher employment test in Korea , 2012 .

[12]  C. Vale,et al.  International Perspectives on Gender and Mathematics Education , 2010 .

[13]  Is 0.999...= 1? , 1999 .

[14]  Hyman Bass,et al.  Knowing Mathematics for Teaching Who Knows Mathematics Well Enough To Teach Third Grade, and How Can We Decide? , 2005 .

[15]  Liping Ma,et al.  Knowing and Teaching Elementary Mathematics Teachers' Understanding of Fundamental Mathematics in China and the United States , 2010 .

[16]  Philipp Mayring.  Qualitative Inhaltsanalyse : Grundlagen und Techniken , 2003 .

[17]  D. Tall,et al.  Students' Mental Prototypes for Functions and Graphs , 1992 .

[18]  Tim Rowland,et al.  The purpose, design and use of examples in the teaching of elementary mathematics , 2008 .

[19]  L. Bauer.  Mathematik, Intuition, Formalisierung: eine Untersuchung von Schülerinnen- und Schülervorstellungen zu $0{,}\overline{9}$ , 2011 .

[20]  L. Shulman.  Those Who Understand: Knowledge Growth in Teaching , 1986 .

[21]  Tim Rowland,et al.  Elementary Teachers’ Mathematics Subject Knowledge: the Knowledge Quartet and the Case of Naomi , 2005 .

[22]  P. Zsombor-Murray,et al.  Elementary Mathematics from an Advanced Standpoint , 1940, Nature.

[23]  Steven J. Chrostowski,et al.  TIMSS 2003 International Mathematics Report: Findings from IEA's Trends in International Mathematics and Science Study at the Fourth and Eighth Grades. , 2004 .

[24]  L. Shulman.  Knowledge and Teaching: Foundations of the New Reform , 1987 .

[25]  G. Schubring.  Historical comments on the use of technology and devices in ICMEs and ICMI , 2010 .

[26]  Daniel Chazan,et al.  Exploring the Practical Rationality of Mathematics Teaching through Conversations about Videotaped Episodes: The Case of Engaging Students in Proving. , 2003 .

[27]  D. Ball,et al.  Unpacking Pedagogical Content Knowledge: Conceptualizing and Measuring Teachers' Topic-Specific Knowledge of Students , 2008, Journal for Research in Mathematics Education.