DEVELOPING PRE-SERVICE TEACHERS’ NOTICING OF STUDENTS’ UNDERSTANDING OF THE DERIVATIVE CONCEPT

This research study examines the development of the ability of pre-service teachers to notice signs of students’ understanding of the derivative concept. It analyses preservice teachers’ interpretations of written solutions to problems involving the derivative concept before and after participating in a teacher training module. The results indicate that the development of this skill is linked to pre-service teachers’ progressive understanding of the mathematical elements that students use to solve problems. We have used these results to make some suggestions for teacher training programmes.

[1]  Brian Bowen,et al.  Prospective teacher learning: recognizing evidence of conceptual understanding , 2013 .

[2]  J. Sarama,et al.  Learning Trajectories in Mathematics Education , 2004 .

[3]  M. G. Sherin,et al.  Mathematics teachers' "learning to notice" in the context of a video club , 2008 .

[4]  C. Fernández,et al.  Primary school teacher’s noticing of students’ mathematical thinking in problem solving , 2013, The Mathematics Enthusiast.

[5]  Megan L. Franke,et al.  Learning to Teach Mathematics: Focus on Student Thinking , 2001 .

[6]  Jere Confrey,et al.  Learning Trajectories in Teacher Education: Supporting Teachers' Understandings of Students' Mathematical Thinking. , 2013 .

[7]  Randall J. Souviney.  Learning to Teach Mathematics , 1989 .

[8]  Samer Habre,et al.  Students’ conceptual understanding of a function and its derivative in an experimental calculus course , 2006 .

[9]  T. P. Carpenter,et al.  Professional development focused on children's algebraic reasoning in elementary school , 2007 .

[10]  John C. Moyer,et al.  An exploratory study of pre-service middle school teachers’ knowledge of algebraic thinking , 2013 .

[11]  David Tall,et al.  Advanced Mathematical Thinking , 1994 .

[12]  Sandy M. Spitzer,et al.  Developing prospective elementary teachers’ abilities to identify evidence of student mathematical achievement , 2011 .

[13]  Rita Schildwacht.  Learning to notice , 2012 .

[14]  Zhonghe Wu,et al.  ENHANCING MATHEMATICS TEACHERS’ KNOWLEDGE OF STUDENTS’ THINKING FROM ASSESSING AND ANALYZING MISCONCEPTIONS IN HOMEWORK , 2012 .

[15]  Gloria Sánchez-Matamoros,et al.  La comprensión de la derivada como objeto de investigación en didáctica de la matemática , 2008 .

[16]  J. Mason.  Researching Your Own Practice: The Discipline of Noticing , 2002 .

[17]  N. Denzin,et al.  Handbook of Qualitative Research , 1994 .

[18]  Ed Dubinsky,et al.  The development of students' graphical understanding of the derivative , 1997 .

[19]  A. Strauss,et al.  Grounded theory methodology: An overview. , 1994 .

[20]  T. Zachariades,et al.  Student perspectives on the relationship between a curve and its tangent in the transition from Euclidean Geometry to Analysis , 2008 .

[21]  Randolph A. Philipp,et al.  Professional Noticing of Children's Mathematical Thinking. , 2010 .

[22]  Mercedes García,et al.  CHARACTERIZING THEMATIZED DERIVATIVE SCHEMA BY THE UNDERLYING EMERGENT STRUCTURES , 2011 .

[23]  Ceneida Fernández,et al.  Learning to notice students’ mathematical thinking through on-line discussions , 2012 .

[24]  Vicenç Font,et al.  Análisis de los niveles de comprensión de los objetos f’(a) y f’(x) de profesores de matemáticas. , 2011 .

[25]  Bernadette Baker,et al.  A Calculus Graphing Schema , 2000 .

[26]  T. Zachariades,et al.  Using Tasks to Explore Teacher Knowledge in Situation-Specific Contexts , 2007 .

[27]  Janine M. Viglietti,et al.  CALCULUS STUDENTS’ AND INSTRUCTORS’ CONCEPTUALIZATIONS OF SLOPE: A COMPARISON ACROSS ACADEMIC LEVELS , 2013 .

[28]  Deborah Loewenberg Ball,et al.  Content Knowledge for Teaching , 2008 .