FOCUSSING STRUCTURAL RELATIONS IN THE BAR BOARD - A DESIGN RESEARCH STUDY FOR FOSTERING ALL STUDENTS' CONCEPTUAL UNDERSTANDING OF FRACTIONS

For fostering conceptual understanding of fractions, connecting different representations is an often used design principle. This paper shows that this design principle is necessary but not sufficient and should be complemented by focussing structural relations. In a design research study in grade 6, different strategies for this principle were developed and empirically investigated with respect to the generated learning processes. The activities were organized around the so-called fraction bar board, a visual model that allows a comprehensive structural view on fractions, order and equivalence.

[1]  Raymond Duval.  A Cognitive Analysis of Problems of Comprehension in a Learning of Mathematics , 2006 .

[2]  Klaus Hasemann.  On difficulties with fractions , 1981 .

[3]  Reinders Duit,et al.  The teaching experiment as a powerful method to develop and evaluate teaching and learning sequences in the domain of non‐linear systems , 2004 .

[4]  Douglas A. Grouws,et al.  Handbook of research on mathematics teaching and learning , 1992 .

[5]  Heinz Steinbring,et al.  The Construction of New Mathematical Knowledge in Classroom Interaction: An Epistemological Perspective , 2005 .

[6]  H. Freudenthal.  Didactical Phenomenology of Mathematical Structures , 1983 .

[7]  G. Bruin Muurling,et al.  The development of proficiency in the fraction domain : affordances and constraints in the curriculum , 2010 .

[8]  Meral Aksu,et al.  Student Performance in Dealing With Fractions , 1997 .

[9]  Richard Lesh,et al.  Rational Number Project: Fraction Lessons for the Middle Grades - Level 1 , 1997 .

[10]  Richard Lesh,et al.  Rational Number Project , 1997 .

[11]  Susan McKenney,et al.  Educational design research: the value of variety , 2006 .

[12]  Richard Lesh,et al.  Applied mathematical problem solving , 1981 .

[13]  A. Treffers.  Three Dimensions: A Model of Goal and Theory Description in Mathematics Instruction ― The Wiskobas Project , 1986 .

[14]  Jan Terwel,et al.  Learning for mathematical insight: a longitudinal comparative study on modelling , 2003 .

[15]  Koeno Gravemeijer,et al.  Design research from a learning design perspective , 2006 .

[16]  B. Moseley.  Students' Early Mathematical Representation Knowledge: The Effects of Emphasizing Single or Multiple Perspectives of the Rational Number Domain in Problem Solving , 2005 .

[17]  Bharath Sriraman.  Probabilistic Thinking: Presenting Plural Perspectives , 2014 .

[18]  D. Geary,et al.  Mathematical learning disabilities. , 2010, Advances in child development and behavior.

[19]  Susanne Prediger,et al.  Fostering German-language learners’ constructions of meanings for fractions—design and effects of a language- and mathematics-integrated intervention , 2013 .

[20]  Leen Streefland,et al.  Fractions in Realistic Mathematics Education: A Paradigm of Developmental Research , 1991 .

[21]  Richard Lesh,et al.  Rational number, ratio and proportion , 1992 .