Promoting a concept of fraction-as-measure: A study of the Learning Through Activity research program

Abstract Promoting deep understanding of fraction concepts continues to be a challenge for mathematics education. Research has demonstrated that students whose concept of fractions is limited to part-whole have difficulty with advanced fraction concepts. We conducted teaching experiments to study how students can develop a measurement concept of fractions and how task sequences can be developed to promote the necessary abstractions. Building particularly on the work of Steffe and colleagues and aspects of the Elkonin-Davydov curriculum, we focused on fostering student reinvention of a measurement concept of fractions. As a study of the Learning Through Activity research program, our goal was to promote particular activity on the part of the students through which they could abstract the necessary concepts.

[1]  Leslie P. Steffe,et al.  Children's Fractional Knowledge , 2009 .

[2]  Ron Tzur.  An Integrated Study of Children's Construction of Improper Fractions and the Teacher's Role in Promoting That Learning , 1999 .

[4]  Hans Freudenthal,et al.  Revisiting mathematics education : China lectures , 1991 .

[5]  Martin A. Simon.  Reconstructing Mathematics Pedagogy from a Constructivist Perspective. , 1995 .

[6]  Distinguishing schemes and tasks in children’s development of multiplicative reasoning , 2013, PNA. Revista de Investigación en Didáctica de la Matemática.

[7]  G. Harel,et al.  Units of quantity: A conceptual basis common to additive and multiplicative structures , 1994 .

[8]  Martin A. Simon,et al.  Participatory and Anticipatory Stages of Mathematical Concept Learning: Further Empirical and Theoretical Development. , 2016 .

[9]  G. Brousseau,et al.  Teaching Fractions through Situations: A Fundamental Experiment , 2013 .

[10]  Martin A. Simon.  Key Developmental Understandings in Mathematics: A Direction for Investigating and Establishing Learning Goals , 2006 .

[11]  Song A. An,et al.  Conceptualizing and organizing content for teaching and learning in selected Chinese, Japanese and US mathematics textbooks: the case of fraction division , 2009 .

[12]  Leslie P. Steffe,et al.  A new hypothesis concerning children’s fractional knowledge ☆ , 2001 .

[13]  Amal Hussain Alajmi,et al.  How do elementary textbooks address fractions? A review of mathematics textbooks in the USA, Japan, and Kuwait , 2012 .

[14]  Martin A. Simon.  Explicating mathematical concept and mathematicalconception as theoretical constructs for mathematics education research , 2017 .

[15]  V. Davydov,et al.  On the Objective Origin of the Concept of Fractions. , 1991 .

[16]  S. Vosniadou,et al.  The development of students’ understanding of the numerical value of fractions , 2004 .

[17]  Nancy K. Mack.  Building on Informal Knowledge through Instruction in a Complex Content Domain: Partitioning, Units, and Understanding Multiplication of Fractions , 2001 .

[18]  Robert E. Reys,et al.  Comparing the Development of Fractions in the Fifth- and Sixth-Graders' Textbooks of Singapore, Taiwan, and the USA. , 2010 .

[19]  Evan McClintock,et al.  A Developing Approach to Studying Students’ Learning through Their Mathematical Activity , 2010 .

[20]  John Olive,et al.  Making sense of instruction on fractions when a student lacks necessary fractional schemes: The case of Tim , 2006 .

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

[22]  P. Thompson,et al.  Fractions and multiplicative reasoning , 2003 .