Making sense of third-grade students’ misunderstandings of the number line

ABSTRACT Researchers collaborated with a team of third-grade teachers in an urban district in the Upper Midwest to examine misunderstandings among students when using the number line as a model for fractions. Researchers looked closely at how the number line can be used as a model to build meaning for fractions for third-grade students. This article focuses on student interviews that discuss preconstructed and blank number line tasks that indicate how and when common misunderstandings occur when using a number line model. Misunderstandings include student misinterpretations of partitioning and tick marks, misunderstanding the unit, and equivalence as it relates to the number line. With these struggles as a basis, instructional implications for using the number line as a model in the classroom are provided. Reflection is included on the role of the number line and how it enhances third graders’ understanding of fractions in ways that other models do not.

[1]  L. Schauble,et al.  Design Experiments in Educational Research , 2003 .

[2]  Paul Cobb,et al.  Experimenting to Support and Understand Learning Processes , 2008 .

[3]  Merlyn J. Behr,et al.  Representations and translations among representations in mathematics learning and problem solving , 1987 .

[4]  Carole Greenes.  Algebra and algebraic thinking in school mathematics , 2008 .

[5]  Mi Yeon Lee,et al.  Relationships between Students' Fractional Knowledge and Equation Writing. , 2015 .

[6]  Kathleen A. Cramer.  Using a translation model for curriculum development and classroom instruction: Models and modeling perspectives on mathematics pr , 2003 .

[7]  Julie L. Booth,et al.  Fractions: Could they really be the gatekeeper’s doorman? , 2012 .

[8]  Kathleen A. Cramer,et al.  The role of representations in fraction addition and subtraction , 2008 .

[9]  R. Siegler,et al.  Early Predictors of High School Mathematics Achievement , 2012, Psychological science.

[10]  Kathleen A. Cramer,et al.  Efficacy of Different Concrete Models for Teaching the Part-Whole Construct for Fractions , 2009 .

[11]  Ipke Wachsmuth,et al.  Rational number learning aids: transfer from continuous models to discrete models , 1988 .

[12]  Robert S. Siegler,et al.  Developing Effective Fractions Instruction for Kindergarten Through 8th Grade , 2010 .

[13]  Identify fractions and decimals on a number line , 2011 .

[14]  Ipke Wachsmuth,et al.  IDENTIFYING FRACTIONS ON NUMBER LINES , 1988 .

[15]  Ronli Diakow,et al.  Towards curricular coherence in integers and fractions: a study of the efficacy of a lesson sequence that uses the number line as the principal representational context , 2013 .

[16]  Thomas R. Post,et al.  Initial Fraction Learning by Fourth- and Fifth-Grade Students: A Comparison of the Effects of Using Commercial Curricula with the Effects of Using the Rational Number Project Curriculum. , 2002 .

[17]  Kathleen A. Cramer,et al.  Unfolding Fraction Multiplication. , 2012 .

[18]  Graeme S. Halford,et al.  Mathematics Education: Models and Processes , 1995 .