Grade 5 children’s drawings for integer addition and subtraction open number sentences

Abstract Three Grade 5 children participated in a microgenetic study embedded in 12-week teaching experiment on integer addition and subtraction. They solved open number sentences in four individual sessions across the 12-weeks and produced drawings. Through the lens of learner-generated drawings and qualitative analysis, these drawings provide perspective into the children’s thinking about integer addition and subtraction. The following categories are described: Single and Double Set of Objects, Number Sequences, Empty Number Lines, Number Lines, Number Sentences, Sign Emphasis, and Answer in Box Only. One student drew sets of objects frequently and the other students drew number lines more. Descriptions of how use of their drawings changed over time are provided. Implications point to a re-examination of integer instructional models and insight into potential learning progressions.

[1]  Irit Peled,et al.  Signed Numbers and Algebraic Thinking , 2017 .

[2]  Detlev Leutner,et al.  Cognitive load and instructionally supported learning with provided and learner-generated visualizations , 2011, Comput. Hum. Behav..

[3]  Sharan B. Merriam,et al.  Qualitative research and case study applications in education , 1998 .

[4]  Patrick W Thompson,et al.  Integers as transformations , 1988 .

[5]  Leslie P. Steffe,et al.  Teaching experiment methodology: Underlying principles and essential elements , 2000 .

[6]  Blaine H. Moore,et al.  The Art of Writing: Drawing as Preparation for Narrative Writing in the Primary Grades. , 1991 .

[7]  Thomas P. Carpenter,et al.  Children's Mathematics: Cognitively Guided Instruction , 1999 .

[8]  Michael T. Battista,et al.  A Complete Model for Operations on Integers , 1983 .

[9]  Leslie P. Steffe,et al.  Schemes of action and operation involving composite units , 1992 .

[10]  Marcia C. Linn,et al.  Learning from Chemical Visualizations: Comparing generation and selection , 2013 .

[11]  L. Verschaffel,et al.  The Impact of Illustrations and Warnings on Solving Mathematical Word Problems Realistically , 2014 .

[12]  Lisa L. C. Lamb,et al.  Obstacles and Affordances for Integer Reasoning: An Analysis of Children's Thinking and the History of Mathematics , 2014 .

[13]  Kevin Crowley,et al.  The microgenetic method , 1996 .

[14]  L. Bofferding.  Negative Integer Understanding: Characterizing First Graders' Mental Models , 2014 .

[15]  Lisa L. C. Lamb,et al.  Integer comparisons across the grades: Students’ justifications and ways of reasoning , 2017 .

[16]  I. Elia,et al.  THE FUNCTIONS OF PICTURES IN PROBLEM SOLVING , 2004 .

[17]  Peggy Noel Van Meter,et al.  Learner-generated drawing as a strategy for learning from content area text , 2006 .

[18]  A. Michael Huberman,et al.  An expanded sourcebook qualitative data analysis , 1994 .

[19]  Lisa L. C. Lamb,et al.  Leveraging Structure: Logical Necessity in the Context of Integer Arithmetic , 2016 .

[20]  L. Bofferding,et al.  Most and Least: Differences in Integer Comparisons Based on Temperature Comparison Language , 2019 .

[21]  P. Herbst.  The Number-Line Metaphor in the Discourse of a Textbook Series. , 1997 .

[22]  P. V. Meter,et al.  The Promise and Practice of Learner-Generated Drawing: Literature Review and Synthesis , 2005 .

[23]  Pamela Liebeck.  Scores and foreits — An intuitive model for integer arithmetic , 1990 .

[24]  Lisa L. C. Lamb,et al.  Using order to reason about negative numbers: the case of Violet , 2014 .

[25]  Aurora Gallardo.  The extension of the natural-number domain to the integers in the transition from arithmetic to algebra , 2002 .

[26]  Jon R. Star,et al.  Model Breaking Points Conceptualized , 2014 .

[27]  Lieven Verschaffel,et al.  Whole number concepts and operations , 2007 .

[28]  A. Sfard.  Thinking as Communicating: Human Development, the Growth of Discourses, and Mathematizing , 2008 .

[29]  L. Bofferding,et al.  Subtraction involving negative numbers: Connecting to whole number reasoning , 2017, The Mathematics Enthusiast.

[30]  Julian Williams,et al.  Using Intuition From Everyday Life in 'Filling' the gap in Children's Extension of Their Number Concept to Include the Negative Numbers , 1999 .

[31]  Andreas Koukkoufis,et al.  Integer instruction: a semiotic analysis of the 'compensation strategy , 2006 .

[32]  Arthur Bakker,et al.  Representing contextual mathematical problems in descriptive or depictive form , 2016 .

[33]  Kevin Crowley,et al.  The microgenetic method. A direct means for studying cognitive development. , 1991, The American psychologist.