Conceptual models for integer addition and subtraction

In this article, we report the findings of a study conducted with 6 Grade 8 students in the United States. The students posed stories for open number sentences involving addition and subtraction of...

[1]  D. Ball With an Eye on the Mathematical Horizon: Dilemmas of Teaching Elementary School Mathematics , 1993, The Elementary School Journal.

[2]  Jinfa Cai,et al.  Problem-Posing Research in Mathematics Education: Some Answered and Unanswered Questions , 2015 .

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

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

[5]  Michelle Stephan,et al.  A Proposed Instructional Theory for Integer Addition and Subtraction , 2012 .

[6]  Baruch B. Schwarz,et al.  Positives About Negatives: A Case Study of an Intermediate Model for Signed Numbers , 1994 .

[7]  Alicia Bruno,et al.  Strategies of pre-service primary school teachers for solving addition problems with negative numbers , 2014 .

[8]  Lisa L. C. Lamb,et al.  Happy and sad thoughts: An exploration of children's integer reasoning , 2012 .

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

[10]  P. Astuti Learning One-Digit Decimal Numbers by Measurement and Game Predicting Length. , 2014 .

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

[12]  Lyn D. English,et al.  The Development of Fifth-Grade Children's Problem-Posing Abilities , 1997 .

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

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

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

[16]  Amy J. Hackenberg,et al.  Constructivist Model Building: Empirical Examples From Mathematics Education , 2014 .

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

[18]  Lisa L. C. Lamb,et al.  ‘Negative of my money, positive of her money’: secondary students’ ways of relating equations to a debt context , 2015 .

[19]  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 .

[20]  I. Greca,et al.  Mental models, conceptual models, and modelling , 2000 .

[21]  Nicole M. Wessman-Enzinger,et al.  Grade 5 children’s drawings for integer addition and subtraction open number sentences , 2019, The Journal of Mathematical Behavior.

[22]  Kemal Altiparmak,et al.  A study on the teaching of the concept of negative numbers , 2010 .

[23]  Patrick W Thompson,et al.  Were lions to speak, we wouldn’t understand , 1982 .