Integrating Integers with Tug-of-War and Two-Sided Counters

Akyüz, D., Stephan, M., & Dixon, J. K. (2012). The role of the teacher in supporting imagery in understanding integers. Egitim Ve Bilim-Education and Science, 37(163), 268.

Akyüz, D., Stephan, M., & Dixon, J. K. (2012). The role of the teacher in supporting imagery in understanding integers. Egitim Ve Bilim-Education and Science, 37(163), 268.)| false
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Bishop, J. P., Lamb, L. L., Philipp, R. A., Whitacre, I., Schappelle, B. P., & Lewis, M. L. (2014). Obstacles and affordances for integer reasoning: An analysis of children's thinking and the history of mathematics. Journal for Research in Mathematics Education, 45(1), 19–61. https://doi.org/10.5951/jresematheduc.45.1.0019

Bishop, J. P., Lamb, L. L., Philipp, R. A., Whitacre, I., Schappelle, B. P., & Lewis, M. L. (2014). Obstacles and affordances for integer reasoning: An analysis of children's thinking and the history of mathematics. Journal for Research in Mathematics Education, 45(1), 19–61. https://doi.org/10.5951/jresematheduc.45.1.0019)| false
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Bofferding, L. (2012). Transitioning from whole numbers to integers. In L. R. Van Zoest, J.-J. Lo, & J. L. Kratky (Eds.), Proceedings of the 34th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 935–942). Western Michigan University.

Bofferding, L. (2012). Transitioning from whole numbers to integers. In L. R.Van Zoest, J.-J.Lo, & J. L.Kratky (Eds.), Proceedings of the 34th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 935–942). Western Michigan University.)| false
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Hill, W. H., Jr. (1968). A physical model for teaching multiplication of integers. The Arithmetic Teacher, 15(6), 525–528. 
https://doi.org/10.5951/AT.15.6.0525

Hill, W. H., Jr. (1968). A physical model for teaching multiplication of integers. The Arithmetic Teacher, 15(6), 525–528. 
https://doi.org/10.5951/AT.15.6.0525)| false
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Khalid, M., & Embong, Z. (2019). Sources and possible causes of errors and misconceptions in operations of integers. International Electronic Journal of Mathematics Education, 15(2), em0568. https://doi.org/10.29333/iejme/6265

Khalid, M., & Embong, Z. (2019). Sources and possible causes of errors and misconceptions in operations of integers. International Electronic Journal of Mathematics Education, 15(2), em0568. https://doi.org/10.29333/iejme/6265)| false
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Khalid, M., & Embong, Z. (2020). Emphasizing concrete representation to enhance students’ conceptual understanding of operations on integers. Turkish Journal of Computer and Mathematics Education (TURCOMAT ), 11(3), 762–773.

Khalid, M., & Embong, Z. (2020). Emphasizing concrete representation to enhance students’ conceptual understanding of operations on integers. Turkish Journal of Computer and Mathematics Education (TURCOMAT), 11(3), 762–773.)| false
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Lamb, L. L., Bishop, J. P., Philipp, R. A., Whitacre, I., & Schappelle, B. P. (2018). A cross-sectional investigation of students’ reasoning about integer addition and subtraction: Ways of reasoning, problem types, and flexibility. Journal for Research in Mathematics Education, 49(5), 575–613. https://doi.org/10.5951/jresematheduc.49.5.0575

Lamb, L. L., Bishop, J. P., Philipp, R. A., Whitacre, I., & Schappelle, B. P. (2018). A cross-sectional investigation of students’ reasoning about integer addition and subtraction: Ways of reasoning, problem types, and flexibility. Journal for Research in Mathematics Education, 49(5), 575–613. https://doi.org/10.5951/jresematheduc.49.5.0575)| false
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National Council of Teachers of Mathematics. (2014). Principles to actions: Ensuring mathematical success for all.

Nurnberger-Haag, J. (2015). How students’ integer arithmetic learning depends on whether they walk a path or collect chips. In T. G. Bartell, K. N. Bieda, R. T. Putnam, K. Bradfield, & H. Dominguez (Eds.), Proceedings of the 37th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 165–172). Michigan State University.

Stephan, M., & Akyüz, D. (2012). A proposed instructional theory for integer addition and subtraction. Journal for Research in Mathematics Education, 43(4), 428–464. https://doi.org/10.5951/jresematheduc.43.4.0428

Stephan, M., & Akyüz, D. (2012). A proposed instructional theory for integer addition and subtraction. Journal for Research in Mathematics Education, 43(4), 428–464. https://doi.org/10.5951/jresematheduc.43.4.0428)| false
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Thurber, B. (2010, January 2). Integer tug of war [Video]. YouTube. https://www.youtube.com/watch?v=AGXc5Jmhw6c

Tsang, J. M., Blair, K. P., Bofferding, L., & Schwartz, D. L. (2015). Learning to “see” less than nothing: Putting perceptual skills to work for learning numerical structure. Cognition and Instruction, 33(2), 154–197. https://doi.org/10.1080/07370008.2015.1038539

Tsang, J. M., Blair, K. P., Bofferding, L., & Schwartz, D. L. (2015). Learning to “see” less than nothing: Putting perceptual skills to work for learning numerical structure. Cognition and Instruction, 33(2), 154–197. https://doi.org/10.1080/07370008.2015.1038539)| false
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University of Cambridge Faculty of Mathematics. (n.d.). Tug of war. Nrich; University of Cambridge. https://nrich.maths.org/5897/note

University of Cambridge Faculty of Mathematics. (n.d.). Tug of war. Nrich; University of Cambridge. https://nrich.maths.org/5897/note)| false
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