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2020 Publications

 

  • Izsák, A., Beckmann, S., & Stark, J. (submitted). Coordinating multiplication equations across topics: A knowledge-in-pieces account. 

 

  • Ölmez, İ. B., & Izsák, A. (in press). Characterizing reasoning about fraction arithmetic of middle grades teachers in three latent classes. Mathematical Thinking and Learning. https://doi.org/10.1080/10986065.2020.1780368

 

2019 Publications

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  • Izsák, A., & Beckmann, S. (2019). Developing a coherent approach to multiplication and measurement. Educational Studies in Mathematics, 101(1), 83–103. doi: 10.1007/s10649-019-09885-8

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  • Izsák, A., Kulow, T., Beckmann, S., Stevenson, D., & Ölmez, İ. B., (2019). Using coordinated measurement with future teachers to connect multiplication, division, and proportional relationships. Mathematics Teacher Educator, 8(1), 49–75.

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  • Izsák, A., Jacobson, E., & Bradshaw, L. (2019). Surveying middle grades teachers' reasoning about fraction arithmetic in terms of measured quantities. Journal for Research in Mathematics Education, 50(2), 156-209. 

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  • Beckmann, S., & Izsák, A. (in press). A potential foundation for trigonometry and calculus: The variable-parts perspective on proportional relationships and geometric similarity. Proceedings of the 23rd Annual Conference on Research in Undergraduate Mathematics Education. 

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  • Izsák, A., & Beckmann, S. (in press). Future teachers’ use of multiplication and division to formulate linear equations. Proceedings of the 23rd Annual Conference on Research in Undergraduate Mathematics Education.

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  • Beckmann, S., & Izsák, A. (2019). Interpretations of number and implications for multiplicative reasoning. In M. Graven, H. Venkat, A. Essien, & P. Vale (Eds.). Proceedings of the 43rd Conference of the International Group for the Psychology of Mathematics Education (Vol. 4, p. 9). Pretoria, South Africa: PME.

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  • Izsák, A., & Beckmann, S. (2019). Future teachers’ use of variables to formulate linear equations. In M. Graven, H. Venkat, A. Essien, & P. Vale (Eds.). Proceedings of the 43rd Conference of the International Group for the Psychology of Mathematics Education (Vol. 4, p. 47). Pretoria, South Africa: PME.

 

2018 Publications

 

  • Izsák, A., Beckmann, S. & Kulow, T. (2018). Uncommon partitions: Partitioning as a problem-solving activity. Mathematics Teaching in the Middle School, 24(3), 164-171.

 

  • Stevenson, D. L., Beckmann, S., Johnson, S. E. & Kang, R. (2018). Quantitative (and non-Quantitative) methods used by future teachers for solving probability-based proportion problems.  Proceedings of the 40th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 687–694), Greenville, SC: Clemson University.

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  • Ölmez, İ. B. (2018). Future teachers’ use of multiplication and fractions when expressing  proportional relationships. In M. Strutchens, R. Huang, D. Potari, & L. Losano (Eds), Educating prospective secondary mathematics teachers (pp. 225 – 244). ICME-13  Monographs. Cham, Springer.

 

  • Ölmez, İ. B., & Izsák, A. (2018). Identifying latent classes of middle grades teachers based on reasoning about fraction arithmetic. In T. E. Hodges, G. J. Roy, & A. M. Tyminski (Eds.), Proceedings of the 40th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 468–475), Greenville, SC: University of South Carolina and Clemson University.

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  • Beckmann, S., & Izsák, A. (2018). Generating equations for proportional relationships using magnitude and substance conceptions. In A. Weinberg, C. Rasmussen, J. Rabin, M. Wawro, & S. Brown (Eds.), Proceedings of the 21st Annual Conference on Research in Undergraduate Mathematics Education (pp. 1215–1223). San Diego, California.

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  • Izsák, A., & Beckmann, S. (2018). Future middle grades teachers’ coordination of knowledge within the multiplicative conceptual field. In A. Weinberg, C. Rasmussen, J. Rabin, M. Wawro, and S. Brown (Eds.), Proceedings of the 21st Annual Conference on Research in Undergraduate Mathematics Education (pp. 852–861). San Diego, California.

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  • Izsák, A., & Beckmann, S. (2018). Future middle grades teachers’ incremental alignment of knowledge within the multiplicative conceptual field. In T. E. Hodges, G. J. Roy, & A. M. Tyminski (Eds.), Proceedings of the 40th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 199–202), Greenville, SC: University of South Carolina and Clemson University.

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  • Beckmann, S., & Izsák, A. (2018). Two senses of unit words and implications for topics related to multiplication. In Bergqvist, E., Österholm, M., Granberg, C., & Sumpter, L. (Eds.), Proceedings of the Forty-Second Conference of the International Group for the Psychology of Mathematics Education, (Vol. 5, pp. 205). Umea, Sweden: PME.

 

  • Izsák, A., & Beckmann, S. (2018). Using equations to develop a coherent approach to multiplication and measurement. In Bergqvist, E., Österholm, M., Granberg, C., & Sumpter, L. (Eds.), Proceedings of the Forty-Second Conference of the International Group for the Psychology of Mathematics Education, (Vol. 5, pp. 155-162). Umea, Sweden: PME.

 

  • Novotna ́, J., Bartolini Bussi, M. G., Beckmann, S., Inpasitha, M., Kaur, B., Sun, X., Venkat, H., & Askew, M. (2018). Professional development models for mathematical models in primary mathematics teacher education: a cross-cultural overview. In Bartolini Bussi, M. G. & Sun, X. (Eds.), Building the Foundation: Whole Numbers in the Primary Grades. The ICMI Study 23. Doi: 10.1007/978-3-319-63555-2 

 

  • Venkat, H., Beckmann, S., Larsson, K., Xin, Y. P., Ramploud, A., & Chen, L. (2018). Connecting whole number arithmetic foundations to other parts of mathematics: Structure and structuring activity. In Bartolini Bussi, M. G. & Sun, X. (Eds.), Building the Foundation: Whole Numbers in the Primary Grades. The ICMI Study 23. Doi: 10.1007/978-3-319-63555-2

 

2017 Publications

 

  • Beckmann, S. & Kulow, T. K. (2017). How future teachers reasoned with variable parts and strip diagrams to develop equations for proportional relationships and lines. In Y. Li, J. Lewis, & J. Madden (Eds.), Mathematics Matters in Education: Essays in Honor of Roger E. Howe. (pp. 117 – 148). Cham, Switzerland: Springer. Doi: 10.1007/978-3-319-61434-2. 

 

  • Izsák, A., & Jacobson, E. (2017). Preservice teachers' reasoning about relationships that are and are not proportional: A knowledge-in-pieces account. Journal for Research in Mathematics Education, 48(3), pp. 301-340. doi: 10.5951/jresematheduc.48.3.0300.

 

 

2016 Publications

 

  • Izsák, A., Beckmann, S., & Bradshaw, L. (2016). Diagnosing reasoning to measure growth in pre-service middle grades teachers' facility with fraction arithmetic. In Wood, M. B., Turner, E. E., Civil, M., & Eli, J. A. (Eds.), Proceedings of the Thirty-Eighth annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, pp. 751-758. Tucson, AZ.

 

  • Kulow, T., Izsák, A. & Stevenson, D. (2016). Measuring shifts in reasoning about fraction arithmetic in a middle grades number and operations content course. In Wood, M. B., Turner, E. E., Civil, M., & Eli, J. A. (Eds.), Proceedings of the Thirty-Eighth annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, pp. 775-782. Tucson, AZ.

 

  • Ölmez, İ. B. (2016). Two distinct perspectives on ratios: Additive and multiplicative relationships between quantities. Elementary Education Online, 15(1), pp. 186-203.

 

 

2015 Publications

 

  • Beckmann, S., Izsák, A., & Ölmez, İ. B. (2015). From multiplication to proportional relationships. In X. Sun, B. Kaur, J. Novotna (Eds.), Conference proceedings of ICMI Study 23: Primary mathematics study on whole numbers, pp. 518 - 525. Macau, China: University of Macau.

 

  • Beckmann, S., & Izsák, A. (2015). Two perspectives on proportional relationships: Extending complementary origins of multiplication in terms of quantities. Journal for Research in Mathematics Education 46(1), pp.17-38. 

 

 

2014 Publications

 

  • Beckmann, S. & Izsák, A. (2014). Why is slope hard to teach? American Mathematical Society Blog on Teaching and Learning Mathematics.

 

  • Beckmann, S., & Izsák, A. (2014). Variable parts: A new perspective on proportional relationships and linear functions. In Nicol, C., Liljedahl, P., Oesterle, S., & Allan, D. (Eds.) Proceedings of the Joint Meeting of Thirty-Eighth Conference of the International meeting of the Psychology of Mathematics Education and the Thirty-Sixth meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, Vol. 2, pp. 113-120. Vancouver, Canada: PME. 

 

  • Bradshaw, L., Izsák, A., Templin, J., & Jacobson, E. (2013). Diagnosing teachers’ understandings of rational numbers: Building a multidimensional test within the diagnostic classification framework. Educational Measurement: Issues and Practice, 33(1), pp. 2–14. DOI: 10.1111/emip.12020

 

  • Jacobson, E. & Izsák, A. (2014). Using coordination classes to analyze preservice middle-grades teachers' difficulties in determining direct proportion relationships. In J. Lo, K. R. Leatham, & L. R. Van Zoest (Eds.), Research Trends in Mathematics Teacher Education, (pp. 47-65). New York, Ny: Springer 

 

 

 

2012 Publications

 

  • Izsák, A., Jacobson, E., de Araujo, Z., & Orrill, C. H. (2012) Measuring mathematical knowledge for teaching fractions with drawn quantities. Journal for Research in Mathematics Education, 43(4), 391–427. 

 

  • Jacobson, E., & Izsák, A. (2012). Using a knowledge-in-pieces approach to explore the illusion of proportionality in covariance situations. 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. 629–636). Kalamazoo, MI: Western Michigan.

 

 

Publications before 2012

 

  • Izsák, A., Orrill, C. H., Cohen, A. S., & Brown, R. E., (2010). Using the mixture Rasch model to assess middle grades teachers’ reasoning about rational numbers. Elementary School Journal, 110(3), 279–300.

 

  • Izsák, A. (2008). Mathematical knowledge for teaching fraction multiplication. Cognition and Instruction, 26(1), 95-143.

 

  • Izsák, A., Tillema, E., & Tunç-Pekkan, Z. (2008). Teaching and learning fraction addition on number lines. Journal for Research in Mathematics Education, 39(1), 33–62.

 

 

 

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