2020 Publications

Izsák, A., Beckmann, S., & Stark, J. (submitted). Coordinating multiplication equations across topics: A knowledgeinpieces 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.
2019 Publications

Izsák, A., & Beckmann, S. (2019). Developing a coherent approach to multiplication and measurement. Educational Studies in Mathematics, 101(1), 83–103. doi: 10.1007/s10649019098858

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.

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), 156209.

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

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.

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.

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 problemsolving activity. Mathematics Teaching in the Middle School, 24(3), 164171.

Stevenson, D. L., Beckmann, S., Johnson, S. E. & Kang, R. (2018). Quantitative (and nonQuantitative) methods used by future teachers for solving probabilitybased 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.

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). ICME13 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.

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.

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.

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.

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 FortySecond 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 FortySecond Conference of the International Group for the Psychology of Mathematics Education, (Vol. 5, pp. 155162). 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 crosscultural overview. In Bartolini Bussi, M. G. & Sun, X. (Eds.), Building the Foundation: Whole Numbers in the Primary Grades. The ICMI Study 23. Doi: 10.1007/9783319635552

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: 10.1007/9783319635552
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: 10.1007/9783319614342.

Izsák, A., & Jacobson, E. (2017). Preservice teachers' reasoning about relationships that are and are not proportional: A knowledgeinpieces account. Journal for Research in Mathematics Education, 48(3), pp. 301340. doi: 10.5951/jresematheduc.48.3.0300.
2016 Publications

Izsák, A., Beckmann, S., & Bradshaw, L. (2016). Diagnosing reasoning to measure growth in preservice middle grades teachers' facility with fraction arithmetic. In Wood, M. B., Turner, E. E., Civil, M., & Eli, J. A. (Eds.), Proceedings of the ThirtyEighth annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, pp. 751758. 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 ThirtyEighth annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, pp. 775782. Tucson, AZ.

Ölmez, İ. B. (2016). Two distinct perspectives on ratios: Additive and multiplicative relationships between quantities. Elementary Education Online, 15(1), pp. 186203.
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.1738.
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 ThirtyEighth Conference of the International meeting of the Psychology of Mathematics Education and the ThirtySixth meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, Vol. 2, pp. 113120. 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 middlegrades 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. 4765). New York, Ny: Springer

Ölmez, İ.B. (2014). Preservice teachers' understandings of division and proportional relationships with quantities. Unpublished M.A. Thesis. University of Georgia: USA
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 knowledgeinpieces 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), 95143.

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