1.
Ball, D. L., & Bass, H. (2003). Toward a practice-based theory of mathematical knowledge for teaching. In E. Simmt & B. Davis (Eds.), Proceedings of the 2002 Annual Meeting of the Canadian Mathematics Education Study Group (pp. 3–14). CMESG/GCEDM.
- Search Google Scholar
- Export Citation
2.
Ball, D. L., & Cohen, D. K. (1999). Developing practice, developing practitioners: Toward a practice-based theory of professional education. In G. Sykes and L. Darling-Hammond (Eds.), Teaching as the learning profession: Handbook of policy and practice (pp. 3–32). Jossey-Bass.
- Search Google Scholar
- Export Citation
3.
Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59(5), 389–407.
- Search Google Scholar
- Export Citation
4.
Bell, C. A., Wilson, S. M., Higgins, T., & McCoach, D. B. (2010). Measuring the effects of professional development on teacher knowledge: The case of developing mathematical ideas. Journal for Research in Mathematics Education, 41(5), 479–512.
- Search Google Scholar
- Export Citation
5.
Ben-Chaim, D., Keret, Y., & Ilany, B. (2007). Designing and implementing authentic investigative proportional reasoning tasks: The impact on pre-service mathematics teachers’ content and pedagogical knowledge and attitudes. Journal of Mathematics Teacher Education, 10(4–6), 333–340.
- Search Google Scholar
- Export Citation
6.
Berk, D., Taber, S. B., Gorowara, C. C., & Poetzl, C. (2009). Developing prospective elementary teachers’ flexibility in the domain of proportional reasoning. Mathematical Thinking and Learning, 11(3), 113–135.
- Search Google Scholar
- Export Citation
7.
Blythe, T., Allen, D., & Powell, B. S. (2015). Looking together at student work. Teachers College Press.
- Search Google Scholar
- Export Citation
8.
Brown, J. S., Collins, A., & Duguid, P. (1989). Situated cognition and the culture of learning. Educational Researcher, 18(1), 32–42.
- Search Google Scholar
- Export Citation
9.
Carney, M. B., Brendefur, J. L., Thiede, K., Hughes, G., & Sutton, J. (2016). Statewide mathematics professional development: Teacher knowledge, self-efficacy, and beliefs. Educational Policy, 30(4), 539–572.
- Search Google Scholar
- Export Citation
10.
Charalambous, C. (2010). Mathematical knowledge for teaching and task unfolding: An exploratory study. The Elementary School Journal, 110(3), 247–278.
- Search Google Scholar
- Export Citation
11.
Common Core Standards Writing Team. (2011, December 26). Progressions for the Common Core State Standards in Mathematics. https://commoncoretools.files.wordpress.com/2012/02/ccss_progression_rp_67_2011_11_12_corrected.pdf
- Search Google Scholar
- Export Citation
12.
Council of Chief State School Officers. (2011, June 1). Common Core State Standards (CCSS) Mathematics Curriculum Materials Analysis Project. Council of Chief State School Officers. https://www.mathedleadership.org/docs/ccss/CCSSO%20Mathematics%20Curriculum%20Analysis%20Project.Whole%20Document.6.1.11.Final.docx.
- Search Google Scholar
- Export Citation
13.
Garet, M. S., Porter, A. C., Desimone, L., Birman, B. F., & Yoon, K. S. (2001). What makes professional development effective? Lessons from a national sample of teachers. American Educational Research Journal, 38(4), 915–945.
- Search Google Scholar
- Export Citation
14.
Hatisaru, V., & Erbas, A. K. (2017). Mathematical knowledge for teaching the function concept and student learning outcomes. International Journal of Science and Mathematics Education, 15(4), 703–722.
- Search Google Scholar
- Export Citation
15.
Hill, H., & Ball, D. L. (2009). The curious—and crucial—case of mathematical knowledge for teaching. Phi Delta Kappan, 91(2), 68–71.
- Search Google Scholar
- Export Citation
16.
Hill, H. C., Ball, D. L., & Schilling, S. G. (2008). Unpacking pedagogical content knowledge: Conceptualizing and measuring teachers’ topic-specific knowledge of students. Journal for Research in Mathematics Education, 39(4), 372–400.
- Search Google Scholar
- Export Citation
17.
Hill, H. C., Kapitula, L., & Umland, K. (2011). A validity argument approach to evaluating teacher value-added scores. American Educational Research Journal, 48(3), 794–831.
- Search Google Scholar
- Export Citation
18.
Hill, H. C., Rowan, B., & Ball, D. L. (2005). Effects of teachers’ mathematical knowledge for teaching on student achievement. American Educational Research Journal, 42(2), 371–406.
- Search Google Scholar
- Export Citation
19.
Hilton, A., Hilton, G., Dole, S., & Goos, M. (2016). Promoting middle school students’ proportional reasoning skills through an ongoing professional development programme for teachers. Educational Studies in Mathematics, 92(2), 193–219.
- Search Google Scholar
- Export Citation
20.
Hoover, M., Mosvold, R., Ball, D. L., & Lai, Y. (2016). Making progress on mathematical knowledge for teaching. The Mathematics Enthusiast, 13(1&2), 3–34.
- Search Google Scholar
- Export Citation
21.
Ilany, B., Keret, Y., & Ben-Chaim, D. (2004). Implementation of a model using authentic investigative activities for teaching ratio and proportion in pre-service teacher education. Proceedings of the 28th conference of the international group for the psychology of mathematics education (Vol. 3, pp. 81–88). https://www.researchgate.net/publication/237801780.
- Search Google Scholar
- Export Citation
22.
Izsak, A., Jacobson, E., & de Araujo, Z. (2012). Measuring mathematical knowledge for teaching fractions with drawn quantities. Journal for Research in Mathematics Education, 43(3), 391–427.
- Search Google Scholar
- Export Citation
23.
Jacob, R., Hill, H., & Corey, D. (2017). The impact of a professional development program on teachers’ mathematical knowledge for teaching, instruction, and student achievement. Journal of Research on Educational Effectiveness, 10(2), 379–407.
- Search Google Scholar
- Export Citation
24.
Johnson, E. M. S., & Larsen, S. P. (2012). Teacher listening: The role of knowledge of content and students. The Journal of Mathematical Behavior, 31(1), 117–129.
- Search Google Scholar
- Export Citation
25.
Kastberg, S. E., D’Ambrosio, B., & Lynch-Davis, K. (2012). Understanding proportional reasoning for teaching. Australian Mathematics Teacher, 68(3), 32–40.
- Search Google Scholar
- Export Citation
26.
Kazemi, E., & Franke, M. L. (2004). Teacher learning in mathematics; Using student work to promote collective inquiry. Journal of Mathematics Teacher Education, 7(3), 203–235.
- Search Google Scholar
- Export Citation
27.
Leavy, A. M., & Hourigan, M. (2016). Using lesson study to support knowledge development in initial teacher education: Insights from early number classrooms. Teaching and Teacher Education, 57, 161–175.
- Search Google Scholar
- Export Citation
28.
Lesh, R., Post, T., & Behr, M. (1988). Proportional reasoning. In J. Hiebert & M. Behr (Eds.), Number concepts and operations in the middle grades (pp. 93–118). Erlbaum; National Council of Teachers of Mathematics.
- Search Google Scholar
- Export Citation
29.
Lesseig, K. (2016). Investigating Mathematical Knowledge for Teaching Proof in Professional Development. International Journal of Research in Education and Science, 2(2), 253–270.
- Search Google Scholar
- Export Citation
30.
Lobato, J., Orrill, C. H., Druken, B., & Jacobson, E. (2011, April 8–12). Middle school teachers’ knowledge of proportional reasoning for teaching [Paper presentation]. As part of the symposium, extending, expanding, and applying the construct of mathematical knowledge for teaching at the American Educational Research Association Annual Meeting, New Orleans, LA, USA.
- Search Google Scholar
- Export Citation
31.
Loucks-Horsley, S., Stiles, K. E., Mundry, S., Hewson, P. W., & Love, N. (2010). Designing professional development for teachers of science and mathematics (3rd ed.). Corwin.
- Search Google Scholar
- Export Citation
32.
Miles, M. B., & Huberman, A. M. (1994). Qualitative data analysis: An expanded sourcebook (2nd ed.). SAGE Publications.
- Search Google Scholar
- Export Citation
33.
Özgün-Koca, S. A., & Kayhan, M. (2009). An investigation of proportional reasoning skills of middle school students. Investigations in Mathematics Learning, 2(1), 26–48.
- Search Google Scholar
- Export Citation
34.
Pianta, R. C., & Hamré, B. K. (2009). Conceptualization, measurement, and improvement of classroom practices: Standardized observation can leverage capacity. Educational Researcher, 38(2), 109–119.
- Search Google Scholar
- Export Citation
35.
Putnam, R. T., & Borko, H. (2000). What do new views of knowledge and thinking have to say about research on teacher learning? Educational Researcher, 29(1), 4–15.
- Search Google Scholar
- Export Citation
36.
Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4–14.
- Search Google Scholar
- Export Citation
37.
Smith, M. S., Bill, V., & Hughes, E. K. (2008). Thinking through a lesson: Successfully implementing high-level tasks. Mathematics Teaching in the Middle School, 14(3), 132–138.
- Search Google Scholar
- Export Citation
38.
Wayne, A. J., Yoon, K. S., Zhu, P., Cronen, S., & Garet, M. S. (2008). Experimenting with teacher professional development: Motives and methods. Education Researcher, 37(8), 469–479.
- Search Google Scholar
- Export Citation
39.
Yoon, K. S., Duncan, T., Lee, S. W.-Y., Scarloss, B., & Shapley, K. (2007). Reviewing the evidence on how teacher professional development affects student achievement (Issues & Answers Report, REL 2007–No.033). U. S. Department of Education, Institute of Education Sciences, National Center for Education Evaluation and Regional Assistance, Regional Educational Laboratory Southwest.
- Search Google Scholar
- Export Citation
