Anderson-Pence, K. L., Moyer-Packenham, P. S., Westenskow, A., Shumway, J., & Jordan, K. (2014). Relationships between visual static models and students’ written solutions to fraction tasks. International Journal for Mathematics Teaching and Learning, 15, 1-18. http://www.cimt.plymouth.ac.uk/journal/default.htm
Andrich, D. (1978). A rating formulation for ordered response categories. Psychometrika, 43(4), 561-573. doi: 10.1007/bf02293814
Ayalon, M., Watson, A., & Lerman, S. (2017). Students’ conceptualisations of function revealed through definitions and examples. Research in Mathematics Education, 19(1), 1-19. doi: 10.1080/14794802.2016.1249397
Baki, A., Kosa, T., & Guven, B. (2011). A comparative study of the effects of using dynamic geometry software and physical manipulatives on the spatial visualization skills of pre‐service mathematics teachers. British Journal of Educational Technology, 42(2), 291-310.
Biggs, J., Kember, D., & Leung, D. Y. (2001). The revised two‐factor study process questionnaire: R‐SPQ‐2F. British journal of educational psychology, 71(1), 133-149.
Bond, T., & Fox, C. M. (2015). Applying the Rasch model: Fundamental measurement in the human sciences. London: Routledge.
Boone, William J., Staver, John R., & Yale, Melissa S. (2014). Person Reliability, Item Reliability, and More Rasch Analysis in the Human Sciences (pp. 217-234). Dordrecht: Springer Netherlands.
Bouck, E. C., & Flanagan, S. M. (2010). Virtual Manipulatives: What They Are and How Teachers Can Use Them. Intervention in School and Clinic, 45(3), 186-191.
Burns, B. A., & Hamm, E. M. (2011). A comparison of concrete and virtual manipulative use in third‐and fourth‐grade mathematics. School Science and Mathematics, 111(6), 256-261.
Carbonneau, K. J., Marley, S. C., & Selig, J. P. (2013). A meta-analysis of the efficacy of teaching mathematics with concrete manipulatives. Journal of Educational Psychology, 105(2), 380–400.
Chao, T., Chen, J., Star, J. R., & Dede, C. (2016). Using Digital Resources for Motivation and Engagement in Learning Mathematics: Reflections from Teachers and Students. Digital Experiences in Mathematics Education, 2(3), 253-277.
Cope, L. (2015). Math manipulatives: Making the abstract tangible. Delta Journal of Education, 5(1), 10-19.
Coupland, M. (2004). Learning with new tools (Unpublished PhD thesis). Department of Information Systems, University of Wollongong. Retrieved from http://adt.caul.edu.au/.
Creswell, J. W. (2013). Research design: Qualitative, quantitative, and mixed methods approaches. Thousand Oaks, CA: Sage publications.
Deterding, S., Dixon, D., Khaled, R., & Nacke, L. (2011). From game design elements to gamefulness: Defining "Gamification". Proceedings from MindTrek '11. Tampere, Finland: ACM.
Dreyfus, T. (1991). Advanced mathematical thinking processes. In Tall D. (ed) Advanced mathematical thinking (pp. 25-41). Springer Netherlands.
Durksen, T. L., Way, J., Bobis, J., Anderson, J., Skilling, K., & Martin, A. J. (2017). Motivation and engagement in mathematics: a qualitative framework for teacher-student interactions. Mathematics Education Research Journal, 29(2), 163-181.
Engeström, Y. (1987). Learning by expanding: An activity-theoretical approach to developmental research. Helsinki: Orienta-Konsultit.
Furner, J. M., & Worrell, N. L. (2017). The Importance of Using Manipulatives in Teaching Math Today. Transformations, 3(1), 1-25.
Gainsburg, J. (2008). Real-world connections in secondary mathematics teaching. Journal of Mathematics Teacher Education, 11(3), 199-219.
Gay, L. R., Mills, G. E., & Airasian, P. W. (2011). Educational research: Competencies for analysis and application (10th ed). Boston: Pearson.
Gravetter, F. J., and Wallnau, L. B. (2007). Statistics for the behavioral sciences. Belmont, CA: Thompson Learning.
Ha, O., & Fang, N. (2018). Interactive Virtual and Physical Manipulatives for Improving Students’ Spatial Skills. Journal of Educational Computing Research, 55(8), 1088-1110.
Hardman, J. (2005). An exploratory case study of computer use in a primary school mathematics classroom: new technology, new pedagogy? Research: information and communication technologies. Perspectives in Education, 23(1), 99-111.
Jurdak, M. (2016). Learning and teaching real world problem solving in school mathematics: A multiple-perspective framework for crossing the boundary. New York: Springer
Kaput, J. J. (1992). Technology and mathematics education. In D. Grouws (Ed.) Handbook on research in mathematics teaching and learning. NCTM Yearbook on Mathematics Education (pp. 515–556). New York: Macmillan.
Karadag, Z., & McDougall, D. (2011). GeoGebra as a cognitive tool. In L. Bu & R. Schoen (Eds.), Model-Centered Learning (pp. 169-181). SensePublishers.
Karakırık, E. (2016). Developing Virtual Mathematics Manipulatives: The SAMAP Project. In Moyer-Packenham P. (ed), International Perspectives on Teaching and Learning Mathematics with Virtual Manipulatives (Vol 17, pp. 147-170). Springer International Publishing.
Kontas, H. (2016). The Effect of Manipulatives on Mathematics Achievement and Attitudes of Secondary School Students. Journal of Education and Learning, 5(3), 10-20.
Ladel, Silke, & Kortenkamp, Ulrich. (2016). Artifact-Centric Activity Theory—A Framework for the Analysis of the Design and Use of Virtual Manipulatives. In P. S. Moyer-Packenham (Ed.), International Perspectives on Teaching and Learning Mathematics with Virtual Manipulatives (pp. 25-40). Cham: Springer International Publishing.
Lee, Chun-Yi, & Chen, Ming-Jang. (2016). Influence of Prior Knowledge and Teaching Approaches Integrating Non-routine Worked Examples and Virtual Manipulatives on the Performance and Attitude of Fifth-Graders in Learning Equivalent Fractions. In P. S. Moyer-Packenham (Ed.), International Perspectives on Teaching and Learning Mathematics with Virtual Manipulatives (pp. 189-212). Cham: Springer International Publishing.
Leont’ev, A. N. (1981). The problem of activity in psychology. In J. V. Wertsch (Ed.), The concept of activity in Soviet psychology (pp. 37–71). Armonk, NY: ME Sharpe.
Lerman, S. (2001). A Review of Research Perspectives on Mathematics Teacher Education. In F.-L. Lin & T. J. Cooney (Eds.), Making Sense of Mathematics Teacher Education (pp. 33-52). Dordrecht: Springer Netherlands.
Linacre, J.M. (2015). A user’s guide to WINSTEPS. Chicago, IL: Winsteps.com.
Moyer-Packenham, Patricia S., & Bolyard, Johnna J. (2016). Revisiting the Definition of a Virtual Manipulative. In P. S. Moyer-Packenham (Ed.), International Perspectives on Teaching and Learning Mathematics with Virtual Manipulatives (pp. 3-23). Cham: Springer International Publishing.
Pallant, J. F., & Tennant, A. (2007). An introduction to the Rasch measurement model: an example using the Hospital Anxiety and Depression Scale (HADS). British Journal of Clinical Psychology, 46(1), 1-18.
Tall, D., (2013). How humans learn to think mathematically: exploring the three worlds of mathematics. New York: Cambridge University Press.
Van Zile-Tamsen, C. (2017). Using Rasch Analysis to Inform Rating Scale Development. Research in Higher Education, 58(8), 922-933.
Wan, Z. H., & Lee, J. C. K. (2017). Hong Kong secondary school students’ attitudes towards science: a study of structural models and gender differences. International Journal of Science Education, 39(5), 507-527.
Wertsch, J. V. (1979). The concept of activity in soviet psychology: An introduction. In J. V. Wertsch (ED), The concept of activity in soviet psychology (pp.03-36). New York: M.E. Sharpe.
Wright, B. D., and Masters, G. N. (1982). Rating Scale Analysis: Rasch Measurement. Chicago: MESA Press.
Yuan, Y., Lee, C. Y., & Wang, C. H. (2010). A comparison study of polyominoes explorations in a physical and virtual manipulative environment. Journal of Computer Assisted Learning, 26(4), 307-316.
Zeynivandnezhad, F., & Bates, R. (2017). Explicating mathematical thinking in differential equations using a computer algebra system. International Journal of Mathematical Education in Science and Technology, 1-25. DOI: 10.1080/0020739X.2017.1409368
Zimmermann, W. & Cunningham, S. (1991). Editor's introduction: What is mathematical visualization? In W. Zimmermann and S. Cunningham (eds.), Visualization in Teaching and Learning Mathematics, (pp. 1-8). Washington, DC: Mathematical Association of America.