Generalization Strategies in Finding the nth Term Rule for Simple Quadratic Sequences

Ainsworth, S. (2006). DeFT: A conceptual framework for considering learning with multiple representations. Learning and Instruction, 16(3), 183–198.

Barmby, P., Andrà, C., Gomez, D., Obersteiner, A., & Shvarts, A. (2014). The use of eye-tracking technology in mathematics education research. In P. Liljedahl, C. Nicol, S. Oesterle, & D. Allan (Eds.), Proceedings of the joint meeting of PME38 and PME-NA36 (Vol. 1, p. 253). Vancouver: PME.

Beitlich, J. T., & Obersteiner, A. (2015). Eye-tracking as a method for identifying mathematical strategies. In K. Beswick, T. Muir, & J. Wells (Eds.), Proceedings of 39th Psychology of Mathematics Education conference (Vol. 1, pp. 93–97). Hobart: PME.

Branch, J. (2000). Investigating the information-seeking processes of adolescents: The value of using think alouds and think afters. Library & Information Science Research, 22(4), 371–392.

Canham, M., & Hegarty, M. (2010). Effects of knowledge and display design on comprehension of complex graphics. Learning and Instruction, 20(2), 155–166.

Carraher, D. W., Martinez, M. V., & Schliemann, A. D. (2008). Early algebra and mathematical generalization. ZDM – The International Journal on Mathematics Education, 40(1), 3–22.

Chumachemko, D., Shvarts, A., & Budanov, A. (2014). The development of the visual perception of the cartesian coordinate system: An eye tracking study. In P. Liljedahl, C. Nicol, S. Oesterle, & D. Allan (Eds.), Proceedings of the joint meeting of PME38 and PME-NA36 (Vol. 2, pp. 313–320). Vancouver: PME.

Confrey, J., & Smith, E. (1994). Exponential functions, rates of change, and the multiplicative unit. Educational Studies in Mathematics, 26, 135–164.

Crisp, R., Inglis, M., Mason, J., & Watson, A. (2012). Individual differences in generalisation strategies. Research in Mathematics Education, 14(3), 291–292.

Cuoco, A. (2005). Mathematical connections: A companion for teachers and others. Washington, DC: Mathematical Association of America, Cambridge University Press.

DfE. (2013). Mathematics programmes of study: Key stage 3. London: Department of Education.

Dörfler, W. (2016). Signs and their use: Peirce and Wittgenstein. In A. Bikner-Ahsbahs, A. Vohns, O. Schmitt, R. Bruder, & W. Dörfler (Eds.), Theories in and of mathematics education ICME-13 topical surveys (pp. 21–31). Switzerland: Springer International Publishing. Available from https://link.springer.com/book/10.1007%2F978-3-319-42589-4 . Accessed 3 Apr 2019

Ellis, A. B., & Grinstead, P. (2008). Hidden lessons: How a focus on slope-like properties of quadratic functions encouraged unexpected generalizations. The Journal of Mathematical Behavior, 27(4), 277–296.

Foster, C. (2004). Differences over difference methods: Pros and cons of different ways of finding the nth term of a sequence of numbers. Mathematics in School, 33(5), 24–25.

Green, H. J., Lemaire, P., & Dufau, S. (2007). Eye movement correlates of younger and older adults’ strategies for complex addition. Acta Psychologica, 125(3), 257–278.

Haider, H., & Frensch, P. A. (1999). Eye movement during skill acquisition: More evidence for the information-reduction hypothesis. Journal of Experimental Psychology: Learning, Memory, and Cognition, 25(1), 172–190.

Huber, S., Moeller, K., & Nuerk, H.-C. (2014). Adaptive processing of fractions – Evidence from eye-tracking. Acta Psychologica, 148, 37–48.

Hyönä, J. (2010). The use of eye movements in the study of multimedia learning. Learning and Instruction, 20(2), 172–176.

Just, M. A., & Carpenter, P. A. (1980). A theory of reading: From eye fixations to comprehension. Psychological Review, 87(4), 329–354.

Knoblich, G., Ohlsson, S., & Raney, G. E. (2001). An eye movement study of insight problem solving. Memory and Cognition, 29(7), 1000–1009.

MacGregor, M., & Stacey, K. (1993). Seeing a pattern and writing a rule. In I. Hirabayashi, N. Nohda, K. Shigematsu, & F. Lin (Eds.), Proceedings of 17th Psychology of Mathematics Education conference (Vol. 1, pp. 181–188). Tsukuba: University of Tsukuba.

Montenegro, P., Costa, C., & Lopes, B. (2018). Transformations in the visual representation of a figural pattern. Mathematical Thinking and Learning, 20(2), 91–107.

Obersteiner, A., Moll, G., Beitlich, J. T., Cui, C., Schmidt, M., Khmelivska, T., & Reiss, K. (2014). Expert mathematicians’ strategies for comparing the numerical values of fractions – Evidence from eye movements. In P. Liljedahl, C. Nicol, S. Oesterle, & D. Allan (Eds.), Proceedings of the joint meeting of PME38 and PME-NA36 (Vol. 4, pp. 337–344). Vancouver: PME.

Panse, A., Alcock, L., & Inglis, M. (2018). Reading proofs for validation and comprehension: An expert-novice eye-movement study. International Journal of Research in Undergraduate Mathematics Education, 4(3), 357–375.

Radford, L. (2008). Iconicity and contraction: A semiotic investigation of forms of algebraic generalizations of patterns in different contexts. ZDM – The International Journal on Mathematics Education, 40, 88–96.

Rayner, K. (1998). Eye movements in reading and information processing: 20 years of research. Psychological Bulletin, 124(3), 372–422.

Rivera, F. D. (2013). Teaching and learning patterns in school mathematics. New York: Springer.

Steele, D. (2008). Seventh-grade students’ representations for pictorial growth and change problems. ZDM – The International Journal on Mathematics Education, 40(1), 97–110.

Sullivan, J. L., Juhasz, B. J., Slattery, T. J., & Barth, H. C. (2011). Adults’ number-line estimation strategies: Evidence from eye movements. Psychonomic Bulletin and Review, 18(3), 557–563.

Tobii Technology. (2010). Tobii eye tracking: An introduction to eye tracking and Tobii eye trackers. Stockholm: Tobii Technology AP.

van Gog, T., & Scheiter, K. (2010). Eye tracking as a tool to study and enhance multimedia learning. Learning and Instruction, 20(2), 95–99.

Was, C., Sansosti, F., & Morris, B. (2017). Eye-tracking technology applications in educational research. Hershey: IGI Global.

Yeşildere, S., & Akkoç, H. (2010). Algebraic generalization strategies of number patterns used by pre-service elementary mathematics teachers. Procedia-Social and Behavioral Sciences, 2(2), 1142–1147.

Zaslavsky, O. (1997). Conceptual obstacles in the learning of quadratic functions. Focus on Learning Problems in Mathematics, 19(1), 20–44.