Middle school students’ patterning performance on semi-free generalization tasks

Anderman, 2006 Anderman, 1998, Motivation and cheating during early adolescence, Journal of Educational Psychology, 90, 84, 10.1037/0022-0663.90.1.84 Behrmann, 2003, Expertise in tactile pattern recognition, Psychological Science, 14, 480, 10.1111/1467-9280.02458 Bilalic, 2010, Mechanisms and neural basis of object and pattern recognition: a study with chess experts, Journal of Experimental Psychology: General, 139, 728, 10.1037/a0020756 Cadez, 2015, Comparison of types of generalizations and problem-solving schemas used to solve a mathematical problem, Educational Studies in Mathematics, 89, 283, 10.1007/s10649-015-9598-y Dörfler, 2008, En route from patterns to algebra: comments and reflections, ZDM, 40, 143, 10.1007/s11858-007-0071-y Devlin, 2008 Duval, 1999, Representation, vision, and visualization: cognitive functions in mathematical thinking, 3 Duval, 2005, Les conditions cognitives de l'apprentissage de la géométrie: développement de la visualisation, différenciation des raisonnements et coordination de leur fonctionnement, Annales de Didactique et de Sciences Cognitives, 10, 5 Duval, 2014, Commentary: linking epistemology and semio-cognitive modeling in visualization, ZDM, 46, 159, 10.1007/s11858-013-0565-8 Jüttner, 1997, Evidence-based pattern classification: a structural approach to human perceptual learning and generalization, Journal of Mathematical Psychology, 41, 244, 10.1006/jmps.1997.1165 Jurdak, 2014, Trends in the development of student level of reasoning in pattern generalization tasks across grade level, Educational Studies in Mathematics, 85, 75, 10.1007/s10649-013-9494-2 Larkin, 1980, Expert and novice performance in solving physics problems, Science, 208, 1335, 10.1126/science.208.4450.1335 Lim, 2011 National Governors Association Center for Best Practices, Council of Chief State School Officers, 2010 National Research Council, 2013 Nilsson, 2011, Flexibility and coordination among acts of visualization and analysis in a pattern generalization activity, Journal of Mathematical Behavior, 30, 194, 10.1016/j.jmathb.2011.07.002 Rivera, 2009, Algebraic reasoning through patterns, Mathematics Teaching in the Middle School, 15, 212, 10.5951/MTMS.15.4.0212 Rivera, 2011, Formation of pattern generalization involving linear figural patterns among middle school students: results of a three-year study, 323 Rivera, 2010, Visual templates in pattern generalization activity, Educational Studies in Mathematics, 73, 297, 10.1007/s10649-009-9222-0 Rivera, 2011 Rivera, 2013 Rivera, 2016, Abduction and the emergence of necessary mathematical knowledge Smith, 2003, Learning to recognize objects, Psychological Science, 14, 244, 10.1111/1467-9280.03439 Tanisli, 2009, The strategies of using the generalizing patterns of primary school 5th grade students, Educational Sciences: Theory & Practice, 9, 1485 Walkowiak, 2014, Elementary and middle schools students’ analyses of pictorial growth patterns, Journal of Mathematical Behavior, 33, 56, 10.1016/j.jmathb.2013.09.004 Wilkie, 2016, Students’ use of variables and multiple representations in generalizing functional relationships prior to secondary school, Educational Studies in Mathematics, 10.1007/s10649-016-9703-x Wu, 2011