Functional thinking ways in relation to linear function tables of elementary school students

Australian Education Council, 1994 Beatty, 2006, Multiple vs. numeric approaches to developing functional understanding through patterns—Affordances and limitations for grade 4 students Blanton, 2004, Elementary grades students’ capacity for functional thinking, 135 Blanton, 2008 Blanton, 2005, Helping elementary teachers build mathematical generality into curriculum and instruction, ZDM Mathematics Education, 37, 34, 10.1007/BF02655895 Bogdan, 1998 Booth, 1988, Children's difficulties in beginning algebra Carpenter, 2000 Carraher, 2008, Early algebra and mathematical generalization, ZDM Mathematics Education, 40, 3, 10.1007/s11858-007-0067-7 Clement, 2000, Analysis of clinical interviews: Foundations and model viability, 547 Confrey, 1994, Exponential functions, rate of change, and the multiplicative unit, Educational Studies in Mathematics, 26, 135, 10.1007/BF01273661 Department of Education and Science, 1991 Department for Education and Skills, 2001 Driscoll, 1999 English, 1998, Introducing the variable through pattern exploration, The Mathematics Teacher, 91, 166, 10.5951/MT.91.2.0166 Ginsburg, 1981, The clinical interview in psychological research on mathematical thinking: Aims, rationales, techniques, For The Learning of Mathematics, 1, 4 Hargreaves, 1999, Children's strategies with number patterns, 67 Hunting, 1997, Clinical interview methods in mathematics education research and practice, Journal of Mathematical Behavior, 16, 145, 10.1016/S0732-3123(97)90023-7 Kaput, 1999, Teaching and learning a new algebra, 133 Kaput, 2008, What is algebra? What is algebraic reasoning?, 5 Kuchemann, 1981, Algebra, 102 Lannin, J. (2002). Developing middle school students’ understanding of recursive and explicit reasoning. Paper presented at the Annual meeting of the American Educational Research Association. Lannin, 2006, Recursive and explicit rules: How can we build student algebraic understanding?, Journal of Mathematical Behavior, 25, 299, 10.1016/j.jmathb.2006.11.004 Lew, 2004, Developing algebraic thinking in early grades: Case study of Korean elementary school mathematics, The Mathematics Educator, 8, 88 Ley, A. F. (2005). A cross-sectional investigation of elementary school student's ability to work with linear generalizing patterns: The impact of format and age on accuracy and strategy choice (Unpublished master's thesis). University of Toronto, Canada. MacGregor, 1995, The effect of different approaches to algebra on students’ perceptions of functional relationships, Mathematics Education Research Journal, 7, 69, 10.1007/BF03217276 Markworth, K. A. (2010). Growing and growing: promoting functional thinking with geometrıc growing patterns (Unpublished doctoral dissertation). University of North Carolina, USA. Martinez, 2006, A third grader's way of thinking about linear function tables, Journal of Mathematical Behavior, 25, 285, 10.1016/j.jmathb.2006.11.003 McMillan, 2004 ME, 1991 Merriam, 1998 Miles, 1994 Ministry of Education of Singapore, 2006 Moss, 2006, Knowledge building and knowledge forum: Grade 4 students collaborate to solve linear generalizing problems, 193 National Council of Teachers of Mathematics, 1989 National Council of Teachers of Mathematics, 2000 Orton, 1999, Pattern and the approach to algebra, 104 Patton, 1990 Philipp, 1999, The many uses of algebraic variables, 157 Rosnick, 1981, Some misconceptions concerning the concept of variable, 313 Samsan, 1999, The influence of different representations on children's generalisation thinking processes, 406 Schliemann, 2001, When tables become function tables Schoenfeld, 1999, On the meaning of variable, 150 Smith, 2008, Representational thinking as a framework for introducing functions in the elementary curriculum, 143 Stacey, 1997, Building foundations for algebra, Mathematics Teaching in the Middle School, 252, 10.5951/MTMS.2.4.0252 Stacey, 2001, Curriculum reform and approaches to algebra, 141 Stephens, 2005, Developing students’ understandings of variable, Mathematics Teaching in the Middle School, 11, 96, 10.5951/MTMS.11.2.0096 Strauss, 1990 Swafford, 2000, Grade 6 students’ pre-instructional use of equations to describe and represent problem situations, Journal for Research in Mathematics Education, 31, 89, 10.2307/749821 Tanışlı, D. (2008). Identifying the primary school 5th grade students’ comprehension and grasp manners regarding patterns (Unpublished doctoral dissertation). Anadolu University, Turkey. Vollrath, 1986, Search strategies as indicators of functional thinking, Educational Studies in Mathematics, 17, 387, 10.1007/BF00311326 Wagner, 1983, What are these things called variables, 316 Warren, 2000, Visualisation and the development of early understanding in algebra, 273 Warren, 2005, Introducing functional thinking in year 2: A case study of early algebra teaching, Contemporary Issues in Early Childhood, 6, 150, 10.2304/ciec.2005.6.2.5 Warren, 2006, Using repeating patterns to explore functional thinking, Australian Primary Mathematics Classroom, 11, 9 Warren, 2008, Generalising the pattern rule for visual growth patterns: Actions that support 8 year olds’ thinking, Educational Studies in Mathematics, 67, 10.1007/s10649-007-9092-2 Warren, 2006, Investigating functional thinking in the elementary classroom: Foundations of early algebraic reasoning, Journal of Mathematical Behavior, 25, 208, 10.1016/j.jmathb.2006.09.006