Levels of participatory conception of fractional quantity along a purposefully sequenced series of equal sharing tasks: Stu's trajectory

The Journal of Mathematical Behavior - Tập 41 - Trang 45-67 - 2016
Jessica H. Hunt1, Arla Westenskow1, Juanita Silva1,2, Jasmine Welch-Ptak1,2
1The University of Texas at Austin, Austin, TX, USA
2Utah State University, Logan, UT USA

Tài liệu tham khảo

Baroody, 2004, Comments on the use of learning trajectories in curriculum development and research, Mathematical Thinking and Learning, 6, 227, 10.1207/s15327833mtl0602_8 Baxter, 2001, Effects of reform-based mathematics instruction on low achievers in five third-grade classrooms, The Elementary School Journal, 101, 529, 10.1086/499686 Baxter, 2002, We talk about it, but do they get it?, Learning Disabilities Research & Practice, 17, 173, 10.1111/1540-5826.00043 Bazeley, 2010, Computer-assisted integration of mixed methods data sources and analyses, 431 Butler, 2003, Fraction instruction for students with mathematics disabilities: Comparing two teaching sequences, Learning Disabilities Research & Practice, 18, 99, 10.1111/1540-5826.00066 Carpenter, 1999, 03801 Charles, 2000, Young children's partitioning strategies, Educational Studies in Mathematics, 43, 191, 10.1023/A:1017513716026 Daro, 2011, Learning Trajectories in Mathematics: A Foundation for Standards, Curriculum, Assessment, and Instruction. CPRE Research Report# RR-68, Consortium for Policy Research in Education Empson, 1999, Equal sharing and shared meaning: The development of fraction concepts in a first-grade classroom, Cognition and Instruction, 17, 283, 10.1207/S1532690XCI1703_3 Empson, 2003, Low-performing students and teaching fractions for understanding: An interactional analysis, Journal for Research in Mathematics Education, 34, 305, 10.2307/30034786 Empson, 2005, Fractions as the coordination of multiplicatively related quantities: A cross sectional study of student's thinking, Educational Studies in Mathematics, 63, 1, 10.1007/s10649-005-9000-6 Empson, 2011 Fuchs, 2014, Does working memory moderate the effects of fraction intervention? An aptitude-treatment interaction, Journal of Educational Psychology, 106, 499, 10.1037/a0034341 Geary, 2012, Independent contributions of the central executive, intelligence, and in-class attentive behavior to developmental change in the strategies used to solve addition problems, Journal of Experimental Child Psychology, 113, 10.1016/j.jecp.2012.03.003 Grbich, 2012 Ginsburg, 1997 Hackenberg, 2013, The fractional knowledge and algebraic reasoning of students with the first multiplicative concept, The Journal of Mathematical Behavior, 32, 538, 10.1016/j.jmathb.2013.06.007 Hecht, 2007, Fraction skills and proportional reasoning, 121 Hecht, 2010, Sources of group and individual differences in emerging fraction skills, Journal of Educational Psychology, 102, 843, 10.1037/a0019824 Hiebert, 2007, The effects of classroom mathematics teaching on students’ learning, 371 Hunt, 2012 Hunt, 2015, Strategies and representations used in equal partitioning problems by students with mathematics learning disability, Learning Disabilities Quarterly, 38, 208, 10.1177/0731948714551418 Hunt, 2013, An exploratory study of the effects of conceptual strategy intervention on knowledge of ratio equivalency for middle school students with mathematics learning disability, The Journal of Special Education, 47, 1 Hunting, 1988, Preschoolers’ cognitions of fractional units, British Journal of Educational Psychology, 58, 172, 10.1111/j.2044-8279.1988.tb00890.x Kieren, 1976, On the mathematical, cognitive and instructional foundations of the rational numbers, 101 Lamon, 1996, The development of unitizing: Its role in children's partitioning strategies, Journal for Research in Mathematics Education, 27, 170, 10.2307/749599 Leech, 2007, An array of qualitative data analysis tools: A call for data analysis triangulation, School Psychology Quarterly, 22, 557, 10.1037/1045-3830.22.4.557 Mazzocco, 2013, Limited knowledge of fraction representations differentiates middle school students with mathematics learning disability (dyscalculia) versus low mathematics achievement, Journal of Experimental Child Psychology, 115, 371, 10.1016/j.jecp.2013.01.005 National Mathematics Advisory Panel, 2008 Nunes, 2009, Children's understanding of fractions, Revista Contrapontos, 8, 509, 10.14210/contrapontos.v17n3.p509-528 Pothier, 1983, Partitioning: The emergence of rational number ideas in young children, Journal for Research in Mathematics Education, 14, 307, 10.2307/748675 Piaget, 1977 Piaget, 1960 Pitkethly, 1996, A review of recent research in the area of initial fraction concepts, Educational Studies of Mathematics, 30, 5, 10.1007/BF00163751 Powell, 2003, An analytical model for studying the development of learners’ mathematical ideas and reasoning using videotape data, The journal of mathematical behavior, 22, 405, 10.1016/j.jmathb.2003.09.002 Simon, 1995, Reconstructing mathematics pedagogy from a constructive perspective, Journal for Research in Mathematics Education, 26, 114, 10.2307/749205 Simon, 2006, Key developmental understandings in mathematics: A direction for investigating and establishing learning goals, Mathematical Thinking and Learning, 8, 359, 10.1207/s15327833mtl0804_1 Simon, 2010, A developing approach to studying students’ learning through their mathematical activity, Cognition and Instruction, 28, 70, 10.1080/07370000903430566 Simon, 2004, Explicating a mechanism for conceptual learning: Elaborating the construct of reflective abstraction, Journal for Research in Mathematics Education, 35, 305, 10.2307/30034818 1997 Steffe, 2002, A new hypothesis concerning children's, Journal of Mathematical behavior, 102, 1 Steffe, 1988 Steffe, 2010 Steffe, 2000, Teaching experiment methodology: Underlying principles and essential elements, 267 Streefland, 1993, Fractions: A realistic approach, 289 Test, 2005, The effects of LAP fractions on addition and subtraction of fractions with students with mild disabilities, Education & Treatment of Children, 28, 11 Tzur, 1999, An integrated study of children's construction of improper fractions and the teacher's role in promoting that learning, Journal for Research in Mathematics Education, 30, 390, 10.2307/749707 Tzur, 2007, Fine grain assessment of students’ mathematical understanding: Participatory and anticipatory stages in learning a new mathematical conception, Educational Studies in Mathematics, 66, 273, 10.1007/s10649-007-9082-4 Tzur, 2013, Distinguishing conceptions and tasks in children's development of multiplicative reasoning, PNA, 7, 85, 10.30827/pna.v7i3.6128 Tzur, 2004, Distinguishing two stages of mathematics conceptual learning, International Journal of Science and Mathematics Education, 2, 287, 10.1007/s10763-004-7479-4 Vukovic, 2012, Mathematics difficulty with and without reading difficulty: Findings and implications from a four-year longitudinal study, Exceptional Children, 78, 280, 10.1177/001440291207800302 Zhang, D. Steckler, P., Huckabee, S., & Miller, R. Strategic development for middle school students struggling with fractions: Assessment and intervention. Journal of Learning Disabilities, 14. http://dx.doi.org/10.1177/0022219414562281 (pre published December).