Students’ reasoning in mathematics textbook task-solving

This study reports on an analysis of students’ textbook task-solving in Swedish upper secondary school. The relation between types of mathematical reasoning required, used, and the rate of correct task solutions were studied. Rote learning and superficial reasoning were common, and 80% of all attempted tasks were correctly solved using such imitative strategies. In the few cases where mathematically founded reasoning was used, all tasks were correctly solved. The study suggests that student collaboration and dialogue does not automatically lead to mathematically founded reasoning and deeper learning. In particular, in the often common case where the student simply copies a solution from another student without receiving or asking for mathematical justification, it may even be a disadvantage for learning to collaborate. The results also show that textbooks’ worked examples and theory sections are not used as an aid by the student in task-solving.

[1]  Johan Lithner,et al.  A research framework for creative and imitative reasoning , 2008 .

[2]  Miroslav Lovric,et al.  Mathematics textbooks and their potential role in supporting misconceptions , 2009, The Best Writing on Mathematics 2010.

[3]  David Pimm,et al.  ‘This is so’: a text on texts , 1996 .

[4]  Manuel Santos-Trigo,et al.  Mathematical Problem Solving , 2015 .

[5]  Torulf Palm,et al.  Mathematical Reasoning Requirements in Swedish Upper Secondary Level Assessments , 2011 .

[6]  J. Hiebert,et al.  THE EFFECTS OF CLASSROOM MATHEMATICS TEACHING ON STUDENTS ’ LEARNING , 2006 .

[7]  Kenneth A. Ross,et al.  Doing and Proving: The Place of Algorithms and Proofs in School Mathematics , 1998 .

[8]  W. Doyle.  Academic Work , 1983 .

[9]  Alan H. Schoenfeld,et al.  Ideas in the air: Speculations on small group learning, environmental and cultural influences on cognition, and epistemology , 1989 .

[10]  J. Törnroos,et al.  Mathematics Textbooks, Opportunity to Learn and Student Achievement. , 2005 .

[11]  Gilbert A. Valverde.  According to the Book: Using TIMSS to investigate the translation of policy into practice through the world of textbooks , 2002 .

[12]  N. Webb,et al.  Promoting effective helping behavior in peer-directed groups , 2003 .

[13]  Torulf Palm,et al.  The relation between types of assessment tasks and the mathematical reasoning students use , 2010 .

[14]  Johan Lithner,et al.  Students' mathematical reasoning in university textbook exercises , 2003 .

[15]  T. P. Carpenter,et al.  Problem Solving as a Basis for Reform in Curriculum and Instruction: The Case of Mathematics , 1996 .

[16]  Birgit Pepin,et al.  An investigation of mathematics textbooks and their use in English, French and German classrooms: who gets an opportunity to learn what? , 2002 .

[17]  J. Hiebert,et al.  Instructional Tasks, Classroom Discourse, and Students’ Learning in Second-Grade Arithmetic , 1993 .

[18]  최영한,et al.  미국 NCTM의 Principles and Standards for School Mathematics에 나타난 수학과 교수,학습의 이론 , 2002 .

[19]  Lovisa Sumpter,et al.  Upper secondary students' task reasoning , 2008 .

[20]  N. Webb.  Task-Related Verbal Interaction and Mathematics Learning in Small Groups. , 1991 .

[21]  William H. Schmidt,et al.  According to the Book , 2002 .

[22]  Johan Lithner,et al.  Mathematical Reasoning in Teachers' Presentations. , 2012 .

[23]  Jeremy Kilpatrick,et al.  International handbook of mathematics education , 1997 .

[24]  Julianna Szendrei,et al.  Concrete Materials in the Classroom , 1996 .

[25]  Monica Johansson.  Mathematical meaning making and textbook tasks , 2007 .

[26]  L. Fuchs,et al.  Enhancing Students' Helping Behavior during Peer-Mediated Instruction with Conceptual Mathematical Explanations , 1997, The Elementary School Journal.

[27]  Mogens Allan Niss,et al.  MATHEMATICAL COMPETENCIES AND THE LEARNING OF MATHEMATICS: THE DANISH KOM PROJECT , 2003 .

[28]  Nicolas Balacheff,et al.  Theory of Didactical Situations in Mathematics , 2002 .

[29]  Monica Johansson,et al.  Teaching mathematics with textbooks : a classroom and curricular perspective , 2006 .

[30]  Johan Lithner,et al.  Mathematical reasoning in calculus textbook exercises , 2004 .

[31]  Frank K. Lester,et al.  Second handbook of research on mathematics teaching and learning : a project of the National Council of Teachers of Mathematics , 2007 .

[32]  Johan Lithner.  Mathematical reasoning and familiar procedures , 2000 .

[33]  Sebastian Rezat,et al.  Interactions of Teachers’ and Students’ Use of Mathematics Textbooks , 2011 .

[34]  E. Silver.  Fostering creativity through instruction rich in mathematical problem solving and problem posing , 1997 .

[35]  William H. Schmidt,et al.  Why Schools Matter: A Cross-National Comparison of Curriculum and Learning , 2001 .

[36]  N. Webb.  Peer interaction and learning in small groups , 1989 .