Mathematical Reasoning Requirements in Swedish Upper Secondary Level Assessments

We investigate the mathematical reasoning required to solve the tasks in the Swedish national tests and a random selection of Swedish teacher-made tests. The results show that only a small proportion of the tasks in the teacher-made tests require the students to produce new reasoning and to consider the intrinsic mathematical properties involved in the tasks. In contrast, the national tests include a large proportion of tasks for which memorization of facts and procedures are not sufficient. The conditions and constraints under which the test development takes place indicate some of the reasons for this discrepancy and difference in alignment with the reform documents.

[1]  Edie Ronhovde,et al.  Making Sense of Word Problems , 2009 .

[2]  A. Su,et al.  The National Council of Teachers of Mathematics , 1932, The Mathematical Gazette.

[3]  Kurt Reusser.  Problem solving beyond the logic of things: contextual effects on understanding and solving word problems , 1988 .

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

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

[6]  G. Harel.  Mathematics education research, its nature, and its purpose: A discussion of Lester's paper , 2006 .

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

[8]  Max Stephens,et al.  Assessment: The engine of systemic curricular reform? , 2000 .

[9]  W. Firestone,et al.  Performance-Based Assessment and Instructional Change: The Effects of Testing in Maine and Maryland , 1998 .

[10]  Fulya Kula.  Verschaffel, L., Greer, B., and De Corte, E. (2000). Making Sense of Word Problems. Netherlands: Swets & Zeitlinger. , 2007 .

[11]  M. Battista.  Applying Cognition-Based Assessment to Elementary School Students' Development of Understanding of Area and Volume Measurement , 2004 .

[12]  M. Hegarty,et al.  Comprehension of arithmetic word problems: A comparison of successful and unsuccessful problem solvers. , 1995 .

[13]  Andreas Schleicher.  Measuring Student Knowledge and Skills: A New Framework for Assessment. , 1999 .

[14]  Dylan Wiliam,et al.  Keeping learning on track: classroom assessment and the regulation of learning , 2007 .

[15]  Douglas K. Brumbaugh.  Reasoning and Proof , 2013 .

[16]  T. Haladyna.  Writing Test Items to Evaluate Higher Order Thinking , 1996 .

[17]  Lyn D. English,et al.  Problem solving for the 21st century , 2010 .

[18]  W. Cox,et al.  Strategic Learning in A-level Mathematics? , 1994 .

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

[20]  Johan Lithner,et al.  Mathematical Reasoning in School Tasks , 2000 .

[21]  David Tall,et al.  Functions and Calculus , 1996 .

[22]  W. A. Mehrens.  Consequences of Assessment: What is the Evidence? , 1998 .

[23]  Jesper Boesen,et al.  Assessing mathematical creativity : comparing national and teacher-made tests, explaining differences and examining impact , 2006 .

[24]  C. Hirsch.  Curriculum and Evaluation Standards for School Mathematics , 1988 .

[25]  Gabriel J. Stylianides,et al.  Reasoning-and-Proving in School Mathematics Textbooks , 2009 .

[26]  N. Sofroniou.  Large-scale Assessment Programs for All Students: Validity, Technical Adequacy, and Implementation , 2004 .

[27]  Torulf Palm,et al.  Impact of authenticity on sense making in word problem solving , 2008 .

[28]  Ewa Bergqvist,et al.  Types of reasoning required in university exams in mathematics , 2007 .

[29]  Denisse R. Thompson,et al.  Assessment and Grading in High School Mathematics Classrooms , 1997 .

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

[31]  Jeremy Kilpatrick,et al.  Adding It Up: Helping Children Learn Mathematics , 2013 .

[32]  G. Brousseau.  Theory of didactical situations in mathematics , 1997 .

[33]  G. Pólya.  Mathematics and Plausible Reasoning , 1958 .

[34]  Yves Chevallard,et al.  A Theoretical Approach to Curricula , 1992 .

[35]  Sandra K. Cimbricz.  State-Mandated Testing and Teachers' Beliefs and Practice , 2002 .

[36]  A. Schoenfeld.  On mathematics as sense-making: An informal attack on the unfortunate divorce of formal and informal mathematics. , 1991 .

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