Abstract
In recent attempts to reform assessment much attention is devoted to the formats of assessment and organizational aspects. Without good problems, however, it is impossible to improve assessment. This article focuses on the role of problems in the development of better assessment. An example of an attempt is given with respect to some key concepts and abilities on percentage. A series of problems for assessing these has been developed inspired by the ideas of Realistic Mathematics Education. The guiding principles were that problems should be meaningful and informative. The problems, which are rather different from the traditional kind have been tried out in two American grade 7 classes. The problems reveal a lot about the different levels of understanding of students. As such they can facilitate instructional decision making. Nevertheless it is clear that this is not the final stage of the search for better assessment problems. As a start to further developmental research, some recommendations will be given for the improvement of the problems.
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Bell, A., H. Burkhardt and M. Swan: 1992, ‘ Balanced assessment of mathematical performance’, in R. Lesh and S. Lamon (eds.),Assessment of Authentic Performance in School Mathematics, AAAS Press, Washington.
Burns, M., and C. McLaughlin: 1990,A Collection of Math Lessons — From Grades 6 through 8, The Math Solution Publications/Cuisenaire Company of America Inc, New Rochelle, NY.
Clarke, D.J., D. M. Clarke and Ch. J. Lovitt: 1990, ‘Changes in mathematics teaching call for assessment alternatives’, in T. J. Cooney and C. R. Hirsch (eds.),Teaching and Learning Mathematics in the 1990's. 1990 Yearbook NCTM, NCTM, Reston, VA.
Davis, R.: 1988, ‘Is ‘Percent’ a Number?’,Journal of Mathematical Behavior 7, 299–302.
De Lange, J.: 1987,Mathematics, Insight and Meaning, OW &CO, Utrecht.
De Lange, J.: in press, ‘Assessment: No Change without Problems’, in T. A. Romberg (ed.),Reform in School Mathematics and Authentic Assessment, SUNY Press, Albany, NY.
Freudenthal, H.: 1968, Why to Teach Mathematics so as to Be Useful?,Educational Studies in Mathematics 1, 3–8.
Freudenthal, H.: 1973,Mathematics as an Educational Task, Riedel Publishing Company, Dordrecht.
Freudenthal, H.: 1983,Didactical Phenomenology of Mathematical Structures, Riedel Publishing Company, Dordrecht.
Gravemeijer, K.: 1982, ‘Het gebruik van contexten’,Willem Bartjens, 1, 4, 192–197.
Gravemeijer, K.: 1990, ‘Context Problems and Realistic Mathematics Instruction’, in K. Gravemeijer, M. van den Heuvel, and L. Streefland,Contexts, Free Productions, Tests, and Geometry in Realistic Mathematics Education, OW&OC, Utrecht, 10–32.
Graue, M. E. and S. Z. Smith: 1992,A Conceptual Framework for Instructional Assessment, National Center for Research in Mathematical Sciences Education, Madison, WI.
Grouws D. A., and S. L. Meier: 1992, ‘Teaching and assessment relationships in mathematics instruction’, in G. Leder (ed.),Assessment and Learning of Mathematics, ACER, Victoria.
Kouba, V., C. Brown, T. Carpenter, M. Lindquist, E. Silver and J. Swafford: 1988, ‘ Results of the Fourth NAEP Assessment of Mathematics: Number, Operations, and Word Problems’,Arithmetic Teacher 36(8), 14–19.
NCTM: 1989,Curriculum and Evaluation Standards for School Mathematics, NCTM, Reston VA.
Romberg, T.A., E. A. Zarinnia and S. Williams: 1988,The Influence of Mandated Testing on Mathematics Instruction: Grade 8 Teachers' Perceptions, NCRMSE, Madison, WI.
Romberg, Th. A., E. A. Zarinnia and K. F. Collis: 1990, ‘A new world view of assessment in mathematics’, in G. Kulm (ed.),Assessing Higher Order Thinking in Mathematics, AAAS, Washington DC, 21–38.
Schoemaker, G.: 1993, ‘Is Mathematics meant to be understood?’, in P. Bero (ed.),Proceedings of the 3rd Bratislava International Symposium on Mathematical Education, Comenius University, Bratislava, 119–124.
Streefland, L.: 1991,Fractions in Realistic Mathematics Education. A Paradigm of Developmental Research, Kluwer Academic Publisher, Dordrecht.
Streefland, L.: 1992, ‘Thinking strategies in mathematics instruction: How is testing possible?’, in R. Lesh and S. Lamon (eds.),Assessment of Authentic Performance in School Mathematics, AAAS Press, Washington.
Streefland, L., and M. Van den Heuvel-Panhuizen: 1992, ‘Evoking pupils' informal knowledge on percents’, in International Group for the Psychology of Mathematics Education,Proceedings of the Sixteenth PME Conference. Volume III, University of New Hampshire, Durham, 51–57.
Stenmark, J. (ed.): 1992,Mathematics Assessment: Myths, Models, Good Questions, and Practical Suggestions, NCTM, Reston, VA.
Sullivan, P., and D. Clarke: 1987, ‘Good teaching and good questions’, in W. Caughey (ed.),From Now to the Future, The Mathematics Association of Victoria, Parkville.
Sullivan, P., and D. J. Clarke: 1991, ‘Catering to all abilities through the use of ‘Good’ questions’,Arithmetic Teacher 39, 2, 14–21.
Treffers, A.: 1987,Three Dimensions. A Model of Goal and Theory Description in Mathematics Instruction — the Wiskobas Project, Reidel, Dordrecht.
Treffers, A.: 1993, personal communication.
Van den Brink, J.: 1984, ‘Numbers in contextual frameworks’,Educational Studies in Mathematics 15, 239–257.
Van den Heuvel-Panhuizen, M.: 1990, ‘Realistic arithmetic/mathematics instruction and tests’, in K. Gravemeijer, M. van den Heuvel, and L. Streefland,Context, Free Productions, Tests, and Geometry in Realistic Mathematics Education, OW&OC, Utrecht, p. 53–78.
Van den Heuvel-Panhuizen, M., and K. Gravemeijer: 1991, ‘Tests are not all bad’, in L. Streefland (ed.),Realistic Mathematics Education in Primary School, CD-B Press/Freudenthal Institute, Utrecht (see also Van den Heuvel-Panhuizen, M., and Gravemeijer, K., 1993, ‘Tests aren't all bad. An attempt to change the face of written tests in primary school mathematics’, in N. L. Webb and A. F. Coxford,Assessment in the Mathematics Classroom, 1993 Yearbook, NCTM, Reston VA, 54–64).
Van den Heuvel-Panhuizen, M., L. Streefland, M. Meyer, J. A. Middleton, and J. Browne: in press, ‘Per Sense’, in T. A. Romberg (ed.),Mathematics in Contexts: A Connected Curriculum for Grade 5–8, Encyclopaedia Britannica Educational Corporation' Chicago.
Van den Heuvel-Panhuizen, M.: 1992,Per Sense Test, Freudenthal Institute, Utrecht (internal publication — draft version).
Van den Heuvel-Panhuizen, M.: 1993a, ‘New chances for paper-and-pencil tests’, paper presented at the CIEAEM 45, Sardinia, Italy.
Van den Heuvel-Panhuizen, M.: 1993b, ‘New forms of assessment, but don't forget the problems’,Proceedings of the Seventeenth International Conference for the Psychology of Mathematics Education, University of Tsukuba, Tsukuba, Ibaraki, Japan, Volume III, 186–193.
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Van Den Heuvel-Panhuizen, M. Improvement of (didactical) assessment by improvement of problems: An attempt with respect to percentage. Educ Stud Math 27, 341–372 (1994). https://doi.org/10.1007/BF01273377
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DOI: https://doi.org/10.1007/BF01273377