Abstract
This chapter consists of two sections. The first, by Mogens Niss, looks at assessment in a general setting, before discussing some possible detailed types of assessment. In section II John Pegg, Angel Gutiérrez & Pedro Huerta describe a type of assessment derived from research on the SOLO Taxonomy that extends the van Hiele “levels”.
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References
Gravemeijer, K., VAN DEN Heuvel, M., & Streefland, L.: Contexts, Free Productions, Tests and Geometry in Realistic Mathematics Education, Utrecht OW & Oc, 1990.
Kulm, G. (ED): Assessing Higher Order Thinking in Mathematics, Washington, DC. American Association for the Advancement of Science, 1990.
DE Lange, J.: Mathematics, Insight and Meaning, Utrecht, OW & OC, 1987.
Leder, G. (ED): Assessment and Learning of Mathematics, Hawthorn, VIC. The Australian Council for Educational Research Ltd., 1992.
Lesh, R., & Lamon, S. J. (EDS): Assessment of Authentic Performance in School Mathematics, Washington, DC. American Association for the Advancement of Science, 1992.
Nelsen, R. B.: Proofs without words, Washington, DC. The Mathematical Association of America, 1993.
Niss, M.: Assessment in Mathematics Education and Its Effects: An Introduction, in [8], pp 1–30.
Niss, M. (ED): Investigations into Assessment in Mathematics Education-An ICMI Study, Dordrecht: Kluwer Academic Publishers, 1993.
Niss, M. (ED): Cases of Assessment in Mathematics Education-An ICMI Study, Dordrecht: Kluwer Academic Publishers, 1993.
Stephens, M., &Z Money, R.: New Developments in Senior Secondary Assessment in Australia, In Niss, [9], pp 155–171, 1993.
Webb, N. L., & Coxford, A. F. (EDS): Assessment in the Mathematics Classroom 1993 Yearbook, Reston, VA. National Council of Teachers of Mathematics, 1993.
References
Biggs, J. & Collis, K.: Multimodal learning and the quality of intelligent behaviour., In H. Rowe (Ed), Intelligence, Reconceptualization and Measurement, 57–76. Lawrence Erlbaum, 1991.
Burger, W.F. & Shaughnessy, J.M.: Characterizing the van Hiele levels of development in geometry, Journal for Research in Mathematics Education, 17, 31–48, 1986.
Campbell, K., Watson, J. & Collis, K.: Volume measurement and intellectual development, Journal of Structural Learning and Intelligent Systems, 11, 279–298, 1992.
Case, R.: The Mind’s Staircase: Exploring the conceptual underpinnings of children’s thought and knowledge, Lawrence Erlbaum, 1992.
Clements, D.H. & Battista, M.T.: Geometry and spatial reasoning., In D.A. Grouws (Ed), Handbook of research on mathematics teaching, 420–464 N.C.T.M.-Macmillan, 1992.
Cole, N.S.: Conceptions of educational achievement, Educational Researcher, 19.3, 2–7, 1990.
Collis, K.F.; Romberg, T.A. & Jurdak, M.E.: A technique for assessing mathematical problem-solving ability, Journal for Research in Mathematics Education, 17.3, 206–221, 1986.
Fischer, K.W. & Knight, C.C.: Cognitive development in real children: Levels and variations, In B. Presseisen (Ed), Learning and thinking styles: Classroom interaction (pp. 43–67). Washington, USA. National Education Association, 1990.
Fuys, D.; Geddes, D. & Tischler, R.: The van Hiele model of thinking in geometry among adolescents, Journal for Research in Mathematics Education Monograph n. 3. N.C.T.M., 1988.
Griffiths, H.B. & Howson, A.G.: Mathematics: Society and Curricula, Cambridge University Press, 1974.
Gutiérrez, A. & Jaime, A.: Towards the designing of a standard test for the assessment of the student’s reasoning in geometry, In Proceedings of the 19th P.M.E. Conference, 3, 11–18, 1995.
Gutierrez, A.; Jaime, A. & Fortuny, J.M.: An alternative paradigm to evaluate the acquisition of the van Hiele levels, Journal for Research in Mathematics Education, 22, 237–251, 1991.
Hofper, A.: Van Hiele-based research, In R. Lesh & M. Landau (Eds), Acquisition of mathematics concepts and processes, 205–227, Academic Press, 1983.
Huerta, M.P.: Los nivelés de van Hiele en relation con la Taxonomia SOLO y los Mapas Conceptuales, (PhD dissertation) Univ. de Valencia, 1997.
Jaime, A.: Aportaciones a la interpretation y aplicaciôn del modelo de Van Hiele. La ensenanza de las isometnas del piano. La evaluation del nivel de razonamiento., (PhD dissertation), Univ. de Valencia. (DAI-C 56/02, p. 314, 1995), 1993.
Jaime, A. & Gutiérrez, A.: Una propuesta de fundamentacidn para la ensenanza de la geometna: El modelo de Van Hiele, In S. Llinares & M.V. Sánchez (Eds), Teoria y prâctica en educaciôn matemâtica, 295–384, Sevilla, Spain. Alfar, 1990.
Jaime, A. & Gutiérrez, A.: A model of test design to assess the Van Hiele levels, In Proceedings of the 18th International Conference for the P.M.E., 3, 41–48, 1994.
Jaime, A. & Gutiérrez, A.: Guidelines for teaching plane isometries in secondary school, The Mathematics Teacher, 88.7, 591–597, 1995.
Niss, M. (ED): Investigations into assessment in Mathematics Education, Kluwer, 1993.
Niss, M. (ED): Cases of assessment in Mathematics Education, Kluwer, 1993.
Pegg, J.: Assessing students’ understanding at the primary and secondary level in the mathematical sciences, In J. Izard & M. Stephens (Eds), Reshaping Assessment Practice: Assessment in the Mathematical Sciences Under Challenge 368–385, Australian Council of Educational Research, Melbourne, 1992.
Pegg, J.: Students’ understanding of geometry: theoretical perspectives, In B. Southwell, B. Perry & K. Owens (Eds), Space-The First and Final Frontier 18–36, Mathematics Education Research Group of Australasia, Sydney, 1992.
Pegg, J.: Learning and Teaching Geometry, In L. Grimison & J. Pegg (Eds), Teaching Secondary Mathematics: Theory into Practice 87–103, Harcourt and Brace, 1995.
Pegg, J. & Faithfull, M.: Analysing higher order skills in deductive geometry, In A. Baturo (Ed), New Directions in Geometry Education 100–105. Brisbane, Australia. Queensland University of Technology Press, 1995.
Pegg, J. & Woolley, S.: An investigation of strategies used to solve a simple deductive exercise in geometry, In G. Bell, et al. (Eds), Proceedings of the 17th Mathematics Education Research Group of Australasia 471–479, Mathematics Education Research Group of Australasia, Lismore, 1994.
Romberg, T.A.: Measures of mathematical achievement, In T. Romberg & D. Stewart (Eds), The monitoring of school mathematics: Background papers: Vol. 2. Implications from psychology; outcomes of instruction. Madison, USA. Wisconsin Center for Education Research, 1987.
VAN Hiele, P.M.: Structure and Insight: a theory of mathematics education, Academic Press, 1986.
Vygotsky, L.S.: Mind in Society, Harvard University Press, 1978.
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Niss, M., Pegg, J., Gutiérrez, A., Huerta, P. (1998). Assessment in Geometry. In: Mammana, C., Villani, V. (eds) Perspectives on the Teaching of Geometry for the 21st Century. New ICMI Study Series, vol 5. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5226-6_9
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DOI: https://doi.org/10.1007/978-94-011-5226-6_9
Publisher Name: Springer, Dordrecht
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