Assessing Higher Order Thinking in Mathematics

By Gerald Kulm | Go to book overview
Figure 10.9. The levels of networks. Each node can be expanded into a lower level network.

well as with broad units at the curriculum level. Figure 10.9 provides a general picture of these relationships. One can focus the assessment on different levels of knowledge, depending upon the goal of assessment, ranging from individual schemas to the integrated curriculum.

The schema theory presented here already has served as the basis for an instructional system and its accompanying assessment. It is a proven way to focus assessment upon the integration of knowledge rather than on fragmentary knowledge. It provides a basis for improving the assessment of mathematical thinking and for incorporating cognitive science into evaluation in related fields. Its value is that it provides the coordination for representing what we want to test, how a student learns it, and how the test measures it.


Acknowledgments

The research described in this chapter was carried out under support from the Cognitive Sciences Program, Office of Naval Research, Contract No. N00014-K-85-0661.


References

Anderson, J. R. ( 1983). The architecture of cognition. Hillsdale, NJ: Erlbaum.

Marshall, S. P. (in press). Assessing schema knowledge. In N. Frederiksen (Ed.), Test theory for a new generation of tests. Hillsdale, NJ: Lawrence Erlbaum.

Marshall, S. P. ( 1989). Affect in schema knowledge: Source and impact. In D. B. McLeod & V. M. Adams (Eds.), Affect and mathematical problem solving. A new perspective (pp. 49-59). New York: Springer-Verlag.

Marshall, S. P., Barthuli, K. E., Brewer, M. A., & Rose, F. E. ( 1989). Story Problem Solver. A Schema Based System of Instruction. (Tech Rep. 89-01, Contract No. N00014-85-K-0661). Arlington, VA: Office of Naval Research.

Minsky, M. ( 1975). A framework for representing knowledge. In P. H. Winston (Ed.), The psychology of computer vision. New York: McGraw Hill.

Rumelhart, D. E. ( 1980). "Schemata: The building blocks of cognition". In R. Spiro, D. Bruce, & W. Brewer (Eds.), Theoretical issues in reading comprehension. Hillsdale, NJ: Erlbaum.

Schank, R., & Abelson, R. ( 1977). Scripts, goals, and understanding. Hillsdale, NJ: Erlbaum.

Usiskin, Z., & Bell, M. ( 1983). Applying arithmetic: A handbook of applications of arithmetic. Part II: Operations. The University of Chicago, Department of Education, Arithmetic and Its Applications Project.

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