change will place a greater reliance upon our knowledge about the learning process in the construction of tests.
In the case of higher order mathematical thinking, early efforts to assess children's performance in clinical settings have been very much in line with the notion of measuring progress and development. Some attempts have been made to use more standardized approaches to problem-solving assessment that are in fine with the traditional purposes of testing ( Charles et al., 1984; Schoen & Oemke, 1979). However, efforts such as these appear to have had little direct impact on instruction. We need to do more to help teachers use the methods developed through clinical studies. In England, the Assessment Performance Unit (APU) has consciously used its testing program as a tool to develop teachers' skills in assessing higher order thinking ( Murphy & Schofield, 1984). There is hope and some anecdotal evidence from APU that involving teachers in the development and administration of higher order thinking assessment programs encourages them to use new instructional strategies. We have already begun to see that little progress can be made in teaching problem solving and other types of higher order mathematical thinking without a concomitant effort to align curriculum with instructional improvement efforts. That alignment is unlikely to be possible without significant advances in the conception and design of approaches to assessment.
American Association for the Advancement of Science ( 1989). Science for aft Americans. Washington, DC: AAAS.
Blumberg, F., Epstein, M., & MacDonald, W. ( 1985). National Assesment of Educational Pmgress higher order skills planning conference. Princeton, NJ: National Assessment of Educational Progress.
Carpenter, T. P. ( 1985). Learning to add and subtract: An exercise in problem solving. In E. A. Silver (Ed.) Teaching and learning mathematical problem solving: Multiple research perspectives. Hillsdale, NJ: Lawrence Erlbaum.
Charles, R., Lester, F., & O'Daffer, P. ( 1984). An assessment model for problem solving. Springfield, IL: Illinois State Board of Education.
Glaser, R. ( 1986). The integration of instruction and testing. In The redesign of testing for the 21st century. Princeton, NJ: Educational Testing Service.
Kulm, G. ( 1982). Analysis and synthesis of mathematical problem solving processes. Final Report, Grant #SED-79-20596, Purdue University, West Lafayette, IN.
Kulm, G. ( 1986). Assessing higher order thinking in mathematics. Paper presented at the NCTM RAC/SIG Research Presession, Washington, DC.
Murphy, P. & Schofield, B. ( 1984). Assessment of Performance Unit science report for teachers. Science at age 13. Department of Education and Science, Welsh Office; Department of Education for Northern Ireland.
National Assessment of Educational Progress. ( 1983). The third national mathematics assessment: Results, trends, and issues. Denver: National Assessment of Educational Progress.
National Council of Teachers of Mathematics. ( 1989). Curriculum and evaluation standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics.
Schoen, H. L. & Oehmke, T. M. ( 1979). The IPSP problem-solving test. Cedar Falls, IA: University of Northern Iowa.
Schoenfeld, A. H. ( 1985). Mathematical problem solving. New York: Academic Press.