Assessing Higher Order Thinking in Mathematics

By Gerald Kulm | Go to book overview

trict, and state data on course content might be compared.

At the outset, we wished to determine the intent behind the institution of higher coursework requirements. This task was accomplished via a series of focused interviews ( Catterall, 1988) with governors' aides, policy makers, and education leaders. In general, these interviews supported our assumptions that more stringent course requirements had been instituted to improve the quality of student performance. McDonnell ( 1988) reported that policy makers described the purpose of coursework reforms both in general terms -- "...kid's potential not being tapped...," -- and as more operational goals -- "...to raise test scores..." (p. 5).

Our second task was to attempt to find new, comprehensive ways to determine the content of particular courses. Most particularly, we were interested in course content level of difficulty. Our data collection involved five types of data: course enrollment data from school rosters, teacher surveys, student surveys, student transcript analyses, and course materials analyses. McDonnell has reported on the utility of such data, their reliability and validity, and the feasibility of collecting and using such information ( McDonnell, Koretz, Catterall, Burstein, & Baker, 1989). To provide a flavor of the work, consider the issue of what it means to have one more course required in a mathematics sequence, with that course intended to increase students' learning of additional mathematics content. However, it is possible that content taught in a Math 1 and Math 2 sequence is simply stretched into a Math 3 course as well. Instruction is slowed down. Does this meet the policy intent? Probably not at first blush, although it is possible that students' overall performance may increase because they have a more extended opportunity to learn a fixed amount of content. To obtain measures of what was actually covered in classes, our project surveyed teachers and students. Another approach involved acquiring samples of student assignments completed by the end of a course and selecting average as well as excellent student work, a post hoc portfolio. Conducting topic analyses of texts and asking teachers to show us how far they covered provided another measure.

Needed analyses are underway to combine findings into composites that either have content validity or can be shown to have construct validity. With curriculum indicators of this sort, we should be able to answer questions about the effects of requirements on students. Do test scores rise because low-performing students have become discouraged with higher standards and have dropped out? Do test scores rise because old content is being learned better over longer periods? Do test scores rise because students are mastering previously unencountered challenging content? Are there short-term dips, as suggested by Koretz ( 1988), because less-able students are taking harder classes? Do we see a predicted drop in average scores and an increase in the variances of students taking those courses? Developing information of this sort, although a complex, time-consuming task, once institutionalized, can greatly contribute to our understanding of all sorts of student performance.


Summary

This chapter explored the definition and impetus for the measurement attention to higher order thinking skills. Through a detailed description, a model development process was presented. This process relied on strong theory, but was firmly grounded as well in concerns for subject matter validity, feasibility, and credibility. This example led to a discussion of educational indicators as an approach to provide context for results of new measures. A brief example of the development of new curriculum indicators was included to demonstrate the complexity and utility of such efforts.


Acknowledgments

The research supported herein was conducted with partial support from the U.S. Department of Education, Office of Research and Improvement, grant number G00869003.

A version of this chapter was presented at the symposium, entitled "Perspectives and Emerging Approaches for Assessing Higher Order Thinking Skills," at the Annual Meeting of the American Association for the Advancement of Science, San Francisco, January 1989.

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