Assessing Higher Order Thinking in Mathematics

By Gerald Kulm | Go to book overview

10
The Assessment of Schema
Knowledge for Arithmetic Story
Problems: A Cognitive Science
Perspective

SANDRA P. MARSHALL

This chapter describes a cognitive science approach to the assessment of higher order thinking. The basic premise here is that to have meaningful changes in our tests, we need to bring into accord three central elements of the instruction and testing cycle: (i) our conceptions about the subject-area domain, (ii) our model of the student's learning in the domain, and (iii) our expectations about the ways that test items reflect the domain and its learning. In the following sections, a psychological theory of memory, learning, and instruction is outlined and applied to the domain of arithmetic story problems. Its implications for a corresponding model of assessment are discussed, and several examples of assessment items are given.


The Existing Problem

Suppose we have a highly simplified representation of the testing process (as in Figure 10.1). The central components are the subject matter to be tested, the student's knowledge about that subject matter, and the test that is intended to tap the student's knowledge. Many considerations come into play in this process. All are governed by our understanding of how the student learns, what he or she learns, and his or her ability to convey this learning. The test represents our best attempt to measure all three of these aspects. The test is the vehicle through which the student demonstrates his understanding.

There are clearly strong connections between the components of Figure 10.1. The test of knowledge, for example, should adequately sample the domain. However, an essential piece is missing from this figure; namely, an integrative model of memory. This model is needed to pull together the student's learning, the subject matter learned, and the test of the subject matter. It can be used to explain how and what knowledge the student encodes in the learning of the domain. It can be used to model the structure of the domain itself in terms of what we would like the student to know. And, it can provide the rationale for the test that estimates the student's learning about the domain. Thus, the model of memory serves as a framework on which the components of the testing process are developed. As shown in Figure 10.2, the model of memory drives the entire testing process by coordinating the different components around a common representation of knowledge. Its advantage lies in the way this representation

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