Assessing Higher Order Thinking in Mathematics

By Gerald Kulm | Go to book overview

12
Investigation of Structured
Problem-Solving Items

MARK WILSON

The ultimate aim of measurement is to gain "objectivity and simplicity" ( Glaser et al., 1987, p. 64) in relating real-world observations to theory. The concept of levels of understanding may be a useful intellectual tool in this process in a range of different situations. When a developmental continuum is postulated and found, levels may provide a convenient way to label portions of the continuum for practical purposes, or may be used to give practical expression to a researcher's doubts about the precision of measurement (i.e., as an alternative to simply reporting standard error of measurement). At the other extreme, as in much qualitative research, researchers may be striving to preserve the full impact of individual differences in development by avoiding standardization of the measurement process.

Nevertheless, the description of some sort of conceptual structure becomes all but inevitable as the researcher proceeds to interpretation. This structure may be more complex than a sequence of developmental levels; often a structure like a (mathematical) lattice will seem more appropriate. Here a sequence of developmental levels may prove useful if considered as a projection of this more complicated structure onto a single dimension. In between these two extremes lie the approaches that are based explicitly on developmental levels, such as the SOLO Taxonomy described in the following section.


The SOLO Taxonomy

The Structure of the Learning Outcome Taxonomy (SOLO; Biggs & Collis, 1982) is a method of classifying learner responses according to the structure of the response elements. The taxonomy consists of five levels of response structure: (i) a prestructural response is one that consists only of irrelevant information; (ii) a unistructural response is one that includes only one relevant piece of information from the stimulus; (iii) a multistructural response is one that includes several relevant pieces of information from the stimulus; (iv) a relational response is one that integrates all relevant pieces of information from the stimulus; and (v) an extended abstract response is one that not only includes all relevant pieces of information, but also extends the response to integrate relevant pieces of information not in the stimulus. This taxonomy is described in more detail by Romberg, Zarinnia and Collis (see chapter 2, this volume).

In the particular type of SOLO item under study ( Collis & Davey, 1986), a short piece of stimulus material which might consist of text, tables, or figures is supplied, then students are asked to answer open-ended questions concerning the material. Together, the stimulus material and the questions are referred to as a "superitem" ( Cureton, 1965). An example is given in Figure 12.1 (see page

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