Assessing Higher Order Thinking in Mathematics

By Gerald Kulm | Go to book overview

1
Developing Comprehensive
Assessments of Higher Order
Thinking

EVA L. BAKER

Testing and related achievement assessment methods undeniably represent one of the most widespread and powerful approaches that are being used to control the quality of schooling. It is also clear that the impact of tests in the service of accountability is not unbridled good. Critics contend that achievement tests may be shallow, corruptible, or incorrect ( Shepard, 1989; Linn, Graue, & Sanders, 1989; Burstein, 1989; Baker, 1989; Koretz, 1989). This chapter will attempt to place in context the renewed attention to assessments that attempt to capture more complex aspects of educational attainments of students.


How Is Higher Order Thinking Conceived and Measured?

Higher order thinking has been conceived both in terms of analyses of intellectual processes and of task characteristics.


Intellectual attributes of higher order thinking

In simplest terms, higher order thinking measures include all intellectual tasks that call for more than information retrieval. Any transformation of information is definitionally "higher order" thinking. Early writers who took the approach of detailing intellectual processes and illustrative tasks included Bloom ( 1956) and Gagne ( 1985). Operating from an assessment perspective, Bloom and his colleagues formulated an analysis that popularized the term "higher order," since the upper levels of their venerable Taxonomy of Educational Objectives (comprehension, application, analysis, synthesis, and evaluation) provided an operational description that influenced test developers and curriculum designers for years. Gagne's analysis of intellectual processes required by tasks, developed from a learning and training perspective, was of similar influence and was also frequently construed to have a hierarchical character. Both analyses rest upon the inference of transformation and construction processes from tasks, and have served as important precursors to many current cognitive analyses.

Other formulations of higher order thinking derive from the general problem-solving literature and emphasize such task components as problem identification and solution testing. These may treat problem solving either as a subject-matter domain independent task, akin to general critical thinking ( Ennis, 1987), or as dependent upon particular content domains. Higher order thinking can also take the form of metacognitive skills, such as planning and self-checking. These skills may be either independent of or embedded in the subject matter task to which

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