Assessing Higher Order Thinking in Mathematics

By Gerald Kulm | Go to book overview

11
Critical Evaluation of
Quantitative Arguments

CURTIS C. McKNIGHT

Higher order thinking, even in mathematics, is not a unitary phenomenon. There is not one form of higher order thinking but, rather, many forms. It might be argued that each form is the same complex of cognitive processes applied to differing domains of knowledge and tasks. However, as seen in this volume, the task and knowledge domains differ so greatly that, even if there are important commonalities in the cognitive processes involved in complex thinking in those domains, pragmatically, it may be more useful to consider the thinking tasks of each domain in terms of their specificity, with a focus on the tasks particular to the knowledge of the domain and the forms of higher order thinking critical to such tasks. Such is the case with the critical evaluation of quantitative arguments.

The entrance of our society into the information age, with its ubiquity of computer-enhanced publishing and presentation graphics, has led to a virtual bombardment of both citizen and student with numerical data and, moreover, with numerical data embedded not in the context of separate treatises or texts on mathematics, but in the context of informative articles which often contain either central or peripheral arguments that have essential quantitative elements. In particular, the quantum leap in the ease with which presentation graphics can be generated has resulted in constant exposure to information presented in graphical form. The ability to think critically in the presence of arguments with essential quantitative elements, often graphical elements, has become an essential skill for educated citizens in our society and will be so even more in the future. Instruction related to the skills necessary for such quantitatively oriented critical thinking will certainly enter the curricula of school mathematics if the new standards for mathematics as reasoning and communication promulgated by the National Council of Teachers of Mathematics ( NCTM, 1989) have their hoped-for impact.

Even with the emergence of these new essential skills of critical thinking that utilize tools for quantitative reasoning and graphical interpretation in contexts that are not "mathematical" in the narrow or disciplinary sense, little investigation has yet been done of the nature of these cognitive skills, their characterization in information-processing terms, and their interaction with noncognitive factors such as anxiety about mathematics. Anecdotal evidence suggests that mathematics anxiety results in the paralysis of critical thinking abilities when quantitative elements are included in the contexts in which individuals must think critically. Further, it has been suggested that the presumed fact of this paralysis of critical facilities, along with the wide spread of such mathematics anxiety, provides at least the possibility for use of numerical data and presentation graphics precisely to eliminate critical evaluation of arguments and claims.

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