The Department of Psychology
QUANTITATIVE ABILITY MASQUERADING AS QUALITATIVE LEARNING
A Response to Inna Glaz
With so much learned enthusiasm, I felt that I should respond. First, I agree with what I feel is the crux of Inna's argument, namely that "if the university catalog states that math knowledge is required, then why not get it before coming to class?" Indeed, I should like to disabuse the misunderstanding that I believe statistics is devoid of some basic knowledge of mathematics or that students should wittingly enroll in classes such as Psy 202 or Psy 302 without first taking the necessary prerequisites. Second, I would like to respond to Inna's comments and her suggestions in some meaningful way. In doing so, however, I must acknowledge that I feel these comments unfortunately fall outside the intended scope of the initial article. For the benefit of the reader who has started at this point, I submitted an article that appeared in the Fall issue of The Looking Glass. In that article I wrote the following:
Clearly, significant prior knowledge does not mean accurate knowledge. Students may do poorly in their statistics courses for a number of reasons (e.g., forgetting how to perform arithmetic and basic algebra, difficulties with the English language, laziness, etc.). Nonetheless, I believe that Inna's claim that "a significant number of students do come to class as 'blank slates' and not very eager to be filled" is unfair and may be misplaced. Suppose, for example, that every student came to Psy 304A prepared (i.e., having taken Psy 202 and Psy 302, receiving, say, grades of B or better). One is still left with several statistical questions. For instance, one might ask whether the proportion of students who ultimately receive A's in Psy 304A differ (i.e., beyond the limits of chance variation) as a function of how well they did in their statistics courses? Perhaps more to the point, what percentage of students would one expect to succeed in Psy 304A if an instructor is required to accept only those who score above a certain arbitrary value in Math 100, say C or better? How might this strategy compare with what would happen if the instructor employed the same approach but instead used students' grades in English 100 as a criteria?
While serving as a lab instructor for the past four quarters, I've learned that probability and statistical concepts are very difficult for students to grasp and often conflict with many of their beliefs and intuitions about data and chance. I suspect this is so because students do not come to class as "blank slates" waiting to be filled, but instead approach learning statistics, as they would approach learning most things, with significant prior knowledge. In learning new concepts, I believe students interpret the new information in terms of the ideas they already have, constructing their own meaning by connecting the new information to what they already believe to be true. Unfortunately, I think this is where most of the flaws in reasoning emerge.
I agree with Inna that statistics is well grounded in mathematics, and therefore requires some rudimentary knowledge of arithmetic and manipulating algebraic equations. However, in mathematics there is (almost always) a clearly defined method for finding the answer, and that answer is usually the only acceptable one. In psychology, however, different research studies can produce very different, often contradictory results (depending on which design is chosen and which statistical technique is employed).
The article that appeared in the Fall issue was intended to stress the importance of the theoretical and practical interpretation of statistical results and the need to show students that they must think about their research questions before they can choose intelligently among the many statistical strategies available. In choosing one strategy over another, it is my opinion that students should be encouraged to (1) look upon their results (including null ones) as being both acceptable and informative outcomes and (2) be critical of their own (and others') research, not on the basis of obtained quantitative results, but on the basis of the qualitative adequacy of procedures and methodology.
(See the article in this issue by Inna Glaz.)
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