Intuitive Strategies and Preconceptions about Association in Contingency Tables

Abstract

The aim of this research was to identify students' preconceptions concerning statistical association in contingency tables. An experimental study was carried out with 213 pre-university students, and it was based on students' responses to a written questionnaire including 2x2, 2x3 and 3x3 contingency tables. In this article, the students' judgments of association and solution strategies are compared with finding of previous psychological research on 2x2 contingency tables. We also present an original classification of students' strategies, from a mathematical point of view. Correspondence analysis is used to show the effect of item task variables on students' strategies. Finally, we include a qualitative analysis of the strategies of 51 students, which has served to characterize three misconceptions concerning statistical association.

The development of chance measurement

“…Noelting also described high level-responses using a between-box measurement of covariation to compare the boxes. This work was closely paralleled by Batanero, Estepa, Godino and Green (1996) who proposed a sequence of development for students assessing associations in twoway tables. Recent research conducted by Konold (1989Konold ( , 1991 with older students has shed light on the beliefs that they hold about probability and how these beliefs influence their judgments in different contexts involving uncertainty.…”

Explaining Student Achievement: the Influence of Teachers’ Pedagogical Content Knowledge in Statistics

“…The work of Author3 and colleagues was consolidated in a scale of statistical literacy (Author3 & Author1, 2003) based on student surveys, and in a scale of statistical understanding reflecting adoption of the concepts of variation and expectation based on in depth student interviews. Many of the items used in these studies drew on the earlier work of other researchers, such as Batanero and her colleagues (e.g., Batanero, Estepa, Godino & Green, 1996).…”

They Don't Show Nothing I Didn't Know: Emergent Tensions Between Culturally Relevant Pedagogy and Mathematics Pedagogy

“…When attempting to reason about the relation between two variables in a data set, students often fail to draw a valid conclusion because they focus on only one aspect of the data. For example, a study by Batanero, Estepa, Godino, and Green (1996) found that when faced with a contingency table about the relation between smoking and Bronchial disease, 70% of a sample of 200 high school seniors were unable to a draw a statistically valid conclusion. The most common error was to only attend to part of the contingency table.…”