Abstract
Statistics education has investigated how to promote formal inferential reasoning from informal inferential reasoning. Nevertheless, there is still a need for proposals that explore and progressively develop inferential reasoning of students and teachers. Concerning this, the objective of this article is to characterize the inferential reasoning that secondary school mathematics teachers show in the practices that they develop to solve problems regarding the Chi-square statistic. To achieve this, we use theoretical and methodological notions introduced by the onto-semiotic approach of mathematics knowledge and instruction. In particular, we have taken a theoretical proposal of levels of inferential reasoning for the Chi-square statistic. Based on the results, the main conclusion was that the proposal above effectively predicted the teachers’ practices, allowing us to distinguish characteristic elements of the levels of inferential reasoning.
Highlights
Teachers on the Chi-Square Statistic.Statistics education has recently developed a particular interest in the education of citizens with the ability to interpret the world around them
Callingham and Watson [2] and Pfannkuch [3] have evidenced that curriculums show elements of statistical inference in years before university education; the notions involved in it are often complex for students and teachers to understand [4,5,6,7,8]
To carry out this study, we used a theoretical proposal of levels of inferential reasoning on the Chi-square statistic, which is based on the theoretical notions we have described and on the research literature of statistics education [26]
Summary
Some studies have emphasized problems that students and teachers present when making inferences with the Chi-square statistic These difficulties include identifying variables, assuming independence, having a unidirectional, deterministic, and localistic conception of association, using a generic interpretation of the hypothesis test, confusing homogeneity with independence, and making errors in the hypothesis statement, with the p-value and the significance level [18,19,20,21,22,23,24,25]. In this sense, this study aims to characterize the inferential reasoning evidenced by. This study seeks to empirically explore if the levels of inferential reasoning on the Chi-square statistic, proposed by Lugo-Armenta and Pino-Fan [26], are predictors of the level of inferential reasoning associated with the practices that teachers can develop when solving problems about this statistic
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