Errors concerning Statistics and Probability in Spanish Secondary School Textbooks

Abstract

Textbooks are considered essential, providing a hierarchical organisation of knowledge, forging the intellectual scaffolding of students and teachers alike, and playing a crucial role in compulsory education. In this paper we discuss, by means of a content analysis, the systematic errors detected in the presentation of questions related to statistics and probability in Spanish secondary school textbooks on mathematics. We found some errors appear systematically in the texts, and the most common are: faulty differentiation between quantitative and qualitative variables, between discrete and continuous variables and between randomness and determinism, confused examples for the bar charts, uncritical choice for graphic representations, inaccuracies in specific vocabulary, and ignoring prior probabilities and a poor consideration about representativeness. We classify the observed errors considering that some of these errors arise from the inherent difficulty of the content and others arise from differences between mathematical and statistical thinking as well as from judgments based on heuristic rules. Knowing the existence of these errors and the reasons why they occur are key points to make them disappear from statistical lessons and to help citizens achieving true statistical literacy.

Keywords

• mathematics
• statistics
• education
• school mathematics content
• statistical literacy
• teaching