Data-Based Work and the Logical Component of Mathematical Competence: The American Experience

Abstract

This article addresses the problem of expanding the methodological toolkit for forming the logical component of basic school students' mathematical competence through data-based work. It is substantiated that statistical thinking is not a separate strand of instruction but a manifestation of the same logical operations – analysis, synthesis, comparison, classification, generalization, proof, and justification – that form the cognitive core of the logical component of mathematical competence. Data literacy is a key requirement of the modern labor market, which gives the teaching of these operations a direct motivational horizon for students. Based on an analysis of American experience – the Guidelines for Assessment and Instruction in Statistics Education (GAISE), the Common Core State Standards (CCSS), and the research of Wild and Pfannkuch, Garfield and Ben-Zvi – it is shown that data constitute a uniquely productive environment for forming all four components of the logical component (motivational-value, cognitive, activity-based, and reflective-evaluative). A correspondence table linking logical operations, dimensions of statistical thinking, and indicators of the logical component was developed, aligning American approaches with the author's own four-component framework. A system of five contextual tasks is proposed, modeling real situations – sociological, price, game-based, and anthropometric data – and targeting different logical operations: comparison, classification, synthesis, and proof. Methodological recommendations for basic school mathematics teachers are formulated.