Mastery of the cardinality principle (CP) is foundational for children's mathematical development. Children's age and subitizing and counting skills contribute to their CP acquisition. This study aimed to investigate the effectiveness of different types of instruction for supporting 3-4-year-olds' CP development and its interplay with child…

The presented article is dedicated to a new way of teaching substitution in algebra. In order to effectively master the subject matter, it is necessary for students to perceive the equal sign equivalently, to learn to manipulate expressions as objects, and to perceive and use transformations based on defining their own equivalences. According to…

Learning to calculate with natural numbers by structuring seems promising but how this can be taught in a sustainable manner remains an open question. An eight-month-long intervention based on the idea of using a structural approach to addition and subtraction, and particularly bridging through ten, was implemented in four Swedish first-grade…

This paper describes a study in which we investigated relationships between defining mathematical concepts--increasing and decreasing infinite sequences--explaining their meanings and classifying consistently with formal definitions. We explored the effect of defining, explaining or studying a definition on subsequent classification, and the…

For decades, educators have advocated using history of mathematics in mathematics classrooms. Empirical research on the efficacy of this practice, however, is scarce. A quasi-experiment was used to investigate the effects of using history as a tool to teach mathematics on grade 11 students' mathematics achievement. Effects in three affective…