We share here results from a quasi-experimental study that examines growth in students' algebraic thinking practices of generalizing and representing generalizations, particularly with variable notation, as a result of an early algebra instructional sequence implemented across grades 3--5. Analyses showed that, while there were no significant…

Educators and several national standards highlight the role that problem solving should play in students' mathematics education: problem solving is recognized as one of the most significant activities of doing mathematics. From the research point of view, nowadays, it is well established that cognitive and affective factors come into play in…

Literature that investigates the factors underlying arithmetic problem-solving achievement extensively evaluates the cognitive components, such as working memory (WM) and processing speed, at the basis of this acquisition. Recently, studies have shown that also the emotional factors, such as math anxiety (MA), could play a crucial role in the…

Although equal sharing problems appear to support the development of fractions as multiplicative structures, very little work has examined how children's informal solutions reflect this possibility. The primary goal of this study was to analyze children's coordination of two quantities (number of people sharing and number of things being shared)…