No abstract

We identify a recent trend in school mathematics as well as in some of the research literature in mathematics education: an emphasis on the practical uses of mathematics and an increased emphasis on verbalizations as opposed to numerical and computational skills. With tools provided by John Dewey, an early advocate of contextual and practical knowledge, we analyse the common research framework for discussing mathematical knowledge in terms of the procedural and the conceptual. We argue that procedural and conceptual knowledge should not be seen as opposites, and that the tendency to treat them as such might be avoided by emphasising the notion of operational skill. We argue that this is important in order for the students to gain both the contextual knowledge and the computational skill entailed in mathematical knowledge.

The aim of the study is to investigate and compare approaches to algebra in the Estonian, Finnish, and Swedish national core curricula (Grades 1-9). Despite the similarities in the school systems of these neighboring countries, the analysis reveals three quite different curricular approaches. The Estonian approach shows influences of the Russian Davydov School. The Finnish approach to some extent resembles the traditional one whereby algebra is addressed first at the lower secondary level and then in a formal manner. However, there are also characteristics typical of the functional view, which dominates the Swedish curriculum. Here, as opposed to the documents from the other two countries, a transition to more formal sophisticated methods at the secondary level is not visible at all. We discuss the results in relation to earlier research and students' different learning outcomes in light of international evaluations.

We characterize the recently included programming content in Swedish mathematics textbooks for elementary school. Especially, the connection between programming content and traditional mathematical content has been considered. The analytical tools used are based on the so-called 5E's, a theoretical framework of action, developed within the ScratchMath project, and Brennan and Resnick's (2012) terms computational concepts and practices. The result uncovers "follow a procedure" as the dominating action, in which the concepts stepwise instruction and repeated pattern were frequent. Bridging between programming and mathematics is weak in the sense that the programming content does not enhance the possibility to explore mathematical concepts and ideas.

This article investigates how the recent implementation of programming in school mathematics interacts with algebraic thinking and learning. Based on Duval's theory of semiotic representations, we analyze in what ways syntax and semantics of programming languages are aligned with or divert from corresponding algebraic symbolism. Three examples of programming activities suggested for school mathematics are discussed in detail. We argue that although the semiotic representations of programming languages are similar to algebraic notation the meanings of several concepts in these two domains differ. In a learning perspective these differences must be taken into account, especially considering that students have to convert between registers with both overlapping and specific meanings.