Representations are key to mathematical activities and meaning-making processes as they are part of modeling, connecting, communicating, and understanding mathematical ideas and concepts. The current study sought to examine a group of novice algebra learners' interactions with different representations from an onto-semiotic approach. A case study…

Self-efficacy in mathematics is related to engagement, persistence, and academic performance. Prior research focused mostly on examining changes to students' self-efficacy across large time intervals (months or years), and paid less attention to changes at the level of lesson sequences. Knowledge of how self-efficacy changes during a sequence of…

Subtraction can be understood by two basic models--taking away (ta) and determining the difference (dd)--and by its inverse relation to addition. Epistemological analyses and empirical examples show that the two models are not relevant only in single-digit arithmetic. As curricula should be developed in a longitudinal perspective on mathematics…

Presents and investigates a theoretical perspective on the development of understandings of mathematical operations with a particular focus on addition. Presents a case study on the development of a young boy and concludes that his attainment of aspects of operation sense supported transitions into algebraic ways of thinking. Contains 46…

The intention of this investigation was to diagnose the retention of some basic skills in some topics in algebra and geometry and to reveal difficult steps in the learning processes in these topics. (MP)

Used are test and interview data to extract evidence as to what level tenth graders have coordinated the worlds of arithmetic and algebra and can move freely between them. More dissociation is shown than was expected. (Author/MVL)