An experiment involving 90 students in the 1st, 3rd, and 5th grades investigated how visual examples and grade (our surrogate for age) affected variability in a drawing task. The task involved using circles as the main element in a set of drawings. There were two examples: One was simple and single (a smiley face inside a circle); the other,…

This study investigated whether German learners of English as a foreign language (EFL) acquire additional recoding strategies that they do not need for recoding in the consistent German orthography. Based on the psycholinguistic grain size theory (Ziegler & Goswami, 2005) we expected students with little experience in EFL to use the same…

The literature seems limited in what is known about conceptual processes that underlie evolution of students with learning disabilities (SLD) conceptions of fractions. This exploratory study examines how a foundational scheme of unit fractions (1/n) may evolve through the mathematical activity of two fifth grade girls. We analyze data segments…

Students explored variation and expectation in a probability activity at the end of the first year of a 3-year longitudinal study across grades 4-6. The activity involved experiments in tossing coins both manually and with simulation using the graphing software, "TinkerPlots." Initial responses indicated that the students were aware of…

Interactions between conceptual and procedural knowledge influence the development of mathematical competencies. However, after decades of research, these interrelations are still under debate, and empirical results are inconclusive. The authors point out a source of these problems. Different kinds of knowledge and competencies only show up…