Prior research shows that representational competencies that enable students to use graphical representations to reason and solve tasks is key to learning in many science, technology, engineering, and mathematics domains. We focus on two types of representational competencies: (1) "sense making" of connections by verbally explaining how…

Prior research shows that representational competencies that enable students to use graphical representations to reason and solve tasks is key to learning in many science, technology, engineering, and mathematics (STEM) domains. We focus on two types of representational competencies: (1) "sense making" of connections by verbally…

The equipartitioning learning trajectory (Confrey, Maloney, Nguyen, Mojica & Myers, 2009) has been hypothesized and the proficiency levels have been validated through much prior work. This study solidifies understanding of the upper level of co-splitting, which has been redefined through further clinical interview work (Corley, Confrey &…

This article reports on 2 studies that attempted to replicate the findings of a study by Szmalec, Loncke, Page, and Duyck (2011) on Hebb repetition learning in dyslexic individuals, from which these authors concluded that dyslexics suffer from a deficit in long-term learning of serial order information. In 2 experiments, 1 on adolescents (N = 59)…

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…

The meaning of fractions with integer multiplication is something that is difficult to understand by students. They tend to think that the product it produces a larger number, while the multiplication of fractions with integers, the result can be any number larger or smaller. This study is a research design that aims to develop a local…

Explaining new ideas to oneself can promote learning and transfer, but questions remain about how to maximize the pedagogical value of self-explanations. This study investigated how type of instruction affected self-explanation quality and subsequent learning outcomes for second- through fifth-grade children learning to solve mathematical…

Although teachers in principle are prepared to make use of science centers, such excursions often fail to facilitate learning processes. Therefore, it is necessary to improve the link between science centers and schools. The design and evaluation of valuable outreach projects may enhance students' out-of-school science learning. In our study, we…

An increasing number of K-12 school teachers have been using handheld, or palmtop, computers in the classroom as an integral means of facilitating education due to the flexibility, mobility, interactive learning capability, and comparatively inexpensive cost. This study involved two experiments in handheld computers: (a) a comparison of the…

To examine how conceptual knowledge about fraction magnitudes changes as students' learning progresses, 5th and 7th-grade students were asked to solve fraction magnitude problems that entailed finding a fraction between two given fractions and then to evaluate solutions for similar problems that were modeled for them. When the given fractions…

Japanese lesson study, in various adapted forms, is becoming increasingly significant in professional development of mathematics teachers in the USA. Our goal in the research reported in this paper was to investigate, in a three-tiered teaching experiment, the cycles of learning of two researchers, six teachers, and the students in three grade 4…

This document contains the second volume of the proceedings of the 30th Annual Conference of the International Group for the Psychology of Mathematics Education. Conference presentations are centered around the theme "Mathematics at the Centre." This volume features 60 research reports by presenters with last names beginning between Abr…