This study investigated how 155 pre-service teachers solved three pattern generalization problems in a two-part written test and sequenced them for teaching purposes to demonstrate their curricular noticing. Participants' solutions were analyzed using inductive content analysis, which showed that only 8.4% of PSTs produced correct answers to all…

In the context of a multiplicative problem, our study investigated young children's ability to visualise and draw equal groups. This paper reports the results obtained from 18 Australian children in their first year of school (age 5-6 years). The task "12 Little Ducks," taught by their classroom teacher, provoked children to visualise…

In the core of computational thinking (CT) practices is problem-solving. However, there is little research on connecting CT with problem solving processes. We developed a computer-based assessment on CT that can log students' problem-solving processes and administered it to a group of fifth graders as a pre- and post- measure of a robotics…

Building from the evidence-based learning progression in geometric reasoning from the RMFII project, this paper presents data from students' solutions to three problems in geometry and measurement situations to identify key components needed to nurture reasoning. To show emerging analytical reasoning students must coordinate multiple pieces of…

Problem-solving skills in creative, open-ended domains are both important and little understood. These domains are generally ill-structured, have extremely large exploration spaces, and require high levels of specialized skill in order to produce quality solutions. We investigate problem-solving behavior in one such domain, the…

Problem-solving and collaboration are regarded as an essential part of 21st Century Skills. This study describes a task-focused approach to network analysis of trace data from collaborative problem-solving in a digital learning environment. The analysis framework builds and expands upon previous analyses of social ties as well as discourse…

This paper explores young children's drawings (6 years old) in early number and addition activities in Malaysia. Observation, informal interviews and analysis of drawings revealed two types of drawing, and gave insight into the transitional process required for children to utilise drawings in problem solving. We argue the importance of valuing and…

This case study contrasts the strategies used by two students in solving bilateral symmetry and reflection tasks, based on the differential properties they attended to. The ninth grader focussed on congruence of sides as the main property of reflection whereas the eighth grader focussed on perpendicularity and equi-distance, as is the normative…

This study on the mental solving of systems of linear equations is part of a larger research program, aimed to gain a better understanding of the potential of mental mathematics activities with topics/objects other than numbers. Through outlining the study details and the activities engaged with, the paper reports on the variety of strategies…

In this paper we report the results obtained when implementing Activities related to the visualization of geometric representations in paper-and-pencil and technological environments with students1 grade 11. This is a qualitative research supported by both the representation theory and the visualization of mathematical objects using technological…

Amongst important and under-researched questions are how introductory lessons can be designed for teaching initial proofs to junior high school students, and how such lessons enrich students' understanding of proofs. With a view to improving the learning situation in the classroom, in this paper we report on the various functions of introductory…

This paper introduces a revised model for the development of basic computation skills. The model draws on four key phases, which have proven to be important for the development of calculation strategies and stresses the use of gestures and the verbalisation of concrete and mental images. This seems to be of crucial importance for children with…

This proposal reports the findings from interviews with construction science students about their visualization of problems in a two-dimensional and a three-dimensional task. The specific research questions focused on the individual characteristics that students identify as influencing their spatial ability to generate internal and external…

This article argues for a shift in how researchers discuss and examine students' uses of representations during their calculus problem solving. An extension of Zazkis, Dubinsky, and Dautermann's (1996) Visualization/Analysis-framework to include physical modes of reasoning is proposed. An example that details how transitions between visual,…

This research team has developed a learning trajectory on 3D visualization for elementary children. This paper focuses on the interchange among the three Spatial Operational Capacity framework representations, namely, 3D models, 2D conventional diagrams, and semiotic abstract representations, and the critical role of a dynamic computer interface…