Findings on children's proportional reasoning abilities strongly vary across studies. This might be due to the different contexts that can be used in proportional problems: fair-sharing, mixtures, and probability. A review of the scientific literature suggests that the context of proportional problems may not only impact the difficulty of the…

In this article, the authors share frameworks for problem types and students' reasoning about integers. The authors found that all ways of reasoning (WoRs) were used across grade levels and that specific problem types tended to evoke particular WoRs. Specifically, students were more likely to use analogy-based reasoning on all-negatives problems…

The implementation of Science, Technology, Engineering, and Mathematics (STEM) at school is one of the challenges of education in the twenty-first century, especially concerning the development of critical thinking during argumentative interactions. In this paper, I refer to an interdisciplinary approach with the aim to analyze the implicit…

This article illustrates and differentiates the unique role cognitive interviews and think-aloud interviews play in developing and validating assessments. Specifically, we describe the use of (a) cognitive interviews to gather empirical evidence to support claims about the intended construct being measured and (b) think-aloud interviews to gather…

This is an exploratory study of how pedagogy in the form of math stories, shapes young learners' perceptions, motivations, and sense-making of math concepts. The research is presented in an exploratory documentary, with audio-video data collected through the iPhone. The pilot test of story-driven math learning solutions was conducted by two…

Analogy is a powerful learning mechanism for children to learn novel, abstract concepts from only limited input, yet also requires cognitive supports. My dissertation sought to propose and examine number lines as a mathematical schema of the number system to facilitate both the development of rational number understanding and analogical reasoning.…

In recent years, the learning and teaching of combinatorics presents particular educational research interest from the primary up to higher education levels. The combinatorial problems constitute a valuable opportunity for mathematical exploration, as combinatorics is a branch of mathematics with many applications, providing a complex network of…

In this study, we analyzed the imprecise (i.e., less mathematically precise) responses that 148 third- to fifth-grade Chinese students made on selected-response problems that were part of a spontaneous mathematical focusing task, the Quantitative Relations Test for Chinese Children (QRTC[superscript 2]). The purpose for this analysis was to…

Process-oriented dynamic testing aims to investigate the processes children use to solve cognitive tasks, and evaluate changes in these processes as a result of training. For the current study, a dynamic complex figure task was constructed, using the graduated prompts approach, to investigate the processes involved in solving a complex figure task…

This research is reviewing students' process of decision making intuitively, analytically, and interactively. The research done by using discount problem which specially created to explore student's intuition, analytically, and interactively. In solving discount problems, researcher exploring student's decision in determining their attitude which…

This study evaluated a new measure for analyzing the process of children's problem solving in a series completion task. This measure focused on a process that we entitled the "Grouping of Answer Pieces" (GAP) that was employed to provide information on problem representation and restructuring. The task was conducted using an electronic…

Recent studies reveal that children can solve proportional reasoning problems presented with continuous amounts that enable intuitive strategies by around 6 years of age but have difficulties with problems presented with discrete units that tend to elicit explicit count-and-match strategies until at least 10 years of age. The current study tests…

In this study we document how a mathematical idea, shared by a student, changes the development of the class discussion. Our work characterizes the flexible and open dynamics in mathematics instruction that a teacher adopts to give her students control of their own mathematical ideas. Our work argues that this flexibility is necessary for teachers…

Research on young children's reasoning show the complex relationships of knowledge, theories, and evidence in their decision-making and problem solving. Most of the research on children's reasoning skills has been done in individualized and formal research settings, not collective classroom environments where children often engage in learning and…

Both additive and proportional reasoning are types of quantitative analogical (QA) reasoning. We investigated the development and nature of primary school children's QA reasoning by offering two missing-value word problems to 3rd to 6th graders. In one problem, ratios between given numbers were integer, in the other ratios were non-integer. These…