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…

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 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…

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…

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…

"Classroom Discussions: Seeing Math Discourse in Action, Grades K-6" provides preservice and inservice instructors, coaches and facilitators with real, classroom-based video examples that illustrate the principles and practices covered in the authors' best-selling book, "Classroom Discussions: Using Math Talk to Help Students Learn, Grade K-6,…

This paper presents a case study examining 3rd, 4th and 5th graders' design fixation and cooperative learning in an engineering design project. A mixed methods instrument, the Cooperative Learning Observation Protocol (CLOP), was adapted to record frequency and class observation on cooperative learning engagement through detailed field notes.…

Analogical reasoning--perceiving similarities in different situations and the transfer of such information--facilitates learning and understanding. However, children with learning disabilities (LD) typically demonstrate deficits in such information processing strategies. In this study, we investigated the analogical problem-solving differences…

Two studies investigated children's metacognition about everyday reasoning, assessing how they distinguish reasoning from nonreasoning and "good" reasoning from "bad." In Study 1, 80 1st graders (6-7 years), 3rd graders (8-9 years), 5th graders (10-11 years), and adults (18+ years) evaluated scenarios where people (a) used reasoning, (b) solved…

The Invisible Wall Project analyzes problem-solving processes of children in Grades 3 and 4 and Grades 8 and 9. The central idea of the research is to use sets of tasks that are all unsolvable, which means they have a goal that cannot be reached. The unsolvability, however, is of a kind that can be understood even by younger children. In our case,…

Metacognitive Performance of four groups of students (hearing high-achieving, hearing average-achieving, hearing underachieving, and deaf and hard of hearing) in first through third grade in the United Arab Emirates was examined and compared. Metacognition was measured using analyses of pictures depicting real-life problematic events, situations,…