This paper builds on our previous research and investigates how students' fractional competence and reasoning can provide clear evidence of non-symbolic algebraic thinking and its progressive transition towards fully generalised algebraic thinking. In a large-scale study, 470 primary students completed a written paper and pencil test. This…

To illustrate primary students' use of argumentation, this study reported on an analysis of elements in argumentation of 168 grade 5 students in Taiwan. This study adopted the van Hiele (vH) model as the main theoretical framework with relevant studies to show the development of argumentation. This study designed a geometric argumentation test…

Problem solving is an essential skill for students to be successful in life and careers. Students need to use efficient strategies to solve problems effectively. In this basic interpretive qualitative study, we aimed to (a) explore children's problem-solving strategies in a game-based tool (i.e., puzzles), and (b) investigate the troubleshooting…

One of the aspects of programming that novices often struggle with is the understanding of abstract concepts, such as variables, loops, expressions, and especially Boolean operations. This paper aims to explore the effects of programming tools with different degrees of embodiment on learning Boolean operations in elementary school. To this end, 67…

The purpose of this study is to examine how the reasoning of elementary school students develops and progresses within a learning progression. In order to do this, we analyzed third, fourth, and fifth grade elementary school students' levels of reasoning about phenomena related to changes of state of water. The results show that higher grades…

In this article we illustrate how one teacher used PhET cannonball simulation as an instructional tool to improve students' algebraic reasoning in a fifth grade classroom. Three instructional phases effective to implementation of simulation included: Free play, Structured inquiry and, Synthesizing ideas.

In the process of problem solving, intuitive thinking leads to findings that go beyond gaps and plays a decisive role in problem solving. Considering that problems often need to be solved in groups rather than by individuals, it is necessary to examine how intuitive thinking expressed by individuals is shared and elaborated among peers in a group…

The aims of the study were (1) to develop a domain-general computer-based assessment tool for inductive reasoning and to empirically test the theoretical models of Klauer and Christou and Papageorgiou; and (2) to develop an online game to foster inductive reasoning through mathematical content and to investigate its effectiveness. The sample was…

Relational reasoning [RR] is the ability to derive meaningful patterns within any information stream. Further, RR can be used as a knowledge activation technique before and during reading, guiding students to notice when their prior understandings are similar to, different from, or in conflict with the text at hand. The purpose of the current…

Eye-tracking studies need adequate theoretical frameworks for producing insights about mathematics learning. The current study uses eye-tracking to investigate the effectiveness of tables and diagrams for supporting covariational reasoning amongst elementary students (n = 60). The theoretical framework emphasizes the cognitive functions of…

Fractions are one of the most difficult areas of mathematics for all students and especially for students with learning disabilities (LD). An incomplete understanding of fractions during the elementary and middle school may be why some students view fractions as "really small" or "less than 1" compared to others who view them…

The purpose of this study was to analyze the problem-solving techniques that students in a fifth-grade classroom applied while solving mathematical word problems. Fifth-grade students in a private school with Ministry of Education curricula in Al Ain, Abu Dhabi, were given a set of 15-word problems to solve with detailed justifications. The…

Building on rich training literature, we examined which skills constituting the control-of-variables strategy (CVS) benefit from a comprehensive training, and which develop similarly during content-focused inquiry at ages 10-12. In addition, we examined whether prior knowledge, reasoning abilities, and reading comprehension explain variation in…

There has been a recent increase in research interest in the ways that visual representation is used to facilitate students' understanding in science classrooms. Yet while many studies have explored individual students' drawing, few studies have looked into drawing as a collective tool to engage students in thinking and talking together in science…

We explored the mediating role of prior knowledge on the relation between intelligence and learning proportional reasoning. What students gain from formal instruction may depend on their intelligence, as well as on prior encounters with proportional concepts. We investigated whether a basic curriculum unit on the concept of density promoted…