Analysis of the experimental results presented in the following chapter reveals experiences with introduction of active learning methods in basic mathematics courses at the Faculty of Mechanical Engineering, Slovak University of Technology in Bratislava. Experiment was implemented in the academic year 2018/19, in basic courses Mathematics I and…

To explain children's difficulties learning fraction arithmetic, Braithwaite et al. (2017) proposed FARRA, a theory of fraction arithmetic implemented as a computational model. The present study tested predictions of the theory in a new domain, decimal arithmetic, and investigated children's use of conceptual knowledge in that domain. Sixth and…

The purposes of the research were 1) to compare the scores of 7th grade students from deductive learning activities management with games on the topic of "Single Variable Linear Equations" to the standardized criteria of 75%, 2) to compare the achievement of the 7th grade students before and after using the deductive learning activities…

Peer assessment is an underutilized tool in mathematics classrooms. We examined how peer assessment could be used in a mathematics course to improve mathematical communication and mathematical proficiency. To describe in what ways peer reviews compared to teacher reviews, we analyzed ratings and feedback of 32 6th graders and their mathematics…

Worked examples are effective learning tools for algebraic equation solving. However, they are typically presented in a static concise format, which only displays the major derivation steps in one static image. The current work explores how worked examples that vary in their extensiveness (i.e., detail) and degree of dynamic presentation (i.e.,…

The visual method in this paper solves linear inequalities in one variable by considering them initially as two competing linear expressions, each of which is then expressed as a linear equation. When the solution of these two linear equations exist, it is viewed as a highlighted area or a line. These linear equations convey the intended visual…

Visualising positive and negative numbers on a number line is helpful for exploring problems involving operations with positive and negative numbers. This is because number lines lend themselves to exploring problems involving continuous linear contexts such as travelling distances and temperature. Teachers in a professional development program…

The aim of this study was to investigate how pictorial representations with different semiotic characteristics affect additive word problem solving by kindergartners. The focus of the study is on three categories of additive problems (change problems, combine problems and equalize problems) and on representational pictures with different semiotic…

This mixed-method study aims to explore the feasibility of using the game-based, multimodal representation of mathematical problems to support middle school students' practice and performance of math problem representation and solving. A three-dimensional architectural simulation game, called E-Rebuild, was developed to engage students in…

Students' problem-solving success depends on more than their knowledge and abilities. One factor that may play a role is the teacher's expectations of students. The current study focused on how a teacher's explicitly-stated expectations influence students' ability to learn from corrective feedback during problem solving. On the one hand, setting…

A typical mathematics assignment consists of one or two dozen practice problems relating to the same skill or concept, yet empirical evidence suggests that there is little or no long-term benefit from working more than a few problems of the same kind in immediate succession. Alternatively, randomized experiments in the laboratory and classroom…

Students' previous knowledge at a superficial level is reviewed when they solve mathematical problems. This action is imperative to strengthen their knowledge and provide the right information needed to solve the problems. Furthermore, Pirie and Kieren's theory stated that the act of returning to a previous level of understanding is called folding…

Mobile eye-tracking research has provided evidence both on teachers' visual attention in relation to their intentions and on teachers' student-centred gaze patterns. However, the importance of a teacher's eye-movements when giving instructions is unexplored. In this study we used mobile eye-tracking to investigate six teachers' gaze patterns when…

Providing students the autonomy and choice to learn when productive struggle becomes unproductive is a core teaching belief in the author's classroom. The author teaches in a multiage classroom where he has 16 first- and second-grade students, ages 6, 7, and 8. Like other educators, he believes in the importance of productive struggle. The author…

If student-centered practices in reading and writing workshops work for students, why aren't these same practices used during mathematical instruction? Workshop models center the instruction on students and offer them the time and freedom to be independent in their work, moving toward high-level, inquiry-based learning. The authors experienced a…