Building effective partnership with parents of young children with language delays has strong face value and is supported by multiple areas of research; however, building and maintaining partnerships to optimize child outcomes in practice can be difficult. This article provides a guide to teachers and speech-language pathologists who work with…

We investigate teacher beliefs about discourses for equation solving and the challenges these beliefs might pose for the implementation of instructional practices that promote deductive reasoning in algebra. To uncover these beliefs, we recorded three video explanations of solutions to the same linear equation with distinct discursive…

Visualization is an effective method for students to internalize concepts and to establish correlations between concepts. Visualization method is especially more important in mathematics which is perceived as the combination of abstract concepts. In this study, whether 6th grade students can solve questions about "Fractions" by using…

Previous studies revealed that many students cannot perform well when it comes to word problem-solving questions. There are various problem-solving strategies that can be applied to help students to overcome the problem. Visualisation techniques in learning have been used to help students enhance their conceptual understanding of the mathematical…

A flipped classroom approach consists of two distinct parts: direct on-line instruction in the students' own time and at their own pace, and interactive group learning and problem solving activities in scheduled classes. This approach has the potential to suit theoretical and practice-based courses such as technology education. This article…

This article presents some paper-folding activities for students to explore a different way to prove some of the angle properties in a circle.

As a foundational evolutionary concept, the Hardy-Weinberg principle should be taught enthusiastically in introductory biology courses. In a companion Perspectives paper, I made the case that students are often given limited or incorrect information on the HW principle due to a lack of mastery or confidence on the part of their teachers. The…

Le Châtelier's principle is used as a basis to derive an expression to calculate solution pH during titrations that involve only strong acids and strong bases. Central to this model are the reaction quotient and a re-equilibration term that represents the extent of neutralization during a titration. Unlike the method traditionally taught to…

In a games-based approach, the idea of understanding is located within the concept of games as decision-laden, problem-solving contexts. However, the concept of "understanding" is largely implicit in much of the germane literature. We are arguing for a more deliberate framework to approach the concept of understanding. We propose that…

The development of universal learning actions [universal'nye uchebnye deystviya] in logic is one of the most important tasks of education. This article explores logical problems as an effective tool for developing logical thinking and the underlying universal learning actions. We outline the basic principles of learning to solve logical problems.…

Through critical interpretation, this paper aims to critically think about some points of Paulo Freire's critical pedagogy and its educational implications. Firstly, this paper explores the influence of life experiences and the Frankfort School on the development of Freire's critical pedagogy. Secondly, it aims to critically assess some points of…

An important but challenging problem-solving technique in introductory mechanics is that of using "tilted axes." For inclined plane and centripetal motion problems, using axes that are aligned relative to the ramp direction or the radial direction (rather than the horizontal and vertical) yields equations that are conceptually more…

For students working on realistic complex modelling problems as autonomously as possible the support by a tutor is indispensable for the students. However, how this support can be realised is still a question that has not been sufficiently answered. Based on prior research, it turned out that teacher interventions based on heuristic strategies…

We share a subset of the 41 underlying strategies that comprise five ways of reasoning about integer addition and subtraction: formal, order-based, analogy-based, computational, and emergent. The examples of the strategies are designed to provide clear comparisons and contrasts to support both teachers and researchers in understanding specific…

Mathematics educators advocate for the use of models as an instructional practice that can potentially aid in building students' understanding of difficult topics. Integers and integer operations are historically problematic for students and are critically important in both arithmetic and the future study of algebra. In this chapter, I explore one…