Automated theorem proving (ATP) for Propositional Classical Logic is an algorithm to check the validity of a formula. It is a very well-known problem which is decidable but co-NP-complete. There are many algorithms for this problem. In this paper, an educationally oriented implementation of Semantic Tableaux method is described. The program has…

Despite advances in evidence-based core instruction and intervention, many students with disabilities continue to achieve poor academic and behavioral outcomes. Many of these students are not sufficiently responsive to standardized programs and require more intensive, individualized supports. While many interventions and school problem-solving…

A model solution to a proof question on an examination is explored and subjected to a detailed analysis in terms of Toulmin's scheme of argumentation. In doing so, the ways in which the scheme has been variously used in the mathematics education and philosophical literature are contrasted. The analysis raises a number of issues concerning the…

The problem-solving process is investigated for five groups of students when solving context-rich problems in an introductory physics course included in an engineering programme. Through transcripts of their conversation, the paths in the problem-solving process have been traced and related to a general problem-solving model. All groups exhibit…

This study aims to investigate plane geometry problem-solving strategies of prospective mathematics teachers using dynamic geometry software (DGS) and paper-and-pencil (PPB) environments after receiving an instruction with GeoGebra (GGB). Four plane geometry problems were used in a multiple case study design to understand the solution strategies…

In recent years, the use of boron-containing reagents in palladium-assisted C-C coupling reactions (the Suzuki reaction) has gained prominence due to the vast array of reagents commercially available. Consequently, the generation of carbon-carbon bonds, namely of functionalized biphenyl systems, is at present considered the backbone of organic…

A visual representation, such as a diagram, can be a powerful strategy for solving mathematical word problems. However, using a representation to solve mathematical word problems is not as simple as it seems! Many students with learning disabilities struggle to use a diagram effectively and efficiently. This article provides a framework for…

This paper provides the formula for the elevation angle at which a projectile has to be fired in a vacuum from a general position to hit a target at a given distance. A spreadsheet application that models the trajectory is presented, and the problem of finding the points of shot and impact of a projectile moving in a vacuum if three points of the…

This study used participant observation to explore students' thinking when learning the concept of factorial functions. First-year university students undertaking a mathematics methodology course were asked to find the number of ways in which five people could sit around a circular table with five seats. Using grounded theory as a qualitative…

Students with mathematics difficulties and learning disabilities (LD) typically struggle with solving word problems. These students often lack knowledge about efficient, cognitive strategies to utilize when solving word problems. Cognitive strategy instruction has been shown to be effective in teaching struggling students how to solve word…

Formative assessment is the process by which teachers and students gather evidence of learning and then use this to adapt the way they teach and learn. I describe a design research project in which we integrated formative assessment strategies into lesson materials that focus on developing students' conceptual understanding and their capacity to…

Background: The shortage of skilled workers choosing STEM (Science, Technology, Engineering, and Math) careers in the USA and worldwide has fueled a movement towards STEAM, in which the "A" addresses the arts and humanities. STEAM education has been proposed as a way to offer relevant problems to solve while drawing on creative and…

Applications and modelling have gained a prominent role in mathematics education reform documents and curricula. Thus, there is a growing need for studies focusing on the effective use of mathematical modelling in classrooms. Assessment is an integral part of using modelling activities in classrooms, since it allows teachers to identify and manage…

The basis of the submitted study are the continuously rising demands to alter the curricula with the aim to develop students' key competences in order to increase their professional versatility. The lack of scientific research and discussions show that little investigation has been done on the issue of development of key competences. Therefore,…

This article reports results from a study investigating the efficacy of a proportional problem-solving intervention, schema-based instruction (SBI), in seventh grade. Participants included 806 students with mathematical difficulties in problem solving (MD-PS) from an initial pool of 1,999 seventh grade students in a larger study. Teachers and…