The purpose of this study was to partially replicate the "Historical Problem Solving: A Study of the Cognitive Process Using Historical Evidence" study conducted by Sam Wineburg in 1991. The Historical Problem Solving study conducted by Wineburg (1991) sought to compare the ability of historians and top level students, as they analyzed…

Within mathematics teaching, ways to help students resolve proportional reasoning problems remains a topical issue. This study sought to investigate how a simple innovative procedure could be introduced to enhance skill acquisition. In two classroom-based experiments, 12-year-old students were asked to solve proportional reasoning mathematics…

Virtual worlds have affordances to enhance collaborative learning in authentic contexts. Despite the potential of collaborative learning with a virtual world, few studies investigated whether it is more effective in student achievements than teacher-directed instruction. This study investigated the effectiveness of collaborative problem solving…

We conducted an intervention-based study in secondary classrooms to explore whether the use of geometric transformations can help improve students' ability in constructing auxiliary lines to solve geometric proof problems, especially high-level cognitive problems. A pre- and post-test quasi-experimental design was employed. The participants were…

This unique volume surveys recent research on spatial visualization in mathematics in the fields of cognitive psychology and mathematics education. The general topic of spatial skill and mathematics has a long research tradition, but has been gaining attention in recent years, although much of this research happens in disconnected subfields. This…

Supporting students to develop an understanding of the meaning of fractions is an important goal of elementary school mathematics. This involves developing partitioning strategies, creating representations, naming fractional quantities, and using symbolic notation. This article describes how teachers can use a formative assessment problem to…

Launched in June 2016, the Smithsonian Learning Lab (SLL) provides access to the digital resources from across the Smithsonian's 19 museums, 9 major research centers, and the National Zoo, to be used as real-world learning experiences. It is designed to aid students in building lasting knowledge and critical skills that take learners from simply…

The pollution of land, water, air, noise, light etc. threatens people, plants, animals and ecosystems. Environmental literacy is at the heart of environmental education, and environmentally literate people are expected to be aware of how to help solve environmental problems such as pollution. The purpose of the present study is to explore 5th…

The present study examines 5- to 8-year-old children's relation reasoning in solving matrix completion tasks. This study incorporates a componential analysis, an eye-tracking method, and a microgenetic approach, which together allow an investigation of the cognitive processing strategies involved in the development and learning of children's…

Solving word problems is a common area of struggle for students with learning disabilities (LD). In order for instruction to be effective, we first need to have a clear understanding of the specific errors exhibited by students with LD during problem solving. Error analysis has proven to be an effective tool in other areas of math but has had…

Counting problems have applications in probability and computer science, and they provide rich contexts for problem solving. Such problems are accessible to students, but subtleties can arise that make them surprisingly difficult to solve. In this paper, students' work on the Groups of Students problem is presented, and an important issue related…

Researchers are currently investigating how calculus students understand the basic concepts of first-year calculus, including the integral. However, much is still unknown regarding the "cognitive resources" (i.e., stable cognitive units that can be accessed by an individual) that students hold and draw on when thinking about the integral. This…

Teachers continue to face the challenge of identifying efficaciously gifted students' learning capacity in its multiple forms. While most educators acknowledge its multidimensional characteristics, the protocols used to identify it are frequently evaluated as unnecessarily restrictive. This study investigates an assessment tool that could…

International trended assessments have long attempted to provide instructional information to educational researchers and classroom teachers. Studies have shown that traditional methods of item analysis have not provided specific information that can be directly applicable to improve student performance. To this end, cognitive diagnosis models…

This article reports on an investigation with first year undergraduate Product Design and Management students within a School of Engineering and Applied Science. The students at the time of this investigation had studied fundamental engineering science and mathematics for one semester. The students were given an open ended, ill-formed problem…