This case study contrasts the strategies used by two students in solving bilateral symmetry and reflection tasks, based on the differential properties they attended to. The ninth grader focussed on congruence of sides as the main property of reflection whereas the eighth grader focussed on perpendicularity and equi-distance, as is the normative…

Background: We tested the effects of an intervention on the learning of introductory thermodynamics principles. This intervention, OEM-Thermo, is designed to prompt the cognitive operations of meaningful learning: organization, elaboration, and monitoring. We also sought evidence to show that execution of these operations was associated with…

This article focuses on how the representational properties of manipulatives affect the strategies children employ in problem solving. Two studies examined the effect of physical materials on 4-7-year-old children's problem solving strategies in a numerical (i.e., additive composition) task. The first study showed how children not only identified…

Worked examples have proven to be effective for knowledge acquisition compared with problem solving, particularly when prior knowledge is low (e.g., Kalyuga, 2007). However, in addition to prior knowledge, executive functions and fluid intelligence might be potential moderators of the effectiveness of worked examples. The present study examines…

Many educational data mining studies have explored methods for discovering cognitive models and have emphasized improving prediction accuracy. Too few studies have "closed the loop" by applying discovered models toward improving instruction and testing whether proposed improvements achieve higher student outcomes. We claim that such…

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…

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…

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…

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…