The 8-coin insight problem requires the problem solver to move 2 coins so that each coin touches exactly 3 others. Ormerod, MacGregor, and Chronicle (2002) explained differences in task performance across different versions of the 8-coin problem using the availability of particular moves in a 2-dimensional search space. We explored 2 further…

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…

Communicative learning progress in industry and education must gain focus and commitment otherwise innovation efforts by new technologies and recent researches will produce scarce results. Frequently, it appears gaps in quality and efficiency due to lack of ideas assimilation, matter that can be noticed. Investigators may discourse about platforms…

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…

Mathematical problem solving typically involves manipulating visual symbols (e.g., equations), and prior research suggests that those symbols serve as diagrammatic representations (e.g., Landy & Goldstone, 2010). The present work examines the ways that instructional design of student engagement with these diagrammatic representations may…

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…

Learning to solve more challenging mathematics problems using multiple strategies has been promoted by research and is a feature of numerous curricula. Yet teachers have been found to be reluctant to incorporate these tasks into their lessons predicting resistance from students. This study examined 87 senior secondary students' reactions to a…

The purpose of the study is to reveal the elementary mathematics student teachers' difficulties encountered in the solution of a modelling problem, the strategies to overcome those difficulties and whether the strategies worked or not. Nineteen student teachers solved the modelling problem in their four or five-person groups, and the video records…

In this study it is investigated to what extent contextualized and non-contextualized mathematics test items have a differential impact on examinee effort. Mixture item response theory (IRT) models are applied to two subsets of items from a national assessment on mathematics in the second grade of the pre-vocational track in secondary education in…

Learning advanced physics, in general, is challenging not only due to the increased mathematical sophistication but also because one must continue to build on all of the prior knowledge acquired at the introductory and intermediate levels. In addition, learning quantum mechanics can be especially challenging because the paradigms of classical…

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…

Halmos (1980) once described problems and their solutions as "the heart of mathematics". Following this line of thinking, one might naturally ask: "What, then, is the heart of problems?" In this work, I attempt to answer this question using techniques from statistics, information visualization, and machine learning. I begin the…

In this paper, an example is offered of a problem-solving task for senior secondary school students which was given in the context of a story. As the story unfolds, the task requires progressively more complex forms of linear programming to be applied. Coding in MATLAB is used throughout the task in such a way that it supports the increasing…

Error analysis is the study of errors in learners' work with a view to looking for possible explanations for these errors. It is a multifaceted activity involving analysis of correct, partially correct and incorrect processes and thinking about possible remediating strategies. This paper reports on such an analysis of learner tests. The tests were…

Background: A potential problem of low-stakes large-scale assessments such as the Programme for the International Assessment of Adult Competencies (PIAAC) is low test-taking engagement. The present study pursued two goals in order to better understand conditioning factors of test-taking disengagement: First, a model-based approach was used to…