Many studies have used fraction magnitude comparison tasks to assess people's abilities to quickly assess fraction magnitudes. However, since there are multiple ways to compare fractions, it is not clear whether people actually reason about the holistic magnitudes of the fractions in this task and whether they use multiple strategies in a flexible…

This study focuses on computer-based formative assessment for supporting problem solving and reasoning in mathematics. To be able to assist students who find themselves in difficulties, the software suggested descriptions - diagnoses - of the encountered difficulty the students could choose from. Thereafter, the software provided metacognitive and…

Extant research has demonstrated that problem-posing and problem-solving mutually affect one another. However, the exact nature and extent of this relationship requires a detailed elaboration. This is especially true when adidactical problem-posing arises within a problem-solving context. In this study, we analyze the scripting journey used by two…

This paper explores student emotion and learning experiences fostered by lecturing-style instruction in Real-Analysis problem-centered lessons. We focus on two lessons that were taught by two reputable instructors and involved challenging, mathematically-related problems the students did not understand. Nonetheless, one lesson evoked negative…

Collaboration scripts and heuristic worked examples have been described as powerful scaffolds to support skill acquisition in CSCL. While CSCL scripts particularly facilitate argumentative discourse within groups, heuristic worked examples provide heuristics and worked out pathways to solve domain-specific tasks. Yet, both scripts and heuristic…

Purpose: Traveling Salesman Problem (TSP) that can be extended and modified in various ways, is a practical and realistic type of problem and forms the basis for the visual and spatial solution of many optimization problems. In this study, 15, 25 and 35 nodes Travelling Salesman Problems were solved by secondary school, high school and…

Engineering educators express concern that undergraduate engineering students solve problems procedurally without the necessary conceptual understanding. While research in engineering dynamics has focused on using technology to improve student performance, this article focuses on using representations for modelling problem solving in the lecture.…

The periodic table is recognized as one of the most powerful tools in science. While it is included in virtually all high school and undergraduate general chemistry curricula, it remains a mystery to many chemistry students who find it impossible to decode. Students are often able to predict periodic trends concerning atomic radius, ionization…

This study explored the use of heuristics in the design space by novice and expert engineers in the initial ideation of a design solution. Verbal protocol analyses were conducted with four engineering students and four professional engineers as they generated ideas to solve a design problem. Overall, both experts and novices used various types of…

Chemical processes can be fully explained only by employing quantum mechanical models. These models are abstract and require navigation of a variety of cognitively taxing representations. Published research about how students use quantum mechanical models at the upper-division level is sparse. Through a mixed-methods study involving think-aloud…

Using data provided by an empirical exploratory study with mathematics undergraduates, this paper discusses some key variables in the interaction between affective and cognitive dimensions in the perplexity state in problem solving. These variables are as follows: heuristics, mathematical processes, appraisal processes [pleasantness, attentional…

Evidence from a range of fields indicates that inventions are often inspired by drawing a parallel to solutions found in nature. However, the cognitive mechanism of this process is not well understood. The cognitive mechanism of heuristic prototype in scientific innovation was tested with 3 experiments. First, 84 historical accounts of important…

Our aim in this article is to elaborate the role of training in representational change theory (RCT), particularly in terms of Ohlsson's (2011) spread of activation explanation (named "redistribution theory"), and to develop novel training manipulations that effect the re-encoding mechanism proposed by RCT (Ohlsson, 1992). Two…

In organic chemistry, spatial reasoning is critical for reasoning about spatial relationships in three dimensions and representing spatial information in diagrams. Despite its importance, little is known about the underlying cognitive components of spatial reasoning and the strategies that students employ to solve spatial problems in organic…

Students experience difficulty learning and understanding chemistry at higher levels, often because of cognitive biases stemming from common sense reasoning constraints. These constraints can be divided into two categories: assumptions (beliefs held about the world around us) and heuristics (the reasoning strategies or rules used to build…