Functional thinking is essential for maritime vocational college students, particularly when solving mathematical problems related to navigation safety. However, limited studies have explored functional thinking among vocational maritime students. This study aims to explore the functional thinking processes of maritime vocational college students…

Heuristics are approaches engineers use for solving problems and making decisions with quick, often approximate, calculations and/or judgement calls. Such approaches have become marginalized in structural engineering education to make room for more theoretical and precise approaches. As a result, engineering students are less confident with…

To solve an unfamiliar mathematics problem, students of the subject must know more than the appropriate prerequisite content knowledge. They must also know how best to strategically apply their knowledge, how to monitor and gauge the effectiveness of their work, and how to respond (both cognitively and emotionally) to unanticipated results.…

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…

The use of heuristics as an instructional strategy enable instructors to provide students with problem-solving strategies that can be adapted and modified for different contexts and experiences. The purpose of this study was to examine the use of heuristics by students and gain insight into the thought process behind their problem-solving skills.…

Researchers point at the need to study the creative processes of students in problem solving, as these may indicate how to encourage creative problem solving. The present research attempts to study, based on the heuristic framework of Polya, pre-service teachers' flexibility processes when they solve a mathematical problem with technology. The…

Understanding chemical models can be challenging for many university students studying chemistry. This study analysed students' understanding of molecular structures using the Lewis structure as a model, and examined what hinders their understanding. We conducted pre- and post-tests to analyse students' conceptions and changes in them. The…

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…

There is a large body of literature concerning the potential of dynamic geometry software (DGS) in the problem solving process. However, questions regarding how teaching should take place to prepare students to use DGS as a heuristic tool in non-routine problem situations seem to be overlooked. To address this gap in the literature, the current…

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…

Although research from a range of fields indicates the importance of innovation for progress in those fields, there is not yet a set of best practices for promoting insights that lead to scientific innovation. This article proposes and tests the hypothesis that function-construction maps based on prototype and heuristic theory lead to increased…

NP-complete problems such as the traveling salesman problem (TSP) play a prominent role in most advanced undergrad/graduate courses in discrete optimization modeling. Teaching such an important topic from a purely mathematical perspective without discussing specific applications may result in reduced student interest and motivation. The DeLand…