In a research study designed to investigate the emergence of collective creativity in elementary classroom settings, and in which teachers' decision-making practices were analyzed alongside both the teachers' observed teaching practices in their classrooms and their students' problem solving actions, the first author developed four metaphors for…

Understanding how physicists solve problems can guide the development of methods that help students learn and improve at solving complex problems. Leveraging the framework of cognitive task analysis, we conducted semistructured interviews with theoretical physicists (N=11) to gain insight into the cognitive processes and skills that they use in…

Isomorphism and homomorphism appear throughout abstract algebra, yet how algebraists characterize these concepts, especially homomorphism, remains understudied. Based on interviews with nine research-active mathematicians, we highlight new sameness-based conceptual metaphors and three new clusters of metaphors: sameness/formal definition, changing…

The aim of this work is to examine pre-architects' use of metaphorical reasoning as a tool for design problem solving exercises in an unfamiliar environment. It is to improve their sense of place, which helps to identify and capture design concepts, as well as define goals and requirements. Regarding the three metaphorical reasoning operations of…

Analogies between old and new concepts are common during classroom instruction. Previous transfer studies focused on how features of initial learning guide later, spontaneous transfer to new problem solving. We argue for a shift in the focus of analogical-transfer research toward understanding how to best support analogical transfer from previous…

The design of solar power plants and the operating principles are learned by engineering students during the last academic year. Typically, this subject is taught using the traditional methodology based on lectures where students are not considered as an active player of the class. The aim of this experience was to implement innovative…

The aim of this paper is to analyse the reasoning and symbolisations used by sixth grade Moroccan students in solving a task based on figurative patterns. Our analysis aims at identifying the systems of actions elaborated by the students to give the general expression of the sequence, according to their perceptions of the sequence of its patterns.…

In this paper I intend to illustrate Vygotsky's Zone of Proximal Development (ZPD) and then extend the discussion to scaffolding and its relationship with the ZPD. This is then followed by some concerns raised in literature regarding scaffolding as a concept and as a metaphor which involves analysing the arguments for regarding the role of…

This conceptual paper proposes a model to describe the quality of student dialogue during participative collaborative problem solving. Drawing on the participation metaphor of learning, we argue that the construct of mathematical sophistication is useful to describe the quality. We then present two frameworks, mathematical competencies and…

Specific acts of problem solving with rates and ratios were interpreted using a journey metaphor derived from Skemp's (1979) construct of director systems. To successfully undertake a problem solving journey a learner must recognise their starting place (present state), have a sense of destination (goal state), and co-ordinate sub-routes along the…

Over the past few decades there has been increased interest in how students and teachers think and learn about negative numbers from a variety of perspectives. In particular, there has been debate about when integers should be taught and how to teach them to best support students' learning. This book brings together recent work from researchers to…

Metaphors are regularly used by mathematics teachers to relate difficult or complex concepts in classrooms. A complex topic of concern in mathematics education, and most STEM-based education classes, is problem solving. This study identified how students and teachers contextualize mathematical problem solving through their choice of metaphors.…

Entropy is often introduced to students through the use of the disorder metaphor. However, many weaknesses and limitations of this metaphor have been identified, and it has therefore been argued that it is more harmful than useful in teaching. For instance, under the influence of the disorder metaphor, students tend to focus on spatial…

This essay proposes a reflection on the learning difficulties and teaching approaches associated with arithmetic word problem solving. We question the development of word problem solving skills in the early grades of elementary school. We are trying to revive the discussion because first, the knowledge in question--reversibility of arithmetic…

In this study, dynamic testing principles were applied to examine progression of analogy problem solving, the roles that cognitive flexibility and metacognition play in children's progression as well as training benefits, and instructional needs of 7- to 8-year-old gifted and average-ability children. Utilizing a pretest training posttest control…