This paper reports on an exploratory study about probabilistic intuition in learning mathematics for decision-making. The analysis was carried out on a group of high school students in relation to their probabilistic intuition in problem-solving, after performing playful learning activities on a simulation platform specifically designed for this…

This paper describes our work to determine the naturalistic images that first-time second-semester university calculus students possess for series convergence. We found that the students we interviewed most frequently determined whether a series converged by imagining a process of appending summands into a running total and examining whether this…

Mathematical modeling is a challenging and creative process. If one considers only interim or final solutions to modeling problems or interviews modelers afterward, often only their "explicit" models are accessible -- those expressed in work products or evinced in verbal and written reflections. The inner world of tacit knowledge and its…

In response to the authors, I demonstrate how threshold concepts offer a means to both contextualise teaching and learning of quantum physics and help transform students into the culture of physics, and as a way to identify particularly troublesome concepts within quantum physics. By drawing parallels from my own doctoral research in another area…

Gestalt psychologists proposed two distinct learning mechanisms. Associative learning occurs gradually through the repeated co-occurrence of external stimuli or memories. Insight learning occurs suddenly when people discover new relationships within their prior knowledge as a result of reasoning or problem solving processes that re-organize or…

Given the privileged status claimed for active learning in a variety of domains (visuomotor learning, causal induction, problem solving, education, skill learning), the present study examines whether action-based learning is a necessary, or a sufficient, means of acquiring the relevant skills needed to perform a task typically described as…

This project examined three hypotheses: (1) teachers can learn to make explicit their own intuitive knowledge as it relates to specific matters and their teaching practice; (2) once a teacher has gained insight into her own knowledge, she can learn to coordinate it with the privileged descriptions of subject matters she is expected to teach; and…

Asserts that the sudden insights that characterize intuitive thinking are as important in effectuating learning as analytical thinking. Claims that intuitive thinking enables students to comprehend complex relationships better, to put things into better perspective, to generate new ideas, and to perceive more ways to integrate facts, concepts, and…

The focus of this paper is on some of the difficulties students experience in learning from texts and in solving other types of academic problems, because of their failure to distinguish between skills needed for everyday thinking and those needed for academic thinking. The paper discusses the types of processing problems children experience when…

Considers the role of evolution and natural selection in the functioning of the modern human brain. Natural selection equipped humans with a mental toolbox of intuitive theories about the world which were used to master rocks, tools, plants, animals, and one another. The same toolbox is used today to master the intellectual challenges of modern…

This paper proposes a theory that can account for differences between everyday and formal mathematics knowledge and a set of processes by which informal knowledge is transformed into formal mathematics. After an introduction, the paper is developed in five sections. The first section lays out the nature of informal, everyday mathematics knowledge.…

This document focuses on evidence from problem solving case studies which indicate that analogy, extreme case analogies, and physical intuition can play an important role as forms of nonformal reasoning in scientific thinking. Two examples of nonformal reasoning are examined in greater detail from 10 case studies of "expert" problem solving.…

Divided into two parts, this article analyzes why some pupils feel reserve about instantaneous velocities and instantaneous flows. The second part relates reactions of pupils facing a problem that implicates the instantaneous rate of change. Describes some characteristics of this problem that enables the authors to explain its instructional…

External representations have a great impact on what and how students learn. One key manner in which environments can operate upon novices' knowledge is through helping them ground their problem solving in an understanding of the situation embodied by the problem. In this paper, students' difficulties in microeconomics problem solving were…