Background and Context: Multiple studies report that experienced instructors lack consensus on the difficulty of programming tasks for novices. However, adequately gauging task difficulty is needed for alignment: to select and structure tasks in order to assess what students can and cannot do. Objective: The aim of this study was to examine…

An underexplored aspect of the relationship between analogical reasoning and creativity is its phenomenology; in particular, the notion that analogical reasoning is related to insight and its associated "aha!" experience. However, the relationship between these phenomena has never been directly investigated. We adapted a set of verbal…

While contemporary mathematics education literature argues that curricular resources, such as textbooks, play a significant role guiding mathematics teachers in what and how they teach, it also shows that these resources often do not do what they say they will do, nor adhere to the standards they claim to further. When it comes to the most…

Despite the seemingly simple mapping between adjectives and perceptual properties (e.g., color, texture), preschool children have difficulty establishing the appropriate extension of novel adjectives. When children hear a novel adjective applied to an individual object, they successfully extend the adjective to other members of the same object…

Mathematical calculations are an important part of chemistry. Those problems are difficult for students, especially if the task is set with a limiting reactant. The aim of this study was development of a Procedure for evaluation of cognitive complexity of the Stoichiometric Tasks with a Limiting Reactant. The procedure created included an…

Due to their abstract nature, representation of mathematical concepts through different registers favors their understanding. In the case of ''sequences and regularities'', it becomes propitious the exploration of different registers of representation in the institution of topics, such as term, order, formation law, and generating expression.…

In science education, representations are necessary inter alia for the understanding of relationships between structures and systems. However, several studies have identified difficulties of students when working with representations. In the present study, we investigated students' responses (regarding their preference, test performance, mental…

The purpose of this study is to explore how an introductory real analysis (IRA) course can be designed to bridge a gap between students' intuition and mathematical rigor. In particular, we focus on a task, called the e-strip activity, designed for the convergence of a sequence. Data were collected from a larger study conducted as a classroom…

We report here on students' views of example generation tasks assigned to them in two first year undergraduate Calculus courses. The design and use of such tasks was undertaken as part of a project which aimed to afford students opportunities to develop their thinking skills and their conceptual understanding. In interviews with 10 students, we…

The aim of the research was to identify how Slovenian primary and secondary school students of various age groups explain the particulate nature of the states of matter of water and air. The qualitative research included five 12, 14, and 16 year old students. A semi-structured interview including four computer-displayed tasks was used for the data…

Existing evidence suggests that children, when they first pass standard theory-of-mind tasks, still fail to understand the essential aspectuality of beliefs and other propositional attitudes: such attitudes refer to objects only under specific aspects. Oedipus, for example, believes Yocaste (his mother) is beautiful, but this does not imply that…

Traditional mathematics education focuses on teaching rote procedures to solve problems, though these procedures are not usually motivated by goals. As a result, students have trouble flexibly using procedures and generalizing their knowledge to solve novel problems that differ from the problems they practice during instruction. In the following…

In daily activities, humans must attend and respond to a range of important items and inhibit and not respond to unimportant distractions. Our current understanding of these processes is largely based on perceptually simple stimuli. This study investigates the interaction of conceptual-semantic categorization and inhibitory processing using Event…

The learning machine described in this paper acquires concepts representable as conjunctive forms of the predicate calculus and behaviors representable as productions (antecedent-consequent pairs of such conjunctive forms): these concepts and behavior rules are inferred from sequentially presented pairs of examples by an algorithm that is probably…

An attempt is made to establish a link between ordinary arithmetical situations and relevant mathematical concepts by the analyzing of complexity of concepts. (MP)