Since the purpose of architecture is to optimize the physical environment, where specific human activities take place properly and in a dignified fashion, architectural design can never be an absolutely push-button process. Accordingly, architecture is truly interwoven with creativity, which should essentially be enhanced or even acquired. In this…

Over the last forty years of mathematics education research, a coherent body of knowledge has accumulated regarding the teaching of limits. On this basis, it remains a challenge to identify goals and design tasks compatible with ordinary teaching conditions. This paper reports on a teaching experiment carried out in France with year 12 students,…

A/r/tography is often considered to be an arts and education practice-based research methodology, but this author explores a/r/tography as a pedagogical strategy that has informed the author's artistic practice and pedagogical experiments. The author tracks his own journey of entering into an a/r/trographic world and where that entering has…

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…

Tzur and Simon (2004) postulated 2 stages of development in learning a mathematical concept: participatory and anticipatory. The authors discuss the affordances for research of this stage distinction related to data analysis, task design, and assessment as demonstrated in a 2-year teaching experiment.

Theories of relational concept acquisition (e.g., schema induction) based on structured intersection discovery predict that relational concepts with a probabilistic (i.e., family resemblance) structure ought to be extremely difficult to learn. We report four experiments testing this prediction by investigating conditions hypothesized to facilitate…

A body of research shows that grammatical gender, although an arbitrary category, is viewed as the system with its own meaning. However, the question remains to what extent does grammatical gender influence shaping our notions about objects when both verbal and visual information are available. Two experiments were conducted. The results obtained…

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…

In this article, we analyze a first grade classroom episode and individual interviews with students who participated in that classroom event to provide evidence of the variety of understandings about variable and variable notation held by first grade children approximately six years of age. Our findings illustrate that given the opportunity,…

In today's competitive global economy characterized by knowledge acquisition, the concept of knowledge management has become increasingly prevalent in academic and business practices. Knowledge creation is an important factor and remains a source of competitive advantage over knowledge management. Constructivism holds that learners learn actively…

Brainstorming research has claimed that individuals are more creative than groups. However, these conclusions are largely based on measuring creativity by the number of ideas generated, and researchers have tended to neglect other important components of creativity, such as the quality of developed ideas. These studies aim to address this gap in…

Three experiments examined conceptual change from reading refutational texts and how such learning interacted with prior knowledge organization. Prior to reading, 3 groups of learners were identified on the basis of their prior knowledge of the targeted concept: 2 groups held misconceptions; 1 group was generally accurate. Experiment 1 tested…

In a series of two "in vivo" experiments, we examine whether correct and incorrect examples with prompts for self-explanation can be effective for improving students' conceptual understanding and procedural skill in Algebra when combined with guided practice. In Experiment 1, students working with the Algebra I Cognitive Tutor were randomly…

The purpose of this study was to investigate in detail the processes involved when the promotion of metaconceptual evaluation facilitates fifth grade students' construction, evaluation, and revision of their explanations for magnetic phenomena. Although much recent research emphasized the importance of student modeling and model construction,…

Adult developmental mathematics students often work under great pressure to complete the mathematics sequences designed to help them achieve success (Bryk & Treisman, 2010). Results of a teaching experiment demonstrate how the ability to reason can be impeded by flaws in students' mental representations of mathematics. The earnestness of the…