This study examines the behavior of individuals when two intuitive rules in their minds lead to two different outcomes concerning a problem. In the absence of the formal knowledge, intuitive rules can affect the mathematical thinking. Hence, studies have usually compared the correct answer of the related formal knowledge with the incorrect one…

The purpose of this study was twofold. First, to explore middle and high school students' intuitively-based (mis)conceptions in probability, particularly availability and representativeness heuristics. Second, to investigate teachers' awareness of these intuitively-based (mis)conceptions and the effectiveness of their instructional practices to…

We present the theoretical argument that the use of mathematics in physics can be productively conceptualized as using a language and that learning to make sense of physics equations and appropriating them into novel scientific inquiry can be understood as a process of learning to read fluently with a high level of reading comprehension and to…

Helping students reach a clear understanding of the cause-and-effect relationship between changes in parameter and the graph of an equation is the focus of the activity outlined in this article. The behavior of phase shifts has been regarded as counterintuitive for many people, and often, because of this, conflict between student intuition and…

In this paper, we investigate the ways in which 15 year-old students conceive interrelated issues of randomness. We deal with these issues of randomness as a whole and not separately from each other, in contrast to the research so far. In order to analyse the students' ways we introduce a modification of Kyburg's Schema [(1974). "The logical…

The purpose of the study was to explore students' consistency in their notions encountering different methods in solving the same task of comparing values of certain infinite series. The participants were 93 male students aged 16-17. Applying cognitive conflict approach and the data were collected through a questionnaire administrated in two…

This paper explores how a professional learning community (PLC) redesigns high school mathematics lessons towards a shared commitment. We describe the nature of a PLC's collective curricular vision to illuminate how teachers can come to new understandings as a group in order to shift the ways students experience mathematics. Using the curricular…

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 this dissertation study, the researcher explored how pedagogy affects the creative process of visual artists who are also higher education art teachers. In order to understand and conceptualize the relationship between pedagogy and art making through the artist-teacher lens, the method and the methodology of Portraiture (Lawrence-Lightfoot…

"Transcendentalism" refers to philosophical, religious, and literary beliefs held by Ralph Waldo Emerson, Henry David Thoreau, Margaret Fuller, Amos Bronson Alcott, and other writers in New England during the 1830s and 1840s. Emerson believed in the significance of one's intuition and individuality. He expresses these beliefs in his…

The term of implicit learning is still subject to controversy. "At least a dozen different definitions have been offered in the field" (Frensch & Rünger, 2003 p.13). While some scholars consider it downright inexistent (see Chun & Jiang, 1998), many others are trying to identify how we seem to acquire knowledge in absence of…

One way to fascinate, engage, arouse curiosity, motivate, and stimulate intellectual development in learning scientific concepts is to use counterintuitive questions. These questions make students aware of the inadequacies of their own thinking by exposing them to situations whose outcomes are inconsistent with what they would expect. In this…

Humans have evolved to follow their intuition, but as any high school physics teacher knows, relying on intuition often leads students to predict outcomes that are at odds with evidence. Over the years, we have attempted to make this intuition-outcome disparity a central theme running throughout our physics classes, with limited success. Part of…

Learning physics often requires overcoming common misconceptions based on naïve interpretations of observations in the everyday world. One proposed way to help learners build appropriate physics intuitions is to expose them to computer simulations in which motion is based on Newtonian principles. In addition, playing video games that require…

Analysis of students' work on tasks relating to reflections, translations and rotations is discussed. Findings from research with regard to students' understanding of a subject would help teachers prepare for the class.