In Principles and Standards for School Mathematics (2000), the (U.S.) National Council of Teachers of Mathematics recommended that students communicate their mathematical thinking in a logical manner, and use the language of mathematics to express their thinking accurately and logically. Students should not only learn mathematics content, but…

Communicating on the mathematical language, problem solving, and reasoning are competencies tested on international test. The aim of this research is to study how secondary school pupils do geometrical constructions, how they give mathematical argumentation and use geometrical notions in their explanations.

Microarray is a high throughput technology to measure the gene expression. Analysis of microarray data brings many interesting and challenging problems. This thesis consists three studies related to microarray data. First, we propose a Bayesian model for microarray data and use Bayes Factors to identify differentially expressed genes. Second, we…

This essay summarizes the discussion on how to engage students in the history of innovation that took place at the Wachman Center's two-day history institute for teachers on this subject held October 18-19, 2008. It was observed that hero innovators generally fail multiple times, and suggested that innovation may be fostered by providing a…

Functional Magnetic Resonance Imaging (fMRI) studies of emotion, personality, and social cognition have drawn much attention in recent years, with high-profile studies frequently reporting extremely high (e.g., > 8) correlations between behavioral and self-report measures of personality or emotion and measures of brain activation. We show…

The optimal development of expertise is dependent on the application of a regimen of deliberate practice. A component of this practice is the development of critical thinking skills related to the solving of complex problems in ill-structured, naturalistic environments. The cognitive steps used to solve problems by experts is frequently not…

Despite generally higher academic achievement, female students display lower academic self-confidence than males. Of particular interest to engineering educators is the difference in confidence in mathematical, scientific and problem-solving skills. Using a multi-method approach that utilizes the rich dataset of the Academic Pathways Study, the…

A number of cars drive along a narrow road that does not allow overtaking. Each driver has a certain maximum speed at which he or she will drive if alone on the road. As a result of slower cars ahead, many cars are forced to drive at speeds lower than their maximum ones. The average velocity in the queue offers a non-trivial example of a mean…

Collaboratively observing tutoring is a promising method for observational learning (also referred to as vicarious learning). This method was tested in the Pittsburgh Science of Learning Center's Physics LearnLab, where students were introduced to physics topics by observing videos while problem solving in Andes, a physics tutoring system.…

The aim of this study is to understand the relationship between metacognition and students' everyday problem solving. Specifically, we were interested to find out whether regulation of cognition and knowledge of cognition are related to everyday problem solving and whether students who perform better in the decision-making problem will better…

In mathematics teacher education, tasks that centre on doing mathematics are used for a variety of purposes, including learning new mathematics. In our research, we focus on doing mathematics as a therapeutic intervention. Many pre-service teachers in our program narrate impoverished mathematics experiences. We engage pre-service elementary school…

Many educators agree that effective teaching helps students to think critically, communicate more clearly, learn self-discipline, develop an understanding of themselves and others, and cultivate the habit of self-education. Today's global, multi-cultural environment requires people to work in teams, which in turn requires collaboration and…

Conventional introduction to computer science presents individual algorithmic paradigms in the context of specific, prototypical problems. To complement this algorithm-centric instruction, this study additionally advocates problem-centric instruction. I present an original problem drawn from students' life that is simply stated but provides rich…

As in many other fields of science and technology, college students in computer engineering do not come into full contact with the key ideas and challenges of their chosen discipline until the third year of their studies. This situation poses a problem in terms of keeping the students motivated as they labor through their foundational, basic…

Pedagogical content knowledge (PCK) has been embraced by many of the recent educational reform documents as a way of describing the knowledge possessed by expert teachers. These reform documents have also served as guides for educators to develop models of teacher development. However, in the United States, few if any of the current models…