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…

In 2016, six of six American Nobel Prize winners in science were immigrants. The numbers of U.S. educated graduates who enter the Science, Technology, Engineering, and Mathematics (STEM) fields have been on the decline, and policymakers and educators have continually sought new policies and programs to try resolve this problem with long-term…

Video games offer an exciting opportunity for learners to engage in computational thinking in informal contexts. This paper describes a genre of learning environments called constructionist video games that are especially well suited for developing learners' computational thinking skills. These games blend features of conventional video games with…

The purpose of this paper is to present a conceptual framework for diagnosing teaching difficulties of a science topic in the science classroom. The development of the framework is presented as well as descriptions of the features of the framework. How the framework can be used is also elaborated? Furthermore, there is a detailed indication of an…

In an innovative, progressive school, students were asked to solve a fairly routine mathematical problem using real money in a "real-world" scenario. Even though the school values students' ideas, the reaction of the teacher to one student's alternative modelling of the problem suggests that he was expecting a particular answer to be…

This study explored the effectiveness of a unique math intervention program in a local school district in Orange County, California in terms of academic achievement and student perceptions about their math abilities as a result of their experiences in the program. As the predominate instructional approach, the program provided students with…

In this paper, we introduce restorying, a pedagogical approach based on social constructivism that employs successive iterations of rewriting and discussing personal, student-generated, domain-relevant stories to promote conceptual application, critical thinking, and ill-structured problem solving skills. Using a naturalistic, qualitative case…

Organic chemistry has the long-standing reputation as a challenging course, and organic synthesis is an aspect of organic chemistry that requires students to make the most links between concepts and requires the highest order of thinking. One-on-one interviews were conducted with students from a second undergraduate organic chemistry course in…

This paper reports results from a case study focused on understanding student practices regarding production-oriented problem-solving with digital media. Thirty-seven students participated in an elective curriculum called, "Techno Savvy," a nine-week course focused on student exploration of global issues, and designed around Web 2.0…

This study addresses the problem of mathematics teachers' resistance to problem-solving models that align with constructivist perspectives because they feel pressure to utilize more teaching approaches that focus on preparing students for high-stakes tests. The purpose of this qualitative study was to explain how ninth grade mathematics students…

Examining how teacher education influences preservice teachers' (PSTs) application of content knowledge, decision making when planning for teaching, creation of innovative teaching practices and design of aligned instruction, has significant implications for understanding learning to teach. The purpose of this study was to explore the extent to…

Self-directed, inquiry-based learning opportunities focused on transdisciplinary real-world problem solving have been shown to foster creativity in learners. What tools might we provide classroom teachers to scaffold them and their students through this creative process? This study examines an online informal learning environment and the role the…

The kindergarten program at the study site transitioned from half day to full day, yet the curriculum was not updated to accommodate the full day schedule, or to include best practices. In order to prepare learners for their future in education, activities were implemented to determine how problem based learning can promote acquisition of the 21st…

Many courses for elementary school are based upon teacher presentation and explanation of basic topics, rather than allowing students to develop their own knowledge. This traditional model may turn elementary-level lessons into an extremely theoretical, boring and non-effective process. In this context, research in mathematics elementary education…

As educational leaders struggle to meet state and federal mandates, many students graduate from high school without the skills necessary to meet the demands of a college education. Guided by the tenets of constructivism, this qualitative case study explored college students' perceptions of their college preparedness through math, science, and…