The purpose of this study was to gain insight into 30, first year calculus students' understanding of the relationship between the concept of vertex of a quadratic function and the concept of the derivative. APOS (action-process-object-schema) theory was applied as a guiding framework of analysis on student written work, think-aloud and follow up…

In this article we study the conceptions of an American and a French group of undergraduate pre-service teachers regarding the concept of independent events. Specifically, we study the role that intuition plays in their answers, ascertain the presence of probabilistic biases, and compare the findings with previous results collected on a different…

When studying a complex research phenomenon, a mixed methods design allows to answer a broader set of research questions and to tap into different aspects of this phenomenon, compared to a monomethod design. This paper reports on how a sequential equal status design (QUAN ? QUAL) was used to examine students' reasoning processes when solving…

The ubiquity of the subject of percentages in our everyday life demands that math teachers and pre-service math teachers demonstrate a profound knowledge and thorough understanding of the concept of percentages. This work, which originated from one specific lesson in an 8th grade math class, studies the conceptual understanding and problem-solving…

There is widespread agreement that science learning always builds upon students' existing ideas and that science teachers should possess knowledge of learners. This study aims at investigating pre-service science teachers' knowledge of student misconceptions and difficulties, a crucial component of PCK, on Newton's Third Law. A questionnaire was…

This paper explores the effectiveness of using "structured examples in concert with prompting reflective questions" to address misconceptions held by mechanical engineering students about thermodynamic principles by employing pre-test and post-test design, a structured questionnaire, lecture room observation, and participants'…

The purpose of this study is to examine the proportional reasoning of pre-service teachers at the beginning of their teacher preparation program using the developmental shifts described by Lobato and Ellis (2010). They cast changes in proportional reasoning as transitions or "shifts" in students' thinking and these shifts can serve as…

This is a descriptive research on the difficulties of Filipino high school students in translating algebraic word problems into mathematical equations. This research is composed of three parts: (1) development of an 11-page "Filipinized" questionnaire; (2) analysis of the mathematical thinking processes of the respondents based on the answers to…

The students' performance in various types of problems dealing with the conservation of matter during chemical reactions has been investigated at different levels of schooling. The participants were 499 ninth grade (ages 14, 15 years) and 624 eleventh grade (ages 16, 17 years) Greek students. Data was collected using a written questionnaire…

Object-oriented analysis and design (OOAD) is not an easy subject to learn. There are many challenges confronting students when studying OOAD. Students have particular difficulty abstracting real-world problems within the context of OOAD. They are unable to effectively build object-oriented (OO) models from the problem domain because they…

We studied students' conceptions of correctness and their influence on students' correctness-related practices by examining how 159 students had analyzed the correctness of error-free and erroneous algorithms and by interviewing seven students regarding their work. We found that students conceptualized program correctness as the sum of the…

Describes a study that investigated probabilistic intuitions held by students (N=98) from grade 7 through college through the use of a questionnaire. Of the misconceptions that were investigated, availability was the only one that was stable across age groups. Contains 20 references. (DDR)

The purpose of this study was to investigate the effects of a problem solving based instructional model on earth science students' achievement and alternative frameworks. Students' opinions toward the instructional method were also investigated. The investigations employed a pretest/posttest control group design to detect any significant change.…

Twelve linear algebra students were interviewed about the concept of a Solution of a System of Equations. The interviews were analyzed using APOS tools, in particular the ideas of Action, Process, Object and Schema, and Genetic Decomposition. The analysis of the interviews revealed several misconceptions of Solution. The analysis also revealed…

The results of an investigation concerned with sequential reasoning in interpreting the current flow in d.c. electric circuits are presented. Analysis of the results of a questionnaire completed by 236 college sophomores shows the presence of a common misunderstanding based on a "local" interpretation of the current flow. A copy of the…