This article reports on an analysis of episodes of invalid or controversial arguments that occurred while two different groups of students worked on similar fraction tasks and examine the role that these types of arguments played in the development of students' reasoning. One group consisted of suburban, middle-class, fourth graders who worked on…

This article discusses an activity designed to encourage writing to learn in mathematics. There were three stages of data collection. An assessment, requiring basic algebra only, was completed by 118 undergraduates from statistics and calculus courses. Students were given summaries of all participant responses, along with the correct answers.…

Learners are all different and teachers are all different, so why do we often ignore this reality when trying to explain, or demystify, some aspect of mathematics in the classroom? Enabling learning can be challenging, demanding of creativity, and needy of alternatives if understanding is the real goal. Here the authors offer ideas that are aimed…

This paper examines students' achievements in solving problems and their misunderstandings when using models. A mixed research methodology was applied. Quantitative research investigated how the performance of students with various levels of high school GPAs correlated with their rating of their lecturers' teaching proficiency. Four lecturers and…

This qualitative case study in a rural school in Umgungundlovu District in KwaZulu-Natal, South Africa, explored Grade 12 learners' mental constructions of mathematical knowledge during engagement with optimisation problems. Ten Grade 12 learners who do pure Mathemat-ics participated, and data were collected through structured activity sheets and…

This paper discusses one step from the scientific method--that of identifying independent and dependent variables--from both scientific and mathematical perspectives. It begins by analyzing an episode from a middle school mathematics classroom that illustrates the need for students and teachers alike to develop a robust understanding of…

Student understanding of biological representations has not been well studied. Yet, we know that to be efficient problem solvers in evolutionary biology and systematics, college students must develop expertise in thinking with a particular type of representation, phylogenetic trees. The purpose of this study was to understand how undergraduates…

Some of mathematics teaching is routine, like an exercise from a textbook for which you have received instruction and already know what to do. On other occasions, however, teaching mathematics is challenging, involving problems of teaching for which the solutions may not be readily apparent. These situations require the application of mathematical…

Climate literacy is an essential component of a strategy to comprehend and confront the grand challenge of global climate change. However, scientific complexity, societal implications, and political associations make climate change a difficult but important topic to teach. In this paper we report on the results of a survey of undergraduate faculty…

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'…

This research was conducted to investigate the effectiveness of BIOMIND portal in enhancing students' 21st century skills and overcoming their misconceptions in Biology subject. 118 Indonesian high school students were involved in this quasi-experimental study. The experimental group underwent learning experiences using BIOMIND portal whereas the…

As partners in a professional development project, the authors jumped at the opportunity to use a real-life problem to engage elementary and middle school teachers in a one-day exploration of the concept of area. "Length times width"--a common response to the question, "What is area?"--is a rote formulaic expression that applies only to certain…

This guidance report focuses on the teaching of mathematics to pupils in Key Stages 2 and 3. It is not intended to provide a comprehensive guide to mathematics teaching. We have made recommendations where there are research findings that schools can use to make a significant difference to pupils' learning, and have focused on the questions that…

Students frequently have difficulty determining whether a given real-life situation is best modeled as a linear relationship or as an exponential relationship. One root of such difficulty is the lack of deep understanding of the very concept of "rate of change." The authors will provide a lesson that allows students to reveal their misconceptions…

Digital games offer an appealing environment for assessing student proficiencies, including skills and misconceptions in a diagnostic setting. This paper proposes a dynamic Bayesian network modeling approach for observations of student performance from an educational video game. A Bayesian approach to model construction, calibration, and use in…