Determining what students know and understand, as well as what misconceptions they have, is essential to planning and providing targeted intervention and support. In this article, a teacher uses formative assessment interviews to uncover evidence of students' understandings and to plan targeted instruction in a mathematics intervention class. The…

The aim of this article is to contribute to the understanding and use of the theory of communities of practice. In order to clarify terms, explore applications for education and reflect on various critiques of the theory in the literature, two educational researchers conducted a series of interviews with the theorist Etienne Wenger-Trayner. The…

One area of algebraic thinking essential for students' success is a relational understanding of the equal sign. Research has indicated a positive correlation between students' relational understanding of the equal sign and their equation-solving performance, suggesting that students' early conception of the equal sign may affect their learning and…

Based on a study with six elementary school teachers and 115 students in grades 3, 4, and 5, this article discusses ways that teachers might support an understanding of variable as students explore pattern-finding activities. The practices emerged from interviews with teachers and a yearlong observation of teaching algebraic thinking during an…

Physics is a subject where pupils hold a great number of deeply seated misconceptions. Sound is a prime example, as it requires the visualisation of a form of energy that moves imperceptibly through an invisible medium. This article outlines some of the common misconceptions that pupils hold regarding the nature of sound and how it is transmitted,…

A story problem about borrowing money, presented in this article, may be represented with positive or negative numbers and thought about in different ways. The authors describe ideas related to integers (both positive and negative) and how students used them in relation to a story problem, and how they related these ideas to equations.

The minus sign is a mathematical symbol that is multi-functional. Yet, how often is its use explicit to the non-mathematician, or more importantly the learner, who is expected to interpret the symbolism appropriately, when often the "meaning" stems from context of its use. From the perspective of the learner, such nuances of use simply…

Instructors are constantly struggling to help students understand mathematical concepts as well as the relevance of mathematics to the real world. In calculus, students possess misconceptions of the limit concept. "Pushing the Limit" refers to a semester-long calculus class project that required students to read about, interview calculus…

It is fascinating to listen to middle school students talk about food for plants and animals and how that food is used. Some students describe ideas that are essentially correct. Some comments suggest that students are familiar with the content, but their understanding is incomplete or includes inaccuracies. Finally, some students have little…

With the implementation of Response to Intervention (RtI) throughout the United States and the strong evidence that validates the use of RtI as a way of supporting struggling students, teachers need ways to understand and reach tier 2 students within their classrooms. One approach to gaining a better understanding of students' misconceptions is…

The gifted remain an often misunderstood and underserved population. In this interview, Dr. Pfeiffer discusses these concerns and provides practitioners with timely information on who exactly the gifted are and the various ways in which they are unique. In this reflective conversation, Dr. Pfeiffer, a noted authority on gifted and talented…

As beginning teachers start to recognize the complexity of teaching mathematics in elementary school classrooms and how their new vision for teaching mathematics creates new challenges, they experience discomfort--a healthy awareness that much is to be learned. Brousseau (1997) notes that changes in the roles that are implicitly assigned to the…

One-day professional development workshops for graduate students and postdocs were held at top National Research Council--ranked chemistry research departments. Attendees intend to pursue academic careers, yet their experience and knowledge about teaching and learning were small. Postsurveys indicated that despite the short duration, the workshop…

We used both student interviews and diagnostic testing to reveal students' misconceptions about number representations in computing systems. This article reveals that students who have passed an undergraduate level computer organization course still possess surprising misconceptions about positional notations, two's complement representation, and…

At present in mainland China, competition in education has become excessive; competition has been increasing, and a competitive mentality is on the rise. The formative causes of excess competition in education are complex; with both practical and conceptual causes. Its roots can be traced to intensifying social competition, a one-sided…