Understanding and knowledge of scientific reasoning skills is a key ability of pre-service teachers. In a written survey (open response format), biology and chemistry pre-service teachers (n = 51) from two German universities claimed central decisions or actions school students have to perform in scientific reasoning in the open inquiry…

This paper addresses the continuing need for mathematics teachers to enrich their mathematical knowledge beyond the school curriculum, in order to effectively engage students in creative and imaginative thinking, particularly, but not exclusively, students who show exceptional promise. The author, a retired university professor, works staff and…

Math teachers' circles are a form of professional development that is recommended by the Conference Board of the Mathematical Sciences in their publication Mathematical Education of Teachers II (2012). However, little research has been published on how effective math teachers' circles are in advancing the mathematical knowledge of teachers and…

This study is based on a Task Design and Analysis activity from a year-long professional development program. The activity was designed to increase teacher growth in several areas, including knowledge of mathematics, understanding of students' cognitive activity, knowledge of good questions, and ability to develop and improve high quality tasks.…

The paper reports an investigation into how a group of elementary and middle school teachers collectively attempted to solve and understand a fraction division problem using an area model. Solving the word problem required that teachers determine how many two-thirds fit into three-fourths. The teachers struggled to conceptualise fraction division,…

Teacher education has become an area of considerable interest among policymakers in many countries over recent years. Teacher's knowledge and skills in qualified teaching is of great importance. The main purpose was to study the level and depth of the school mathematics and related teaching knowledge attained by prospective Ukrainian secondary…

Borderlands of practice are spaces where teachers are engaged in negotiating multiple conceptions of "best practices" within their daily teaching practice. Teachers at work in borderlands must actively negotiate varied conceptions, expectations, and assumptions about what is "best" for their students. These conceptions often…

In this brief article, the author argues that if society defines schools as testing centers instead of learning centers where young people go to watch adults work, then teacher education programs are replaceable. Online technologies allow for the transmittal of information without the need for traditional classroom settings. However, if schools…

This paper documents the ways mathematical knowledge for teaching (MKT) and curriculum materials appear to contribute to the enactment of a 7th grade "Connected Mathematics Project" lesson on comparing ratios. Two teachers with widely differing MKT scores are compared teaching this lesson. The comparison of the teachers' lesson enactments suggests…

Math Teachers' Circles have been spreading since their emergence in 2006. These professional development programs, aimed primarily at middle-level mathematics teachers (grades 5-9), focus on developing teachers' mathematical problem solving skills, in line with the Common Core State Standards-Standards of Mathematical Practice. Yet, to date,…

This study focused on the mathematical content knowledge of prospective teachers in Iceland. The sample was 38 students in the School of Education at the University of Iceland, both graduate and undergraduate students. All of the participants in the study completed a questionnaire survey and 10 were interviewed. The choice of ways to measure the…

Teaching computer science (CS) in high schools, rather than just programming or even computer literacy, is important as a means of introducing students to the true nature of CS, and enhancing their problem-solving skills. Since teachers are the key to the success of any high school educational initiative, any discussion of high school programs…

The purpose of this paper is to capture the pedagogical content knowledge (PCK) of university professors about quantum chemistry. More specifically, we aimed to identify and analyze relationships between specific PCK components, using an adapted version of the model of PCK of Magnusson "et al.". A sample of university professors (n = 6)…

Argues for a reconceptualization of teaching expertise based on psychological similarities of expert teachers to one another. The authors offer a prototype-based categorization model, drawn from psychological research, on which the family resemblance among expert teachers may be founded. The authors discuss several implications of the prototype…

Recent research explaining the influence of teacher knowledge and beliefs on instruction tends to illustrate what teachers cannot do by describing their limited beliefs about mathematics or gaps in mathematics knowledge. Those studies illustrating what teachers can do tend to focus on one teacher. This paper describes what nine secondary level…