To improve mathematics achievement of U.S. students and to assure that "what and how students are taught should reflect not only the topics within a certain academic discipline, but also the key ideas that determine how knowledge is organized and generated within that discipline" are dual goals of the Common Core State Standards for…

Instructional design principles for visuals in student materials have been developed through findings based on student-level measures. However, teacher viewpoints may be a rich source of information to better understand how visuals can be optimized for student learning. This study's purpose is to examine teacher viewpoints on visuals. In a…

The purpose of this article is to present five examples of teacher leadership from within secondary mathematics classrooms. These vignettes come from a larger study that resulted in a teacher leader continuum. This article offers classroom teacher examples that highlight each of five positions along that continuum. The argument is made that a wide…

The purpose of this study was to determine the extent to which the modeling of deductive reasoning and proof-type thinking occurs in a mathematics course in which students are not explicitly preparing to write formal mathematical proofs. Algebra was chosen because it is the course that typically directly precedes a student's first formal…

Too many students and educators view the senior year and graduation from high school as an end point, rather than one vital step along the education pipeline. Students who engage in a fourth year of math tap into and build upon their advanced analytic skills and are more likely to have better success in postsecondary course work, as they have…

With GeoGebra introduced into mathematics instruction the teaching/learning process is not improved in terms of speed and quality only. Mathematical concepts, rules and procedures must be adjusted to the new environment. On the other hand, characteristics of the computer and the educational software in use must be thoroughly examined and a…

Taylor series convergence is a complicated mathematical structure which incorporates multiple concepts. Therefore, it can be very difficult for students to initially comprehend. How might students make sense of this structure? How might experts make sense of this structure? To answer these questions, an exploratory study was conducted using…

This article analyses the experiences of 55 secondary pre-service teachers (PSTs) in a mandated professional development course that used Halliday's systemic functional linguistics (SFL) and related pedagogical practices to support PSTs' development of disciplinary linguistic knowledge for working with linguistically diverse students in the United…

This article introduces a model entitled, "Responsive Teaching through Problem Posing" or RTPP, that addresses a type of reform oriented mathematics teaching based on posing relevant problems, positioning students as experts of mathematics, and facilitating discourse. RTPP incorporates decades of research on students' thinking in…

This study investigated the use of interdisciplinary learning activity task to construct students' knowledge in Mathematics, specifically on the topic of scale drawing application. The learning activity task involved more than one academic discipline, which is Mathematics, English Language, Art, Geography and integrating the Brunei Darussalam…

In this article we present the prototype of a workshop on naive set theory designed for high school students in or around the seventh year of primary education. Our concept is based on two events which the author organized in 2006 and 2010 for students of elementary school and high school, respectively. The article also includes a practice report…

Mathematics learning is a continuous process in which students face some abrupt episodes involving many changes of different natures. This work is focused on one of those episodes, transition from primary to secondary school, and targets teachers and their mathematical knowledge. By characterising the mathematical knowledge that teachers of…

This paper being an extension of Bhattacharjee (2012) is very much relevant to Year 9 to Year 10A in the "Australian Curriculum: Mathematics". It also falls within the purview of class IX to class XII curriculum of Mathematics in India (Revised NCERT curriculum) for students aged 14-17 years. In Bhattacharjee (2012), the discovery of…

How many squares can be found on a typical 5 × 5 geoboard? Teachers who are unfamiliar with this question may wish to stop here and reflect a bit. The question can lead to wonderful student discourse: How can someone tell if something is a square? Should squares be counted that are the same size (but in a different location) or just different…

One of the most common household polyhedra is a cereal box. For over 100 years, American companies like Kellogg's™ have packaged cereal in containers shaped like rectangular prisms. Why is a rectangular prism the most commonly used solid for holding cereal? Would another design work equally or more efficient? This article describes an…