This article describes reflections of two mathematicians and a mathematics teacher educator who collaborated on the development and implementation of courses (probability and statistics connections, number concept connections, and middle school mathematics methods) for middle school mathematics preservice teachers. The instructors of the courses,…

Forming part of a wider research study, the current study investigated prospective middle school mathematics teachers' ways of covariational reasoning on tasks involving simultaneously changing quantities. As the introductory theme of a larger unit on derivative, a model development sequence on covariational reasoning was designed and experimented…

The present study aimed to examine lower secondary students? images of mathematics comprised of stated attitudes to and perceived needs for mathematics, and their views about mathematicians and their work. A group of 1284 lower secondary students drew a picture of mathematicians and described their drawings. The students? drawings fell into two…

The paper describes one problem solving strategy -- the Use of false assumption. The objective of the paper is to show, in accordance with Phylogenesis and Ontogenesis Theory, that it is worthwhile to reiterate the process of development of the concept of a variable and thus provide to pupils one of the ways helping them to eliminate usual…

Performance in Mathematics among pupils in lower primary schools in Kenya is a problem that continues to be a concern to parents, teachers and stakeholders in education. Teacher related factors and in particular teacher preparedness has been cited as a major contributing factor to poor teaching methods which fundamentally translates to pupils'…

This study explores components of ambitious teaching practices for teaching multiplicative properties that can give teachers opportunities to learn through a quick images activity in a cycle of enactment and investigation. Throughout the cycle, it is found that the participants have opportunities to learn the following components of ambitious…

Despite repeated discussions and practice, algebra students continue to make variable errors, in many ways, year after year. This same problem appeared thirty years ago in a list of common errors that math teachers today would immediately recognize, many involving exponents and distribution (Marquis 1988). Similar complaints even appeared in the…

An exploratory study was conducted to investigate the use of magic activities in a math course for prospective middle-school math teachers. This research report focuses on a lesson using two versions of math magic: (1) the "5-4-3-2-1-½ Magic" involves having students choose a secret number and apply six arithmetic operations in sequence…

Despite growing up in a world that is permeated by mathematics, students graduating from US schools are woefully unprepared for the mathematical challenges that await them in the workplace or in higher educational pursuits. Mathematical competencies underpin not only success in college but also increase job opportunities for students after…

The purpose of this research was to study the procedure of think pair share, the type of cooperative learning models, which can be implemented in mathematics instruction in Manokwari, West Papua Indonesia. This study was conducted at Senior High School in Manokwari (SMA Negeri 1), Manokwari West Papua Indonesia. The research was carried out using…

Due to the embeddedness of digital technologies in mathematics education of today, we often see examples of students simultaneously using their mathematical competencies and digital competencies. In relevant literature, however, these are not seen as a connected whole. Based on reviewing existing competency frameworks, both mathematical and…

In this article I present some notes and reflections on possible ways to be adopted in teaching practice in Mathematics for the incorporation of meanings in teaching and learning of school mathematics in face of the cultural diversity in which the school is situated and constituted in the 21st century through the perspective of globalization. It…

Background: This article is focused on the role of the facilitator in the professional development of mathematics teachers. It is a feature of several frameworks for using video that teachers are invited to comment on the detail of what they saw and heard, and base comments on evidence from the video. It is also a common finding that it is hard to…

Recently, claims of a 'new and straightforward' method of solution to second-order linear difference equations have appeared in the mathematics education literature from Rivera-Figueroa and Rivera-Rebolledo. The claim of novelty is based on an assumption that 'since the equation is worked in its canonical form', the method within this context must…

We examine opportunities and challenges of applying a single, explicit definition of multiplication when modeling situations across an important swathe of school mathematics. In so doing, we review two interrelated conversations within multiplication research. The first has to do with identifying and classifying situations that can be modeled by…