Specialists in the field of mathematical education consider that the learning of multiplication has an extremely important role not only in the area of mathematics, but also in day to day life. We can distinguish two different stages in the process of teaching-learning multiplication: a first step implies the discovery of the results within the…

Composition of functions is one of the five big ideas identified in NCTM's "Developing Essential Understanding of Functions, Grades 9-12" (Cooney, Beckmann, and Lloyd 2010). Through multiple representations (another big idea) and the use of The Geometer's Sketchpad[R] (GSP), students can directly manipulate variables and thus see dynamic visual…

Shifting your high school's math program to new Common Core standards is much easier when teachers and leaders have this handy guide. Getting a copy for every staff member involved in the process ensures everyone knows: (1) How the six conceptual categories throughout the math standards are connected and reinforced; (2) How the modeling standards…

Against the backdrop of half a century of research in mathematics problem solving, Polya's last stage is especially conspicuous--by the scarcity of research on it! Much of the research focused on the first three stages (J.M. Francisco and C.A. Maher, "Conditions for promoting reasoning in problem solving: Insights from a longitudinal…

The concept of function is a central but difficult topic in secondary school mathematics curricula, which encompasses a transition from an operational to a structural view. The question in this paper is how the use of computer tools may foster this transition. With domain-specific pedagogical knowledge on the learning of function as a point of…

Learning mathematics is challenging. It requires discipline, logic, precision, perseverance, and accuracy. It can also be fun. When mathematics is set in a context that inspires students to want to solve interesting problems, students will have an intrinsic desire to learn the necessary skills to accomplish a specific goal. The game of Crypto! was…

This article describes a professional development initiative for fifteen mathematics teachers in the use of dynamic geometry software GeoGebra. A four-day introductory workshop was given in Nepal to provide an overview of GeoGebra and its possible integration in the teaching/learning of secondary school mathematics there. Teachers' impressions and…

In this paper, we introduce a new approach to compute the partial fraction decompositions of rational functions and describe the results of its trials at three secondary schools in Hong Kong. The data were collected via quizzes, questionnaire and interviews. In general, according to the responses from the teachers and students concerned, this new…

This article describes a project that focuses on numeracy in secondary school mathematics. During the course of the project a teacher had the chance to develop and trial new tasks and styles of teaching and learning numeracy. She became increasingly comfortable with using more extended tasks for learning mathematics. However, she believes that it…

Is the time allowed for National Assessment Program Literacy and Numeracy (NAPLAN) numeracy tests sufficient? Is there any evidence that students run out of time and, if so, what are the implications for teachers who prepare students for NAPLAN numeracy tests? In each of the 2010 Years 7 and 9 numeracy tests students were required to complete 32…

Teaching through Problem Solving (TtPS) is an effective way to teach mathematics "for" understanding. It also provides students with a way to learn mathematics "with" understanding. In this article, the authors present a definition of what it means to teach through problem solving. They also describe a professional development vignette that…

In the United States, researchers argue that proof is largely concentrated in the domain of high school geometry, thus providing students a distorted image of what proof entails, which is at odds with the central role that proof plays in mathematics. Despite the centrality of proof, there is a lack of studies addressing how to integrate proof into…

In two experiments we explored the instructional value of a cross-domain mapping between "number" and "line" in secondary school students' understanding of density. The first experiment investigated the hypothesis that density would be more accessible to students in a geometrical context (infinitely many points on a straight…

Students can use geometric representations of numbers as a way to explore algebraic ideas. With the help of these representations, students can think about the relations among the numbers, express them using their own words, and represent them with letters. The activities discussed here can stimulate students to try to find various ways of solving…

Developmentally, middle school students progress from being concrete thinkers and learners to abstract thinkers. Traditional middle school mathematics instruction introduces a curriculum that is intuitive and taught within a natural trajectory of the content. However, with this traditional approach, students may miss out on being exposed to…