There has been a recent push to reframe curriculum and pedagogy in ways that make school more meaningful and relevant to students' lives and perceived needs. This "relevance imperative" is evident in contemporary rhetoric surrounding quality education, and particularly in relation to the junior secondary years where student disengagement with…

This paper analyses the responses of 247 middle school students to items requiring the concept of average in three different contexts: a city's weather reported in maximum daily temperature, the number of children in a family, and the price of houses. The mixed but overall disappointing performance on the six items in the three contexts indicates…

Professional development is important for all teachers, and in low socio-economic schools where the challenges of teaching are greater this need is crucial. A model involving a combination of one-on-one peer mentoring integrated with group peer mentoring was piloted with experienced mathematics teachers of senior students in low socio-economic…

The opening lines of "How the Grinch Stole Christmas!" (Geisel 1957) set the tone for an inspiring change-of-heart story about a grumpy creature that comes to value humanity and the Christmas spirit. Although the book is often considered inspirational for other reasons, the authors were particularly moved by Dr. Seuss's interesting conjecture…

In intermediate and college algebra courses there are a number of methods for factoring quadratic trinomials with integer coefficients over the integers. Some of these methods have been given names, such as trial and error, reversing FOIL, AC method, middle term splitting method and slip and slide method. The purpose of this article is to discuss…

This paper extends work in the area of quantitative reasoning related to rate of change by investigating numerical and nonnumerical reasoning about covarying quantities involved in rate of change via tasks involving multiple representations of covarying quantities. The findings suggest that by systematically varying one quantity, an individual…

This article describes a lesson study on the area of a parallelogram for year 7 students. In Singapore, students in secondary schools are streamed into ability bands. Normal (Academic) is the label for the middle band. The teachers were convinced that Lesson Study provided a valuable platform for professional development. The authors followed the…

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…

This note presents demonstrations of quadratic expressions that come about when particular problems are posed with respect to matchsticks that form regular triangles, squares, pentagons and so on. Usually when such "matchstick" problems are used as ways to foster algebraic thinking, the expressions for the number of matchstick quantities are…

In this note, primarily intended for high school students and high school teachers, characterizations of a right triangle and an equilateral triangle in the Euclidean plane are presented using the nine-point circle of a given triangle. Geometrical applications are explored along with their possible uses in the teaching environment. (Contains 4…

The purpose of the present article is to investigate how 15-year-old Iranian students interpret the concept of equation, its solution, and studying the relation between the students' equation understanding and solving. Data from two equation-solving exercises are reported. Data analysis shows that there is a significant relationship between…

In the United States, students' learning experiences around proof is generally concentrated in the domain of high school geometry with a focus on its verification function. Thus, providing students with a limited conception of what proof entails and the role that it plays in performing mathematics. Moreover, there is a lack of U.S.-based studies…

A structural equation model of relationships among testing-related motivation variables (test value, effort, self-efficacy, and test anxiety), test-taking strategies (test tactics and metacognitive strategies), gender, and math test performance were examined with a sample of 10th graders (N = 438; 182 males and 256 females). In general, motivation…

Discourse requires students to evaluate and interpret the perspectives, ideas, and mathematical arguments of others as well as construct valid arguments of their own. That is, students develop deeper understandings of mathematics when they engage in meaningful social interactions such as whole class discourse. Both the National Council of Teachers…

A key characteristic of successful mathematics teachers is that they are able to provide varied activities that promote student learning and assessment. Web 2.0 applications can provide an assortment of tools to help produce creative activities. A Web 2.0 tool enables the student to enter data and create multimedia products using text, graphics,…