This article offers an engaging application that adds meaning to the binomial theorem. (Contains 8 figures.)

This study investigates the role of graphing calculators in multiple representations for knowledge transfer and the omission of oversimplification in complex function graphs. The main aim is to examine whether graphing calculators were used efficiently to see different cases and multiple perspectives among complex function graphs, or whether…

Recent international studies have highlighted the success of students from Hong Kong in mathematics and problem-solving, and have begun to suggest some of the factors associated with this success. Other studies have suggested that Hong Kong students are averse to risk-taking, favouring memorisation and imitation in their solution strategies. Year…

This article describes the A, E, I, O, U technique, designed to help teachers ensure that teaching and learning are not mutually exclusive in the classroom. Most teachers would agree that motivating average teenagers to communicate how they got an answer or justify their problem-solving strategies can be as difficult as teaching a dog to whistle.…

The authors have attempted to implement "less is more" in a variety of educational contexts. The schools they have been part of include a pilot school in Boston, New Mission High School(New Mission), a charter school in Fitchburg, North Central Charter Essential School (NCCES), and a charter school in Devens, Francis W. Parker Charter…

This article presents some identities on the sum of the entries in the first half of a row in Pascal's triangle. The results were discovered while the author was working on a problem involving Laplace transforms, which are used in proving of the identities.

This article considers an old version of the classical pursuit problem as posed by Francis Godwin in 1599, who imagines a wedge of swans flying from the earth to the moon in twelve days, always flying at constant speed toward the moon. The return trip, during which the swans always fly toward the earth at the same speed, takes eight days. A little…

This text has been centered on two main ideas: the specifications of a good problem to be introduced in a classroom; and according to Freudethal's view, the importance of teaching the students how to apply mathematics in their own real life problems. Putting these two ideas together, we may conclude that historical real world problems fit the…

This study examined practices of teachers in Wake County Public Schools (WCPSS) high school Algebra I classes. Regression analyses of standardized state testing results allowed for identification of the most effective and least effective Algebra I teachers and schools. The study used surveys, observations, and focus group interviews to compare and…

In order to collaborate effectively in group discourse on a topic like mathematical patterns, group participants must organize their activities in ways that share the significance of their utterances, inscriptions, and behaviors. Here, we report the results of a ethnomethodological case study of collaborative math problem-solving activities…

This article deals with evaluating an interactive learning environment (ILE) during the iterative-design process. Various aspects of the system must be assessed and a number of evaluation methods are available. In designing the ILE Ambre-add, several techniques were combined to test and refine the system. In particular, we point out the merits of…

A case study approach was adopted to investigate two thinking skills programmes for a maximum variation sample of five- to six-year-olds in four schools, in two local authorities (LAs), in England and Wales, using multiple methods. School staff interviewed felt that thinking skills programmes enhanced critical thinking skills and improved use of…

In this book, Bob Hogan and Char Forsten introduce American mathematics educators to the model drawing process adapted from the much-acclaimed Singapore approach. They explain what model drawing is and why it's such an effective problem-solving tool. They show exactly how teachers can guide their students through the process, tell which key points…

The aim of this study is to characterize the discourse of two problem-solving courses for prospective teachers. The data, consisting of audio recordings and field notes, were examined from a dialogical approach combined with the theory of contextualization. I show not only the substantial differences between the two classroom discourses but also…

"Mathematical literacy" implies that a person is able to reason, analyze, formulate, and solve problems in a real-world setting. Mathematically literate individuals are informed citizens and intelligent consumers. They have the ability to interpret and analyze the vast amount of information they are inundated with daily in newspapers, on…