This Brief Report summarizes case studies of the classroom teaching practices of 2 algebra teachers. The data consist of videotaped classroom observations during 1 academic year. The study identifies and characterizes specific teaching practices that establish the norm that the teacher is the sole arbiter of mathematical correctness in the…

In the move from elementary to middle school mathematics, students encounter major changes in instructional materials and approaches, work expectations, school structure, and general level of difficulty in material. Research shows that, in general, students suffer significant declines in academic achievement in the transition from elementary…

These Proceedings are a written record of the research presented at the 33rd Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (PME-NA 2011) held in Reno, Nevada, October 20-23, 2011. The theme of the conference is Transformative Mathematics Teaching and Learning. The Proceedings…

This article draws on the 21st Century Skills Movement and the successful teaching practices of Asian schools in order to provide five suggestions that secondary math teachers can incorporate into their classrooms in order to promote the skill set necessary for an ever-changing global economy. Problem-based instruction, student-led solutions, risk…

For more than a hundred years there has been a debate about the sequence in which high school science should be taught. Many advocates of "Physics First" support a more conceptual ninth-grade physics course followed by chemistry and then biology while supporters of mathematically rigorous physics favor a sequence of biology-chemistry-physics. This…

This article describes one prevalent practice that a group of 6th- and 7th-grade students engaged in when they used fractions in the context of area and perimeter, decimal operations, similarity, and ratios and proportions. The study's results revealed that students did not simply take the concepts and skills learned in formal fractions units and…

The mathematics methodology subjects the author undertook in the early 1980s encouraged him to adopt a very expository style of teaching in which each new concept is introduced by its formal definition. The teacher should then explain a few carefully chosen examples for students to copy into their books, and then provide plenty of graded practice…

This article presents a guided investigation into the spacial relationships between the centres of the squares in a Fibonacci tiling. It is essentially a lesson in number pattern, but includes work with surds, coordinate geometry, and some elementary use of complex numbers. The investigation could be presented to students in a number of ways…

Students often struggle with the connection between algebraic and graphical representations of functions. This overview of the history of the Cartesian coordinate system helps the classroom teacher consider new ways to aid students in making the "Cartesian connection." (Contains 7 figures.)

This "Brief Report" summarizes results from a study that investigated joint effects of two innovations adopted at a high school in an affluent suburban community in the northeast United States: 4 x 4 block scheduling and the "Standards"-based curriculum, the Interactive Mathematics Program (IMP).

Left to their own devices, many students are happy to work within their comfort zone of skill and understanding, a level where they are confident that they will achieve regular success. The job of the classroom teacher is to help students reach beyond this and to help them make this level their new comfort zone. Clearly, teachers need to employ a…

Algebra is one of those hard-to-teach topics where pupils seem to struggle to see it as more than a set of rules to learn, but this author recently used the software "Grid Algebra" from ATM, which engaged her Year 7 pupils in exploring algebraic concepts for themselves. "Grid Algebra" allows pupils to experience number,…

Proportional thinking is the mathematical basis of a wide range of topics in the middle-school mathematics curriculum. While the concept is obvious in the traditionally-named ratio and proportion sections, proportional thinking is also the key to such diverse topics as rate, gradient of a linear function, similarity, trigonometry and percentage,…

We often look for a best-fit function to a set of data. This article describes how a "pretty good" fit might be better than a "best" fit when it comes to promoting conceptual understanding of functions. In a pretty good fit, students design the function themselves rather than choosing it from a menu; they use appropriate variable names; and they…

This article describes an activity for developing the notion of association between two quantitative variables. By exploring a collection of scatter plots, the authors propose a nonstandard "intuitive" measure of association; and by examining properties of this measure, they develop the more standard measure, Pearson's Correlation Coefficient. The…