In this book, the author offers a wide selection of student engagement strategies for math teachers in grades K-12. He shares his class-tested ideas in a clear and spirited voice, with his devotion to the teaching profession and his students apparent on every page. With invaluable ideas to help students remain engaged for longer time periods, this…

This phenomenological study investigates conceptions of statistical variation that secondary mathematics teachers who are recognized leaders in AP Statistics exhibit. This study also investigates perceptions and recollections of activities and actions that teachers who exhibited robust understandings of variation suggest contributed to their…

Learning in educational settings emphasizes declarative and procedural knowledge. Studies of expertise, however, point to other crucial components of learning, especially improvements produced by experience in the extraction of information: perceptual learning (PL). We suggest that such improvements characterize both simple sensory and complex…

Many academics like to isolate a piece of the world to study: an important social issue, a central philosophical problem, a key moment in history. They know they're oversimplifying but they do it anyway--it's the only way to make progress, and what's more, their little worlds are often more beautiful than the real one. This paper shares a story of…

This article presents data from a group of secondary pre-service teachers who used vee diagrams to illustrate their conceptual and methodological analyses of a problem, as part of a required mathematics methods course assignment. The individually constructed vee diagrams were analysed in terms of the extent to which they displayed principles and…

We describe how 1 Algebra I teacher and her 8th-grade students used meta-representational knowledge when generating and evaluating equations to solve word problems. Analyzing data from a sequence of 4 lessons, we found that the teacher and her students used criteria for evaluating equations, in addition to other types of knowledge (e.g., different…

The objective of this study was to investigate and characterize the geometric thinking and understanding of four pre-service middle and secondary mathematics teachers while considering their spatial ability levels. To investigate the differences, if any, that existed among these pre-service middle and secondary teachers with different spatial…

In November 2007 a joint ATM/MA team began working together to consider how ICT can be used to support the teaching and learning of topics that are considered to be "hard to teach" in secondary mathematics, within a project that complements that of the Secondary National Strategy. In the best subject association spirit, it was decided to…

From preliminary analysis of teacher-nominated examples of successful technology-supported practice in secondary-school mathematics, the use of graphing software to teach about algebraic forms was identified as being an important archetype. Employing evidence from lesson observation and teacher interview, such practice was investigated in greater…

Handheld graphing technologies have fundamentally been utilized in the teaching and learning of many secondary school and college mathematics concepts. In order to observe the effects of these new kinds of technologies on students' learning of mathematics, their teachers need to decide whether it is reasonable to do, learn, and teach mathematics…

Rapid increases in knowledge and technology call for the use of such tools as a personal digital assistant (PDA) to increase the quality of education and student performance. PDAs evolved from personal organizers, but today's handhelds can be effective tools that help students organize facts and concepts, develop written documents, understand…

In this article, the authors share an episode from an after-school program and focus on eight of the twenty-four urban, sixth-grade students who volunteered to work on mathematical problem solving. When students are given a supportive environment, open-ended tasks, and thoughtful teacher questioning, their reasoning can develop naturally. By…

If students are to understand inferential statistics successfully, they must have a profound understanding of the nature of the sampling distribution. Specifically, they must comprehend the determination of the expected value and standard error of a sampling distribution as well as the meaning of the central limit theorem. Many students in a high…

For over a decade, research studies of mathematics education in high-performing countries have pointed to the conclusion that the mathematics curriculum in the United States must become substantially more focused and coherent in order to improve mathematics achievement in this country. To deliver on the promise of common standards, the standards…

The end of 7th grade provides an important moment to assess how prepared California's students are to succeed in the more advanced math curriculum that starts with algebra. At a minimum, all California students are required to successfully pass Algebra I in order to receive a high school diploma. But Algebra I also functions as the gateway to more…