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,…

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…

In the literature of mean and covariance structure analysis, noncentral chi-square distribution is commonly used to describe the behavior of the likelihood ratio (LR) statistic under alternative hypothesis. Due to the inaccessibility of the rather technical literature for the distribution of the LR statistic, it is widely believed that the…

Benford's law of the "first digits" states that in spite of intuitively expected equal frequency of 1/9 of the decimal digits r = 1, ... , 9 appearance on the first place of any number, various empirical studies show another pattern of these frequencies distribution, which is log[subscript 10](1 + 1/r). The article considers this law and other…

Shortly after starting work for the University of Chichester in the School of Teacher Education, the author was planning a session relating to algebra and found herself inspired by an article in MT182: "Algebraic Infants" by Andrews and Sayers (2003). Based on the making of families of "Multilink" animals, Andrews and Sayers…

In his 1976 book, "Proofs and Refutations," Lakatos presents a collection of case studies to illustrate methods of mathematical discovery in the history of mathematics. In this paper, we reframe these methods in ways that we have found make them more amenable for use as a framework for research on learning and teaching mathematics. We present an…

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 research report describes the findings of a study on teachers' ways of interpreting student responses to tasks involving equivalent expressions. The teachers in this study were engaged in model-eliciting activities designed to promote the development of their knowledge and reveal their models (or interpretations) of their students' algebraic…

We designed and implemented curriculum intended to be used by students in an algebra-based introductory physics laboratory course. Our curricular goal was to foster, through observations in the lab, a coherent framework in students' understanding of general principles presented in the introductory mechanics course, while addressing known student…

Here is the only reference book you will ever need for teaching primary school mathematics and statistics. It is full of exciting and engaging snapshots of excellent classroom practice relevant to "The New Zealand Curriculum" and national mathematics standards. There are many fascinating examples of investigative learning experiences,…

This research explored the experiences of students in a school district that limited early access to the study of algebra and to inform education policymakers of the impact of such tracking policies on the lives and futures of the students. Quantitative analysis had already yielded a snapshot of inequities deriving from the policies surrounding…

Engaging all students in grade-level mathematics is often a challenge for teachers, especially in diverse urban classrooms. Too often in her role of supporting the development of effective practices with middle school teachers, the author observes traditional classroom instructors presenting information and demonstrating procedures. In this…

This study examined the effect of foster care experience and characteristics on educational outcomes. The typical strategy in examining the effect foster care has on educational outcomes is to compare the educational achievement of youth with foster care experience to that of their peers or to national norms. This strategy fails to take selection…

This is a summary of the May 2009 EdSource report, "Algebra Policy in California: Great Expectations and Serious Challenges." The report focuses on California's policies regarding mathematics, in particular state standards for when students should take Algebra I. It also provides a comprehensive look at state data related to both student…

To ensure that all high school graduates are prepared for the opportunities and challenges that await them, states have increasingly been focused on aligning their end-of-high school expectations with the demands of the real world. In 2005, no state had aligned their expectations with real world demands; now 29 states have adopted college- and…