The importance of student understanding of the concept of place value cannot be underestimated. Place value is a "gate keeper" in developing mathematical understanding. The purpose of this study was to examine and develop a teacher-made test of place value knowledge. The questions were developed using the progressions from the Number…

In 2002/03, the Charlotte-Mecklenburg Schools in North Carolina initiated a broad program of accelerating entry into algebra coursework. The proportion of moderately-performing students taking algebra in 8th grade increased from half to 85%, then reverted to baseline levels, in the span of just five years. We use this policy-induced variation to…

Defining what teachers need to know to teach algebra successfully is important for informing teacher preparation and professional development efforts. Based on prior research, analysis of video, interviews with teachers, and analysis of textbooks, we define categories of knowledge and practices of teaching for understanding and assessing teachers'…

There is wide acceptance that there are teacher shortages, particularly in physics, chemistry and mathematics, and in rural and hard to staff schools. An issue that arises because of this shortage is teachers teaching subjects that they are not qualified to teach. In this paper, I draw on my research and that of others to outline the issues for…

There remains a lack of empirical evidence about the relationship between the level of mathematics studied at high school and within tertiary degrees and primary school pre-service teachers' success in curriculum subjects. Further, there is little evidence to inform the structure and delivery of mathematics teacher preparation. In this study, the…

With increased accountability attached to students' results on national testing in Australia, teachers feel under pressure to prepare students for the tests. However, this can lead to shallow teaching of a narrowed curriculum. An alternative approach involves using data to identify common errors and misconceptions, discussing strategies aimed at…

Teachers can use geometric patterns to promote students' understanding of functional relationships. In this article, the authors first look at a problem-solving process that supports the use of figural reasoning to explore and interpret geometric pattern tasks and generalize function rules. Second, the authors discuss a framework for…

This study reports how the difficulty of simple worded percentage problems is affected by the problem structure and the complexity of the numbers involved. We also investigate which methods students know. Results from 677 Year 8 and 9 students are reported. Overall the results indicate that more attention needs to be given to this important topic.…

This paper explores the infusion of financial literacy into the Mathematics curriculum in a secondary school in Singapore. By infusing financial literacy, a core theme in the 21st century framework, into mathematics education, this study investigated the impact of using financial literacy-rich mathematics lessons by using validated learning…

"PLATO[R] Achieve Now" is a software-based curriculum for the elementary and middle school grades. Instructional content is delivered via the PlayStation Portable (PSP[R]) system, allowing students to access learning materials in various settings. Software-based assessments are used to customize individual instruction, allowing students…

For nearly three decades, during which the author taught everything from basic algebra to advanced placement calculus, the author thought of himself as a secondary school mathematics teacher. The notion of teaching elementary school math never appealed to him because of its simplicity. The author stresses that anyone could teach children to count,…

During the last decades of the twentieth century, changes in school curricula have resulted in proof-free or proof-lite curricula. In this article, the author argues that proof is, and should be seen to be, a central component in the school curriculum--from at least the middle of the primary years and upwards. He identifies proof with problem…

The transformations found in secondary mathematics curriculum are typically limited to stretches and translations (e.g., ACARA, 2010). Advanced students may find the transformation, twist, to be of further interest. As most available resources are written for professional-level readers, this article is intended to be an introduction accessible to…

The increase in the diversity of students and the complexity of their needs can be a rich addition to a mathematics classroom. The challenge for teachers is to find a way to include students' interests and creativity in a way that allows for rigorous mathematics. One method of incorporating the diversity is the development of "open-ended…

A mathematical theory of peer instruction describing the increase of the normalized number of correct answers due to peer discussion is presented. A simple analytic expression is derived which agrees with class data. It is shown that our theory is connected to the mathematical learning models proposed by Pritchard et al. It is also shown that…