When questioned, secondary mathematics teachers in rural and regional schools in Australia refer to their limited opportunities to engage and share experiences with peers in other schools as an under-utilised and cost-effective mechanism to support their professional learning and enhance their students' learning. The paper reports on the creation…

This study empirically evaluated the effectiveness of the instructional design, learning tools, and role of the teacher in three versions of a semester-long, high-school remedial Algebra I course to determine what impact self-regulated learning skills and learning pattern training have on students' self-regulation, math achievement, and…

The 2012 National Survey of Science and Mathematics Education was designed to provide up-to-date information and to identify trends in the areas of teacher background and experience, curriculum and instruction, and the availability and use of instructional resources. A total of 7,752 science and mathematics teachers in schools across the United…

Teach For America (TFA) and the Teaching Fellows programs are an important and growing source of teachers of hard-to-staff subjects in high-poverty schools, but comprehensive evidence of their effectiveness has been limited. This report presents findings from the first large-scale random assignment study of secondary math teachers from these…

Teach For America (TFA) and the Teaching Fellows programs are an important and growing source of teachers of hard-to-staff subjects in high-poverty schools, but comprehensive evidence of their effectiveness has been limited. This report presents findings from the first large-scale random assignment study of secondary math teachers from these…

The reflective ability in mathematics is a highly individual mental process, which is engaged in the course of certain types of mathematics activity. This article describes the basic meaning, characteristics, and developmental features of reflectivity in mathematics. It is suggested that reflective ability in mathematics and its relations with…

The National Council of Teachers of Mathematics [NCTM] requires students in grades nine through 12 to be able to explain inequalities using mathematical relational symbols and be able to understand the meaning of inequalities and their solutions (NCTM, 2000). Studies have shown that not only middle and high school students have difficulties with…

The current financial crisis and recession in the United States present an opportunity to discuss relevant applications of some topics in typical first-and second-year algebra and precalculus courses. Real-world applications of percent change, exponential functions, and sums of finite geometric sequences can help students understand the problems…

A proof's potential to promote understanding and conviction is one of the main reasons for which proof is so important for students' learning of mathematics. Unless students realise the limitations of empirical arguments as methods for validating mathematical generalisations, they are unlikely to appreciate the importance of proof in mathematics.…

This study compares the Programme for International Student Assessment (PISA) 2003 Mathematics results with the Trends in International Mathematics and Science Study (TIMSS) 2003 Grade 8 mathematics results, using country mean scores for 22 participants of both studies. It is found that Western countries generally performed better in PISA than in…

Prime numbers are often described as the "building blocks" of natural numbers. This article shows how the author and his students took this idea literally by using prime factorizations to build numbers with blocks. In this activity, students explore many concepts of number theory, including the relationship between greatest common factors and…

An old chestnut goes something like this. The surface area of a pond in the form of an annulus is required, but the only measurement possible is the length of the chord across the outer circumference and tangent to the inner circumference. It is a beautiful example of invariance. Invariance in mathematics usually refers to a quantity that remains…

This article gives a general overview of an alternative instructional sequence that can be used to teach integer concepts and operations. The sequence follows three heuristics from Realistic Mathematics Education (RME) that encourage curricula to be reinforced with real-world applications (financial net worth): move students gradually, yet…

The goal of this article is to present a sketch of what, following the German social theorist Arnold Gehlen, may be termed "sensuous cognition." The starting point of this alternative approach to classical mental-oriented views of cognition is a multimodal "material" conception of thinking. The very texture of thinking, it is suggested, cannot be…

This article demonstrates the significant benefits of integrating talking and writing in middle school mathematics classrooms.