Ensuring a high quality of teaching mathematics to students is inextricably linked with teaching how to solve creative mathematical problems. These problems traditionally include tasks of high educational, developmental and diagnostic value. Teaching how to solve such problems allows training graduates with the highest level of the subject…

The present study focused on the lack of knowledge of the double use of brackets in arithmetic expressions and the difficulty in the operatively of expression for mathematics application at the school level. Learning the other rules and formulas of mathematics involves learning the use of a bracket. Binding is useful in both arithmetic and…

Searching for loci belongs to classical topics of school curricula at schools of different levels all over the world. In the text investigation of loci by GeoGebra using the command "LocusEquation," the tool which has recently been implemented into GeoGebra and which brings a new approach in searching for loci of points, is given. This…

The International Association for the Evaluation of Educational Achievement (IEA) Research for Education series represents a further effort by IEA to capitalize on it's unique datasets, so as to provide powerful information for policymakers and researchers. Each report focuses on a specific topic and is produced by a dedicated team of leading…

This book is inspired by Roger E. Howe's contributions to the international communities of mathematics and mathematics education. Renowned for his research contributions in the fields of representation theory, automorphic forms, harmonic analysis, and invariant theory, Dr. Howe has also fundamentally deepened our understanding of the mathematics…

New strategies can ignite teachers' imagination to create new lessons or adapt lessons created by others. In this article, the authors present the experience of an algebra teacher and his students solving linear and literal equations and explain how the use of ideas found in past NCTM journals helped bring this lesson to life. The…

This article explores the potential for aspects of abstract algebra to be influential for the teaching of school algebra (and early algebra). Using national standards for analysis, four primary areas common in school mathematics--and their progression across elementary, middle, and secondary mathematics--where teaching may be transformed by…

Teachers' knowledge of the early algebra content that is to be taught is crucial for effective pedagogy and ensuring that the students' understanding of early algebra is not flawed. This article reports the findings of two of the activities that a group of in-service teachers participated in during a professional learning intervention program that…

We would like to share with you our ongoing experiences with "hands-on statistics" lessons we have recently carried out. We have developed a new experimental path for teaching young students using fundamental concepts of "statistics": uncertainty of the measurement, the uncertainty of the mean, the mean itself, etc. The methods…

Research supports special educators' use of progress-monitoring data for instructional decision-making purposes as an evidence-based practice for improving student achievement. This article describes the Professional Development for Algebra Progress Monitoring (PD-APM) system. PD-APM, is an online system that includes two "hubs" that…

In 2000, the "National Council of Teachers of Mathematics" recommended that Algebra Standards, "instructional programs from prekindergarten through grade 12 should enable all students to use mathematical models to represent and understand quantitative relationships." In this article, the authors suggest the "Balance"…

Many students have trouble grasping algebra. In this book, bestselling authors Judith, Gary, and Erin Muschla offer help for math teachers who must instruct their students (even those who are struggling) about the complexities of algebra. In simple terms, the authors outline 150 classroom-tested lessons, focused on those concepts often most…

Teachers of mathematics recognize the difficulty of reaching every student when the range of student abilities puts a considerable strain on the classroom discussion and time. In a response to the problem, students are grouped so that those with greater mathematical aptitude help those who have difficulties. While this approach is to be…

In-service teacher professional development has been used to improve teacher effectiveness. In Kentucky, the National Science Foundation funded a large professional development program called the Appalachian Math and Science Partnership (AMSP) to provide content-based professional development to teachers in rural schools. We show that students…

Algebraic structures are a necessary aspect of algebraic thinking for K-12 students and teachers. An approach for introducing the algebraic structure of groups and fields through the arithmetic properties required for solving simple equations is summarized; the collective (not individual) importance of these axioms as a foundation for algebraic…