Arithmetic was the first mathematical subject to enter the school curriculum in the United States in a formalized manner. Until the first quarter of the nineteenth century, the prevailing pedagogy of this subject revolved around the tenets of mental discipline theory and the rules method of teaching, which valued memorization and repetitive drill…

There is a vital need in the mathematics and science teaching and learning community at the secondary school level for assistance for teachers in adapting curricular materials to meet the many district, state, and national demands and to facilitate high-quality learning of students and their ability to transfer this learning and apply it as they…

With the adoption of the "Common Core State Standards for Mathematics" (CCSSM), the process of mathematical modeling has been given increased attention in mathematics education. This article reports on a study intended to inform the implementation of modeling in classroom contexts by examining students' interactions with the process of…

Mathematical problem posing is an important skill for teachers of mathematics, and relates readily to mathematical creativity. This article gives a bit of background information on mathematical problem posing, lists further references to connect problem posing and creativity, and then provides 20 problems based on the multiplication table to be…

Teaching and learning of mathematical modelling has become a key competence within school curricula and educational standards in many countries of the world. The term mathematical modelling, its meaning, and how it can be implemented in mathematics lessons have been intensively discussed during several Conferences of the European Society for…

The dictionary definition of constraint is one-sided, solely restrictive. The problem-solving definition is two-sided. Constraints come in pairs. One retains its restrictive function, precluding something specific; the other directs search for its substitute. The paired constraint model is applied to both domain and classroom. I discuss the…

This paper discusses an alternative approach for developing problem solving experiences for students. The major argument is that students can develop their creativity by engaging in collaborative problem solving activities in which they apply a variety of mathematical methods creatively to solve problems. The argument is supported by: considering…

With the implementation of the National Council of Teachers of Mathematics recommendations and the adoption of the Common Core State Standards for Mathematics, modeling has moved to the forefront of K-12 education. Modeling activities not only reinforce purposeful problem-solving skills, they also connect the mathematics students learn in school…

The purpose of this article is to present five examples of teacher leadership from within secondary mathematics classrooms. These vignettes come from a larger study that resulted in a teacher leader continuum. This article offers classroom teacher examples that highlight each of five positions along that continuum. The argument is made that a wide…

Leaders in mathematics are responsible for implementing positive change within their school districts and motivating teachers of mathematics to improve their practices. One way mathematics leaders can achieve this goal is by establishing professional collaborations. We analyzed the research and summarized the common attributes found in successful…

During the last few decades, equity concerns have become a priority for some researchers and mathematics (education) organizations. Scholars have begun to address issues of equity through a critical lens (e.g., Boaler, 2007; Darling-Hammond, 2005; Martin, 2003) in their work and scholarship. In this article, the author seeks to add to the equity…

This paper aims to tell how the Russian national examination in mathematics (the Uniform State Examination or USE) has been conducted most recently. The author must say at once that the history of the system of secondary school graduation examinations or even the history of the USE will be covered only to the small degree that is necessary for…

The National Curriculum Framework 2005 envisions a reformed curriculum that connects knowledge and learning to the child's context. While concerns of equity, accessibility, and social transformation have been aimed through education, the crucial link of "teacher"--instrumental in realizing these aims--seems missing. This study explores…