Twenty-five years of teaching grades 8-12 mathematics has shown the author that students learn best when they can construct their own knowledge (constructivism) and that students, given appropriate guidance, can and will take on responsibility for their own learning (self-regulation theory). This article describes some classroom tools that she has…

Retaining mathematical knowledge is difficult for many students, especially for those who learn facts and procedures without understanding the meanings underlying the symbols and operations. Repeated practice may be necessary for developing skills but is unlikely to make conceptual ideas stick. An idea is more likely to stick if students are…

Research shows that the greatest gains in student learning in mathematics classrooms occur in classrooms in which there is sustained use of high cognitive demanding tasks throughout instruction (Boston and Smith 2009). High cognitive demanding tasks, which this article will refer to as rich tasks, are mathematics problems that are complex, less…