As a beginning teacher, the author was often surprised when marking tests. She thought students understood the material, but their tests told a different story. She had simply been assuming that students understood, but she had not actually checked until it was too late to do anything about it. She needed some quick ways to gauge student…

Assessment and instruction are interwoven in mathematically rich formative assessment tasks, so employing these tasks in the classrooms is an exciting and time-efficient opportunity. To provide a window into how these tasks work in the classroom, this article analyzes summaries of student work on such a task and considers several students'…

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…

In many mathematics classrooms, the teacher provides "worked examples" to demonstrate how students should perform certain algorithms or processes. Some students find it difficult to generalize from the examples that teachers provide and cannot apply what they have learned in new situations (Watson and Mason 2002). Instead, teachers might…

The lesson study model of professional development that originated in Japan is becoming increasingly popular in the United States. At its core, lesson study is a means of bringing teachers together to carry out the process of planning a lesson, implementing and observing it, and then examining it during a debriefing session. The debriefing…

Presents a technique used during the first five minutes of class that elicits from students written responses to questions of their understanding of mathematical content or their attitudes toward their mathematics class specifically, or mathematics in general. Provides sample questions from algebra, geometry, and general mathematics. (MDH)

Describes a project to explore how mathematics teachers can use assessment of students' learning to shape their own instructional practices. The project had two goals: (1) to make sense of what students understand, how they understand it, and what counts as evidence of understanding; and (2) to use analysis of materials that document students'…