|Second Look - Asking Good Questions|
Talking about the Greek Cross
Meaningful mathematical discourse occurs when tasks are chosen carefully and the teacher steps back and allows students to move to the forefront of their own learning.
Investigating Mathematical Thinking and Discourse with Ratio Triplets
Describes a unique task structure that helps foster classroom discourse and reveals students' mathematical conceptions. The example involves a proportional reasoning task set within a best-buy context. Three versions of the task are provided which encourage students to consider the meaning of ratios in multiple ways. Several student responses are provided and analyzed.
Talking Generally or Generally Talking in an Algebra Classroom
The ways in which four eighth-grade girls, each with varying levels of algebraic understanding, share ideas, debate, and gradually move toward generalizations inherent in the “Painted Cube” problem. The intent of this article is to examine how students move to progressive formalization and to provide insights into the ways that teachers can foster similar processes among their students.
Illuminations Lesson: Classic Middle-Grades Problems for the Classroom
lesson presents two classic problems (Mangoes Problem and Sailors and Coconuts)
that can be represented and solved in several different ways. Middle-grades
students work in groups on the problems to promote communication of
mathematical ideas, and a variety of classroom solution attempts are described.
Communication Standard - Pre-K through Grade 12
Instructional programs from prekindergarten through grade 12 should enable all students to— organize and consolidate their mathematical thinking through communication; communicate their mathematical thinking coherently and clearly to peers, teachers, and others; analyze and evaluate the mathematical thinking,