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December 2007, Volume 14, Issue 5


Assessing Students' Understanding through Conversations
Cecilia Vanderhye and Cynthia Zmijewski Demers
How teachers can use students' conversations to assess their mathematical understanding. Examples from third, fourth, and fifth grade classrooms highlight how mathematical conversations were used in different lessons to assess student understanding and differentiate instruction. Teachers will gain a clear understanding of questioning and communication techniques to better assess student learning.

Mathematics and the Learning Cycle: How the Brain Works As It Learns Mathematics
Ronald Zambo, Debby Zambo

The authors of this article merge information about the learning cycle with NCTM's constructivist view to help teachers of mathematics understand their students. By learning about how the brain works and how the learning cycle happens in the brains of children, teachers will better understand how to approach teaching and learning in the mathematics classroom.

Assessing Students’ Levels of Understanding Multiplication through Problem Writing
Jill Mizell Drake and Angela Barlow
The potential of problem writing as a technique for assessing the depths of students' mathematical understandings. Discussions include sample student-generated word problems and connections between problem writing and the Process Standards. Teachers will understand how to use problem writing as assessment in the mathematics classroom.

Read how you can use this journal article as a Professional Development Experience.

Using Item Analyses and Instructional Conversations to Improve Mathematics Achievement
Douglas Fisher and Donna Kopenski
The significant gains in student achievement in an urban elementary school when teachers worked together to develop, administer, and review assessment items. In grade-level teams, teachers completed item analyses and engaged in instructional conversations about students’ needed instruction. Readers of this article will learn how to plan for, write, and assess student assessments to guide teaching and student learning.

What's Your Angle on Angles?
Christine Browning, Gina Garza-Kling, and Elizabeth Hill Sundling
How several key activities can be used to help elementary students develop a more complete understanding of the concept of angle. Includes student examples from a sixth grade class. Teachers will learn how to develop strong lessons to teach or re-teach this concept in the mathematics classroom.

Preparing for Problem Solving
Becky Holden
A first grade teacher incorporates Cognitively Guided Instruction (CGI) into her lessons and cultivates the learning environment necessary to support CGI. Readers of this article will learn how to assess student learning and differentiate in the classroom for more effective mathematics instruction using CGI.

Watch What You Say
Sally Roberts
Student misconceptions about quadrilateral properties make a case for the importance of teachers not only knowing where their students have been and where they are in terms of their learning, but also where their current learning will lead them. Suggested classroom activities are included for teachers to gain a clearer understanding of how to teach students about quadrilaterals.

Read how you can use this journal article as a Professional Development Experience.

Curriculum Focal Points: What's Your Focus and Why?
Francis Fennell
This article from NCTM president Skip Fennell introduces a four-part series exploring the use of Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics: A Quest for Coherence (NCTM 2006). Readers will gain information on how the Focal Points will help with math education in the classroom.