Helping and Getting Help—Essential Skills for Effective Group Problem Solving

Seventh grade teacher: “My students have been working together in groups for a while now. They're getting along fine. But I'm finding that a lot of them still don't understand the work. I tell them to ‘work together’ and that it is all right to help each other. Sometimes I worry that they are only giving each other the answers. How can I get them to focus on problem solving and not just putring down the right answer?”

Implementing The Professional Standards for Teaching Mathematics: Linking Teaching, Learning, and Assessment

The sixth standard in the Professional Standards for Teaching Mathematics (NCTM 1991) focuses on analyzing and interconnecting teaching and learning. The standard calls for the analysis of teaching and learning to be ongoing by “[o]bserving, listening to, and gathering other information about students to assess what they are learning.” Teachers examine the “[e]ffects of the tasks, discourse, and learning environment on students' mathematical knowledge, skills, and dispositions.”

Research into Practice: Concrete Materials and Teaching for Mathematical Understanding

Today we find common agreement that effective mathematics instruction in the elementary grades incorporates liberal use of concrete materials. Articles in the Arithmetic Teacher no longer exhort us to use concrete materials, nor does the Professional Standards for Teaching Mathematics (NCTM 1991) include a standard on the use of concrete materials. The use of concrete materials seems to be assumed unquestioningly.

IDEAS

The “IDEAS” section for this month focuses on connections among mathematics, concern for the environment, and conservation of natural resources. Each activity allows opportunities for communicating, reasoning, and problem solving as students become personally involved in helping to conserve natural resources. This investigative approach that connects mathematics to students' everyday lives is recommended in the Curriculum and Evaluation Standards for School Mathematics (NCTM 1989).

Teacher to Teacher: Making Story Problems Relevant

My third-grade class struggled with understanding “story” problems—that is, mathematics problem written in sentences— until one day I decided to put problems into a familiar form, making them relevant to children's lives.

Empowering Students with “The Math Connection”

In Franklin County, Massachusetts, students, are making mathematical connections with “The Math Connection” television show, and the results are quite exciting.