Guidelines for Teachers

The themes of problem-solving, communication, reasoning, and making mathematical connections have been integrated throughout the content at all grade levels. The importance of understanding the reasoning processes used to accomplish the following must be continually emphasized:

• Solve problems,
• Communicate mathematical ideas and concepts in verbal and written form,
• Connect concepts within mathematics, and
• Connect mathematics to realistic situations.

Teachers will rely heavily on cooperative learning to promote active student involvement. Diverse instructional techniques, materials, resources, and technology will be used at all levels to promote the concepts and applications of mathematics.

To provide effective mathematics instruction, teachers should:

• Develop an environment that encourages students to learn through risk-taking and exploration,
• Maintain heterogeneous grouping while providing opportunities for individual and group experiences,
• Require oral and written communication as a major component of the mathematics program,
• Promote and facilitate mathematical discussions,
• Structure mathematical discussions, questions to challenge student thinking through analyzing, synthesizing, and evaluating,
• Structure lessons that require students to think about their own thinking and the thinking of others,
• Promote problem solving, problem formation, and mathematical reasoning as an integral part of the mathematics curriculum,
• Model problem solving behaviors,
• Connect mathematical concepts to other mathematical ideas as well as to everyday life,
• Design lessons that progress from manipulation of concrete objects to pictorial understanding to abstract, symbolic representation,
• Structure lessons that encourage students to experience and develop concepts over an extended, continuous period,
• Monitor groups and individuals to encourage and facilitate student participation,
• Provide opportunities for students to become immersed in problem solving activities and encourage students to be persistent in problem solving,
• Derive mathematical activities from everyday experiences and provide opportunities for applications of acquired skills.
• Utilize student portfolios, journals, interviews, and observations of group work for assessment,
• Link conceptual understanding to skill development,
• Utilize materials, references, and personnel from outside the classroom,
• Integrate mathematics throughout the curriculum.

To promote active learning, teachers should ensure that students will:

• Participate in cooperative or collaborative learning experiences,
  
• Develop and use a variety of strategies that facilitate problem solving,
  
• Have access to manipulative materials appropriate for their grade level,
  
• Have access to hand-held calculators at all times appropriate for their grade level,
  
• Have access to computers for demonstration, individual and group use,
  
• Integrate mathematical concepts into everyday life,
  
• Participate in mathematically-based projects,
  
• Communicate mathematically, in oral and written form,
  
• Participate in study trips whenever appropriate,
  
• Develop habits of persistence and tenacity in problem solving situations
  
• Apply reasoning skills to problem solving situations.