Glen Richgels' 7 Teaching and Learning Principles

1. Teach the way kids learn.

This is the number one and primary principle. Pay attention to your students. Pay attention to their learning. They are more important than rigid, sequential curricula.

2. Use group work.

Groups should not be homogenous. Try for as much heterogeneity as possible. There should be 3-4 students in a group. Sometimes groups of 2 are better, but in general 3-4. Change groups approximately once a month. Watch so that more average achievers get help and attention.

3. Utilize student <=> student communication

Group work will facilitate this. There is no replacement for time for students to digest what the teacher has been saying or for students to make their own discoveries.

4. Utilize teacher <=> student communication

Too many teachers teach in only one direction, the teacher as source of knowledge in the classroom. The teacher needs to take the time to listen, and this is in many forms observation, discussion, journals, … . The teacher knows what they said, teachers need to take the time to find out what the students heard. Based upon what the students heard, instruction may have to be altered.

5. Encourage multiple solution paths

The old practice of having all students do things exactly the same way destroys creativity; destroys student motivation to problem solve. In traditional instruction students waited for the teacher to dispense how to do things and then follow the steps like mindless robots. Allowing/encouraging multiple solution paths will mean more work for the teacher, but does help sustain and encourage creativity. This is needed more as we prepare students for unknown futures. This has been an NCTM priority since the 1980s.

6. Utilize problem solving and contextual settings for material

Students who see how mathematics is used and use it to solve problems, retain the material longer and learn it deeper than through rote memorization or with naked symbol practice.

7. Assessment

Assessment has two purposes. The evaluation of what students have learned for the assignment of grades is the first purpose. This is a necessary evil of the teaching profession. Second and more important is the assessment of student learning for the purpose of altering instruction. As a teacher assesses students over time, the teacher learns how students learn, this impacts principle one. Teachers should consolidate what they learn about student learning through assessments to help them refine their ideas/knowledge of how students learn.