Guiding Principles for Teaching Mathematics


“The type of mathematics instruction that involves students actively and intellectually requires much from the teacher. Without thoughtful decisions about the particular activities and without thoughtful interactions with students, potentially powerful mathematical experiences can become little more than interesting activities ….” 

                                                                                    – Kathy Richardson


1.      Our top priority is the development of students’ thinking and understanding. Students need to verify their thinking for themselves rather than depend upon an outside authority to tell them if they are right or wrong. We must see our job as setting up appropriate situations, asking questions, listening to students, and focusing the attention of the students on important elements rather than trying to teach a concept through explanations.

                                  Student Discourse: Finding Half from (Chris) on Vimeo.

2.      We must not expect all students to get the same thing out of the same experience. We must provide activities that have the potential for being understood at many different levels. Further, activities must be provided over time so that students develop skills and proficiencies from their understanding.

                                  Hearing All Voices from (Chris) on Vimeo.

3.      We recognize that partially grasped ideas and periods of confusion are a natural part of the process of developing understanding. When a student does not reach the anticipated conclusion, we must resist giving an explanation. Instead, we must ask a question or pose a new problem that will give the student the opportunity to contemplate evidence not previously considered.

                                  Grappling with Fractions from (Chris) on Vimeo.

4.      We must help students develop persistence in solving problems. Only in a learning environment in which mistakes and confusion are considered to be a natural part of the learning process can students believe they do not have to come up with quick, right answers.

                                  Field Day Conversation from (Chris) on Vimeo.

5.      We must value the development of mathematical language, both written and verbal.  Language serves to internalize and clarify thinking and to communicate ideas. Putting thought into words requires students to organize their thinking and to confront their incomplete understanding.

                                  Ansol Solves Division Problems from (Chris) on Vimeo.