# Guiding Philosophies and Beliefs

Complementary Mathematics / Guiding Philosophies and Beliefs

## Guiding Philosophies and Beliefs– Complementary Mathematics

**On Teaching:**

- Teaching is among the most honorable of all professions –and also among the most challenging and demanding.
- We all can improve our practice; you don’t have to be bad to get better.
- Teachers are the decision makers in their classrooms –
**not**the text books. - Teachers should strive for a “Profound Understanding of Fundamental Mathematics”.(Liping Ma)
- Great teachers see themselves as part of a larger collaborative process.
- Great questions posed by students need to be recognized and rewarded (in addition to great answers).
- Clarity and transparency carry the day.
- Don’t assume you know what the students are thinking –ask.
- Any topic can be presented in the most interesting and engaging manner imaginable as well as in the most boring and disconnecting manner possible –or at any stage in between.
- Balance, variety and differentiation are essential components in the development of mathematical programming (as well as to most other endeavors in life).
- The teacher should not be working harder than his/her students. If this is the case, the students could be learning more.
- There is no single best way to teach everybody, anything.

**On Learning:**

- Competence leads to confidence which leads to fulfillment. Incompetence leads to anxiety which leads to aversionand avoidance (for both students and teachers).
- Students need to experience success in mathematics early and often.
- Students can be great collaborators. Have students help select and/or develop learning activities, homeworkassignments and assessments whenever possible and appropriate.
- Students need to play an active and on-going role in the development of math programming.
- There is no concept or skill too difficult to learn if the prerequisite understandings are firmly in place and thestep to the new understanding is not too large.
- Students should always be in the process of mastering mathematical facts, equivalents, conversions, etc., (
**with deep understanding**) building on past competencies. - Rote memorization (memorization absent understanding) is largely inefficient and ineffective –and perpetuates the notion that math is mystical and cannot be fully understood. Understanding should precede formulas.
- Learning targets should be clearly defined and easily understood by students (and parents/guardians). Progress towards these targets should be documented for students to see. Students will work hard when they see measureable improvement.
- If you want to measure change, don’t change the measure.

All strategies and recommendations are supported by each of the following four seminal documents: The Common Core State Standards for Mathematics, 2010; Principals and Standards for School Mathematics (National Council of Teachers of Mathematics, 2000); Adding It Up-Helping Children Learn Mathematics (National Research Council, 2002); and Principles to Actions: Ensuring Mathematical Success for All (National Council of Teachers of Mathematics, 2014).

**Favorite quote regarding the goal of public education:….The general objects of this law are to provide an education adapted to the years, to the capacity, and the condition of every one, and directed to their freedom and happiness. **

**-Thomas Jefferson, 1782**