1. Activity-Oriented Mathematics
"Good mathematics is NOT how many answers you know… but how you behave when you don't know." Author unknown
A teacher establishing an effective learning environment for mathematics recognizes this and encourages behaviors and actions of learners that promote mathematical understanding.

2. Activity-Oriented Mathematics
Question: How do you decide how much time to provide learners to explore sound math and grapple with significant math problems?
Question: How does the way you've arranged the room (e.g., the seating, the location of materials, etc.) affect the learners' learning of mathematics?
Question: How does one provide appropriate contexts to encourage the development of mathematical skills and proficiency?

3. Activity-Oriented Mathematics
Question: What do you do about the learner who says that he/she doesn't like math or is afraid of math?
Question: Do learners ask questions in math or make conjectures? Do you encourage this? How?
Question: What do your learners do that sends the message that they are making sense of math? How do you encourage that?

4. Creating the Environment
Provide sufficient time for learners to explore significant mathematics.
Provide sufficient time to grapple with important ideas and problems.
Consult your schools curriculum documents to aid you in identifying those important ideas.

5. Creating the Environment
Consider the ways children think and learn mathematics.
Make use of appropriate models.
Use the physical space available in your classroom in ways that facilitate understanding of mathematics.

6. Creating the Environment
Think about the value and utility of the mathematics that you want the learners to learn.
Share with your learners this value and utility. Where in the world might they encounter such mathematics? Make their learning relevant whenever possible.

7. Creating the Environment
Become as knowledgeable of the mathematics content as you can.
Become as knowledgeable of the effective ways of learning that content as you can.
Be aware that there is no requirement that children must like mathematics, but that your job may be to help them to develop an appreciation for mathematics.

8. Creating the Environment
Encourage all learners to work independently or collaboratively as needed to make sense of mathematics.
Encourage learners to ask questions, to make and share mathematics conjectures, and have them provide reasons to support their conjectures.
Provide a "risk-free" environment that encourages meaningful "grappling" with significant mathematics.