1. The Development of Mathematical Proficiency: Using Learning Research, Assessment, and Effective Instruction

2. the understanding how students learn math;
There are 3 essential parts needed to develop mathematical proficiency of all students in a world of differences:
the understanding how students learn math;
the application of assessment techniques to analyze student learning;
the planning and execution of quality mathematical experiences to ensure continued growth based on what was learned during the assessments.

3. Brain research adds new insights for mathematics instruction.
Many studies fit well with the developmental learning theories that stress active learning with growing complexity of mental structures. The insights have led educators to coin the phrase, “Learning is Action”.
Still, other insights fit well with the theories of information processing and their diversified ways of storing and retrieving information in the brain, leading to the phrase, “Learning is Process”.

4. “Learning is Action”
Our brains are resilient and flexible. One part of the brain is capable of taking over the actions normally done by another part if the need arises. The more stimulation children receive in their environment, the more they can interact with the things around them. The more interaction a person has with the environment, the more diversified neural connections are made inside the brain. These connections, or networks, are how we learn and remember. Thus, the more mentally active the learning task, the greater the brain activity – thus Learning is Action.

5. “Learning is Process”
If the neural connections are not continually activated, knowledge governed by that network connection will be lost. Brain research supports the idea that neural connections must be used if they are to remain vital in the life of human beings. There must be a constant encoding, storing, and retrieving of learned information if it is to remain vital – “use it or lose it.”

6. Learning Theories & Math Instruction
Learning is Action
Cognitive/Constructivist Theories~ believed that children must be allowed to experiment physically with the things around them if they are to learn.
Jean Piaget
Lev Vygotsky
Learning is Process
Information Processing Theories~ there must be a constant encoding, storing, and retrieving of learned information if it is to remain vital.
Sensory Pathways
Thought Processing
Learning Styles
Multiple Intelligences