Brain Research: Implications for Mathematics Education

2 The Best Learning Comes from Emotionally Safe Non-threatening Environments

The Brain is Designed for Survival  Physical  Social  Emotional

4 The Brain is Poorly Designed for Formal Instruction. It is not designed for efficiency and order.

5 New Concepts are Difficult to Grasp at First Because There are No Networks to Create the Associations

Three Factors Critical to Constructing Meaning  Relevance  Emotion  Context/Pattern

You Can Either Have Your Students’ Attention OR They Can Be Making Meaning For Themselves, But Never at the Same Time 7

Rate of Learning and Rate of Retrieval are Independent 8

All Learning Requires the Appropriate Mental State  Curiosity  Anticipation  Suspense  Low-Moderate Anxiety  High Challenge  Temporary Confusion

 Best - First  Second Best - Last  Least - Just Past the Middle Prime Time

Creating the Right Mental State Learners who know how to process negative moods optimize learning time. They model good decision making and critical thinking, and they have a sense of belonging. Visualization and goal setting activities, decision-making scenarios, and activities that require logical thinking and brainstorming help create the right mental state.

Motions and Actions Help Learning  Cross Body Motions Help  The Best Teachers Have the Learners Attention Less Than 20% of the Time  Right-Brain Left-Brain Research Shows the Two Hemispheres are Highly Integrated  The Brain Needs Something New Every 20 Minutes

David Sousa’s Hierarchy 6 6 Lecture Read Audiovisual Demonstration Discussion Group Practice by Doing Teach Others/Immediate Use of Learning Average Retention Rate After 24 Hours 5% 10% 20% 30% 50% 75% 90%

For Long-Term Memory Retention Rehearsal Is Necessary

 Problem Solving  Reasoning and Proof  Communication  Connections  Representations  Problem Solving  Reasoning and Proof  Communication  Connections  Representations Process Standards

Teachers are the primary source of feedback for their students. Feedback 16

Rules for Feedback  More Often  More Immediate  More Specific  More Appropriately Presented - Celebrations are better than rewards

Stages of Learning  Preparation  Acquisition  Elaboration  Memory Formation  Functional Integration

Preparation This stage provides a framework and sets up possible connections with the learner’s background and the new information. 19

Acquisition During this stage the learner is receiving sensory input. This may be in the form of data, written material, lecture, etc. This may also include talking and doing. The brain feeds on meaningful exposure to larger models, patterns, and experiences through manipulation, experimentation, discussion, and revisiting ideas. 20

Elaboration During this stage learners need to practice and refine their thinking. They need lots of feedback from the teacher but also from each other. 21

Memory Formation Many factors such as adequate rest, emotional intensity, context, nutrition, quality and quatity of associations, stage of development, learner states and prior learning contribute to memory formation. It is the memory formation that allows the learning to be retrieved 22

Functional Integration This stage provides for practice and use so that the new learning is reinforced and expanded upon. 23

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