1. Successfully using math requires special math aptitude. In the last century, it was thought reading required reading aptitude; there were readers and non-readers. Today we know everyone can learn to read. Similarly everyone can successfully learn to use math on a much higher level than we are now achieving; no special aptitude is required.
2. People who are good at math know the answer and solve problems in one step. This is rarely true. Usually problems must be broken into a series of smaller problems to arrive at an answer.
3. To be skilled using math means never making mistakes. This is also false. Everyone makes mistakes. This is why the eraser is on the pencil. Further mistakes often illuminate the process. Learning to recognize a mistake when the answer doesn't make sense is the art
4. People who are good at math aren't expressive, creative or interesting. They are usually nerds. Not true. Some of us are right brained. Math and music talent seem to correlate. Some of the best problem solving is done using intuition. See myth #1.
Memory:
Memory is developed by building pathways in the brain. Imagine walking across a field of grass in the spring. The first few times the grass pops back to hide your footprints but if you continue to walk across the same area, eventually a path is made. Hebbs work showed every time a brain cell is used there is a bit of energy that is fed back to the cell, making it stronger. I subscribe to the 'Use It or Lose It' theory of memory. Research has shown that learning can take place at all ages. Memory can be improved however if there is a storage strategy and/or many associations with the information. Good organization and retrieval strategies improve memory and learning.
Models:
Using familiar models such as the clock and money enhance math learning. Many third graders who protest they can't multiply will, when presented with six quarters, tell you it's worth $1.50. Similarly most know if the minute hand is pointing at the 9 on the clock, 45 minutes have past since the hour began. Visualization increases retention and reduces time needed to teach a concept. The clock model provides a strategy to reconstruct the 5's until long term memory that 9 x 5 = 45 is developed.
Metaphor:
Learning math is a metaphor for life. Many times when faced with new math topics, students feel lost, frustrated and want to quit. They can only succeed if they risk stepping into unknown territory, and persist with the struggle to learn. This process needed to incorporate new concepts into their math foundation is a wonderful metaphor for life.
Meta Learning:Meta learning is learning how to learn. Students have different learning styles: some learn predominantly by reading, some by watching, some by listening and others by hands on, experimenting with various approaches.
The process of solving problems in math often involves using many resources, breaking the problem into a series of smaller, less complex steps or solving a similar but easier problem to see the process. This method of problem solving can viewed as one way of 'learning how to learn' and can be applied across the curriculum.
Multimedia:
Multimedia is an effective tool to enhance learning because with visualization, sound, and interactivity, all learning modalities are used.
Learning is emotional. Color, music, and animation enhance the experience. Interactivity allows students to follow different paths, explore and discover. Interactive students become active learners. Immediate feedback helps students develop strategies and confidence. Using multimedia reduces the time need to learn a concept and increases retention.
Miracles:
There are no miracles needed to learn math and no magic required to solve math problems. Developing math sense involves the step-by-step building of a solid math foundation with both information and relationships.