The system is based on five underlying principles of learning.
When there is meaning, mathematics is easier to learn and much easier to remember. Meaning is usually found in complex activities such as: problem posing, problem solving, working on projects. Sports, cooking, nutrition, data collection, measurement, and student-created puzzles are excellent sources of meaning. Projects – designing and planning a four-room house, planning a party, purchasing school supplies, or picking stocks – bring mathematics to life and connect to the student’s community.
The brain has difficulty remembering material that is not connected to previous learning. The more choice built into the learning process – the greater the success of learning. Choice is provided when students generate student-written problems and when they are allowed to write tests or “All the Facts” sheets in order of their choosing. Students doing the “How Many Ways” and “What Do I Know” activities find themselves challenged and during the participation in these activities many students become very creative with ‘number’. In addition, the games which are provided further give students ‘choice” as there are many levels of challenge. Projects almost always involve students choosing information relevant to their homes, school or community.
Students who are asked “How did you get your answer?” or “Can you do it another way?’ learn to feel that their methods and ideas are valued. Trusting that your peers and teachers value your thinking is an important step in creating self-esteem and risk-taking in mathematics. Teachers who use this program develop increasingly respectful questioning techniques that encourage creativity and risk-taking.
Because all students bring different experiences to the classroom, they learn differently and make connections differently. When this diversity is valued by teachers and students, a sense of risk-taking envelops the class and the whole process of learning mathematics becomes creative and joyful.
Traditional textbooks often teach in units – some topics such as decimals, fractions, geometry, measurement and even multiplication and division are not taught until later in the school year. This means that students receive less practice in these areas and often forget the material as there can be as many as twelve months between units. Because their previous learning experiences are so varied, all students require ‘differing amounts of time’ to learn new material The curriculum should be learned, left, reviewed and re-learned within new contexts (projects). The Yearly Plans in the Teachable Moment System ensure that the main concepts throughout the entire curriculum are covered monthly. Assessment drives instruction. Mastery is developed over long periods of time. This approach to math instruction parallels the way reading is taught and language is learned.