Math Was Created
Mathematics is an innately creative and discovery based process. All math stems from very simple laws and truths. This means that all of math can be discovered and created using our unique individual ability to think logically and problem solve.
All mathematical truths have been discovered. No one sat down with Newton and said “here’s how you do calculus.” He studied. He struggled. He hypothesized. He experimented. He failed. And then he discovered.
All of our students can, and will if given the opportunity, discover, on their own and in their own way, every mathematical truth, rule and procedure. No longer is the textbook or the online program or the teacher or the parent the “all-knowing math authority,” the student is their own authority.
The Discovery Method
The Discovery Method is based on the principles of the scientific method: students observe patterns, hypothesize rules, test their working-hypotheses, prove their own theorems, and record their findings in their own journal. When they need help or forget a rule later on, they look to their own record as the authority. Now, they own their knowledge! The Discovery Method allows students to create math systems that spawn from their own unique way of thinking.
Here is a brief outline of the steps in the Discovery Method:
Step 1: Discover
Students are given problems to solve using their logical thinking and problem solving skills.
Step 2: Collect and Organize Data
Students take the problems and answers that they discovered and create a list in order to look for patterns.
Step 3: Observe Patterns
Students look for patterns and relationships in their data to find a generalized hypothesis that will work for all similar problems.
Step 4: Hypothesize
Students create a step by step process that is uniquely their own.
Step 5: Experiment/Test Hypothesis
Students then test their hypothesis on a myriad of different problems by checking the logical answer with the answer they got by following their hypothesis.
Step 6: Theorize
Once their hypothesis has been tested and proven correct, students record their finalized step by step process as their theorem.