Creativity and Learning

Creativity, innovation, intuition and discovery might be appropriate for specific topics at different developmental stages.

For example:

1.  What is the appropriate age (brain development) for students to use addition to detect and correct subtraction errors (and the reverse)?

2.  What is the appropriate age (brain development) for students to use multiplication to detect and correct division errors (and the reverse)?

From my limited experience, using addition with subtraction or multiplication with division to detect and correct errors does not appear to be integrated into the elementary school math curriculum.  The student is dependent on the teacher to detect and correct math errors in grades four and five.

When using the appropriate process to build a dynamic model of a system, there are steps to test, verify and validate the model.  As a result, detecting and correcting errors is integrated with the process of building the model.  Thus the student modeler has the responsibility for detecting and correcting errors.  This is what leads to someone developing creativity, innovation, intuition and discovery.

There are many quantitative and qualitative methods of detecting and correcting errors in different subjects.  A teacher-centered classroom is where the teacher is the focal point of detecting and correcting errors.  When students learn a process for detecting and correcting their own errors they begin to take responsibility for their own learning.

The existing education system is primarily teacher-centered and is immune to any change toward a student-centered classroom. Probably only as high school extra-curricular activity or college level will anyone have a chance at introducing processes for students to learn how to detect and correct their own errors. I'm encouraged to learn about websites that are introducing these methods.