Below are the key areas related to true mastery of mathematics. All areas are desired to have a comprehensive understanding of mathematics.
Computation – Having the skills and strategies available to quickly apply the correct process to the problem presented. (How to do the problem)
Concept – Having the understanding to carefully reason through each step of the process, prioritizing higher function and accuracy. (The reason Why each process and step is chosen)
Application – Knowing which process to apply to the given problem in each situation. (When to use which process)
Memorization – Committing to memory the processes and reasoning skills to move from proficiency to fluency to automaticity or unconscious response.
Reflection & Mastery – What did you learn? Can you teach it to someone else?
Students need to master skills at each level of arithmetic, including complex applications of those skills, in order to become a true master of their craft. Also, a student teaching back what has been learned is a critical demonstration of the student's ability to:
- Grasp the problem
- Choose a process
- Develop a solution
- Articulate the reasoning behind their choices
- or… Reveal where there are gaps in their understanding
Perceptions is designed as a SUPPLEMENTAL INTENSIVE INTERVENTION. Ideally, students will be given enough time to master the materials found in each lesson. However, due to the nature of this course, that may not be achievable to the depths that might be desired, especially for students that have significant issues with memorization or math facts application.
Math facts are NOT covered in this level. Proficiency in the math facts is a key pre-requisite skill. Without fact proficiency a student may struggle to develop the needed understanding in the time allotted.