Since my retirement from 32 years of being a high school mathematics teacher, I have tutored numerous students from second to eighth grade. What I learned is that each of them was capable of mastering concepts that many teachers and parents would describe as not being age appropriate. I was able to accomplish this by doing several things:

(1) All advanced concepts were divided into more fundamental concepts. I made sure that each fundamental concept was mastered before progressing to the more advanced concept.

(2) After each lesson I developed special practice materials where students could demonstrate mastery of what I had taught. When appropriate, problems where common errors were likely to occur were included in the materials that I wrote.

(3) At the beginning of each new lesson I made an effort to test for mastery of previous concepts taught by verbally testing the students.

4) An integral part of the learning process was the use of psychology.

The student was made aware of the fact that the concepts being learned were those traditionally taught to students that were older than them or from grade levels that were much higher than what they were enrolled in. Being aware of how they were able to learn concepts from higher-level courses motivated them to want to learn more. By making success an integral part of the learning experience, I was able to enhance their experience and foster a love for continually learning of mathematics.

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