like +terms + smret + ekil = 2eikl + 2emrst
factoring + expressions = oirn(factg + e2ps3)
How Do We Know? – Yes, You Can Learn Algebra!
Metacognition, Operant Conditioning,
a little humor and Sunny and Bunny too!
Now Available
Comments from others:
It made difficult math seem easy.
It made math, that at one time was miserable, more enjoyable and easier to understand.
It was helpful having the rules at the top of the pages so I didn’t have to look back all the time.
-Jacob Moore, Happy Student, Greensburg, Louisiana
Your book is fabulous!
Your book is a personal god-send for me. It makes math review fun.
-Mary Spafford, Home Schooling Grandparent, Capitola, California
….even my wife might have “understood” algebra with this text but, then, what would I have used as comic relief examples in the classroom.
-Larry Wier, MA, High School Administrator and Math Science Teacher, Mendon Utah
QUOTES:
The most beautiful thing we can experience is the mysterious.
It is the source of all true art and science.
Einstein, What I Believe, 1930.
The whole of science is nothing more than a refinement of everyday thinking.
Einstein, Physics and Reality, 1936,
Certainly few things are more mysterious to a high school freshman than trying to link physical relationships and measurement to the world of mathematics and arithmetic he/she has previously experienced. Yet if science is just a "refinement" of everyday thinking, how can it be such a mystery? Probably a paradox there somewhere.
How Do We Know? Presents a system for review of arithmetic and algebra which can remove the “mystery” of arithmetic calculations and enable students to see the beauty and mystery of mathematics and science.
How Do We Know? Contains operant conditioning in the form of Precision Teaching which is behavoristic conditioning using a conditioned response approach, and reflexive thinking in the form of justification tables reminiscent of formal geometric proofs.
There is a reflexive nature in most of the Precision Teaching exercises that is an introduction to a reflective or metacognitive process. One definition of metacognition is thinking about how we think.
Operant conditioning in the form of Precision Teaching, and reflexive thinking in the form of justification tables reminiscent of formal geometric proofs. Linking reflexive thinking and operant conditioning, probably a paradox there somewhere also.
Precision Teaching is a powerful tool for motivating students to learn. It has found wide acceptance in the field of Special Education. Extensive research has validated this approach to operant conditioning in educational settings. I hope I have presented a structure to help introduce this system to mainstream teachers.