**WHY I WROTE MY CRYSTAL BOOKS**

**I've taught or tutored most of my life, all ages, often as a volunteer. I wrote**

THESE ARE TIPS FOR GATE-KEEPERS: STANDARDIZED TESTS AND MATH:

1. PRACTICE for Standardized tests. These are speed and basic knowledge tests, and you can improve your score! I've helped people increase their scores by 100, 200, up to 280 points on SAT and GRE. Don't let the gate-keepers stop you!

Take practice tests from a book with a timer. Grade your test to find what’s wrong. Correct your understanding, and find a tutor if you need one. Work on your speed. Investing about two hours of effort per week for nine months generally brings a 100 point increase in actual test score.

More practice brings a greater increase, up to a point; it’s hard to improve scores beyond a 250 point increase. Naturally, you can't improve beyond a perfect score. I helped a student increase her GRE score by 280 points, so that she could be accepted into a specific program. This was her only dream, and now she’s a music professor.

2. IF A STUDENT DOESN’T “GET” MATH, it's often because they have not really learned fractions in 4th or 5th grade. Make sure they can add 1/2 + 1/2 and NOT get 2/4. Draw pizza circle pictures with fraction slices to make it visual and real. Can they add 1/3 + 1/5 correctly? The answer is 8/15, NOT 2/8 or 2/15. Basic fractions are important even in Calculus; misunderstanding this will cause problems.

It can be hard to understand why 9 divided by 1/3 = 27. Draw 9 pizza circles and put a dot in the center of each circle. Draw lines to divide each circle into thirds. Now count the slices. 27! There are three thirds in each pizza. Use pretend food to get their attention, and quicker comprehension. It’s very satisfying when you see the lightbulb click on and they say, “I get it!”

Find a tutor if needed. People make up rules when they don’t understand, and use these forever. When I tutor someone, regardless of their age, I give a quick basic test to find these holes in understanding. Fix this foundation before moving to more involved math.

3. MUCH OF CHEMISTRY IS BASIC MATH. One needs fractions to balance those chemical equations!

4. BASIC MATH IS EASIER THAN WRITING ONCE YOU UNDERSTAND IT. Improving a math score takes less time than increasing a verbal score, though you can help both. Writing has more "rules" and "variables" than math, which makes it a delightful challenge. Advanced math subjects, beyond the basics, can be exquisite. Don't let the gate-keepers stop you from reaching your dreams!

*Crystal Geometry*and*Crystal Colors*to help students understand math and chemistry, using fun activities. Hold crystals to feel the chemical angles; measure a huge fossil shark's tooth to discover "How big was the shark." Math, science, and art have beautiful connections.THESE ARE TIPS FOR GATE-KEEPERS: STANDARDIZED TESTS AND MATH:

1. PRACTICE for Standardized tests. These are speed and basic knowledge tests, and you can improve your score! I've helped people increase their scores by 100, 200, up to 280 points on SAT and GRE. Don't let the gate-keepers stop you!

Take practice tests from a book with a timer. Grade your test to find what’s wrong. Correct your understanding, and find a tutor if you need one. Work on your speed. Investing about two hours of effort per week for nine months generally brings a 100 point increase in actual test score.

More practice brings a greater increase, up to a point; it’s hard to improve scores beyond a 250 point increase. Naturally, you can't improve beyond a perfect score. I helped a student increase her GRE score by 280 points, so that she could be accepted into a specific program. This was her only dream, and now she’s a music professor.

2. IF A STUDENT DOESN’T “GET” MATH, it's often because they have not really learned fractions in 4th or 5th grade. Make sure they can add 1/2 + 1/2 and NOT get 2/4. Draw pizza circle pictures with fraction slices to make it visual and real. Can they add 1/3 + 1/5 correctly? The answer is 8/15, NOT 2/8 or 2/15. Basic fractions are important even in Calculus; misunderstanding this will cause problems.

It can be hard to understand why 9 divided by 1/3 = 27. Draw 9 pizza circles and put a dot in the center of each circle. Draw lines to divide each circle into thirds. Now count the slices. 27! There are three thirds in each pizza. Use pretend food to get their attention, and quicker comprehension. It’s very satisfying when you see the lightbulb click on and they say, “I get it!”

Find a tutor if needed. People make up rules when they don’t understand, and use these forever. When I tutor someone, regardless of their age, I give a quick basic test to find these holes in understanding. Fix this foundation before moving to more involved math.

3. MUCH OF CHEMISTRY IS BASIC MATH. One needs fractions to balance those chemical equations!

4. BASIC MATH IS EASIER THAN WRITING ONCE YOU UNDERSTAND IT. Improving a math score takes less time than increasing a verbal score, though you can help both. Writing has more "rules" and "variables" than math, which makes it a delightful challenge. Advanced math subjects, beyond the basics, can be exquisite. Don't let the gate-keepers stop you from reaching your dreams!