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Questions and Answers about Geometry

Question:  My daughter was always good in math. But the first report card came home this year and she has a C- in Geometry. What's going on? What can I do to help her?

Answer:  Geometry is half new language and half mathematics. Also, a new way of thinking is required. It can be quite a handful for a teenager. We will answer the question in parts:

The Language Part — Textbooks give a symbol, definition, naming convention, theorem or postulate one time and expect the student to recognize it and understand how to use it for the rest of the school year.

     Tutor in a Book's Geometry presents the new information, explains it, illustrates it, repeats it, and gives visual memory helpers to aid the student's retention of the information.

    
     The connection that the student is supposed to make when the new
    information is used in a proof or problem, is clearly stated. This ensures
    that the student understands what it is that he or she is being asked to
    do in each particular problem.
    Graphic organizers containing the new information and its purpose are
    provided so that student's can more easily study and prepare for exams.

The Math Part — Even students who were strong in algebra often struggle with
applying their algebra skills to geometry because they do not recognize the
mathematical connections.

     For review and as a reference, Tutor in a Book's Geometry includes and
    explains examples of how to set up and balance, each type of algebraic equation.
     

     As each new geometry topic is introduced, Tutor in a Book's Geometry
    immediately points out the algebra connection and explains it, using illustrations
    where helpful. Then the right demonstration problem(s) are solved using clear
    and consistent methods. Memory tips are included to help the student recognize
    similar problems and remember how to solve them.

     Exercises are then given for the student to practice and reinforce the concept
    and gain confidence. (Complete solutions for exercises including explanations
    and illustrations are in the book's Answer Section.)


Now the Thinking Part — Understanding the meaning and the significance of new
ideas and information is the foundation for thinking through problems and proofs.
As the student becomes familiar with and confident about using the new ideas and
information, thinking is facilitated. In fact, proofs and problems are very predictable.
Tutor in a Book's Geometry points out the patterns to the student and teaches
them how to look for, recognize, and use, the information that the problem is giving.

     As each new fact is introduced, Tutor in a Book's Geometry, clearly states
    and illustrates the meaning of the new information and its connection to
    previously introduced concepts. Then the right sample proof(s) and/or
    problem(s) are done so that the student can learn how to correctly combine
    the new fact with previously learned information.
     

     Many facts (definitions, theorems, postulates) are supposed to prompt
    the student to make a particular connection. Once the student is made aware
    of this connection, he or she can recognize and remember it.

    Explanations and illustrations are designed to help the student understand
    how to think through a problem and put the pieces of information together
    logically and correctly.

     Related facts are combined in graphical organizers that include examples
    of how each fact is used in proofs or problems.



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