Q&A #19885

Geometry for "gifted" student

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From: Marielouise (for Teacher2Teacher Service)
Date: Oct 23, 2008 at 21:20:03
Subject: Re: Geometry for

>HI.  Wondering if you had any thoughts on whether it is possible to
>"extend" 9th grade Geometry class material for a gifted student --
>extending it, say, into her areas of interest, which are Biology and
>Biomedical research?  The problem is that she hasn't yet studied Physics,
>Trig or Calculus?  Would it just be better for her to complete the regular
>9th grade curriculum, and look for Geometry applications as she moves into
>Physics, Trig and Calc.?  Thanks for any thoughts!
>I am a parent, not a teacher, trying to get my gifted daughter's math needs
>met, EITHER by finding some kind of appropriate YEAR-LONG approaches and
>materials to "extend" the reach of the course while she is in the 9th grade
>Geometry course,
>OR by obtaining permission for her to move through the course at her own
>pace and finish by mid-year (to fit in some other course).  I'm not a
>"math" person, per se, hence the questions.
>I was hoping that someone could tell me if 9th grade high-school geometry
>COULD even be "meaningfully extended" to make the course beneficial and of
>academic value to her ALL YEAR -- IS it possible to go into fluid
>mechanics, for example, without having yet studied Physics --
>or would she be better off just moving thru this regular 9th-grade course
>material at her own accelerated pace, perhaps with some "extended asides"
>as appropriate, and then moving on -- being done with this course, and
>knowing to expect to see other types of geometry later on in college or
>graduate studies, after she'd had more science and more math to tie into
>it --
>It just occurred to me that you might not be aware of the typical 9th-grade
>Geometry course contents (and we're here in Pennsylvania, too).  These
>statements are from the high-school's website, and will put the course in
>perspective for you.  My daughter is extremely discouraged by the painfully
>SLOW movement through course material, and the redundancy of the
>presentations -- and she has the "top" teacher and the "top" level class
>offered.  She's a very visual person and likes math; she "gets" this stuff
>the first time through (and sits bored thru umpteen repetitions until the
>others get it), and she NEEDS to either move through and be done, OR have
>it "extended" in some way that has value to her professional goals... but
>that's what I'm trying to ascertain -- CAN it be "extended" now, with her
>having ZERO background in Physics or Trig or Calculus or Statistics -- or
>does it make sense to acquire what's here and be done, for now?
>Thanks, Karen
>In this course, you will develop skills in defining terms, thinking
>logically, and arriving at conclusions, both geometric and non-geometric.
>Lines, angles, circles, triangles, quadrilaterals and other geometric
>figures are studied. Students become familiar with two-column, paragraph,
>and indirect proofs. The relationship of geometry to arithmetic, algebra,
>and right triangle trigonometry is emphasized.  You will also learn and
>develop some basic concepts of solid geometry, coordinate geometry, and
>          In Geometry, you will study basic definitions and concepts
>relevant in Geometry.  You will learn how to use deductive structure in
>which conclusions are justified by means of previously assumed or proved
>statements.  You will learn the concept of congruent angles, segments, and
>triangles.  You will also learn the concept of similar figures, the
>Pythagorean Theorem, circles, area, surface area and volume of various
>geometric figures.

 -Marielouise, for the T2T service

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Hi, Karen,

I read your question on the CPAM website and it intrigued me.  I fully 
support Claudia's response to 
you about using other texts ...especially Discovering Geometry and the 
computer program 
Geometer Sketchpad. Both of these will challenge your daughter's creative 
instinct.  Geometry is 
more than just what your Pennsylvania curriculum states.  I have always 
considered it the mental 
structure upon which much of mathematics is built.  The Geometer Sketchpad 
enables students to 
explore without the tediousness of constructions by hand.  

Has your daughter built three dimensional models of standard figures as well 
as the Platonic solids 
and Archimedian solids?  Use straws, rubber bands or "stick-um" (used to 
hold candles upright in 
their bases) to build open models and see what happens to diagonals of the 

Has your daughter explored origami?

Has your daughter asked herself what happens to the equation of a line when 
it moves off the two 
dimensional plane and is seen in three dimentional space?  What happens to 
the equation of the 
line in three space?  How does the equation of a plane relate to the 
equation of a line?  If the 
solution of a system of two equations in two unknowns is either void or a 
point in a two 
dimentional sysstem, what is the solution of the system of three equations 
in three unknowns?  
This is coordinate geometry in three space.  This is important because once 
the mind abstracts and 
is able to see the progression from one to two to three space, then n-
dimensional space is easier to 
comprehend.  Can a geometry student do this?  Yes, I have seen many do 
it.    However, this is a 
situation where building models with manila board and string not only helps 
one see the solution of 
problems but also develops the "eye" for being able to draw and read three-
dimensional figures.
Unfortunately, for me, I have been out of the high school classroom for more 
than 10 years and 
cannot direct you to texts that can help you.

Has she studied probability?  Geometric probability is a good problem 
solving method for some 

Hopefully this will give you the idea that there is more to geometry than is 
in high school 

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