Q&A #19885

Geometry for "gifted" student

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From: Karen Atwood <crakeha5556@verizon.net>
To: Teacher2Teacher Service
Date: Oct 23, 2008 at 23:26:08
Subject: Re: Geometry for

Thank you, both MarieLouise and Claudia (and Richard Tchen)!  Very helpful!  
was interested to read that you both suggested the Geometer Sketchpad; I was 
just reading about that this afternoon.  And you mentioned Origami and 3-D 
space -- my daughter has loved Origami for years (perhaps this has already 
benefitted her), and literally just over the weekend (!) she had asked me if 
knew anything about Geometry in "3-dimensional space" or about Geometry that 
would deal with curves -- so what you suggest sounds like a good match for a 
direction for her, at least for now.  I don't know that these would hold her 
all year, though.  Not familiar with "n-dimensional space," but that sounds 
interesting, too.  Thank you, and other suggestions continue to be welcome, 
anyone has more.  -- Karen

>>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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>this possibility:
>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 dimentional models of standard figures as well
as the Platonic solids
>and Archimedian solids?  Use straws, rubber bands or "stick-um" (used to 
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 
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 
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 
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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