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 23:19:37
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 >> >>COURSE DESCRIPTION: GEOMETRY, LEVEL I >>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 >>probability. >> >>COURSE TOPICS: >> 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 > > >Thanks for visiting our on-line community. >Visit Teacher2Teacher again at http://mathforum.org/t2t/ > >It is now possible to make a financial contribution to help The Math Forum. Please read more about >this possibility: >http://www.drexel.edu/ia/mathforum/. > >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 hold candles upright in >their bases) to build open models and see what happens to diagonals of the solid. > >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 >problems. > >Hopefully this will give you the idea that there is more to geometry than is in high school >textbooks. >Marielouise > >

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