Download Technology Review: Cinderella

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Technology Review: Cinderella
General Information
An innovation in Java based interactive software written and developed by RichterGebert and Ulrich Kortenkamp, Cinderella offers a dynamic geometry environment in which
users can build, construct, and explore figures within the given realm of Euclidean, Elliptic, and
Hyperbolic geometry. “[Cinderella]...it replaces pencil, ruler, compass and paper and enables
you to do exact geometric drawings with the mouse. Although the software is easy enough to use
to make it the perfect tool in K-12 geometry education, its mathematical foundation is powerful
enough to serve college and high school students as well as advanced geometry researchers”
(“The Interactive Geometry Software Cinderella”). Currently, the latest version Cinderella.2 can
be downloaded free of charge at http://www.cinderella.de/tikiindex.php?page=Download+Cinderella.2. If one would like to personalize and make copyrights
of their constructions within Cinderella.2, the ability to purchase a license is $10. Given the
various operating systems, Windows 95/98/NT/XP/Vista/7, Mac OS X, Mac OS 9, Linux and
Generic Unix there is a list of instructions to be followed when downloading Cinderella.2.
Common Core Standards
With the use of Cinderella in the classroom, students are able to explore various Common
Core State Mathematical Standards and Objectives. Listed below are some of the geometry
standards students will explore through the use of Cinderella:
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Experiment with Transformations in the Plane
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CCSS.Math.Content.HSG.CO.A.1
Know precise definitions of angle, circle, perpendicular line, parallel line, and line
segment, based on the undefined notions of point, line, distance along a line, and distance
around a circular arc.
CCSS.Math.Content.HSG.CO.A.2
Represent transformations in the plane using, e.g., transparencies and geometry software;
describe transformations as functions that take points in the plane as inputs and give other
points as outputs. Compare transformations that preserve distance and angle to those that
do not (e.g., translation versus horizontal stretch).
CCSS.Math.Content.HSG.CO.A.5
Given a geometric figure and a rotation, reflection, or translation, draw the transformed
figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence
of transformations that will carry a given figure onto another.
Prove Geometric Theorems:
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CCSS.Math.Content.HSG.CO.C.9
Prove theorems about lines and angles. Theorems include: vertical angles are congruent;
when a transversal crosses parallel lines, alternate interior angles are congruent and
corresponding angles are congruent; points on a perpendicular bisector of a line
segment are exactly those equidistant from the segment's endpoints.
CCSS.Math.Content.HSG.CO.C.10
Prove theorems about triangles. Theorems include: measures of interior angles of a
triangle sum to 180°; base angles of isosceles triangles are congruent; the segment
joining midpoints of two sides of a triangle is parallel to the third side and half the
length; the medians of a triangle meet at a point.
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
CCSS.Math.Content.HSG.CO.C.11
Prove theorems about parallelograms. Theorems include: opposite sides are congruent,
opposite angles are congruent, the diagonals of a parallelogram bisect each other, and
conversely, rectangles are parallelograms with congruent diagonals.
Make Geometric Constructions:
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CCSS.Math.Content.HSG.CO.D.12
Make formal geometric constructions with a variety of tools and methods (compass and
straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.).
CCSS.Math.Content.HSG.CO.D.13
Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.
Understand and Apply Theorems About Circles:
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CCSS.Math.Content.HSG.C.A.2
Identify and describe relationships among inscribed angles, radii, and chords. Include the
relationship between central, inscribed, and circumscribed angles; inscribed angles on a
diameter are right angles; the radius of a circle is perpendicular to the tangent where the
radius intersects the circle.
CCSS.Math.Content.HSG.C.A.3
Construct the inscribed and circumscribed circles of a triangle, and prove properties of
angles for a quadrilateral inscribed in a circle.
CCSS.Math.Content.HSG.C.A.4
(+) Construct a tangent line from a point outside a given circle to the circle.
Use Coordinates to Prove Simple Geometric Theorems Algebraically:
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CCSS.Math.Content.HSG.GPE.B.7
Use coordinates to compute perimeters of polygons and areas of triangles and rectangles,
e.g., using the distance formula.*
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Standards of Mathematics Practices
Cinderella’s dynamic geometry environment allows ample opportunity to explore and
address various ideals of the Standards of Mathematics Practices. Listed below are five of the
eight Standards of Mathematics Practices and how Cinderella.2 is aligned with the standards.
1. Make sense of problems and preserve in solving them.
Within Cinderella.2 students are given the ability to visualize, analyze, and investigate
the relationship amongst data through the creation of functions, graphs, and diagrams.
Through their investigation, students are able to explain the meaning of a problem and
restate the problem in their own words.
2. Reason abstractly and quantitatively.
Within Cinderella’s dynamic geometry environment, “…students have the ability to
translate a word problem into an equivalent number sentence, function, or graph.
Additionally, students recognize that all relevant information within the problem has a
quantitative value that is expressed with a numeric symbol. After successfully solving the
problem, students are able to explain how the numeric representations are related to the
original word problem” (“Reason Abstractly and Quantitatively”).
3. Model with mathematics.
With Cinderella’s dynamic geometric environment, students are able to create and
manipulate graphs and figures with the given data, showing the relationship amongst
various variables. Allowing for the student to become transparent in their learning, and
able to link real-world scenarios with mathematical representations of those scenarios.
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4. Use appropriate tools strategically.
With the aide of Cinderella.2 students are able to use the dynamic geometric environment
to visualize the appropriate answer while solving the problem using given rules. Being
able to conceptualize linear, quadratic, exponential, etc. functions within the software and
then being able to prove their answers using paper and pencil. Cinderella.2 offers the
ability as a tool to make conjectures, to prove, and check their mathematical calculations.
5. Attend to precision.
“Students are able to specify units of measure, and label axes clearly; calculate accurately
and efficiently, and express answers with a degree of precision appropriate to the context
of the problem” (“Attend to Precision”).
Description of the Technology and Associated Written Materials
According to Wardhaugh, “Cinderella is an interactive geometry software, meaning it
presents us with a digital blank slate and a set of tools for doing all sorts of exciting things, like
drawing points, lines, circles, perpendiculars, bisectors, loci, and so forth. All the classical
constructions possible with compasses and straight-edge are provided for, as are the new-fangled
facilities of ruler and protractor”. Cinderella is an excellent tool to teach students about various
geometrical topics while encouraging the possibility of explanations and investigations to their
solutions. Cinderella ultimately lives up to my expectations by exceeding the goal of geometric
understanding(s) through the use of an interactive environment. Through this intense interaction,
students are given the ability to manipulate and explore various properties to see if they hold true
and why.
Being that I had experience with an interactive geometry software prior to Cinderella, I
found the ease in using this software to be relatively stress-free. Even though Cinderella offers a
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wonderful teaching environment for students to gain a deeper understanding of geometrical
topics, I find the program a little difficult to navigate through. In comparison to other
geometrical software I thought the ease of use would develop over a few days of play, but I had
to find videos and read the manual to get a grasp of the software. The ability to enhance a
student’s conceptual understanding is present within Cinderella, amongst various websites, video
tutorials, and manuals online I was able to find lesson plans that incorporated Cinderella into the
lesson with students taking the reign of their own learning through investigative research-type
questions. In comparison with other interactive geometry software I would not recommend
Cinderella for purchase to a school and/or school system. There are other user friendly software
available that incorporates more into their software, compared to software like Geometer’s
Sketchpad, I think Cinderella.2 is mediocre at best.
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Works Cited
"Attend to Precision." Read Tennessee. N.p., n.d. Web. 06 Oct. 2014.
<http://www.readtennessee.org/math/teachers/teachers_mathematics_toolkit/mathematica
l_practices/attend_to_precision.aspx>.
"Cinderella." Cinderella : Download 2. N.p., n.d. Web. 30 Sept. 2014.
<http://www.cinderella.de/tiki-index.php?page=Download+Cinderella.2>.
"Mathematics Standards." Home. N.p., n.d. Web. 30 Sept. 2014.
<http://www.corestandards.org/Math/>.
"Reason Abstractly and Quantitatively." Read Tennessee. N.p., n.d. Web. 06 Oct. 2014.
<http://www.readtennessee.org/math/teachers/teachers_mathematics_toolkit/mathematica
l_practices/reason_abstractly_and_quantitatively.aspx>.
"The Interactive Geometry Software Cinderella - HOME - Overview." The Interactive Geometry
Software Cinderella - HOME - Overview. N.p., n.d. Web. 26 Sept. 2014.
<http://antique.cinderella.de/en/overview.html>.
Wardhaugh, Benjamin . "The Interactive Geometry Software - 'Cinderella' Version 1.2."
plus.maths.org. N.p., 1 Dec. 2000. Web. 6 Oct. 2014.
<http://plus.maths.org/content/interactive-geometry-software-cinderella-version-12>.