C882 Task 1
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Western Governors University *
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Mathematics
Date
Feb 20, 2024
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docx
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6
Uploaded by JusticeFlowerWolverine37
1
Dynamic Software in the Geometry Classroom
There are a few different websites that aid in teaching geometry. One dynamic geometry software that can be used is GeoGebra. GeoGebra is a powerful and versatile tool that combines geometry, algebra, calculus, and other mathematical concepts. It offers various features that facilitate student learning in different geometry topics. One feature that GeoGebra provides that facilitates student learning is examining the congruence and similarity of geometric shapes.
The features in GeoGebra for examining congruence and similarity include dragging and
transformations, measurement tools, transformation tools, and interactive worksheets. Students can easily manipulate geometric shapes by dragging their vertices, sides, or angles. This feature allows them to explore how congruent and similar shapes can be transformed through translations, rotations, reflections, and dilations. GeoGebra provides tools to measure lengths, angles, and areas of geometric shapes. Students can compare measurements between different shapes to determine congruence or similarity. GeoGebra offers a variety of transformation tools, such as "Congruence" and "Similarity" transformations. These tools automatically determine if two shapes are congruent or similar based on the given transformations. GeoGebra allows teachers to create interactive worksheets that guide students through specific activities related to congruence and similarity. These worksheets can include step-by-step instructions, dynamic examples, and interactive questions to reinforce understanding.
Exploring with Dynamic Features
To explore the geometric theorem "If M is the midpoint of line AB, then AM is congruent to MB" using GeoGebra, the following steps can be followed:
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1.
Open GeoGebra and create a coordinate system or a line segment AB.
2.
Use the point tool to place point M on the line segment AB.
3.
Use the midpoint tool to mark M as the midpoint of AB.
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4.
Use the distance or measurement tool to measure AM and MB.
5.
Observe and analyze the measurements of AM and MB.
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6.
Drag the endpoints of AB and observe how the measurements of AM and MB change.
7.
Make a conjecture or conclusion based on the observed measurements and the dynamic action.
Identifying Misconceptions
Often when teaching new concepts to students, they often have some misconceptions. The first misconception that a student could have is assuming that only vertical or horizontal lines have midpoints. A second misconception is thinking that the concept of midpoint applies only to line segments and not to lines or rays.
To identify the first misconception the teacher can ask the question “Can a diagonal line have a midpoint? Why or why not?” By asking about a diagonal line, we can gauge if the student
understands that midpoints can exist on lines with any orientation. A second question that could be asked is “True or False: Only vertical or horizontal lines have midpoints.” By presenting this
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question, we can assess whether students have an accurate understanding of midpoints in line segments. The correct answer is "False." Midpoints can be found on any line segment, regardless
of its orientation or slope. It is important to address this misconception and help students understand that midpoints are determined by dividing a line segment into two equal parts. To address the misconception, GeoGebra can be used to construct various lines with different orientations and show that midpoints can be placed on them. By manipulating and exploring different lines, students can visually see that midpoints are not restricted to specific orientations.
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References
GeoGebra. (2020). GeoGebra | Free Math Apps - used by over 100 Million Students & Teachers Worldwide. GeoGebra. https://www.geogebra.org/?lang=en
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