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Mayville State University
Math 389: Modern Geometry Spring 2017
Instructor: Mr. Fred Strand Office: CB108B
Hours of Availability: 9:00am or By appointment
Work Phone: 788-4684 Cell Phone: 701-371-4393
Campus Email Address: fred.strand@mayvillestate.edu
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Class Schedule: 2:00pm – 2:50pm M-W-F Final Test: Tuesday, May 9 2:00 pm
CREDIT: Three(3) semester hours.
Course Description
A study of K-12 and undergraduate topics. K-12 topics: polygons, platonic solids, tessellations, transformations
and congruent triangles. Undergraduate topics: axiomatic Euclidean geometry, finite geometries, fractals,
projective geometry, and non-Euclidean geometries. The study includes the integration of effective research based
teaching strategies to use geometry to model mathematical ideas and methods for mathematical proofs. Pre-
requisite: Math 103 or equivalent.
Purpose of the Course
Geometry students will learn about and review the breadth of knowledge that geometry entails today. Geometry
fulfills a core requirement for mathematics and mathematics education majors and minors. It is designed to prepare
students in geometry who will be elementary and secondary teachers as well as those who will pursue further study
in mathematics. The course includes Euclidean geometry from an axiomatic view (commonly taught in high
schools) and Non-Euclidean geometry (which deals with three dimensional structures).
Course Objectives
1. Students will be able to identify the various types of geometric shapes, their algebraic equations and whether
they occur in Euclidean or Non-Euclidean geometries.
2. Students will be able to recognize the names of mathematicians who contributed to the field of geometry.
3. As part of a competency in technology:
a. Students will use GeoGebra to demonstrate how to: draw circles, make measurements and constructions.
Transform given objects by translating, reflecting and rotating.
b. Students will construct a 12 slide PowerPoint presentation on either a geometrical concept(s) or the life
and works of a mathematician who made a contribution to the field of geometry.
c. Students will demonstrate the skills to use the internet to find and review(evaluate) videos that show
geometric math and post their evaluations to the Moodle discussion board.
d. Students will explore GeoGebra, a dynamic program used to combine geometry with algebra.
e. Students will explore non-Euclidean geometry, which is the geometry of spheres, cones and hyperbolic
shapes; Sierpinski’s and Pascal’s triangles; and Koch’s snowflakes and fractals through internet lessons.
Program Student Learning Outcomes (SLOs) Addressed in This Course
The Academic Program Student Learning Outcomes document can be found in your Moodle course shell. It
contains all learning outcomes pertaining to Essential Studies courses and all majors and minors. The document has
an index so you can quickly find the degree you are pursuing. As part of Mayville State’s effort to demonstrate
continuous improvement in achieving student learning outcomes, this course will assess SLO #5, Integrating
Techonology, as part of the Mathematics Major/Minor. Students will use the internet to research and use GeoGebra
to complete associated work.
Course Timeline
This course includes chapter assignments and exams, due dates to be announced on Moodle. The exams will cover
the textbook material. The projects found on Moodle can be worked on and completed anytime during the semester.
Student presentations will be held throughout the semester.
Course Improvements Based on Most Recent Assessment Findings
To improve communication skills students will be asked to present their completed projects in a format of their
choosing.
Required Materials: Geometry(2004), McDougal Littell, a division of Houghton Mifflin Company, Evanston, IL.
ISBN: 0-618-25022-0(this textbook will be provided). A calculator and computer access for internet use.
Instructional Strategies
Class discussion, lecture, cooperative grouping, written assignments, instructor feedback- both oral and written,
exams, board work, internet programs/research and other methods that may occur during the course.
Learning Experiences
1. Participate actively in class discussions and activities.
2. Assignments will be given in class or in a detailed handout.
3. Submit all assignments on designated due dates.
Reduction in points earned if late.
4. Exams will be taken on the scheduled date unless arrangements are made ahead of time.
5. Read all reading assignments.
Expectations/Protocols
Students will be completing written assignments, which they will be sharing with their classmates
on a daily basis.
Course notes will be taken and used on quizzes and exams.
Class discussions will be an integral part of this course and students are expected to participate in
our class discussions and projects.
Class attendance is expected.
Instructor/Student Communication
Students are accountable for all academic communications sent to their Mayville State University e-mail
address. And, are responsible to check the Moodle course shell regularly.
Students can expect me as your instructor, to respond to your correspondence in a timely manner. Generally, I
will respond within hours of receiving your contact, but definitely I will respond within 24 hours.
Evaluation and Grading
Overall grades will be assigned by weighting your averages in the sections according to the following scheme:
Textbook assignments 25%
Textbook chapter tests 35%
Internet lessons 10%
GeoGebra exploration 10%
Presentations(2 – 3) 10%
Final Exam 10%
Final letter grades will be assigned based on the usual 90-80-70-60 scale:
A: 90% or higher B: 80%-89.9% C: 70%-79.9% D: 60%-69.9% F: 0%-59.9%
Note: The course website contains an online gradebook where all scores for the course will be posted whenever
they are recorded. You are encouraged to check your grades online often and to notify the instructor of any
questions you have about your scores.
Important Student Information
“Important Student Information” can be found in your Moodle course shell.
English Proficiency and Other Academic Concerns
Starfish Early Alert System
Students with Disabilities
Academic Honesty
Emergency Notification
Continuity of Academic Instruction for a Pandemic or Emergency
Family Educational Rights and Privacy Act of 1974 (FERPA)
Notes:
Interstate New Teacher Assessment and Support Consortium Standards (InTASC)
1 The teacher understands how learners grow and develop, recognizing that patterns of learning and
development vary individually within and across the cognitive, linguistic, social, emotional, and physical
areas, and designs and implements developmentally appropriate and challenging learning experiences.
2 The teacher uses understanding of individual differences and diverse cultures and communities to ensure
inclusive learning environments that enable each learner to meet high standards
3 The teacher works with others to create environments that support individual and collaborative learning,
and that encourage positive social interaction, active engagement in learning, and self-motivation.
4 The teacher understands the central concepts, tools of inquiry, and structures of the discipline(s) he or
she teaches and creates learning experiences that make these aspects of the discipline accessible and
meaningful for learners to assure mastery of the content.
5 The teacher understands how to connect concepts and use differing perspectives to engage learners in
critical thinking, creativity, and collaborative problem solving related to authentic local and global
issues.
6 The teacher understands and uses multiple methods of assessment to engage learners in their own
growth, to monitor learner progress, and to guide the teacher’s and learner’s decision making..
7 The teacher plans instruction that supports every student in meeting rigorous learning goals by drawing
upon knowledge of content areas, curriculum, cross-disciplinary skills, and pedagogy, as well as
knowledge of learners and the community context..
8 The teacher understands and uses a variety of instructional strategies to encourage learners to develop
deep understanding of content areas and their connections, and to build skills to apply knowledge in
meaningful ways.
9 The teacher engages in ongoing professional learning and uses evidence to continually evaluate his/her
practice, particularly the effects of his/her choices and actions on others (learners, families, other
professionals, and the community), and adapts practice to meet the needs of each learner.
The teacher seeks appropriate leadership roles and opportunities to take responsibility for student
10 learning, to collaborate with learners, families, colleagues, other school professionals, and community
members to ensure learner growth, and to advance the profession.
Reminder:
Please refer to the Important Student Information document found at the top of the Moodle site for this course.
This information will be presented to the class at the beginning of the semester as well by the instructor.
For information regarding to specific Academic Student Learning Outcomes (SLO) for each major or program,
please refer to the MSU Academic Student Learning Outcomes document provided at the top of the Moodle site for
this course.
Changes
The instructor reserves the right to amend, adjust, or otherwise modify the syllabus at any time during the course.
Project: GeoGebra Exploration Name:____________
Students will be able to:
1. Use GeoGebra to make geometric drawings with analytical and algebraic measurement capabilities.
2. Use a companion website found at http://tube.geogebra.org/ with a variety of topics to investigate.
PROJECT INSTRUCTIONS:
Drawings & Calculations using GeoGebra…
You will submit 4 GeoGebra files containing the items listed below. Make sure to include each of
the indicated parts for each file to be submitted. When you are giving an answer or sharing
information use a textbox to do that (use as many as you need). You are being asked to use features
that we have not used before, if you need help with any of them, please contact me.
File #1: Draw 3 circles differing in size.
Measure the radii, circumferences, diameters and areas of each circle.
Save this file as CirclesYourName (Ex. CirlcesFredStrand). Submit using this name.
File #2: Draw 3 polygons, no triangles. Use Polygon, Regular Polygon and Rigid Polygon from the
dropdown menu to create the polygons.
Measure the sides, angles, perimeters and areas of each polygon.
Save this file as PolygonsYourName. Submit using this name.
File #3: Draw 2 triangles, one of which is equilateral.
Construct the midpoints of the sides.
Construct the medians- label the point of concurrency M.
Construct the angle bisectors- label the point of concurrency A.
Construct the perpendicular bisectors- label the point of concurrency P.
Save this file as TrianglesYourName. Submit using this name.
Notice: when you change the label of an object the program will automatically use a subscript(such as M
and M1).
File #4: Construct a polygon and a line not intersecting the polygon. Reflect the polygon about the line.
Construct a triangle and a point outside the triangle. Dilate the triangle about the point by a
factor of 0.5.
Write a description of each using good terminology and notation.
Save the file as TransformYourName. Submit using this name.
PROJECT: GeoGebra Exploration
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