Download Artifact one - Angela Patterson Digital Portfolio

EDTC 614 Online Course Proposal Template
Proposed Course Title: (EDU-0314) Teaching Geometry in the High School Setting
Instructor: Angela Patterson
Course Description:
This course is offered to third year undergraduate level mathematics and secondary education
students. It explores appropriate mathematical pedagogy for high school level prospective
teachers, specifically focusing on the subject of Geometry. Candidates will review the postulates
and theorems associated with Geometry and create practical teaching applications such as
lessons, assessments, and projects for their educational portfolios and future employment
opportunities.
Course Pre-requisites: Introduction to Educational Theories (EDU-0123), Developmental
Psychology (PSYC-0216), Adolescent Psychology (PSYC-0225), and Teaching Algebra I in the
High School Setting (EDU-0310)1.
Number of Sessions/Weeks/Hours/Credits: 16-week sessions, approximately 45 hours, 3 credits.
Subsequent Appropriate Courses: Teaching Algebra II in the High School Setting (EDU-0318)1,
Observation and Analysis (EDU-0328)1, Principles and Practices of Secondary Education (EDU0432), Effective Teaching Strategies for K-12 (EDU-0455), and Student Teaching (EDU-0462).
(1can be taken as a co-requisite with Teaching Geometry in the High School Setting)
Modes of Delivery: Asynchronous: 100%
Synchronous: 0%
Platform Software Package: WebCT
E-mail:
WWW: 
Printed text: 
CD-ROM:
Video Cassette: ____ Audio Cassette: ____ Interactive Video Disc: ____
Video Conferencing:____
Telephone: ____
Chat: ____
Other: Math Type 5.0 Equation and Geometer’s Sketchpad version 4.0.
Course Topics (short list): The basic structure of Geometry, lines and their relationships,
congruent and similar shapes, geometric shapes and their properties, types of transformations,
area, perimeter, and volume of various shapes, and conceptualizing proofs.
Rationale for Offering/Taking/Teaching This Course Online:
Traditionally, mathematics majors that are also a dual major with education or minor in
education are expected to know the content upon entering the field of teaching. However, many
colleges and universities only focus on the pedagogical aspect of teaching, never addressing the
content that the students could potentially teach when successfully being hired for their first
teaching job in a high school setting. As mathematics majors, undergraduate students typically
study more advanced mathematics beyond the high school curriculum such as Calculus, Number
Theory, and Abstract Algebra. Although studying advanced mathematics provides the
prospective teacher with an appreciation and plethora of knowledge to use in the classroom,
rarely are such topics taught in a high school setting.
Through the introduction of this course, prospective mathematics teachers will be given the
opportunity to review the subject of Geometry and explore creating lesson plans, assessments,
and projects in preparation for a future employment opportunity at the secondary level in
education. The use of an online setting will provide these students with the opportunity to work
independently with the technology that they will be using first hand in their classrooms. The
convenience of an online setting will also allow the students to be able to take additional courses
that will satisfy their mathematics and education majors.
Expected Student Outcomes:
At the conclusion of this course, students will be expected to:

Develop Geometry lesson plans that incorporate the NJCCCS and NCTM standards for
teaching mathematics.

Develop activities and projects that utilize multiple learning abilities (e.g., inductive
reasoning vs. deductive reasoning, cooperative learning)

Develop activities and projects that utilize technology (e.g., researching Pythagoras on
the Internet) and mathematics software programs (e.g., Geometer’s Sketchpad).

Develop assessments that contain various forms of questioning including multiple choice,
short answer, and open-ended questions. This will act as a precursor to preparing the
prospective teachers’ students for standardized testing (e.g., New Jersey High School
Proficiency Assessment).
Description of Content:
This course is offered online in 16 weekly sessions. Students are able to access lectures (using
the Lessons module), complete assignments (submitted in the Drop Box), and interact with their
classmates and the instructor using the Discussion Board and e-mail. The Chat room feature
will be available for students to use at their own discretion.
Session 1: Introductions & Sketchpad Orientation.
Students will provide a brief introduction of themselves and complete an activity to familiarize
themselves with one of the programs utilized throughout the course.
Session 2: The Basic Structure of Geometry.
 (2.1) Define and use symbolic notation for points, lines, planes, line segments, rays, and
angles.
 (2.2) Define Segment and Angle Addition Postulates.
 (2.3) Define congruent, midpoint, segment bisector, angle bisector, and perpendicular.
Use distance formula to calculate the distance between two points.
 (2.4) Explore conditional and biconditional statements and identify their parts.
 (2.5) Review the properties of Algebra and explore the properties of congruence.
 (2.6) Define and use vertical angles, linear pairs of angles, complementary and
supplementary angles.
Session 3: Lines in a Plane.
 (3.1) Define parallel, perpendicular, oblique, and skew lines. Apply the properties for
parallel and perpendicular lines.
 (3.2) Relate solving systems of equations algebraically to their geometric counterparts
using lines.
 (3.4) Differentiate between the three styles of proofs (paragraph, flow-chart, and twocolumn) and apply them to proving various theorems.
 (3.5) Define angles formed with parallel lines and their relationships amongst each other.
 (3.6) Use angle relationships to prove two lines are parallel.
Session 4: Congruent Triangles.
 (4.1) Discover the parts that make two triangles congruent. Classify triangles by their
sides and angles.
 (4.2) Determine measures of angles of a triangle.
 (4.3) Prove triangles are congruent using the Side-Side-Side and Side-Angle-Side
congruence postulates.
 (4.4) Prove triangles are congruent using the Angle-Side-Angle and Angle-Angle-Side
congruence methods.
 (4.5) Prove corresponding parts of congruent triangles are congruent.
 (4.6) Use properties of right and isosceles triangles to find missing parts and prove
triangles are congruent.
Session 5: Properties of Triangles.
 (5.1) Discover properties of perpendicular and angle bisectors.
 (5.2) Identify special segments such as perpendicular bisectors, angle bisectors, medians,
and altitudes of a triangle.
 (5.3) Identify and construct midsegments of triangles.
 (5.4) Ordering sides and angles of a triangle and the triangle inequality.
 (5.5) Use the hinge theorem and its converse.
Session 6: Polygons.
 (6.1) Identify, name, and classify polygons.
 (6.2) Find the measures of the angles of polygons.
 (6.3) Discover properties of parallelograms.
 (6.4) Prove that quadrilaterals are parallelograms.
 (6.5) Identify parallelograms that are rhombuses, rectangles, and squares.
 (6.6) Identify trapezoids, isosceles trapezoids, and their properties.
 (6.7) Identify kites and their properties.
Session 7: Transformations.
 (7.1) Identify the three basic rigid transformations in a plane and use transformations to
identify patterns.
 (7.2) Use properties of reflections.
 (7.3) Use properties of rotations.
 (7.4) Use properties of translations.
 (7.5) Use properties of glide reflections and compositions of transformations.
Session 8: Midterm Review.
Students will create two forms of review for midterms.
Session 9: Continue working on the Midterm Review.
Session 10: Similarity.
 (8.1) Compute ratios and proportions.
 (8.2) Use properties of proportions to solve problems.
 (8.3) Identify similar polygons.
 (8.4) Identify and use similar triangles.
 (8.5) Prove triangles are similar using Side-Side-Side and Side-Angle-Side similarity
theorems.
 (8.6) Use proportionality theorems to solve problems.
 (8.7) Identify and solve dilation problems.
Session 11: Right Triangles.
 (9.1) Use properties of right triangles.
 (9.2) Use the Pythagorean Theorem.
 (9.3) Use the Converse of the Pythagorean Theorem.
 (9.4) Find the lengths of sides of isosceles right and 30-60 right triangles.
 (9.5) Use sine, cosine, and tangent of an acute angle.
 (9.6) Solve a right triangle by using the inverse sine, cosine, and tangent.
Session 12: Circles.
 (10.1) Use vocabulary associated with circles.
 (10.2) Use properties of tangents to solve problems.
 (10.3) Measure central angles and arcs of circles.
 (10.4) Use properties of chords and arcs to solve problems.
 (10.5) Use inscribed angles to solve problems.
 (10.6) Measure angles formed by secants, tangents, and chords.
Session 13: Perimeter, Area, and Volume.
 (11.1) Find perimeter of polygons.
 (11.2) Find area of parallelograms and triangles.
 (11.3) Find area of trapezoids and kites.
 (11.4) Find area of regular polygons.
 (11.5) Find circumference and arc length of a circle.
 (11.6) Find area of circles.
 (12.1) Identify polyhedrons.
 (12.2) Find surface area of prisms and cylinders.
 (12.3) Find surface area of pyramids and cones.
 (12.4) Find volume of prisms and cylinders.
 (12.5) Find volume of pyramids and cones.
 (12.6) Find surface area and volume of a sphere.
Session 14: Final Exam.
Students will design an end of the year final exam.
Session 15: Continue working on the Final Exam.
Session 16: Wrap up and Evaluation.
Course Requirements:




Each student will be expected to read each chapter of the textbook and complete various
assigned exercises from the textbook. These exercises as well as any responses to lecture
notes must be posted to the discussion board for students to collaborate on weekly.
Each student must read at least 90% of the discussion board postings.
Each student is expected to respond to at least two other discussion board postings each
week. (This interaction will provide student-to-student feedback for the topic discussions
as well as the solutions to problems each student has posted).
Each student is expected to create lesson plans, assessments, and projects based upon
reading the textbook material and lecture notes. Although lesson plans, assessments, and
some activities will be individually completed, two projects will be completed in
assigned groups.
Course Evaluation:
Grades will be based on a point system.
10 points – for both (two) discussion board responses to classmates’ postings weekly
15 points – for each textbook exercise assignment or discussion topic posted to the discussion
board weekly
25 points – for each lesson plan submitted
25 points – for each Sketchpad activity submitted
25 points – for each assessment submitted
50 points – for each project/activity submitted
The overall grade will be based on the percentage of the total points (points earned out of total
points).
Required Resources:
Course Text (Primary):
Larson, R. E., Boswell, L., & Stiff, L. (1995). Geometry: An integrated approach. Lexington,
MA: D. C. Heath and Company. ISBN: 0-669-31667-9.
Supplemental Text(s):
Larson, R. E., Boswell, L., & Stiff, L. (1995). Geometry: An integrated approach. Formal
assessment. Lexington, MA: D. C. Heath and Company. ISBN: 0-699-31672-5.
System Requirements:
The following hardware and software are requirements for online learning:
 Computer with Macintosh or Windows operating system and 128MB of RAM
 Modem with baud rate of 56K
 Account with an Internet Service Provider
 Anti-virus software updated on a regular basis
 A WebCT supported browser
 The Geometer’s Sketchpad version 4.0
 Math Type 5.0 Equation
Course Syllabus:
*Assignments are due at 9pm on the Friday of each week.
Week Dates
Topic
Readings
1
Jan. 14-18
Introductions &
Sketchpad
Orientation
Assignments*
I) Post a brief one-paragraph
description introducing yourself to
your classmates and instructor.
Include the following:
 why are you taking the class
 what other education classes
have you taken during your
course of undergraduate
studies
 why you chose mathematics
and education as a major
 what you would like to learn
from taking this online
course
II) Download the instructions and
activities to familiarize yourself
with Geometer’s Sketchpad and its
functions from the drop box.
Submit a print screen of the
completed activity to the drop box.
2
Jan. 22-25
The Basic
Structure of
Geometry
Chapter 2
Lessons 2.12.6
I) Post to the discussion board a
relationship using the properties of
reflexive, symmetric, and transitive.
II) Design a lesson plan for one of
the six topics/sections in Chapter 2
to be submitted via the drop box.
3
Jan. 28-Feb. 1
Lines in a Plane
Chapter 3
I) Discussion board problems
Lessons 3.1- posting:
3.6 (skip 3.3) Page 114-115 #15 – 18, 20, 26
Page 130 #16
Page 145 #16
II) Design an inductive activity for
students to explore the angles
formed with parallel lines using
Geometer’s Sketchpad to be
submitted via the drop box.
4
Feb. 4-8
Congruent
Triangles
Chapter 4
Lessons 4.14.6
I) Discussion board problems
posting:
Page 173 #20, 22
Page 180 #11, 12
Page 186 #15, 16
Page 194 #14
II) Design lesson plans for sections
4.3 and 4.4 including a cooperative
learning activity in each to be
submitted via the drop box.
5
Feb. 11-15
Properties of
Triangles
Chapter 5
Lessons 5.15.5
I) Post to the discussion board the
pedagogical approach you would
use to assist your students in
learning about the special segments
of a triangle (section 5.2).
II) Design an activity using
Geometer’s Sketchpad to promote
your students’ learning of the topic
of perpendicular and angle bisectors
(section 5.1) using the program as
an inductive or deductive tool for
the learning process to be submitted
via the drop box.
6
Feb. 19-22
Polygons
Chapter 6
Lessons 6.16.7
I) Post to the discussion board the
pros and cons of providing
Geometry students with the formula
for finding the angles of a polygon
with a table showing how the
formula is derived (see Page 273) as
opposed to just giving the students
the formula and working with it.
II) Create a test for the assessment
of chapter 6. Be sure to include
multiple choice, short answer, and
open-ended questions. Submit it to
the drop box.
7
Feb. 25-29
Transformations Chapter 7
Lessons 7.17.5
I) Many textbooks do not include
special rules for rotating about the
origin using a 90, 180, and 270
rotation. Research using the
Internet or other resources and find
the rules. Post them to the
discussion board along with the
resource you have found them in.
II) Design a lesson plan for section
7.5 to be submitted via the drop
box.
8
March 3-7
Midterm
Review Project
Create two types of review for a
Geometry midterm. One must be a
formal review such as a review
sheet with sample questions and the
other must be creative such as a
game or Power Point slide show.
*This project will be completed in
assigned groups.
9
March 10-14
Midterm
Review Project
Midterm Review Project submitted
via the drop box.
10
March 17-20
Similarity
Chapter 8
Lessons 8.18.7
I) Discussion board problems
posting:
Page 377 #40, 42
Page 397 #10 – 12
Page 404 #12, 14
Page 416 #11 – 14
II) Design an inductive activity for
students to explore the properties of
similar triangles using Geometer’s
Sketchpad to be submitted via the
drop box.
11
March 24-28
Right Triangles
Chapter 9
Lessons 9.19.6
I) Post to the discussion board three
word problems that involve the use
of right triangles and trigonometric
ratios to solve. Provide the solution
in a separate posting.
II) Create a test for the assessment
of chapter 9. Be sure to include
multiple choice, short answer, and
open-ended questions. Submit it to
the drop box.
12
March 31-April 4
Circles
Chapter 10
Lessons
10.1-10.6
I) Discussion board problems
posting:
Page 488 #15 – 22
Page 497 #46, 48
Page 508 #15 – 18
Page 514 #16, 18
II) Design a lesson plan for section
10.6 to be submitted via the drop
box.
13
April 7-11
Perimeter, Area, Chapter 11
& Volume
Lessons
11.1-11.6
Chapter 12
Lessons
12.1-12.6
I) Discussion board problems
posting:
Page 583 #5 – 16
Page 637 #9 – 16
14
April 14-18
Final Exam
Project
Design an end of course cumulative
70-question final exam for
Geometry students. The exam must
contain 3 parts (as a typical
assessment): multiple choice, short
answer, and open-ended questions.
50 questions must be multiple
choice, 15 questions must be short
answer, and 5 questions must be
open-ended. An answer key must
be submitted with the final exam.
*This project will be completed in
assigned groups.
15
April 21-25
Final Exam
Project
Final Exam and Answer key must
be submitted via the drop box.
16
April 28-May 2
Wrap up,
Evaluation, &
Reflection
I) Complete the evaluation of the
course through the online
questionnaire.
II) Post to the discussion board a
follow-up reflection based upon
your initial posting of what you
wanted to learn by taking this
course.