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St. Francis Xavier University
P.O. Box 5000
Antigonish, Nova Scotia
B2G 2W5
Pedagogical Foundations for Elementary Mathematics Education III:
Geometric Reasoning - Education 403
Instructor: Tara Taylor
Office: Nicholson Annex 22A
Office Phone: 867-3395
Email: ttaylor@stfx.ca
Web: http://people.stfx.ca/ttaylor/EDUC403/summer2014/geo2014.html
Office Hours: by appointment (will also be available before and after classes, and on
breaks)
This course is designed to help elementary teachers develop a better understanding
of geometry. This will be achieved through hand-on activities and discussions of
relevant concepts, problems, and applications of geometry.
Course Goals:
1. Pedagogy of Topology
 Investigate and explore aspects of topology including its origins and
history
 Make and test conjectures in relation to topology: connectivity,
orientability, simple closed curves, Poincare conjecture
2. Pedagogy of Euclidean Geometry
 Investigate and explore the properties of 2D shapes: regular polygons,
triangles, quadrilaterals, etc
 Investigate and explore the properties of solids: Platonic solids, etc
 Make and test conjectures and examine minimum and sufficient
conditions in relation to geometric figures and solids
3. Pedagogy of Transformational Geometry
 Explore the effect of various transformations on geometric figures:
translations, rotations, reflections

Explore and apply symmetries: symmetries of the square, other
shapes
4. Pedagogy of Geometric Constructions
 Explore geometric constructions: using straight-edges and compasses,
Geometer’s sketchpad
 Make and test conjectures in relation to geometric constructions
5. Pedagogy of Non-Euclidean Geometry
 Investigate and explore aspects of non-Euclidean geometries, such as
hyperbolic geometry, and the origins and history
 Make and test conjectures in relation to non-Euclidean geometries
6. Pedagogy of Fractals
 Investigate and explore aspects of fractal geometry: self-similarity,
dimension, examples, etc
 Make and test conjectures in relation to fractal geometry
Materials:
All Materials will be provided on the website
http://people.stfx.ca/ttaylor/EDUC403/summer2014/geo2014.html.
University Policy on Academic Integrity
St. Francis Xavier University values academic integrity. Please familiarize yourself with
the policy in section 3.9 of the academic calendar. Any infractions will be dealt with
according to this policy.
Attendance
Students are reminded that attendance is mandatory for all classes. If you are unable to
attend class and have a legitimate reason for doing so, you should send an email prior to
the class advising me of the reason why you are unable to attend. You will be expected to
make up any missed time through alternate assignments.
Class Plans - Please check website for class plans and updates. Our tentative outline is as
follows:
Date
Topic
July 8 (AM)
Introductions, what is geometry, “straight”, start topology
July 8 (PM)
More topology
July 9 (AM)
Origins of Euclidean Geometry, Pythagorean Theorem, Distance
July 9 (PM)
Transformations, Congruence, Parallel Lines, Sum of angles
July 10 (AM)
Symmetries of the Square, similar triangles, the golden ratio
July 10 (PM)
Summary of week and open-book quiz
July 15 (AM)
Discussion of geometry paper, constructions
July 15 (PM)
More constructions, tilings, solids
July 16 (AM)
Explorations of non-Euclidean geometries
July 16 (PM)
Fractals
July 17 (AM)
Summary and open-book quiz, presentations
July 17 (PM)
Presentation/discussion of portfolios and meaningful activities
Grading Scheme
Evaluation Tool
Portfolio
Quiz 1 on first week material
Quiz 2 on second week material
Class Participation
Meaningful activity (group presentation)
Score
30%
15%
15%
15%
25%
100%
Portfolio (30%)
The portfolio will be your record of the course that will hopefully be useful for you in
future teachings. This is where you can record key concepts, examples, questions,
reflections, ideas for activities that are meaningful and relevant to you. The portfolio
doesn’t need to be formal- it should organically develop- it can have doodles and be
hand-written. You can include interesting references/websites that you have found.
Time will be given each day to work on your portfolio.
The final version will be shared and discussed on the last day.
Quizzes (30%)
Each week will end with a summary of the important concepts from the week and an
open-book quiz based on the concepts. You can use any materials- books, notes,
calculators, etc. The quizzes are done individually. The questions will be similar to
exercises that we do in-class, as well as more reflective questions about the deeper
meanings of the concepts.
Class Participation (15%)
The course needs your participation and active engagement. Please ask lots of questions,
provide feedback for what is working and what isn’t working, comments on how
concepts could be used in your classrooms.
Meaningful Activity (25%)
Alone or in groups of at most 3 people, you will come up with a geometry based activity
that you could do with your own students. The activity should help the students
understand some aspect of geometry and needs to be meaningful and relevant to them.
The goal of this is to develop more examples of hands-on activities that you can take
back to your students. The activities will be shared with the rest of the class for feedback
and discussion. The activity can take on any form and focus on any geometry aspects that
we have discussed in the course or that you have seen elsewhere.
On Grading
While individual excellence will be rewarded, it is expected that the class average of marks will normally
fall between 78 and 84. The following descriptors highlight the typical grade range:
A+ = 85+ Exceptional: from all or most others
 Knowledge (subject matter): In-depth, exceptional, well developed, superior, relevant knowledge
and understanding of subject matter and relevant, related areas
 Arguments (differing viewpoints): Logical, exceptional, creative, thought-provoking, critical
compelling awareness of all related arguments is demonstrated
 Reasoning (analyzes, evaluates, synthesizes): Cogent analysis, exceptional, convincing critical
thinking skills: analyzes, refutes, critiques, examines, and values all relevant sources
 Position/stance (formulates ideas and concepts): A convincing, exceptional, perceptive, careful
and very well-developed argument is presented throughout
 Communication (written, oral, visual): Exceptional mastery of style, tone, language structure and
conventions
 Demonstration: Efficient, exceptional, consistent, compelling demonstration of knowledge and
ability to create/perform the skill at hand with finesse
A = 80-84 Excellent
 Knowledge (subject matter): In-depth, well-developed knowledge of subject matter and relevant,
related areas
 Arguments (differing viewpoints): Logical, critical awareness of all salient arguments is
demonstrated
 Reasoning (analyzes, evaluates, synthesizes): Convincing, excellent critical thinking skills:
analyzes, refutes, critiques, examines, and values all relevant sources
 Position/stance (formulates ideas and concepts): A convincing, well-developed, careful argument
is presented throughout
 Communication (written, oral, visual): Excellent style, tone, language structure and conventions
 Demonstration: Consistent, excellent demonstration of knowledge and ability to create/perform the
skill at hand
B = 75-79 Very Good
 Knowledge (subject matter): Proficient knowledge of subject matter and related areas
 Arguments (differing viewpoints): Logical awareness of all the arguments is demonstrated
 Reasoning (analyzes, evaluates, synthesizes): Proficient critical thinking skills: analyzes,
refutes, critiques, examines, and values all relevant sources
 Position/stance (formulates ideas and concepts): A careful argument is presented throughout
 Communication (written, oral, visual): Proficient style, tone, language structure and conventions
 Demonstration: Proficient demonstration of knowledge and ability to create/perform the skill at
hand
B- = 70-74 Good

Knowledge (subject matter): Sufficient knowledge of subject matter and related areas
 Arguments (differing viewpoints): Sufficient awareness of all the arguments is demonstrated
 Reasoning (analyzes, evaluates, synthesizes): Sufficient critical thinking skills
 Position/stance (formulates ideas and concepts): A sufficient argument is presented throughout
 Communication (written, oral, visual): Sufficient style, tone, language structure and conventions
 Demonstration: Sufficient demonstration of knowledge and ability to create/perform the skill at
hand
C+ = 65-69 Fair
 Knowledge (subject matter): Partial but developing knowledge of subject matter and related areas
 Arguments (differing viewpoints): Awareness of the arguments is relevant but limited




Reasoning (analyzes, evaluates, synthesizes): Limited and developing critical thinking skills
Position/stance (formulates ideas and concepts): A limited, relevant argument is presented
throughout
Communication (written, oral, visual): Limited style, tone, language structure and conventions
Demonstration: Limited demonstration of knowledge and ability to create/perform the skill at hand
C- = 60-64 Minimal Pass
 Knowledge (subject matter): Limited and in places inadequate knowledge of subject matter and
related areas
 Arguments (differing viewpoints): Awareness of arguments is limited and irrelevant in places
 Reasoning (analyzes, evaluates, synthesizes): Limited and in places inadequate critical thinking
skills
 Position/stance (formulates ideas and concepts): A limited and, in places, irrelevant argument is
presented throughout
 Communication (written, oral, visual): Limited and in places inadequate knowledge of style,
tone, language structure and conventions
 Demonstration: Limited demonstration and, in places, inadequate knowledge and ability to
create/perform the skill at hand
F = less than 60 Failure
 Knowledge (subject matter): inadequate knowledge of subject matter and related areas
 Arguments (differing viewpoints): Awareness of arguments is inadequate and irrelevant in places
 Reasoning (analyzes, evaluates, synthesizes): inadequate critical thinking skills
 Position/stance (formulates ideas and concepts): inadequate and irrelevant argument is presented
throughout
 Communication (written, oral, visual): inadequate knowledge of style, tone, language structure
and conventions
 Demonstration: inadequate demonstration and knowledge and ability to create/perform the skill at
hand
Classroom Equity Policy
For all members of our class to learn effectively, this classroom must be a safe learning environment. To
ensure safety for all students, the policy in this class is that no one shall be discriminated against or
harassed on the basis of age, race, colour, religion, creed, sex, sexual orientation, physical disability or
mental disability, an irrational fear of contracting an illness or disease, ethnic, national or Aboriginal origin,
family status, marital status, source of income, political belief, affiliation or activity, an individual's
association with another individual or class of individuals having any one or more of the characteristics
referred to in the list above. Whether a person intended their words or actions to be discriminatory or
harassing does not matter; it is the effect of words and actions that is the focus of equitable treatment.
Discrimination is the distinctive treatment of a person with one or more of the above characteristics which,
in the view of a reasonable person, has the effect of imposing a burden, obligation or disadvantage or limits
and withholds benefits and advantages to an individual or a class of individuals. Harassment (including
sexual harassment) is offensive or objectionable conduct or comment toward another person or persons that
is known or ought to be known from the perspective of a reasonable person in the position of the
complainant to be intimidating, offensive or unwelcome.
Please feel free to discuss with me any questions or concerns you have about discrimination or
harassment. If I cannot help you resolve your problem, you may discuss the matter further with the Human
Rights and Equity Advisor, Marie Brunelle (mbrunell@stfx.ca)