Title: The Art of Mathematics

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Title The Art of Mathematics
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Title The Art of Mathematics
Teacher Planning and Management
The Cité des Jeunes A.M. Sormany is a
Comprehensive Francophone High School, opened in
Edmundston, New Brunswick, Canada in 1972. 
Student enrolment originally reached around 2000
students a year from grades 10 to 12 with 600/700
students graduating each year.  Presently, there
are around 1350 students from grades 9 to
12, including students with special needs. With
a wide, diversified curriculum, the school is
considered one of the best in the province.
Equipped with a modern communication system,
it allows students and teaching staff to link up
with other learning institutions.   The school's
aims and objectives are to provide students with
a learning environment, where, within an
atmosphere of mutual respect between students and
staff, they are able to realize their full
potential. The school's fundamental values are
based on self-reliance, respect
and social responsibility. The school strives to
guide students through their intellectual,
creative and social pursuits so as to enable them
to play their full, positive role in an
ever-changing society. The school
also encourages students to have a sense of pride
in their francophone identity. 
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Title The Art of Mathematics
Teacher Planning and Management
The project I am presenting to you now, has been
used for the past three years, both in the
classroom environment and via the internet,
throughout the province. I have found
this project encourages and motivates students.
It allows them to explore numerous possibilities
offered by this approach and to develop their
artistic abilities. It also facilitates them to
gain a better understanding of various
mathematical concepts. By using this approach, I
came to realize that students were able to
master mathematical concepts related to the
project. They showed little or no difficulties
during the review period. The effectiveness of
this approach is also evident from the
results of the final examination. All the schools
using this programme via the internet also have
access to a software called GrapheEasy. This
makes the use of the programme a lot easier.
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Title The Art of Mathematics
Teacher Planning and Management
This project meets the requirements of the
Department of Education for the Province of
New-Brunswick as to the mathematical content of
its curriculum. Students can apply their
knowledge pertaining to the graphing of functions
such as Linear, Constant, Quadratic, Square Root,
Absolute value, Exponential, Logarithmic and
Trigonometric (sinus, cosine). More importantly,
students learn how to modify these accordingly to
certain parameters. This project allows students
not only to learn mathematical concepts, but to
apply and use them and master them while building
a challenging drawing. Applying mathematical
concepts to a practical, visual project is a very
challenging and gratifying experience. This is
not a new concept and has existed for a long
time. Very often, teachers would decline this
initiative because it is time consuming and very
tedious to correct. With the arrival of
computers and the availability of easy to use
software, we can now make drawings with a great
deal of precision. Also, this approach
necessitates few corrections since an error can
be readily observed with the software.
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Title The Art of Mathematics
Teacher Planning and Management
Programe of studies This project includes many
concepts proposed by the Provincial Department of
Education for students of the grades 11 and 12
levels. https//portail.nbed.nb.ca/Topics/Educate
urs/Ressources20pedagogiques20et20pro/Mathemati
ques/Pages/default.aspx Math 30311 (Grade
11) Specific learning skills Able to solve
problems and analyse situations using quadratic
functions and their graphs i.e. problems of
maximum and minimum values as applied to everyday
situations. Math 30321 (Grade 11) Graphical
representation of absolute values, square roots,
rational expressions. Math 30411 (Grade
12) Graphical representation of trigonometric
functions such as sinus and cosine and the
ability to use them in problem solving situations
concerning the amplitude, the period and phase
shift. Math 30421 (Grade 12)  To recognize
algebraically and graphically the characteristics
of functions domain, range, use of parameters,
the use of symmetry in relations the x and y
axes. Being able to recognize the
characteristics and to transform specific
functions such as linear, quadratic, cubic,
rational, square root, absolute values,
exponential, logarithmic and trigonometric.
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Title The Art of Mathematics
Teacher Planning and Management
Canadian Planning and Management The
mathematical concepts previously mentioned can be
found in all Canadian provincial curricula. The
concepts can be observed at different grade
levels such as grade 10, 11 or 12. Details can
be observed from the following sites Québec,
http//www.mels.gouv.qc.ca/DGFJ/dp/programmes_etud
es/secondaire/pdf/mat536.pdf Manitoba
http//www.edu.gov.mb.ca/k12/cur/parents/senior/gr
ade12.htmlmath Nova Scotia
https//sapps.ednet.ns.ca/Cart/items.php?CA12UID
20071001163058204.82.241.153 Alberta
http//www.education.gov.ab.ca/french/Math/10-12/P
rogram/Applique/appl.asp Prince Edward Island
http//www.gov.pe.ca/photos/original/ed_sps_0708.p
df Newfoudland and Labrador http//www.ed.gov.nl
.ca/edu/sp/sh/math/math3206.pdf
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Title The Art of Mathematics
Teacher Planning and Management
The Francophone section of the Department of
Education purchased the license of the software
GrapheEasy allowing its installation in each of
the French schools throughout New-Brunswick.
When teaching on line, all of my students have
access to computers furnished by the schools.
This allows them to work independently on their
project using the software GrapheEasy. When
teaching in a classroom situation, students are
invited to produce their choice of a drawing
using the two computers available in the
classroom. Also available to them are computer
laboratories where some 30 computers are
installed. They have access to these during
lunch period, after school or during their
laboratory courses. In order to get started on
their project, brief examples of several graphs
are available through tutorials, (see annexe
A). The purchase of the license also allows the
teachers to download the software at their home
for their personal use (software available in
English and French). This allows them to
familiarize themselves and to master the content
of the software. This is a semestrial project
offered over a four month period. This approach
allows students to work at their own rate on
these mathematical concepts and apply the learned
knowledge to produce a practical, visual project.
The teacher is available to answer questions
either on the software or the mathematical
concepts. The teacher acts as a guide throughout
these learning experiences..
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Title The Art of Mathematics
Teacher Planning and Management
As explained, students can work individually at
their computer but can also help each other. For
those who have a computer and the internet at
home, they can download a temporary version of
the software in order to experiment with various
functions. However, this version will not allow
them to save their work. In the following pages,
you will find drawings made by my students. With
each drawing, you will find the name of the
students and also the numbers of equations
required in order to construct their drawings. It
must not be forgotten that the drawings are made
of segments of straight lines, curves and areas
completely defined by the students. All
equations and functions are represented by a
limited domain and range that students have to
define in order to arrive at a desired result.
Please notice the small details.
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Title The Art of Mathematics
Work Samples, Teacher and Student Reflection
Student Julie Leblanc. Approximately 135
mathematical equations
Logarithmic function
circle
linear
sinus function
quadratic function
quadratic function
logarithmic function
sinus function
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Title The Art of Mathematics
Work Samples, Teacher and Student Reflection
Student Megan Approximately 135 mathematical
equations
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Title The Art of Mathematics
Work Samples, Teacher and Student Reflection
Student Valérie Lang Approximately 225
mathematical equations
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Title The Art of Mathematics
Work Samples, Teacher and Student Reflection
Student Tristan Martin Approximately 210
mathematical equations
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Title The Art of Mathematics
Work Samples, Teacher and Student Reflection
Student Sophie Chiasson Approximately 135
mathematical equations
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Title The Art of Mathematics
Work Samples, Teacher and Student Reflection
Student Stacey Morris Approximately 225
mathematical equations
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Title The Art of Mathematics
Work Samples, Teacher and Student Reflection
Student Billy Nowlan Approximately 105
mathematical equations
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Title The Art of Mathematics
Work Samples, Teacher and Student Reflection
Student François Laplante Approximately 270
mathematical equations
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Title The Art of Mathematics
Work Samples, Teacher and Student Reflection
Student Chantal Richard Approximately 90
mathematical equations
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Title The Art of Mathematics
Work Samples, Teacher and Student Reflection
Student Stéphanie Turner. Approximately 120
mathematical equations
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Title The Art of Mathematics
Work Samples, Teacher and Student Reflection
Student Gisèle Doiron. Approximately 165
mathematical equations
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Title The Art of Mathematics
Work Samples, Teacher and Student Reflection
Student Clément Savoier. Approximately 75
mathematical equations
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Title The Art of Mathematics
Work Samples, Teacher and Student Reflection
Student Stéphanie Caissie. Approximately 255
mathematical equations
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Title The Art of Mathematics
Work Samples, Teacher and Student Reflection
Student Clément Savoie. Approximately 75
mathematical equations
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Title The Art of Mathematics
Work Samples, Teacher and Student Reflection
Student Joline Poirier. Approximately 120
mathematical equations
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Title The Art of Mathematics
Work Samples, Teacher and Student Reflection
Most of the time, when the project is completed,
the students own expectations are exceeded.
Teachers and students are fascinated by the
ideas, creativity and the complexity of the
chosen equations which make up the drawing. At
the beginning, students will often ask the number
of equations required in order to meet the
teachers objectives. I have never required a
minimum number of equations. Through
self-motivation and interest toward their
project, students often surpass themselves and
produce very creative work indeed. The sharing
of the projects at the end of the semester, is
much appreciated by all students and their peers
show a keen and intelligent interest in each
others work. Once they are involved in their
project, they will often ask how they could
improve their drawing by making use of other
mathematical functions. This challenge brings
them to explore mathematical concepts that are
not taught at their grade level (for example,
application of the integral calculus). After a
few explanations on the teachers behalf, they
apply these new applications to their drawings
thereby exceeding the course outlines and the
objectives set for that grade level. Clearly,
without the technological advances now available,
all this would be impossible. I presented this
approach in 2005 and also in 2007 at an Atlantic
convention called APTICA (Pedagogical Advancement
of Technologies and Communications in the
Atlantic Provinces). The enthusiasm that I
received was very reassuring.
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Title The Art of Mathematics
Work Samples, Teacher and Student Reflection
The success of the students depends very much on
the time spent working on his project. To help
the student, it is essential that the teacher
requires a rough sketch by mid-semester in order
that the student does not undertake his project
at the last moment. This is a semestrial project
and without establishing this deadline of
mid-semester, many students might postpone
starting their project until the end, thus
producing an inferior drawing with less
mathematical content. Generally, students are
very enthusiastic to work on the project. When
teaching mathematics, a teacher often hears the
following comments Why are we learning this and
what use will it be? Using this approach, I have
never heard that remark when studying vertical or
horizontal translations. The necessity of these
concepts is indispensable for their project and
gives meaning to their learning experience. After
offering a few explanations and examples,
students demonstrate little difficulty initiating
their project. Naturally, throughout the
semester, certain students will ask precise
questions pertaining to the use of the software.

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Title The Art of Mathematics
Teaching Resources

• Student Project Overview
• Tasks Required
• Explain the project at the beginning of the
  year when presenting the course outline.
• Ensure all students have access to a computer and
  the software.
• Teach the students the necessary mathematical
  concepts and familiarize them with the software,
  its environment and applications.
• Use the software for the graphing of equations
  and inequalities.
• Specify a date, at mid-semester, for their
  submission of a sketch of their proposed drawing.
• Specify the method of evaluation in order that
  students are aware of the criteria of assessment.

Documents
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Title The Art of Mathematics
Assessment and Standards
Assessment Rubrics Grading procedures will
vary with different teachers. For example, I
offer the following suggestion. The weight and
the evaluation of the project are based on the
following criteria's (calculated on a value of
40) - Creativity of the drawing
0 2 4 6 8 10
points - Level of difficulty of equations
0 2 4 6 8 10
points - Variety of equations linear, cubic,
absolute value, inequalities, circle,
quadratic, logarithmic, exponential,
trigonometric..
0 2 4 6 8 10 points - Appearance
color, design, thickness of curves 0 2 4
6 8 10 points Mapping the Standards This
project allows students to explore and master
mathematical concepts as prescribed by the
Department of Education in all Canadian
Provinces. We can expect learning experiences
that are reliable, lasting and transferable.
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Title The Art of Mathematics
Annexe A
ltInformation about school and teachergt
Students write their mathematical equations here
The graphs related to their equations appear here.
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How to work with GrapheEasy ?

Title The Art of Mathematics
Annexe A
Step 1  Click here in order to write your first
equation
ltInformation about school and teachergt
Step 2  What form do you want? Click on the
quadratic form and the software will propose
different type of equations for the parabola.
Choose the first form i.e. the standard form
A(x-B)2 C. Click next.
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Then
Title The Art of Mathematics
Step 3  Choose 2 for the value of A, B and C,
that is, the equation of the form y (x)
2(x-2)22
Assessment and Standards
Step 4  Choose the desired color blue and a
thicker curve. Click end.
Click on the    sign in order to have more
information on the equation and curve
Your first equation.