Web 2.0 Tools and Project Based Learning Kim Peacock, B.Ed., M.Ed.
AuthorsRobert Levesque, DSS, B.Sc., B.Ed., M.Ed. To apply and master different.
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Transcript of AuthorsRobert Levesque, DSS, B.Sc., B.Ed., M.Ed. To apply and master different.
<Enter Title>
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Authors Robert Levesque, DSS, B.Sc., B.Ed., M.Ed.
To apply and master different mathematical concepts in relation to art Drawings
Objectives
DescriptionThe Art of Drawing requires creative and intrinsic thinking processes. Once a drawing is dissected into its various constituent parts; i.e. segments comprising straight lines, parabolas, circles, areas, etc., parts of a whole can be observed. Henceforth, springs a visualising, an approach into the world of Mathematics. In other words, a clear relationship between the world of mathematics and the world of art can be established. Drawings are represented according to their function and regions of inequalities within a restricted range or domain. Therefore, it is possible to create an image, a creative drawing, using various mathematical functions. This pragmatic activity presupposes a high intellectual challenge. This cognitive reflection allows the opportunity to experience the relationship between two fields that have been considered poles apart: Mathematics and Art. This multi-disciplinary project provides an opportunity for students to express themselves visually using mathematical skills. Being able to make use of various mathematical functions, applying them, translating them vertically and horizontally, positioning these lines and curves at a desired, precise location, enables students, once the individual graphs are connected together, to create a work of art. The use of computers enables us to observe the fusion of these two distinct worlds.
Learning Areas Mathematics
Levels 16-17-18 year olds
Project Overview
Title: The Art of Mathematics
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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.
Title: The Art of Mathematics
GrapheEasy; MS Office; Desire2Learn (content platform for distance learning); Interwise (communication platform for distance learning)
Software
Drawings, graphs, grapheEasy, functions, horizontal translation, vertical translation, Art, constructive learning, mathematics, project, mathematical parameter
Keywords
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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.
Title: The Art of Mathematics
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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.
Title: The Art of Mathematics
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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/Educateurs/Ressources%20pedagogiques%20et%20pro/
Mathematiques/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.
Title: The Art of Mathematics
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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_etudes/secondaire/pdf/
mat536.pdf
Manitoba: http://www.edu.gov.mb.ca/k12/cur/parents/senior/grade12.html#math
Nova Scotia: https://sapps.ednet.ns.ca/Cart/items.php?
CA=12&UID=20071001163058204.82.241.153
Alberta:
http://www.education.gov.ab.ca/french/Math/10-12/Program/Applique/appl.asp
Prince Edward Island: http://www.gov.pe.ca/photos/original/ed_sps_0708.pdf
Newfoudland and Labrador: http://www.ed.gov.nl.ca/edu/sp/sh/math/math3206.pdf
Title: The Art of Mathematics
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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..
Title: The Art of Mathematics
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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.
Title: The Art of Mathematics
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Work Samples, Teacher and Student Reflection
Student: Julie Leblanc.
Approximately 135 mathematical equations
Title: The Art of Mathematics
sinus function
quadratic functionlogarithmic function
sinus function
Logarithmic function
circle
linear
quadratic function
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Work Samples, Teacher and Student Reflection
Student: Megan
Approximately 135 mathematical equations
Title: The Art of Mathematics
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Work Samples, Teacher and Student Reflection
Student: Valérie Lang
Approximately 225 mathematical equations
Title: The Art of Mathematics
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Work Samples, Teacher and Student Reflection
Student: Tristan Martin
Approximately 210 mathematical equations
Title: The Art of Mathematics
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Work Samples, Teacher and Student Reflection
Student: Sophie Chiasson
Approximately 135 mathematical equations
Title: The Art of Mathematics
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Work Samples, Teacher and Student Reflection
Student: Stacey Morris
Approximately 225 mathematical equations
Title: The Art of Mathematics
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Work Samples, Teacher and Student Reflection
Student: Billy Nowlan
Approximately 105 mathematical equations
Title: The Art of Mathematics
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Work Samples, Teacher and Student Reflection
Student: François Laplante
Approximately 270 mathematical equations
Title: The Art of Mathematics
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Work Samples, Teacher and Student Reflection
Student : Chantal Richard
Approximately 90 mathematical equations
Title: The Art of Mathematics
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Work Samples, Teacher and Student Reflection
Student: Stéphanie Turner.
Approximately 120 mathematical equations
Title: The Art of Mathematics
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Work Samples, Teacher and Student Reflection
Student: Gisèle Doiron.
Approximately 165 mathematical equations
Title: The Art of Mathematics
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Work Samples, Teacher and Student Reflection
Student: Clément Savoier.
Approximately 75 mathematical equations
Title: The Art of Mathematics
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Work Samples, Teacher and Student Reflection
Student: Stéphanie Caissie.
Approximately 255 mathematical equations
Title: The Art of Mathematics
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Work Samples, Teacher and Student Reflection
Student: Clément Savoie.
Approximately 75 mathematical equations
Title: The Art of Mathematics
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Work Samples, Teacher and Student Reflection
Student: Joline Poirier.
Approximately 120 mathematical equations
Title: The Art of Mathematics
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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 teacher’s 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 other’s 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 teacher’s 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.
Title: The Art of Mathematics
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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.
Title: The Art of Mathematics
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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
Title: The Art of Mathematics
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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.
Title: The Art of Mathematics
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Annexe A
<Information about school and teacher>
Students write their
mathematical
equations here The graphs related to
their equations
appear here.
Title: The Art of Mathematics
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Annexe A
<Information about school and teacher>
Title: The Art of Mathematics
Step 1 : Click here in order to write
your first equation
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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Assessment and Standards
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)2
+2 Step 4 : Choose the desired
color “blue” and a thicker
curve. Click end.
Your first equation.
Click on the « + » sign in order
to have more information on
the equation and curve