2005 CANADIAN MATHEMATICS EDUCATION FORUM
May 68, 2005
FIELDS INSTITUTE

FORUM CANADIEN 2005
SUR L'ENSEIGNEMENT DES MATHÉMATIQUES
68 mai 2005
L'INSTITUT FIELDS

SHARING SUCCESSES/ PARTAGEONS NOS RÉUSSITES
Abstracts
S1a) L'EXPÉRIENCE MENÉE AU CÉGEP
DE RIMOUSKI DANS LES COURS DE MATHÉMATIQUES
Personne resource: Philippe Etchecopar (Cégep de Rimouski)
etchecop@globetrotter.net
L'expérience menée au Cégep de Rimouski dans les
cours de mathématiques (quatre cours de 75 périodes sur
deux ans) du programme de Sciences de la nature consiste à actualiser
l'enseignement des mathématiques.
Cette expérience vise à montrer aux élèves
l'utilité des mathématiques dans différents domaines
en utilisant les NTIC, logiciels de calcul symbolique et Internet. Elle
vise également à leur présenter les mathématiques
sous un aspect plus vivant que celui des calculs et des cours magistraux
en incluant dans chaque cours un volet culturel. Ce volet montre comment
les mathématiques se sont développées et comment
elles ont participées aux débats d'idées.
Les logiciels de calcul symbolique sont utilisés pour résoudre
des problèmes par modélisation et
simulation, les deux grands changements que les ordinateurs ont introduit
en sciences. Résoudre un
problème ce n'est plus rechercher une solution numérique,
c'est comprendre un phénomène. Cette
recherche du modèle mathématique permettant de traduire
et de reproduire un phénomène naturel met
en évidence le rôle des mathématiques comme langage
de la nature. Les simulations permettent aux
élèves de développer leur autonomie et leur esprit
critique, l'expérimentation reprend sa place en mathématique.
Par l'utilisation des ressources mathématiques disponibles sur
Internet, les élèves apprennent à trouver, évaluer,
classer et utiliser l'information.
Cette utilisation des NTIC a demandé une nouvelle approche pédagogique
et la rédaction de manuels adéquats. Le travail en laboratoire
représente environ 20% des cours.
L'introduction d'une certaine culture scientifique dans chaque cours
présente d'abord aux élèves une autre vision des
mathématiques, des mathématiques à visage humain.
En montrant le cadre dans lequel se sont développés les
concepts, les idées qui les ont portés, les polémiques
qu'elles ont suscitées, les élèves voient en quoi
les mathématiques sont un élément majeur de notre
culture, ils voient que, loin d'être une discipline figée,
les mathématiques sont dynamiques et qu'il y a place à
la controverse, ce qui est un secret bien gardé.
Le volet culture permet aussi de vulgariser des sujets qui autrement
ne seraient traités qu'à l'université, comme l'infini.
Les élèves comprennent mieux des concepts comme la limite
d'une fonction quand ce concept est replacé dans son cadre historique
qui s'étale sur près de deux siècles.
Les thèmes abordés sont, par exemple, l'histoire des
nombres, l'histoire du calcul différentiel, la nature des mathématiques,
l'infini, les géométries non euclidiennes et fractales,
le chaos, etc.
Les travaux prennent la forme de fiches de lectures, recherches, etc,
en coordination avec des cours de formation générale,
philosophie en l'occurrence. Ces travaux comptent pour 5% de la note
finale. Cette expérience est menée depuis une dizaine
d'années et cette actualisation de l'enseignement des
maths est très appréciée des élèves,
les évaluations annuelles en font foi.
Elle est également très stimulante pour les enseignantes
et les enseignants et un professeur convaincu
est beaucoup plus convaincant.
S1b) COLLEGE EXPERIENCE: TEACHING MATHEMATICS IN
CONTEXT
Presenter: Dragana Martinovic (Sheridan Institute of Technology and
Advanced Learning)
dragana.martinovic@sheridaninstitute.ca
My proposal for a success story draws from my love for mathematics
and belief that everybody
can find enjoyment in it and be empowered by learning how to think mathematically.
Mathematics teachers at colleges have special challenge to overcome:
Our students are interested
in obtaining skills and not necessarily general knowledge and they need
to be convinced that
what they are learning will be put in some use later in school or at
some point in the workplace.
Although mathematics textbooks contain more and more examples of applications
(i.e., "In a
simple electronic circuit, find the resistance for given voltage and
current," is mathematically
equivalent to: "For how long you should invest certain amount of
money with a given interest rate in order to earn given interest?"),
they often appear superfluous, because either students know nothing
about resistance yet or they know that the simple interest is not used
in banking at all.
The following are some elements of successful approach to teaching
mathematics at Sheridan:
1. It is beneficial to teach across disciplines in a program. My experience
in teaching
mathematics (in schools of engineering, business, and information technology),
computer
science, and involvement in curriculum development help me to be aware
of the sequencing of
courses and their overall outcomes. In other words, I teach trade using
math and math using
trade. This approach provides students with challenging topics and helps
them explore relatively
simple applications of mathematics in what they already have studied.
I would like to share with
you some examples from statistics, calculus and computer science courses
that were "AHA!"
moments for my students and consequently ended in successful learning
experiences:
I found both of [math] courses to be full of valuable information that
will no doubt
become even more vital in later years (1st semester student, evaluation
of the program).
2. Communicating mathematics is important skill and in almost all of
math courses at Sheridan,
students work on group or individual projects and present their investigations
orally and in a written form.
3. Students have laptops which provides for simulation, exploration
using analytical software
(i.e., Maple), organization of data (spreadsheets), and visualization
of findings.
4. The colleges deal with a diverse population of students. Although
the concept of culturefree
mathematics (in a research community) is almost abandoned, it is upon
math educators to
become 'mathematical enculturators' (Bishop, 1991) and talk about cultural
aspects of
mathematics, about values in mathematics, and about different histories
of mathematics. There
are plenty of excellent (but not widely popularized) examples of contributions
from all over the
globe that our students benefit from: development of numerical systems,
famous constants,
approximations, etc. Our professional development meetings are good
opportunity for
exchanging such teachable moments and putting mathematics in context
for our students.
Bishop, A.J. (1991) Mathematical Enculturation: a Cultural Perspective
on Mathematics
Education, Dordrecht, Holland: Kluwer.
S1c) LEARNING HOW TO TEACH AND LEARN MATHEMATICS

"TEACHING MATHEMATICS" COURSE AT MCMASTER UNIVERSITY
Presenter: Miroslav Lovric (McMaster University)
lovric@mcmaster.ca
The course "Teaching Mathematics" has been designed in an
attempt to improve the quality of instruction delivered by undergraduate
teaching assistants in mathematics at McMaster University. Problems
traditionally experienced by our teaching assistants range from a lack
of knowledge of mathematics content, and lack of guidance by lecturers
and course coordinators, to rudimentary teaching skills without opportunities
for improvement, to low motivation, and inadequate preparation for a
tutorial session.
A group of undergraduate students are enrolled in the "Teaching
Mathematics" course and concurrently work as teaching assistants
for a firstyear calculus course. In other words, they are both teachers
and learners at the same time. A framework for the "Teaching Mathematics"
project is that of a learning partnership on several levels: partnership
between undergraduate students, i.e., between undergraduate teaching
assistants, and between undergraduate teaching assistants and students
in their tutorial groups. It is also a learning partnership between
"Teaching Mathematics" course instructor and the students
(in the "Teaching Mathematics" course). Such framework is
an echo of the fact that education must be an active and inspired twoway
communication.
In this session, I plan to briefly outline the design of the "Teaching
Mathematics" course, and to discuss various issues related to both
the course and to my students' performance as teaching assistants. Teaching
assistants work on improving their written and oral communications skills
through writing about mathematics, conducting tutorial sessions and
through oneonone sessions with their students during office hours.
In "Teaching Mathematics" sessions, we discuss and analyze
elements that constitute good teaching practice  especially preparation
(knowledge of mathematics) and communication. By reading and criticizing
journal and newspaper articles and books we get introduced to theoretical
aspects of teaching, and, in particular, teaching mathematics. By learning
how to teach mathematics we also learn how to learn mathematics  certainly,
a very valuable asset  especially for those students who plan to major
in mathematics.
"Teaching Mathematics" course provided me with an opportunity
to constantly monitor the work of my students  my teaching assistants
(we used evaluations, selfevaluations and personal interviews). I have
collected valuable data and information that I plan to discuss in my
session.
S1d) MATHEMATICS UNPLUGGED  CONNECTING MATHEMATICALLY
WITH THE GENERAL PUBLIC SCIENCE WORLD & BCAMT COLLABORATIVE
Presenters: Pamela Hagen (BCAMT) and Rob Sidley (BCAMT)
pamelahagen@telus.net rsidley@dccnet.com
Since the fall of 2002 the BCAMT & Science World, Vancouver, BC
have joined together to
present weekends of mathematical activities entitled, Mathematics Unplugged.
Science World's curator, Rob Lunde, who wanted to bring mathematics
into more prominence at Science World, as well as gradually develop
more public awareness about mathematics, initiated this collaboration.
Plans were developed whereby the Association asked for volunteers from
its' members to attend Science World on a designated weekend and to
take a handson activity that would be relevant and appealing to under
13 year olds, and their family; Science World's target audience. The
BCAMT would have a designated area within Science World's public areas
where the Association's conference booth and banner were set up. Tables
were also made available for having a book display and carrying out
the
activities.
The Association and Science World collaborated to produce a pamphlet
giving information
about mathematics including web sites, games and books that would help
foster the development of Numeracy.
The weekend was established for attendance by the Association on Saturday
and Sunday on a
preselected weekend between 11.00 am and 4.00 pm. A call was put out
to members to volunteer for a 2.5hour shift with another volunteer,
and a schedule was drawn up for volunteers. Science World provided free
entry and parking for volunteers and a small honorarium, which paid
for material expenses for volunteers. Each volunteer prepared once or
two handson math activities of their own choosing, such as model versions
of math problems, i.e. Bridge of Konnisburg, paper constructions of
polyhedra, probability games with lollipops. In recent visits mathematics
trails within the facility have been developed and a prize made available
through a draw, for those completing the math trail.
This collaboration has occurred at least once a year or twice a year
since that time and has become a portfolio of the Association under
the auspices of the Outreach Committee. Initially only members of the
Association's Executive signed up to attend this weekend. However this
has expanded to all members of the Association, including mathematics
and education faculty as well as education and mathematics students
at local universities and colleges. More volunteers than can be accommodated
on the schedule now step forward to take part in communicating about
and with mathematics to the general public.
This collaboration has proven to be very successful for both parties
and given volunteers an
opportunity to provide information and answer a myriad of questions.
It is felt to be an activity that could easily be replicated between
any mathematical group and an institution as a means of broadening the
public awareness about Numeracy and mathematics.
S2a) BRINGING SURVEYS AND DATA ANALYSIS TO LIFE
IN THE CLASSROOM WITH CENSUS AT SCHOOL
Presenter: Joel Yan (Statistics Canada)
joel.yan@statcan.ca,
Other contributors: Stewart Craven (Toronto District School Board)
Members of the Census at School Teacher Advisory Committee: Anna Spanik
(Halifax
Regional School Board), France Caron (Université du Québec
à Montréal), Tom Steinke
(OttawaCarleton Catholic DSB), Florence Glanfield (University of Saskatchewan);
Bradd Hart (McMaster University)
Students aged 8 to 18 from across Canada are getting involved in the
international Census
at School project. They respond in class to an online survey, covering
topics such as their height, pets or favorite school subject. Then they
'play detective' with the anonymous results, discovering interesting
patterns and comparisons that bring their lessons to life. Students
have fun experiencing this survey about themselves, while gaining important
skills in using information technology to understand their world and
make informed decisions. They become aware of the important role of
the national census in collecting information to help us understand
our country and its people.
"We worked on measurement, data management, graphic displays of
data, estimating, and different ways of recording data. It's a lot more
fun to use data of a personal nature."
Kimberly Burstall, primary teacher, Halifax, Nova Scotia
"My students got more out of this project than any text book or
teacher could communicate."
Larry Scanlon, primaryintermediate special education teacher, Waterloo,
Ontario
The Census at School international project began in the United Kingdom
in 2000. It now boasts database of results from Australia, New Zealand,
South Africaand, as of summer 2004, Canada! Statistics Canada is responsible
for the Canadian component of the project. The Canadian survey includes
some questions that are common to all participating countries and others,
on topics such as bullying and allergies, which were developed by an
advisory board of mathematics teachers from across Canada. These teachers
have also created over 15 online learning activities for grades 4 to
12.
Depending on their grade level, students can use these to:
" create different types of graphs to answer questions such as
"Do boys and girls eat different breakfast foods?"
" explore relationships between variables: "Does foot size
increase with height?"
" analyse a phenomenon like bullying and determine which age group
is most at risk: "Bullying  studying to curb it".
Students can compare their class results to national and international
data available on the
website.
"Kids connect best with data they can see themselves in. Census
at School makes it painless to collect data in electronic format, so
that students can spend more time analyzing the data. Census at School
data has a nice balance of numeric and categorical variables, which
allow for a rich array of representations and analyses."
 Tom Steinke, Educational Consultant, OttawaCarleton Catholic School
Board
"Through this project, students see statistics (and math in general)
as a set of conceptual tools that help them better understand the complexity
of the world in which they live in"
France Caron, Education professor, Université du Québec
à Montréal, Québec.
"I believe [the Census at school] was a valuable learning experience
because it gave me... a better
understanding of designing survey questions. Also, reading the questions
provided insight as to how
the data may be grouped or analyzed later on."
 Grade 12 student, class of Amy Scales, Listowel, Ontario
Over 8,000 Canadian students completed the survey last school year.
A series of summary results tables are posted on the www.censusatschool.ca
site under "Data and results". The survey found that math
was the second favorite subject of high school students after physical
education, while elementary school students preferred physical education
followed by art. In high school, 25% of girls and 21% of boys said they
don't eat breakfast.
The project is even more popular this year: over 13,000 students have
already responded as of February, 2005. Students and teachers find working
with data about their class and their peers an interesting way to learn
data analysis skills. Join in at www.censusatschool.ca
S2b) PROTIC: UN PROGRAMME OÙ LES TECHNOLOGIES
APPUIENT L'APPRENTISSAGE DANS UN CONTEXTE D'APPROCHE PAR PROJET
Personne resource: Sébastien Simard (École secondaire
Les CompagnonsdeCartier)
sebastien@protic.net
Reconnu au niveau international par l'OCDE (Organisation de coopération
et de développement économique, secteur éducatif)
en 2003, le programme Protic accueille des élèves de la
première
à la cinquième secondaire. Les valeurs pédagogiques
avantgardistes de Protic le situent au
coeur de la réforme québécoise, et ce, bien avant
le début de celleci. Ce programme vise à
favoriser le développement des compétences de jeunes dans
un environnement où les technologies sont facilitées.
Protic permet à chaque jeune de travailler son autonomie à
travers l'utilisation de son propre ordinateur portable en classe. Les
TIC sont donc privilégiées comme soutien aux apprentissages
et elles sont un prétexte et un déclencheur des activités
pédagogiques menant à la construction des apprentissages.
L'enseignement se fait prioritairement par projets et par mises en situation
initiés par les enseignants, les élèves et le milieu.
Le modèle d'enseignement intègre les matières (interdisciplinarité)
et privilégie les apprentissages de type coopératif.
S2c) MATHEMATICAL MODELING IN THE CURRICULUM: IMPLEMENTATION
IN ONTARIO
Presenter(s): Christine Suurtamm (University of Ottawa)
Geoffrey Roulet (Queen's University)
rouletg@educ.queensu.ca
Over the past quarter century curriculum change projects in many jurisdictions
have contained calls for a focus on applications and modelling, but
progress in this direction has been slow. Papers presented at the February,
2004 conference connected to the ICMIStudy 14: Applications and Modelling
in Mathematics Education showed that mathematical modelling is appearing
as a curriculum theme in isolated classrooms around the world, usually
the sites of focussed research. In
contrast to this, Ontario has recently issued new secondary school mathematics
curricula which present modelling as the core activity of the inquiry
process by which course content is to be developed. This official systemwide
curriculum emphasis has been accompanied by significant efforts in support
of implementation. The results of this program can be observed in the
appearance of modelling and applications activities in classrooms across
the province and in Ontario's results in the 2003 PISA study which emphasized
"situations in which students encounter mathematical problems and
relevant knowledge and skills are applied". Ontario's success in
moving forward with an applications and modelling curriculum is being
highlighted in the upcoming ICMIStudy 14 Volume. It is valuable to
look back at the history of this relative curriculum change success
and note the features that appear to have supported progress.
With the 1985 Curriculum Guideline: Mathematics: Intermediate and Senior
Divisions, Ontario officially joined the international movement to emphasize
mathematical modelling and applications in the school curriculum. Here,
in the introductory Process Components section, the Ministry of Education
set out a sixstep problemsolving/modelling process and stated, "Whenever
possible, skills and concepts should be related from the beginning,
to their applications". Although some objected to the weakness
in the 1985 Guidelines' "suggestions", these statements, encouraging
the use of applications, modelling, and experiential approaches to teaching
and learning, supported mathematics teachers who wished to experiment
with alternate styles of instruction. These teachers expanded upon the
Guidelines brief discussions of new approaches and the use of information
technology in the learning of mathematics. When, in 1996, the Ministry
of Education announced its intention to rewrite the secondary school
program there existed a core leadership group that could effectively
participate in the curriculum writing process and provide related teacher
support activities.
The release of the new guidelines has been followed by significant implementation
support: Ministry of Education licencing of computer software and funding
for the purchase of graphing calculators, teacher workshops and weeklong
institutes organized by the professional associations, and websites
providing teachers with easy access to resources and model student projects.
Although beneficial at all grade levels, these activities appear to
have had significant impact in relation to the Grade
12, Mathematics for Data Management course. Much of the content of this
course: statistics, iteration, database organization, flowcharting,
graph theory, networks, and coding; was relatively unfamiliar to teachers,
and the course organization, with a large independent student project,
was a new challenge for many. Teachers attending professional development
workshops in support of this course experienced learning in an investigative,
technology supported environment similar to that envisioned for their
students. In this, teachers' images of both mathematics and its teaching
and learning were challenged.
S2d) CHANTIER D'APPRENTISSAGES MATHÉMATIQUES
INTERACTIFS : UN MARIAGE FRUCTUEUX DE LA TECHNOLOGIE, DE LA RÉSOLUTION
DE PROBLÈMES ET DE LA COMMUNICATION
Presenter: Viktor Freiman (l'Université de Moncton)
freimanv@umoncton.ca
The Internet based project CAMI (Chantier d'apprentissages mathématiques
interactifs,
www.umoncton.ca/cami ) has been created in 2000 in order to help New
Brunswick francophone students from K12 to get access to electronic
resources in mathematics. 4 years of collaboration between the Université
de Moncton and the provincial Ministry of Education and School Districts
allowed school children to solve more than 500 challenging mathematical
problems and to communicate their solutions electronically. At the same
time, university students involved in math education courses had a chance
to correct these solutions and to send a personal feedback to each
participant getting thus a deeper insight into children's mathematical
thinking and reasoning. With the time, the collaborative virtual community
CAMI has attracted many new members from New Brunswick and other provinces.
The functioning of CAMI is quite simple: every Monday, four new problems
of four different levels are posted on the Internet site. Schoolchildren
have a week to choose a problem of their taste, solve it, fill in an
electronic form and send it to the Universtié de Moncton. A team
of preservice teachers is ready to evaluate solution and to send a
personal comment to the child by email. A general comment written by
the university students with the most interesting solutions is being
posted on the site. The project gives also an opportunity for inservice
teachers to make a search for problems in the archive and use them in
the classroom. The project team does regular surveys in order to get
a feedback from all groups of participants of the project and to make
necessary adjustments and improvements. The statistical information
collected about the project shows that it gains popularity and has a
positive impact on the use of technology in mathematics classroom and
in a preservice teacher's training.
The project team works in close collaboration with the authors of the
CAMI, Nancy Vezina (University of Ottawa) and Maurice Langlais (School
District 1, NB), the Ministry of Education of New Brunswick, school
administrators and teachers, as well as with Information Technology
specialists of the Université de Moncton. The operation and development
are getting strong support of the provincial Ministry of Education,
the New Brunswick Innovation Fund and the Canadian Mathematical Society.
S3a) MATHEMATICS, SCIENCE, AND ABORIGINAL STUDENTS:
BUILDING RELATIONSHIPS AT THE UNIVERSITY OF SASKATCHEWAN
Presenter: D. Cowan, H. Fraser, L. Wilson (University of Saskatchewan)
Dave.Cowan@usask.ca
Close to 1800 students at the University of Saskatchewan have identified
themselves as Aboriginal. Most of these students do not choose mathematics
or science as their primary area of study  in most science or applied
science programs no more than 6% of the students enrolled are Aboriginal.
Despite the low participation rate in the sciences, the University of
Saskatchewan is among the leading postsecondary institutions in the
country in serving Aboriginal students and seeing them to completion
of their degree programs. Our experience has convinced us that the most
important factors in improving the numbers of Aboriginal students who
successfully complete our mathematics, science and applied science programs
are (i) strengthening our relationships with Aboriginal communities,
students, and leaders; and (ii) adapting the culture of the university
to better reflect our student population (and that of the province).
While this might appear to be obvious, how we set about doing these
things is not. Thus the focus of our 'success story' is not in the mathematical
content of our courses and the pedagogical methods we employ, but in
the relationships we are building between the university and Saskatchewan
Aboriginal communities and the context in which we deliver our programs.
The University of Saskatchewan has implemented a number of programs
for Aboriginal students with the aim of improving student success in
science and mathematics, but with the fortunate consequence of building
strong relationships between the university and the Aboriginal community.
It is through these experiences that we have come to recognize the barriers
(in all their complexity) that many students face when they begin their
university studies. Creating a social and intellectual environment that
is meaningful to Aboriginal students is critical to improving the experience
(and the participation and success rates) of our students. Key factors
in achieving this include:
" Greater dialogue between community leadership and the university;
" Improved cooperation between the K12 systems and postsecondary
institutions;
" Quality instruction;
" Recognition of the importance of Aboriginal languages in programming
and the role language plays in our support of Aboriginal students;
" Creating an environment on campus that better reflects the student
body and the people of the province  this includes enriching the culture
of the campus by including more Aboriginal driven academic activities
(courses, seminars, visiting scholars, languages, public lectures and
debates, and so on).
We recognize that many of the problems we face at university begin
in the K12 system and that there is little that we can do independently.
Little can be accomplished by tinkering with course content in university
mathematics; much more can be done by working closely with the K12
systems in making a student's learning experience continuous and seamless
as they move from one system to the next. The University of Saskatchewan
and the province's Aboriginal communities are strengthening their partnerships
and continuing the ongoing task of relationship building. It is this
'work in progress' that is our true success story.
S3b) A PRIMARY PARADIGM SHIFT: THE JOURNEY FROM
AN INSTRUCTIONAL PHILOSOPHY TO A COMMUNITY OF LEARNERS
Presenters: Cheryl Shields, Barb Labas & Trish Reeve (South Corman
Park School)
cshields@sesd.sk.ca; blabas@sesd.sk.ca; preeve@sesd.sk.ca
As a team, we would like to thank the Canadian Mathematical Society
for the opportunity to take
the time to reflect on the work we have been involved in since September
2004. We did not realize
the amount of growth and change in our teaching practice until we were
asked to write about it. Our
experience has both been informed by and has informed a chain reaction
in our school, our
division, and neighboring divisions building on a constructivist philosophy.
Teachers are now
questioning their own math philosophy and teaching strategies. This
experience has been timely
and extremely worthwhile.
As a group of professional learners we have reviewed math research
including the work of Dr.
Grayson Wheatley; Kathy Richardson; Early Numeracy and Teaching Number
(Australia); Math
Recovery Programme (Australia); and theories based on a constructivist
approach to teaching and
learning mathematics. All of the research has challenged our own math
philosophy, and math
teaching. We recognize from national and international data that our
children are struggling in
math, particularly in the area of math reasoning. This alone has prompted
us to change our
teaching practice. As well, through the work of Dr. Grayson Wheatley
we have seen the value of
asking and listening to children articulate their math strategies and
reasoning skills with their peers.
This listening and sharing piece is invaluable as it has changed our
role from primarily direct
teaching to one of facilitating student learning.
We strongly believe that this approach to teaching is not yet "another
bandwagon" as we have
seen evidence to support math development within our kindergarten and
grade one classrooms.
Along with the 'regular' population, our students with special needs
in grade one have been
included and met success in the regular classroom. In kindergarten student's
developmental stages in math are identified, indicating individual programming
needs. Our traditional approach of assessment has developed to a higher
level, as we are able to gain greater insight using "The Stages
of Early Arithmetical Learning" from Early Numeracy (2000  Australia).
As well, we assess
our student's mathematical reasoning with the use of videotaped interviews,
math journaling,
anecdotal records and group sharing of strategies. This is where our
growth as teachers has flourished.
Changes to our teaching practice and challenging our own math philosophy
has not been a simple
task. We constantly feel the struggle to keep up to the curriculum,
and the pull to revert back to the
traditional and comfortable teaching methods of our past. This paradigm
shift is one that we could
not endure alone. The fact that we are able to work together as a team,
to maintain dialogue, to
celebrate successes and to share failures, has enabled us to translate
this theory into practice. The
changes we have made as teachers is vast, though it does not compare
to the growth we feel our
students have made when given the opportunity to think, share and construct
their own math
reasoning skills in a meaningful context.
We are prepared to share our success story at the CMS Forum 2005 through
dialogue, power point, video clips, and written documentation.
S3c) OUR STORY OF COLLABORATION (BETWEEN FIVE SCHOOL
DIVISIONS AND A UNIVERSITY)
Presenters: Karen Campbell (Sask. Mathematics Teacher Society)
Florence Glanfield (Univ. of Sask.)
Sharon Compton (Saskatoon East School Division)
kd1campbell@yahoo.com
Our proposal for a success story is the story of collaboration between
five school divisions and a university. Our collaborative efforts have
focused on mathematics education, primarily from K  middle years. Our
goal is to improve mathematics teaching and learning in all five school
divisions and at the university. Presently we have three separate committees:
the Saskatoon Regional Assessment Consortium, the Early Numeracy Committee,
and a summer institute committee, working towards this goal. Not only
is there collaboration between the school divisions and the university,
but also between the committees.
Together we have initiated various ongoing projects. The Saskatoon
Regional Assessment Consortium has been working on a project that focuses
on the question "What might be good assessment tasks if students
are learning fractions in a constructivist manner?" What this initiative
required was not only the development of the assessment tasks, but also
the professional development of teachers. The professional development
of teachers included activities that focused on teachers own mathematical
and pedagogical knowledge. In addition to learning more about fractions,
teachers in all 5 school divisions were involved in the development
of a common assessment tool. In March 2005, teachers will come together
with these common assessments to discuss the results and reflect on
future directions.
The Early Numeracy Committee is working towards the development of
an early screening instrument to identify students at risk of learning
difficulties in mathematics. We are engaged in reading research from
both the educational psychology perspective and the mathematics education
perspective around students at risk. Once a screening instrument has
been developed, the committee will look for effective practices to support
mathematics instruction.
The summer institute committee emerged from the Early Numeracy Committee
because of the importance of teacher learning identified in some of
the research articles. This committee organized a summer institute in
August 2004. The two day institute not only delves into teachers' philosophical
beliefs and understandings about teaching mathematics, but also addresses
teachers' identity as mathematics teachers, and teachers' understanding
of mathematical concepts. The format of the institute was such that
there was a focus on teachers sharing their own stories, understandings,
and wonderings about coming to know mathematics and teaching mathematics.
The threads of the program were related to teacher identity, children's
literature, learning mathematics, teaching mathematics, and conversations
with colleagues. The result of this two days has spurred the teachers
in different ways to come together to talk about early numeracy and
teaching mathematics. The institute was a huge success and the planning
committee is currently planning for the summer of 2005.
Not only would we like to share some of our work, but we would like
to share the way in which the individuals involved from the five school
divisions and the university have benefited from this collaboration.
S3d) PRIMARY PROBLEMS TO PONDER AND INTERMEDIATE
INVESTIGATIONS TO INSPIRE: NUMERACY RESOURCES TO SUPPORT ELEMENTARY
PROBLEM SOLVING
Presenter: Carole Saundry (BCAMT)
csaundry@richmond.sd38.bc.ca
The BC Association of Mathematics Teachers' Executive is a group of
educators devoted to
supporting their peers across the province in the teaching of mathematics.
Two members of that
executive, Janice Novakowski and Carole Saundry, took on a special project
in the fall of 2003 in
order to provide support specifically for nonmath specialist teachers
at the primary level.
Operating from the belief that problemsolving should be at the heart
of every math lesson, Janice and Carole began generating lessons for
primary classrooms that were openended, engaging and conceptuallybased.
They visited classrooms from kindergarten to grade 3, trying out the
lessons, gathering work samples and video of students working. The result
was a numeracy resource entitled Primary Problems to Ponder. The book
features 12 problemsolving lessons for K3 that covers each of the
strands, and includes annotated work samples, an assessment rubric and
a lesson planning template so that primary teachers can develop their
capacity to design rich problembased lessons of their own. To support
teachers in using the resource, Carole and Janice have offered several
afterschool workshop series, where participating teachers learn the
big ideas behind teaching through problemsolving at the primary level,
watch video samples of children working through the problems, then try
out lessons with their own students and bring samples back to share.
The response to the resource and the workshops which support it have
been overwhelming. Now in its third printing, the
resource has been shared with more than 500 teachers across the province.
Intermediate grade teachers heard their colleagues at primary speaking
about the Primary
Problems to Ponder resource and began to inquire after a resource suitable
for their grade
levels. In response, Janice and Carole went out into schools again,
this time to explore mathematical investigations  a projectbased approach
to math. Intermediate Investigations to Inspire is for grades 48 and
features 5 investigations covering each of the 4 strands, and includes
a fifth investigation that integrates logical reasoning and Palm technology.
Once again, video footage was gathered, and a series of movies showing
the background building lessons, extensions and the investigations was
produced. The movies and work samples are an integral part of the after
school workshop series for this group of teachers. Each of the investigations
is a mathematical performance task. As such, an observational checklist
and a final assessment rubric are included to assist teachers in making
informed judgments about their students' capacity to reason and communicate
mathematically. Supported by assessment tools, suggested online resources
and literature connections for their lessons, this resource has "inspired"
intermediate teachers to try a rich projectbased approach to mathematics
teaching.
The significance of this BCAMT "Success Story" is in the
thoughtful conversations it is provoking
among teachers of primary and intermediate grades. Teachers are trying
these lessons, testing
out these new methods and talking with pride about the range of ways
in which their students
have responded. Teachers are finding they are able to reach more students
through these
openended problems; they are commenting on the level of engagement
they have noticed
while their students really "do" math. Most importantly, they
are talking about how their students
are thinking  and about how this thinking is being communicated in
a variety of ways.