MATHEMATICS EDUCATION

April 19, 2014

2005 CANADIAN MATHEMATICS EDUCATION FORUM
May 6-8, 2005
FIELDS INSTITUTE

FORUM CANADIEN 2005
SUR L'ENSEIGNEMENT DES MATHÉMATIQUES
6-8 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 "A-HA!"
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 culture-free
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 first-year 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 two-way 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 one-on-one 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, self-evaluations 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 hands-on 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
pre-selected weekend between 11.00 am and 4.00 pm. A call was put out to members to volunteer for a 2.5-hour 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 hands-on 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
(Ottawa-Carleton 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, primary-intermediate 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 Africa-and, 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, Ottawa-Carleton 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 Compagnons-de-Cartier)
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 avant-gardistes de Protic le situent au
coeur de la réforme québécoise, et ce, bien avant le début de celle-ci. 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 ICMI-Study 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 system-wide 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 ICMI-Study 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 six-step problem-solving/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 re-write 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 week-long 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 K-12 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 feed-back 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 pre-service teachers is ready to evaluate solution and to send a personal comment to the child by e-mail. 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 in-service 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 feed-back 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 pre-service 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 post-secondary 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 K-12 systems and post-secondary 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 K-12 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 K-12 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 non-math specialist teachers at the primary level.
Operating from the belief that problem-solving should be at the heart of every math lesson, Janice and Carole began generating lessons for primary classrooms that were open-ended, engaging and conceptually-based. 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 problem-solving lessons for K-3 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 problem-based lessons of their own. To support teachers in using the resource, Carole and Janice have offered several after-school workshop series, where participating teachers learn the big ideas behind teaching through problem-solving 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 project-based approach to math. Intermediate Investigations to Inspire is for grades 4-8 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 on-line resources and literature connections for their lessons, this resource has "inspired" intermediate teachers to try a rich project-based 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
open-ended 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.