'I
S.94-61
. ?
SIMON FRASER UNIVERSITY
Office of the Vice-President, Academic
MEMORANDUM
To:
?
Senate
From:
?
J.M. Munro, Chair
Senate Committee on Academic Planning
Subject:
?
Master's Programs in Mathematics Education and
changes to M.Sc. Program in Secondary Mathematics
Education - SOAP Reference: SOAP 94-37, SCAP 94-40
Date:
?
September 15, 1994
Action undertaken by the Senate Committee on Academic Planning and the Senate
Graduate Studies Committee, gives rise to the following motion:
Motion:
?
"that Senate approve and recommend approval to the Board of
Governors, as set forth in S.94-
61
the proposed Master's
Programs in Mathematics Education, including new courses
EDUC 844, EDUC 845, MATH 601, MATH 602; and revisions to
the M.Sc. Program in Secondary Mathematics Education"
The attached documentation was prepared earlier and held up because the Math courses were still going
through the approval stages. As a result some of the events written in the future tense have now take
place. The following changes should be read in the documentation:
Page 1, paragraph 2. The third intake into the Secondary Mathematics Education program took place in
fall 1993.
Page 1, paragraph 7. ?
The first intake into the Mathematics Education program is projected to take place
in 1995-2.
Page 2, Note ***
?
This course [EDUC 844] was offered as a special topics course during the 1993-2
semester.
Master's Programs in
Mathematics Education
In the following we propose
1.
A change in the currect M.Sc. Program in Secondary Mathematics Education
2.
Establishment of the new M.A./M.Ed. emphasis in mathematics education
justification
The program in Secondary Mathematics Education (offered jointly by
the Faculty of Education and the Department of Mathematics and Statistics)
which was instituted in 1989 has been very successful in attracting qualified
secondary mathematics teachers. The second cohort is currently completing
its program, and we are looking forward to the third intake in the fall of 1993.
This program addresses the interests and needs of a very specific group,
secondary mathematics teachers, in that one-half of the course work is taken
in the department of mathematics.
Over the years, we have encountered strong candidates who are
interested in mathematics education at the elementary and intermediate levels,
that is, up to grade 10. However, the advanced level of mathematics content in
the existing program did not meet their needs and interests in pedagogical
matters of mathematics. Until now such students were enrolled in the
. ?
Computers in Education, General Curriculum, or Individual Programs and took
part of their course work with the cohort in. secondary mathematics education.
The Faculty of Education and the Department of Mathematics and
Statistics wish to respond to this small but growing number of students by
institutionalizing a program in mathematics education with two routes: M. Sc.
in Secondary Mathematics Education and a new route of M.A./M.Ed in
Mathematics education. The new, M.A./M.Ed. program will keep the spirit of
collaboration between the Faculty of Education and the Department of
Mathematics and Statistics. Thus, the mathematics content courses will be
designed such as to address the background of the candidates.
Characteristics
Recent documents on the nature of teaching and learning of
mathematics (Year 2000; NCTM Standards 1989) emphasized the need for new
approaches in mathematical pedagogy. This program incorporates recent
developments in theory (such as constructivism) as well as new emphases in
curriculum and pedagogy (problem solving, the use of technology).
Potential Students
The appropriate target group would be teachers with assignments at the
elementary and intermediate grade levels that include the instruction of
mathematics.
•
?
?
A bi-annual intake of 10- 15 students is anticipated. This intake
alternates with the bi-annual intake of students in the Secondary Mathematics
Education. The first intake is projected for the 1994-2 semester.
I.
Course Requirements
M.Sc. in Secondar
y
Mathematics Education*
The requirements for the M.Sc. in Secondary Mathematics Education
include course work with a minimum of 25 credit hours in education and
mathematics and masters thesis.
Core courses
Math 603-4 Foundations of Mathematics
Math 604-4 Geometry
Math 605-4 Mathematical Modeling
Educ 846-4 Foundations of Mathematics Education
Educ 847/S-4 Teaching and Learning Mathematics
Educ 844-5 The Research Basis of Mathematics Education**,***
M.A./ M.Ed. in Mathematics Education
The requirements for the MA in Mathematics Education include course
work with a minimum of 25 credit hours in education and mathematics and a
masters thesis. The requirements for a M.Ed. in Mathematics Education
include a required course work of 25 credit hours in education and
mathematics, a minimum of 15 hours of electives in education and/or
mathematics, and a comprehensive examination. Alter the first 4 courses in
the program, the students in consultation with faculty members will choose
either the MA or M.Ed. option. At this point, the M.
candidates will be
provided with a list of critical readings which will serve as the basis for
the comprehensive examination to be taken alter all the course work
(required and elective) has been completed. The core courses will be
completed together by the MA and M.Ed. candidates.
Core cours
es
Math 6xx-4 Discovering Mathematics I
Math 6xx-4 Discovering Mathematics Il
Educ 846-4 Foundations of Mathematics Education
Educ 847/G-4 Teaching and Learning Mathematics
Educ 844-5 The Research Basis of Mathematics Education**,***
Educ 845-4 Learning Mathematics with Computers**, ****
Electives
Graduate level courses in the Faculty of Education or in the Department of
Mathematics and Statistics.
Notes
* The M.Sc in Secondary Math Education has been approved. We propose
an amendment by adding the course Educ 844-5, The Research Basis of
Mathematics Education.
* *
?
New courses are printed in bold-face type. Course descriptions
areenclosed.
* * * This course is offered as a special topics course during the 1993-2
semester
* * * * This course was offered as a special topics course during the 1991-2 and
1992-2 semesters
IStaffing
The courses Educ 846-4 Foundations of Mathematics Education, and Educ
844-5 The Research Basis of Mathematics Education will be taught jointly to
students in both M.Sc and M.A./M.Ed routes. However, the course Educ 847-4
Teaching and Learning Mathematics will be taught separately.
The proposed change in the M.Sc. route of the program involves one
new course taught every second year. The proposed M.A./M.Ed route involves
three new courses, taught every second year, one in education, and two in
mathematics. Members of the Department of Mathematics and Statistics will
continue the tradition to serve on thesis committees which has been
established for the program in secondary mathematics education over the past
four years.
The total additional commitment in terms of faculty teaching time for
both programs will be 3/8 FTE (3 courses over 2 years) in the Faculty of
Education and 1/4 FTE ( 1 course/year) in the Department of Mathematics and
Statistics.
0
C^ -
Form GS.8
SIMON FRASER UNIVERSITY
New Graduate Course Proposal Form
Calendar Information:
Department: FACULTY OF EDUCATION
?
Course Number: Educ. 844-5
Title: The ResearcltBasis of Mathematics Education
Description:
An examination of critical issues, current research and research practices in mathematics education.
Credit Hours:
?
5 ?
Vector. 3-0-2 Prerequisite(s) if any: EDUC 847
Enrollment and Scheduling:
Estimated Enrollment:
?
15-20 ?
When will the course
first
be offered: ?
95-2
How often will the course be offered:
?
once every 2 years
Justification:
This course builds
?
on the theoretical foundations of mathematics education acquired in the
0
prerequisite course EDUC
847,
Foundations of Mathematics Education
Resources:
Which Faculty member will normally teach the course:Dr. Wolff-Michael Roth
What are the budgetary implications of mounting the course: ?
1/8 FTE
Are there sufficient Library resources (append details): Appended literature resources locall
y available
Appended: a) Outline of the Course.
b)
An indication of the competence of the Faculty member to give the course.
c)
Library and faculty resources
Approved:
Faculty Graduate Studi
es
Co mittee: / t
1
tV "
?
'
—
Date: &(
I/
'39..2
Date: /f
6?.1
'72
Faculty:
Senate Graduate Studies Committee:)Q(}
2
- ?
DateL--
/995
.
4
Research in Math Ed
Page 1
.
?
THE RESEARCH BASIS
OF
MATHEMATICS
EDUCATION
(8445)
This course was developed for graduate students in the program(s) of mathematics
education. It builds on the theoretical foundations of mathematics acquired by the students in the
prerequisite course EDUC 847, Teaching and Learning of Mathematics. Students will examine the
highlights of contemporary research and research practices in mathematics education as they pertain
to teaching, learning, and knowing of mathematics.
T
he course will deal with current and critical issues in the area of mathematics education
such as situated cognition, social constructivism, communities of practice/socio-cultural issues,
collaborative problem solving, technology in mathematics education, gender and mathematics,
constructivism, sociology of knowledge, ethnomathematics and cultural issues, mathematical
cognition/problem solving, and students' beliefs. The course will examine the influence of these
issues on the specific research methods used by researchers.
The topics of the course are circumscribed by, but not limited to the major readings listed
below with each topic. The specific selections may change depending on the participants in the
course. That is, the specific research articles to be read in the offering for elementary teachers
would focus on the research done by researchers in the elementary classrooms such as by Paul
Cobb and colleagues, Maggie Lampert, and Gaea Leinhardt. For secondary education majors, the
research done at Cornell by Jere Confrey or by Allan Schoenfeld at Berkeley would be more
central. In the context of published research and original data sources, the student will be
introduced to the relevant research methods in mathematics education.
Textbook
Grouws, D.A. (Ed.) (1992).
Handbook of research on mathematics teaching and learning.
New
York. MacMillan Company.
Competence of a Faculty Member
Dr. Wolff-Michael Roth completed a Ph.D. in Science Education with a secondary emphasis in
research methods. In addition to science, he taught mathematics and computer science in middle
and high schools. Over the past five years, he investigated problem solving, ratio reasoning, and
the learning of mathematics in the context of science classrooms using both quantitative and
qualitative methods. His current research includes the construction/acquisition of mathematics
knowledge in settings which focus on situated learning and communities of mathematical practice.
Sociology of Knowledge! Social Constructivism
Cobb, P. (1989). Experiential, cognitive, and anthropological perspectives in mathematics
education. For the Learning of Mathematics, 9,32-42.
Cobb, P., Wood, T., & Yackel, E. (1991). Analogies from the philosophy and sociology of
science for understanding classroom life.
Science Education, 75(1),
23-44.
Cobb, P., Wood, T., Yackel, E., Nicholls, J., Wheatley, G., Trigatti, B., & Perlwitz, M. (1991).
Problem-centered mathematics projects.
Journal of Research in Mathematics Education,
22(1), 3-29.
Cobb, Paul; And Others (1991). Assessment of a Problem-Centered Second-Grade Mathematics
Project Journal for Research in Mathematics Education, 22, 3-29.
Livingston, E. (1986). The ethnomethodological foundations of mathematics. London and New
York. Routledge and Kegan PauL
JA(r.
Research in Math Ed
Page 2
Lynch, M. (1990). The externalized retina: Selection and mathematization in the visual
documentation of objects in the life sciences. In M. Lynch & S. Woolgar (Eds.),
Representation in scientific practice (pp.
153-186). Cambridge, MA: The
MIT Press.
Lynch, M. (1990). The externalized retina: Selection and mathematization in the visual
documentation of objects in the life sciences. In M. Lynch & S. Woolgar (Eds.),
Representation in scientific practice (
pp.
153-186). Cambridge, MA: The MIT Press.
Lynch, M. (1991). Method: measurement--ordinary and scientific measurement as
ethnomethodological phenomena. In G. Button (ed.), Ethnomethodology and the human
sciences (j)p. 77-108). Cambridge: Cambridge University Press.
EthnomathematicslCultural Issues
Crump, T. (1990). The anthropology of numbers. Cambridge, UK: Cambridge University Press
Lave,
J. (1988).
Cognition in practice: Mind, mathematics and culture in everyday life.
Cambridge: Cambridge University Press.
Lave, J., Murtaugh, M., & de la Rocha, 0. (1984). The dialectic of arithmetic in grocery
shopping. In B. Rogoff
& J. Lave (Eds.),
Everyday cognition: Its development in social
context
(pp.
67-94). Cambridge, MA: Harvard University Press.
Saxe, G.
B. (1991).
Culture and cognitive development: Studies in mathematical understanding.
Hillsdale, NJ: Lawrence Eribaum Associates.
Schliemann, A.D. & Acioly,
N.M. (1989). Mathematical knowledge developed at work: The
contribution of practice versus the contribution of scooling
Cognition and Instruction, 6(3),
185-221.
Scribner, S. (1986). Thinking in action: some characteristics of practical thought. In R.J.
Sternberg & R.K. Wagner (Eds.),
Practical intelligence: Nature and origins of competence in
the everyday world (pp.
13-30). Cambridge: Cambridge University Press.
Situated Cognition
Brown, J.S., Collins, A., & Duguid, P. (1989). Situated cognition and the culture of learning.
Educational Researcher, 18(1), 32-42.
Collins, A., Brown, J. S., & Newman, S. (1989). Cognitive apprenticeship: Teaching the craft of
-reading, writing, and mathematics. In L. Resnick (ed.), Cognition and instruction: Issues and
agendas
(pp.
453-494). Hillsdale, NJ: Lawrence Eribaum Associates.
Greeno, J.G. (1988). Situated activities of learning and knowing in mathematics. In M. Behr, C.
Lacampagne, M.M. Wheeler (Eds.), Proceedings of the 10th Annual Meeting of the PME-NA.
DeKaib, IL
Greeno, J.G. (1991). Number sense as situated knowing in a conceptual domain.
Journal
for
Research in Mathematics Teaching, 22,
170-218.
Greeno, J.G. (1991). Number sense as situated knowing in a conceptual domain. Journal for
Research in Mathematics Teaching, 22, 170-218.
Kaput, J.J. (1987). Towards a theory of symbol use in mathematics. In C. Janvier (Ed.),
Problems of
representation in the teaching and learning
of
mathematics (
pp.
159-195).
Hillsdale, NJ: Lawrence Eribaum Associates.
Kilpatrick, J. (1987). Problem formulating: Where do good problems come from? In A.
Schoenfeld (ed.), Cognitive science and mathematics education (
pp.
123-147). Hillsdale, NJ:
Lawrence Eribaum Associates.
Roth, W.-M. (in press). Bridging the gap between school and real-life: Toward an integration of
science, mathematics, and technology in the context of authentic practice.
School Science and
Mathematics.
Roth, W.-M. (in press). Problem-centered learning or the integration of mathematics and science
in a constructivist laboratory: A case study.
School
Science and Mathematics.
Saxe, G.B. (1992). Studying children's learning in context: Problems and prospects.
The Journal
of
the Learning Sciences,
2, 215-234.
Research in Math Ed
Page 3
• ?
Communities of Practice/Socio-Cultural Issues
Brown, J.S., Collins, A., & Duguid, P. (1989).
Situated
cognition and the culture of learning.
Educational Researcher, 18(1),
32-42.
Cazden, C.B. (1986). Classroom discourse. In M. C. Wittrock (Ed.),
Handbook for research on
teaching
(3rd ed.), (pp.
432-463). New York: Macmillan.
Eisenhart, M.A. (1988). The ethnographic research tradition and mathematics education research.
Journal for Research in Mathematics Education,
19,99-114.
Lampert, M. (1986). Knowing, doing, and teaching multiplication.
Cognition and Instruction,
3(4),
305-342.
Lampert, M. (1990). When the problem is not the question and the solution is not the answer:
Mathematical knowing and teaching.
American Educational Research Journal,
27(1), 29-63.
Lo, J.J., Wheatley, G.H., & Smith, A.C. (1991, April). Learning to talk mathematics. Paper
presented at the annual meeting of the American Educational Research Asociation. Chicago,
IL.
McArthur, D., Stasz, C., & Zmuidzinas, M. (1990). Tutoring techniques in algebra.
Cognition
and Instruction, 7,
197-244.
Technology in Mathematics Education
Adams, D.D., & Shrum, J.W. (1990). The effects of microcomputer-based laboratory exercises
on the acquisition of line graph construction and interpretation skills by high school biology
students. Journal of Research in Science Teaching,
27(8), 777-787.
Hare!, I. (1991).
Children designers:
Interdisciplinary constructions for learning and knowing
mathematics in a computer-rich school Norwood, NJ: Ablex.
Hard, I., & Papert, S. (1991). Software design as a learning environment. In L Harel & S.
Papert, Constructionism: Research reports and essays, 1985 - 1990
(pp.
41-84). Norwood,
•
?
NJ: Ablex.
Kaput, J. (1986). Information technology and mathematics: Opening new representational
windows. Journal of Mathematical Behavior, 5,
187-207.
Pea,
R. D.
(1987). Cognitive technologies for mathematics education. In A. Schoenfeld (ed.),
Cognitive science and mathematics education
(pp.
89-122). Hillsdale, NJ: Lawrence Eribaum
Associates.
Mathematical Cognition/Problem -Solving
Dufour-Janvier, Bednarz, N., & Belanger, M. (1987). Pedagogical considerations concerning the
problem of representation In C. Janvier (Ed.), Problems of representation in the teaching and
learning of mathematics (pp. 109-122). Hillsdale, NJ: Lawrence Eribaum Associates.
Kaput, J.J. (1987). Towards a theory of symbol use in mathematics. In C. Janvier (Ed.),
Problems of representation in the teaching and learning of mathematics
(pp.
159-195).
Hillsdale, NJ: Lawrence Eribaum Associates.
Mason, J.H. (1987). What do symbols represent? In C. Janvier (Ed.), Problems of
representation in the teaching and learning of mathematics
(pp.
73-81). Hillsdale, NJ:
Lawrence Erlbaum Associates.
Roth, W.-M. (1991). The development of reasoning on the balance beam.
Journal of Research in
Science Teaching,
28,
631-645.
Schoenfeld, A. (1985).
Mathematical problem solving.
Orlando, FL: Academic Press.
Schoenfeld, A.H. (1992). On paradigms and methods: What do you do when the ones you know
don't do what you want them to? Critical issues in the analysis of data in the form of
videotapes. The Journal of
the
Learning Sciences, 2,
179-214.
Wilensky, U. (1991). Abstract meditations on the concrete and concrete implications for
mathematics education. In L Harel & S. Papert,
Constructionisnv Research reports and
essays, 1985 - 1990 (pp.
193-203). Norwood, NJ: Ablex.
Gender and Mathematics
Burton, L.
(1990).
Gender and mathematics: An international perspective.
London: Cassell
1
Research in Math Ed
Page 4
Fennema, E., & Leder, G.C. (1990).
Mathematics and gender.
New York: Teacher's College.
Walkerdine, V. (1990).
Counting girls out.
London: Virago.
?
0
Constructivism
Cobb, P., Yackel, E., Wood, T. (1992). A constructivist alternative to the
representational view
of mind in mathematics education.
Journal for Research in Mathematics Education, 23(1),
2-
33.
Davis, P.J. & Mason, J.H. (1989). Notes on
a radical constructivist epistemethodology applied to
didactic situations. Journal
of
Structural Learning,
10,
157-176.
von Glasersfeld, E. (1987). Preliminaries to any theory of representation. In C. Janvier (Ed.),
Problems of
representation in the teaching and learning
of
mathematics
(pp.
215-225).
Hillsdale, NJ: Lawrence Eribaum Associates.
Wheatley, G.H. (1991). Constructivist perspectives on science and mathematics learning.
Science
Education, 75,
9-2 1.
Collaborative Problem Solving
Kroll, D.L. (1989). Cooperative problem solving and metacognition: A case study of three pairs
of women. (Doctoral dissertation, Indiana University, 1988). Dissertation Abstracts
International, 49, 2958A. (University Microfilms No. 89022500)
Smith, E., & Confrey, J. (1991, April).
Understanding collaborative learning: Small group work
on contextual problems using a
multi-representational software tool.
Paper
presented at the
annual meeting of the American Educational Research Association, Chicago, IL.
Students' Beliefs
Lester, F.K., Garofalo, J., & Kroll, D.L. (1989). Self-confidence, interest, beliefs, and
metacognition: Key influences on problem solving behavior. In D. McLeod & V. Adams
(Eds.), Affect and mathematical problem solving: A new perspective (pp.
75-88).
New York:
Springer-Verlag.
?
0
Stodolsky, S.S., Salk, S., & Glaessner, B. (1991). Student views about learning math and
social
studies. American Educational Research Journal, 28(1),
89-116.
f.
.Form
SIMON FRASER
GS.8
UNIVERSITY
New Graduate Course Proposal Form
Calendar Information:
Department: FACULTY OF EDUCATION
?
Course Number:
Educ.845
Title:
Learnin
g
Mathematics with Computers
Description:
Experience in incorporating computers in mathematical problem solving, adaptation of materials for
use in intermediate mathematics classroom.
Credit Hours:
?
4 ?
Vector. 2-0-2 Prerequisite(s) if any:
Enrollment and Scheduling:
Estimated Enrollment:
?
10-15 ?
When will the course first be offered: 199573
How often will the course be offered:
?
every second year
Justification:
Following the Year 2000 Document and the change in the focus of teaching mathematics found in
the NCTM Standards, there is a repeating recommendation to incorporate technology in a process
of constructing mathematical knowledge. The proposed course attempts to familiarize the learner
with the highlights of educational software for teaching mathematics through a variety of personal
hands on experiences and through related literature.
Resources:
Which Faculty member will normally teach the course: Rina Zazids
What are the budgetary implications of mounting the course: -1/8 FTE
Are there sufficient Library resources (append details): Appended literature resources locall
y
available
Appended: a) Outline of the Course.
b)
An indication of the competence of the Faculty member to give the course.
c)
Library resources
Approved:
Faculty Graduate Studies Copimittee:
?
tI2t1
&
Faculty:
?
Date-
,t -
a2
•
?
Senate Graduate Studies Committee:
?
Date,9
Senate: ?
Date:________________
.
al
Learnin g
Mathematics with Computers
?
I*
Objectives:
The similar belief in learning theories of Dewey, Montessori, Piaget and Papert is
that people learn by "doing and thinking about what they did". Therefore this course
has a dual goal: to provide the intellectual challenge of "doing" hands on problem
solving and to provide the theoretical unders
tanding--based
on the constructivist
views on the learning of mathematics—Of "what they did", and how it is applicable
for children's learning of mathematics.
Description
The course will
of
integrate
Course:
two main formats: Computer Laboratory and Seminar. The
Computer Laboratory will involve students in a variety of mathematical problem
solving activities (that is, "doing mathematics"), that invite students to use a
computer to explore unfamiliar environments and to experience the process of
construction a new mathematical knowledge. The Seminar will involve students in
discussions on these activities (that is, "thinking about what they did"), addressing
mathematical problems and methodological issues. Classroom implementations,
including adaptation and modification of such activities will be suggested.
Furthermore, through the seminar discussions and related literature, students will
become familiar with the contemporary research on the uses of computers in
mathematics
The software
classroom.
will include programming languages LOGO and ISETL, spreadsheet,
Geometric Supposer, Cabri Geometry or Geometer's Sketchpad, Function machines,
among other software packages and microworids.
Assignments and expectations:
Attendance and active participation in discussions
Presentation to the class
Paper based on literature review
? -
Project based on designing mathematical activities using computers
Assessment and grading:
The above items - 25% each.
Bibliography: Available upon request
S
J0
SMON FASEF QJOVESOTY
•
?
FACULTY OF EDUCATION
MEMORANDUM
To: ?
Ron Heath
Senate Graduate Studies Committee
From: ?
Robin Barrow
Dean, Faculty of Education
Re: ?
Library Assessment
Educ 844-5 - Research Basis of Mathematics Education
Date:
?
December 7, 1993
The Faculty of Education will support the one-time costs for the above
course. at $1029.
.
RB/cp
c.c.: M. Manley-Casimir
?
S. Kanehara
0
SOMON FRASER UNDVERSDTY
FACULTY OF EDUCATION
?
•
MEMORANDUM
To:
?
Ron Heath
Senate Graduate Studies Committee
From:
?
Robin Barrow
Dean, Faculty of Education
Re: ?
Library Assessment
Educ 845-5 - Learning Mathematics with Computers
Date:
?
June 24, 1994
Further to my memorandum of December 7, 1993 the Faculty of
Education will cover the costs associated with the profile change through a one-
time budget transfer (see attached memorandum from J. Munro).
I trust this now enables the speedy approval of Education 845-5.
RB/cp
c.c.: M. Manley-Casimir
?
S. Kanehara
K. Kirkland
.
ri
S
SOON FRASER UNJOVERSOTY
?
FACULTY OF EDUCATION
MEMORANDUM
To:
?
Ron Heath
Senate Graduate Studies Committee
From: ?
Robin Barrow
Dean, Faculty of Education
Re: ?
Library Assessment
Educ 845-5 - Learning Mathematics with Computers
Date:
?
December 7, 1993
The Faculty of Education will support the one-time costs for the above
course at $486.
The Faculty does not support the recommended profile charges of $764
of recurring costs.
RB/cp
c.c.: M. Manley-Casimir
?
S. Kanehara
S
MEMORANDUM
W.A.C. Bennett Library, Simon Fraser University
?
Burnaby, British Columbia, Canada V5A 1S6
Date: 17 Seotember, 1993
From: Ralph Stanton (Collections Librarian)
To: ?
Cornel Hamm, Acting Dean of Education (3643)
Re:
?
Library Course Assessment for Master's Programme in
Mathematics Education
I have assessed the Library's ability to support the new
Master's Programme in Mathematics Education, here are the
results.
This new Master's programme involves the introduction of
four new courses, two in Mathematics and two in Education.
We have not received an assessment request for the two
mathematical courses designated in the documentation as MATH
6xx-4 Discovering Mathematics I and MATH 6xx-4 Discovering
Mathematics II.
Book Prices:
The average price of books in this field is $54
(BNA07/10/93 direct).
EDUC 844-5 The Research Basis of Mathematics Education
This course will first be offered in 95-2 to 15 to 20
students and every 2 years after.
There are 29 monographs listed in the course reading list
of which 6 are not in the catalogue, they should be bought
at a cost of $324. A further 13 are on loan and should have
added copies purchased for $705. Catalogue checking for both
courses was done August 1993 when use is low.
One time costs:
Monographs not in the catalogue
Added copies of monographs
Total
$324
R
r
p
Gr- I
am
$705
SO
$i
.
14.
EJ
EDUC 845-5 Learning Mathematics With Computers
This course will first be offered in 94-3 to between 10
and 15 students and every two years after that.
There are 13 monographs listed in the course reading list
of which 8 are not in the catalogue, they should be bought
at a cost of $432. Another title is on loan and should have
an added copy purchased for $54. Of the 5 serials citations
1 is not available from Library resources, it is Logo
Exchange at $29. This resource could be provided through
inter-library loan or other arrangement.
One time costs:
Monographs not in the catalogue $432
Added copies of monographs
?
$ 54
Total ?
$486
PROFILE CHANGES
For both these courses we recommend profile changes as
follows:
S .
?
?
In the sub-profile 003 Science Books
-
the non subject
parameter 14/08 (teaching of pre-college mathematical)
should be switched on. This would produce 11 books at an
average cost of $54 for a total of $594 per year and a
further 6 forms (of which we expect to select 2 per year) at
an average cost of $40 each for an annual cost of $80 per
year.
Add to sub-profile 022 Education Books the subject
describer Math in the curriculum BNA #36645480 which will
add an estimated 3 titles per year at a cost of $30 each for
a total of $90 per year.
The total cost of profile changes $594 + $80
+
$90
=
$764.
THE TOTAL RECURRING COSTS FOR PROFILE CHANGES
ARE
$764
PER
PLUS
YEAR
$1,029
TRANSFER
FOR A TOTAL
FROM BASE
OF $1,515.
BUDGET.
ONE
TIME COSTS
ARE
$486
Please contact me to discuss this assessment if you have
any concerns or questions (Phone 5946).
• ?
c.c. Michael Manley-Casimir, Director, Graduate Programs
?
Stan Kanehara, Assistant to the Dean
Sharon Thomas, Head, Library Collections Management
i^.
OCT-21-1993 16:8 FROM SFU LIBRARY r'1t1ENT
?
TO ?
8O
P.2/03
MEMORANDUM
W.A.C.
Burnaby,
B
ennett
British
Library
Columbia,
Simon
Canada
Fraser
V5A
University156
?
Date: 17 September, 1993
From: Ralph Stanton (Collections
Librarian)
Cornel Hamm, Acting
lDean. of Education (3E43)
Library Course Assessment for Master's Programme in
Mathematics Education
I have assessed the Library's ability to support the new
Master's Programme
in
Mathematics Education, here are the
results.
This new Master's programme involves the introduction of
four new Courses, two in Mathematics and two in Education.
We have not received an assessment request for the
two
mathematical courses designated in the documentation as MATH
6xx-4 Discovering
Mathematics
I
and MATH 6xx-4 Discovering
Mathematics II.
Book
The
Prices:
average
?
price of books in this field is $54
.
0
(NA07/10193 direct)
EDtJC
844-5 TbeRe
p
rch Basis of Math=tir,5 Education
This course will first be offered in 95-2 to 15 to 20
students and every 2 years after.
There are 29 monographs listed in the course reading list
of which 6 are not in the catalogue, they should be bought
at a cost
of $324. A further 13 are on
loan and should have
added copies purchased for $705. Catalogue checking for both
courses was done August 1993 when use is low.
One time costs:
Monographs not in the catalogue $324
Added copies of monographs ?
$705
Total
?
029
11:;.
OCT-21-1993 16:09 FROM SFU LIY MANAGEMENT
?
TO
?
P.
003/003
U
This course will first be offered in 94-3 to between 10
and 15 students and every two years after that.
There are 13 monographs listed in the course reading list
of which 8 are not in the catalogue
s
they should be bought
at a cost of $432. Another title is on loan and should have
an added copy purchased for $54. Of the 5 serials citations
3. is not available from Library resources, it is Logo
Exchange at $2, This resource could be provided through
inter-library loan or other arrangement.
One time costs:
Monographs not in the catalo
g ue $432
Added copies of monographs
?
$ 54
Total
?
$486
PROFILE CHANGES
For both these courses we recommend profile changes as
follows:
•
?
? In
the sub-profile 003 Science Books the non su.bect
parameter 14/08 (teaching of pre-college mathematical)
should be switched on. This would produce 11 books at an
average cost of $54 for a total of $594 per year and a
further 6 forms (of which we expect to select 2 per year) at
an average cost of $40 each for an annual cost of $80 per
- year.
Add to sub-profile
022
Education Books the subject
descriptor Math in the curriculum BNA $36645480 which will
add an estimated 3 titles per year at a cost of $30 each for
a total of $90 per year.
me total cost of profile changes $594 + $80 + S90 = $764.
THE TOTAL RECURRING COSTS FOR PROFILE CHANGES ARE $764
?
PER YEAR TRANSFER FROM BASE BUDGET. ONE TI COSTS AR9 $426
PLUS $1,029 FOR A TOTAL OF
$1,515.
Please contact me to discuss this assessment if you have
any concerns or questions (Phone 5946)
c.c. Michael Manley-Casimir, Director, Graduate Programs
Stan Kanehara, Assistant to the Dean
Sharon Thomas,
Head,
Library Collections Management
I
TOTAL P.003
IT
PROPOSAL FOR
?
MATH 601-4 ANQ MATH 602-4?
AS PART OF THE
?
MATHEMATICS/EDUCATION MASTER'S PROGRAM
The two courses described on the following pages are an integral part of the new Master's
Program in Mathematics Education recently approved by the Faculty of Education. They
are designed to give the student both breadth and understanding of four fundamental
areas of mathematics and will complement the mathematics currently taught in the
elementary and intermediate grades. Each course covers more than one area: Discover
Mathematics I - Arithmetic, Algebra and Geometry; and Discovering Mathematics II -
Discrete Mathematics, Probability and Statistics, and will be taught in two parts (usually
with a different instructor teaching each part). In each case the goal will be to give the
students a hands-on exploratory experience which will lead to mathematical
understanding and discovery. This will be achieved by the use of projects, videos, guest
speakers, experiments and discussions. No formal mathematics background will be
assumed and material will be presented in a non-theoretical manner. At all times efforts
will be made to ensure that the material is related to the so-called "real world", a variety
of applications will be presented and students will be encouraged to relate the material to
their own interest and experiences.
No suitable text is available for either course. Further, no reference materials are known
which would be accessible to students with no more than a high school mathematics
background. Suitable handouts and notes will be prepared.
fl'
('6'.
Department of Mathematics and Statistics
.
?
Application for new graduate courses
Appendix
Proposal:
We want to introduce two new graduate courses, MATH 601-4, Discovering Mathematics I,
and MATH 602-4, Discovering Mathematics
II
Justification:
Over four years ago, in the Fall 1989 semester, the Department of Mathematics and Statistics
and the Faculty of Education introduced a Master's Program in Secondary School Mathematics
Education. This program has proved to be very successful and highly popular. It has served as a
paradigm for a similar program at the University of Victoria.
Members of the Faculty of Education and the Department of Mathematics and Statistics felt
that it was time to introduce a Master's Program in Mathematics Education to meet the needs of
practicing teachers who have assignments in the elementary and intermediate grades
(approximately grades 4 to 10). This program, like the one for secondary school teachers, will
consist of courses in both the Education Faculty and the Department of Mathematics and
Statistics. The courses, MATH 601-4, Discovering Mathematics I, and MATH 602-4,
Discovering Mathematics II, will be the Department of Mathematics and Statistics part of the
program.
Course descriptions:
MATH 601-4, Discovering Mathematics I
A discussion of the basic ideas of the arithmetic and geometry of the elementary and junior
secondary school. Emphasis will be on the students understanding though exploration and
discovery. Topics will include some of the following: language of mathematics, number systems,
fractions, decimals and percents, estimation and measurement, algebraic systems, classification
of plane and solid figures, properties of Euclidean geometry, transformation geometry, and other
geometries.
MATH 602-4. Discovering Mathematics
II
An exploration of discrete mathematics and Statistics with emphasis on the ways in
which
they arise and are used in "real world" applications.. Emphasis will be on understanding and
discovery and students will see how these topics can be addressed in their own teaching. Topics
will include: counting, graphs as models, algorithms, scheduling, coding theory, measuring,
interpreting data, testing, experimental design, uses of statistics.
Budgetary implications:
See attached memo from Kathy Heinrich.
Competence of
faculty teaching
the course:
The faculty chosen to teach these courses are certainly competent to do so.
Library resources:
No new library resources will be needed. The material for these courses will be developed
by the instructors.
Iq.
SIMON FRASER UNIVERSITY
MEMORANDUM
Date: ?
February 23, 1994
To: ?
H. Gerber
From: ?
Katherine Heinrich, Chair
Department of Mathematics
& Statistics
Subject: ?
Math 601 and 602
It is proposed that Math 601 and 602 (two new courses to be offered in Mathematics
Education by our department) would be offered in alternate years. We currently offer 20
graduate courses, 2 of which are offered jointly with undergraduate courses. In the
calculations I have been doing regarding our teaching resources for the future, I have
assumed no undergraduate/graduate courses offered simultaneously (although we should
encourage such), 20 graduate courses a year and "space" for one or two special topics
courses.
On that basis alone I believe we have sufficient resources to offer these two courses.
Further, as indicated by the attached e-mail message from the Dean of Education, in
recognition of the graduate courses we offer to their graduate students, each year a faculty
member in education, as part of her/his regular assignment will teach a course in this
department. Last year Rina Zazkis taught Math 190 and it was very successful.
This is an excellent opportunity, both to be part of a new joint program with Education,
and in support of our teaching program. I believe we have the resources to support it.
KH:jc
^0..
Simon Fraser University
?
New Graduate Course Proposal Form
CALENDAR INFORMATION:
Department:
?
Mathematics/Statistics
?
Course Number:
Math 601-4
Title:
?
Discovering Mathematics I
Description:
?
See attached.
Credit Hours: ?
Four ?
Vector:
400
?
Prerequisite(s) if any:
Acceptance into the
Master's program in Mathematics Education or permission of the department. Graduate
Students in the Department of Mathematics and Statistics cannot take this course to
satisfy their degree requirements.
ENROLLMENT AND SCHEDULING:
Estimated Enrollment: ?
25 ?
When will the course first be offered:
How often will the course be offered:
?
Once every two years
• ?
JUSTIFICATION:
See attached
RESOURCES:
Which Faculty member will normally teach the course:
J. L. Berggren, H. Gerber
What are the budgetary implications of mounting the course:
Are there sufficient Library resources (append details):
?
Yes
Appended: ?
(a) Outline of the Course
(b)
An indication of the competence of the Faculty member to give the course
(c)
Library resources
Approved: ?
Departmental Graduate Studies Conur
?
Date: i-I
rc ?
1 I
Faculty Graduate Studies çommittet:
?
Date:
Faculty: ?
-Date:
Senate:Senate ?
Graduate Studies Committee:
QQ_-f
.L__-Date:
_Date:
1
Ig ?
9
S
I.
MATH 601-4?
DISCOVERING MATH I?
OUTLINE
Arithmetic and geometry form the core of the elementary school curriculum. The fundamental
concepts in both these areas of mathematics will be approached through exploratory exercises
and problems as well as in projects. The students will work both singly and in groups to explore
the ideas of mathematics. The presentations will be non-theoretical.
Among the topics to be discussed are some of the following:
PART I: ARITHMETIC
1. The language of mathematics
2.
Number Systems
a)
Evolution and description of base-ten system
b)
Other base systems
c)
Operations of addition and multiplication
d)
Primes, factors and perfect numbers
3. Fractions
a)
Ratios and commensurability
b)
Models of fractions
c) Operations on fractions
d)
Density and other properties
4. Decimals and percents
a)
Development of decimals
b)
Operations on decimals
c)
Periodic decimals and fractions
d) Percents
5.
Estimation and measurement
a) Estimation
b) Measurement
6. Algebraic Systems
(2
weeks)
a)
Modular Arithmetic and coding•
b) Dihedral groups
c) Matrices
PART II: GEOMETRY
1. Classification of plane and solid figures
a)
Terminology - polygons, polyhedra, vertices, edges, etc.
b)
Symmetries of figures
c)
Regular figures
2.
Properties of Euclidean Geometry
a) Congruence
b)
Parallel properties and angles of figures with applications to tessellations
c) Pythagorean theorem
d) Distance in the plane
?
0
.
Me
e) Areas and volumes
S
f) Similarity properties
g) Possible and impossible constructions
3. Transformation geometry
a)
Motions of the line and plane
b)
Translations
c)
Reflections
d) Rotations
4. Fractal Geometry
CALENDAR DESCRIPTION
MATH 601-4 Discovering Mathematics I
A discussion of the basic ideas of the arithmetic and geometry of the elementary and junior
secondary school. Emphasis will be on the students understanding though exploration and
discovery. Topics will include some of the following: language of mathematics, number systems,
fractions, decimals and percents, estimation and measurement, algebraic systems, classification
of plane and solid figures, properties of Euclidean geometry, transformation geometry, and other
geometries.
Prerequisite:
Acceptance into the Master's program in Mathematics Education or permission of
the department. Graduate students in the Department of Mathematics and Statistics cannot take
this course to satisfy their degree requirements.
2
0
A.
Simon Fraser University
?
New Graduate Course Proposal Form
CALENDAR INFORMATION:
Department: ?
Mathematics/Statistics
?
Course Number: ?
Math 602-4
Title: ?
Discovering Mathematics II
Description: ?
See attached
Credit Hours:
Four
Vector:
400
Prerequisite(s)
if
any:
Math
601
and acceptance
into the Master's program in Mathematics Education, or permission of the department.
Graduate
course to
students
satisfy their
in the
degree
Department
requirements.
of
Mathematics
and Statistics cannot take this
ENROLLMENT AND SCHEDULING:
Estimated Enrollment:
25
?
When will the course first be offered:
Fall 1995
How often will the course be offered:
Once every two years.
.IUSTIFICATJON:
See attached.
RESOURCES:
Which Faculty member will normally teach the course:
?
K. Heinrich, C. Dean
What are the budgetary implications of mounting the course:
Are there sufficient Library resources (append details):
?
Yes
Appended: ?
(a) Outline of the Course
(b)
An indication of the competence of the Faculty member to give the course
(c)
Library resources
Approved: ?
Departmental Graduate Studies Co
?
g
ft^_ ?
Date: / cc k
17
Faculty Graduate Studies Committee:
Date:
Faculty:
?
Date: fl
?
/
/
(?YY
Senate Graduate
Studies CommitteeT2,
p
4 ?
Date: ?
____________
^4-
MATH 602-4
• ?
DISCOVERING MATH II
Discrete Mathematics is used in computer communications, scheduling and transportation
problems. Statistics is encountered by each of us every day in the newspapers and on
television as medical findings, sporting results and economic strategies are discussed.
These are two of the most accessible areas of modern applied mathematics and many
problems and the ideas behind their solution can be understood and appreciated by
students with only a modest mathematical background. Several topics in these areas and
their relationship to "real-world" problems will be explored. The exploration will be
done through a series of projects with students often working in teams and making
presentations of their discoveries. The presentation will be non-theoretical.
Topics:
PART 1: DISCRETE MATHEMATICS
1. Counting
• ordered and unordered selections
• permutations and combinations
• elementary probability
• pigeon-hole principle
2.
Graph Theory
• graphs as models
?
•
?
• trees and their properties and uses
• eulerian walks and applications
• games on graphs
• graph algorithms
• networks
3.
Graphical designs
• graph decompositions
• tournament scheduling
• Hamilton cycles and 1-factors in complete graphs
• Steiner triple systems
• applications
4.
Coding Theory
• binary arithmetic
• error correction and detection
• Hamming distance
• codes from graphs and designs
PART 2: STATISTICS
1.
Measuring and Averages
• measures of central tendency
• measures of dispersion
• elements of graphing data - univariate, bivariate, multiway data
X5 -
2.
Designing Experiments
• randomization
• binomial, hypergeometric, normal probability distributions
• double - blind experiments
• paired comparisons
3. Interpreting Data
• components of a test of hypothesis
• hypothesis tests for means and proportions
• two
-
sample tests
• standard error of an estimator
4.
Seminars
• Environmental Statistics
• Statistics and Medicine
• Statistics in Sport
CALENDAR DESCRIPTION ?
MATH
602-4 DISCOVERING MATHEMATICS
II
An exploration of discrete mathematics and statistics with emphasis on the ways in which
they arise and are used in "real world" applications. Emphasis will be on understanding
and discovery and students will see how these topics can be addressed in their own
teaching. Topics will include: counting, graphs as models, algorithms, scheduling,
coding theory, measuring, interpreting data, testing, experimental design, uses of
statistics.
Prerequisite:
MATH 601 and acceptance into the Master's program in Mathematics
Education, or permission of the department. Graduate students in the Department of
Mathematics and Statistics cannot take this course to satisfy their degree requirements
fl
c.c. Sharon Thomas, Head Collections Management
.
V
MEMO
•
TO:
?
Katherine Heinrich, Chair Department of Mathematics
and Statistics
FROM: Ralph Stanton (Library Collections Management
Office)
RE: ?
New Course Proposal for MATH 601 and MATH 602 Dated
February 23, 1994
DATE: 11 July 1994
I have examined the Library's holdings for MATH 601
Discovering Mathematics I and 602 Discovering Mathematics
II. These 4 unit courses will be offered once every 2 years
to 25 students
The Library has no record of receiving the course outline or
other documents until the agenda of SGSC meeting of July 11,
1994 was received. No reading list is attached to these
courses.
• ?
The Library has completed a course assessment for EDUC 844-5
and EDUC 845-5 which cover topics in the teaching of pre-
college Mathematics. Changes to the Library profile made for
these courses should be adequate to support MATH 601 and
602.
The serial
Arithmetic Teacher
is
in the collection. The
Mathematics Department has indicated it has not set a text
for either course and that it will allocate up to $200 per
course to allow for the purchase of texts related to these
courses. The Mathematics department has indicated it is
satisfied with Library Resources as currently planned.
MAXIMUM TOTAL OF ALL ONE TIME COSTS IS $400. NO OTHER COSTS
ARE ATTACHED TO THESE COURSES.
RS
A.
