SiMON FRASER UNIVERSITY
?
MEMORANDUM
From ......
.SENAIE.,.GJADUATh ... S.TUD......COMMITTEE..............
Date.......
JIJNE1Q.,.,.1.9.75 .................... ..................................... ..............
.
MOTION:
?
"That Senate approve, and recommend approval to
the Board of Governors, the M.Sc. (EDUC) Program
in Mathematical Education, as set forth in S.75410
including the new courses:
MATH 601-5 - Trends and Developments in Mathematics, I
MATH 602-5 - Trends and Developments in Mathematics, II
which do not carry credit toward the M.Sc. or the Ph.D.
degrees in the Faculty of Science, but toward the M.Sc.
(EDUC) degree."
0
SIMON FRASER UNIVERSITY
To: Members of Senate
Subject: M.Sc.(Educ) Program
in Mathematical Education
S7
5-
//o
From: Office of the Dean
of Graduate Studies
Date: June
10, 1975
.
MOTION: That Senate approve the M.Sc.(Educ) Program in
Mathematical Education
This program was approved by the Senate Graduate
Studies Committee on June
9, 1975.
Jon Wheatley
Dean of Graduate Sbicjies
.
From ?
Jon Wheatley,
Dean of Graduate Studies
Date ?
March
24, 1975.
SiMON FRASER UNIVERSITY.
?
S. ?
-
MEMORANDUM
U
I enclose a proposal for an M.Sc. (Ed) Program in Mathematical
Education: It is my ruling that it is not a new program. I checked this
ruling with the Academic Planning Committee to make sure I would not be
over-ruled at a later time with consequent loss of time: the Academic
Planning Committee concurred in my ruling. Thus the proposal may go forward
toSenate without reference to the Assessment Committee for New Programs
However, because it is a course package, rather than simply one or two
new courses, I would like it to go before the Senate Graduate Studies
Committee (if it passes the Executive Committee) before it goes to Senate.
Jon Wheatley
cc: Dr. B. Wilson, Chairman Academic Planning Committee
Dr. S. Aronoff, Dean of Science
Dr. A. H. Lachlan, Chairman Mathematics
enc • ? - -. --- -.
MAI 25 1975
.
S1MON FRASER UNIVERSITY
?
MEMORANDUM
.
To......................M. McGinn,Secreary
Senate Grad Studies Committee
Subject ...... M...S.c... ..... (.Ed..) ... Program ... in ......... ..........
.... ......... .... .
From .......
.......S...
..Aro.n.o.ff..
...... ..........
Dean
...of...Sciercce. ...
.....................................................
Date...............
March ...S.....i.c.7.5 ... ..... ........... ......... ................ ....................
At its meeting of February 27, 1975, the Faculty of Science passed the
following motions:
"That the Faculty approve the proposal for a Master of Science (Education)
Program in Mathematics Education and forward to 56,5C
for consideration."
"That the Faculty approve course proposal MATH 601-5, 'Trends and Develop-
ments in Mathematics, I' and forward toSGSC for consideration."
"That the Faculty approve course proposal MATH 602-5, 'Trends and Develop-
ments in Mathematics, II' and forward to 565L for consideration."
The supporting documentation for these proposals is attached.
/pe 1
End.
.
0
SiMON FRASER UNIVERSITY
?
MEMORANDUM
.
To ?
... ?
Dr. S. Aronoff
Dean of Science
Subject. ?
M.
Sc.:.
(Ed.)
.
Program
?
tics
Education
From .........
...
Dr.A.H.Lachlan.
Chairman
Mathematics Department
Date
...Qcpbe.c,.
22,1974.. ........................................ ..........
....
This proposed new program has crystallized and the proposers of
it would like it to be mounted in the academic year 75-76. In the
past I indicated to you that I hoped we could make our contribution to
this program without any additional faculty members. At that time it
seemed that the requirement would be for six hours teaching a year. The
Department now has a very strong feeling that it has been the victim of
too tight a squeeze in terms of manpower and that on no account should we
undertake anything new without receiving the necessary additional help
at faculty level.
The requirements for the program would be 15 hours over two years.
I think that the best way to provide the necessary teaching would be to
• ?
employ persons with recent Ph.D.'s either to teach some of our tutorials
or to teach some of our lowest level calculus courses. Of course I
should say we are alive to the necessity for all introductory courses
to be taught not only competently but well. I feel that a sum in the
neighborhood of $10,000 over two years could be used to fund the teaching
in this way. Our Appointments Committee felt that it would be prudent to
use this approach rather than requesting yet another faculty position
because it is not yet certain that the M.Sc. Education Program can be
offered continuously.
1A
I
A.H. Lachlan
AHL/lh
att. current information about program
0
SiMON FRASER UNIVERSITY
MEMORANDUM
To .....
Prof.A.H. Lachlan
..
..
.
From.,
?
L.
.Berggren
.................
Chairman, Math Department
?
. ?
.
Subject
.............. ...................... ........................ . ......................................................... .
Date ...... ..... .8 ...
October ?
1974 .....
Dear Aliatair,
I am writing to
request that you call an early meeting
of the Appointments
and Long-Range Planning Committee to consider the implications for future
staffing of the new M.Sc. (Ed.) Program in Mathematics Education. The Program
itself is to be offered by the Education Faculty but it has been drawn up with
close cooperation between two members of that Faculty (Professors Dawson & Trtvett)
and ?
a committee from the Math. Department.
?
.
The mathematics component of. the program will consist of two 13-week courses,
one of which will be offered each year. (It is a two-year program and all students
will take both courses.) Each course will meet one evening per week, from
4:30-
9:30 with a 45 minute break for dinner. In addition a member of our department ;ill
have the responsibility of supervising the writing of an extended essay (for which
the student receives 5-hour credit) by each student in the program. As the program
will be based on close cooperation betwe4n the person teaching the education
.._-
?
courses and the person teaching the mathámatics course it will be desireable if each
attends a fair portion of the courses gien by the other, I thus put the time
commitment of a person teaching in the piogram at 15 hours over 2 years (10 hours
teaching the mathematics courses,f 5 hourq from directing essays) and this is the
number of teaching hours I feel must be 41located 1y the Department. Because of
the number of students involved (between lO and 15 I feel it would be less than
fair to give under 5 hours teaching credit to the person supervising the extended
essays.
My own view is that there are several persons in the department capable of
and interested in teaching in this program. What I would like the ALRP Committee
to consider is whether or not we can make our contribution to the program without
bringing in a new faculty member to cover the hours we will loose by using one of
our present faculty for this program.
I enclose a draft of the description of the program.
Yours very truly,
LB: lc
/
GRADUATE PROGRAM IN MATHEMATICS EDUCATION
Introductjon
The following
brief
desc Iption of the proposed Graduate
:P.
r
ogram in Mathematics Educat on has been generated as a result
of discussions between the Faulty ofEducatlon and the Mathe-
1atics Department.
The proposed 'program is designed to provide practising
tachcrs with an opportunity to update their knowledge base in
the fields of education and mathematics.
Degree to be awarded
• ?
On successful completion of the Graduate Program in Mathe-
matics Education, a candidate will be awarded the degree of
Master of Science (Education).
..\d-isionjeguirements
The Graduate Program in Mathematics Education, seeks h'.
calibre candidates who are interested--in improving the qualLty
of educational practice in their classrooms. Applicants
f3r,
adrisson must be practising teachers who n:t the regular
adrissio. ruirements to the Faculty of Education. In addi-
tion,
?
requirénients imposed by the Mathematics Deparent
must be me;.
4
S
The Graduate Program in Mathematics Education will
?
ve
initial intake of fifteen students in September, 1975. If fifteen
I
suitable candidates are not identified, the program
will..
be
mounted.
Applications for admission must be made before
I
?
?
Applications wi1lbe sent to the Faculty of Education for
documentation. A joini Faculty of Education-Mathematics Cepart-
net comuittee will rule on t}e admissibility of candiate,
with
the
final decision for admissibility reserved by the Ficlty of
Education Graduate Studies Committee.
Meeting Times
The Graduate Program in Mathematics Education is desizrii
for practising teachers whose family and occupational res.:
bi]ities require them to continue employment while they
take graduate work. For this reason, meeting times will
Tuesdays and Thursdays commencing at4:30 p.m and
con:inuin
through the dinner hour until 9:30 P.M.
Program Content,
Sequencing
and Staffing ?
S
To complete the Graduate Program in Mathematics Educ-tion
and to qualify for the M.Sc. (Education) degree, a candia:o
will be required to complete aminimum of forty semester hours
of work icluding two extendd essays of five semester hours
work each.
.3
.
H
Program
content, sequencing and
staffing for
the two
year
period i
?
shown on the following pages.
It should be notcd
that all students must follow the program
sequencing that
is
'outlinedq
SEMESTER
CALENDAR
?
COURSE
SHORT CONTENT
NUMBER
DESCRIPTION
Fall ?
1975
Education 814
Research. Design
S
(75-3)
a
Mathematics 601
Trends ?
.
Develop-
5
-
ments in Math.
?
I
Spring 1976
**
Education
Trends ?
Develop-
S
(76-1)
ments in Math.
•
Education I
Education 881
Extended Essay
S
Suer 1S176
formal course work
(76-2)
Fall 197*
*
Mathematics 602
Trends ?
Develop-
5
:
(76-3)
I
"ments in Mathe-
matics ?
II
Optiona1 Course
(1.1athematics
?
or
S
•
Edjcation]
Spring 1977
**
Education
Trends ?
Develo:-
(77-1)
-
ments ?
in Mathea-
tics ?
Education
?
:1
Education 882
Extended Essay
S
A ?
See
Appendix A
** ?
See
Appendix B
A**
?
See
.
Appendix C
****
?
See
Appendix D
V
(
I,
sc.rvisoryCOTTUtitteeS
Each.candidate'Will have a Supervisory Committee of two
members, one from the Faculty
1
of Eductiofl and one from the
athrat'icsDep3Ttment. Init.atiofl and supervision of each
candidate's program will be undertaken pursuant to Senate
Graduate Studies Regulations.
Program Coordinator
is recommended as Program Coordinator
for the
?
in Mathematics Education. It is further
rccoended that the Program Coordinator be assisted by a sali
consultatjVe committee whose members have a major commitment
to and involvement in the program (3 or 4 professors
at most)
The program Coordinator will work closely with Senior
Super-
visors of the candidates in the program and the Director of
Graduate Studies, faculty of Education, in order to foster the
expedience and orderly progress of candidates towards their
degrees.
Financial
Assistance
No
financial
assistance will be available for applicants
to the Graduate Program in Mathematics Education.
.5...
•
?
APPENDIX
AL
• ? Mathematics 601
H
Mathematcs 602
H
From
.........P...
S.K. Thomason .....
Graduate Studies Committee
Mathematics ..epartment
Date .....
.......
Noveiiiber25
.....1974
....................... .. ........ ...
................
SiMON FRASER UNIVERSITY
?
MEMORANDUM
Enclosed are New Graduate Course Proposal Forms for Math 601-5
and 602-5, approved by the Department Graduate Studies Committee on
November 21, 1974. Please note that they were approved subject to the
condition that they will not carry credit towards the M.Sc. or Ph.D.
degrees in Mathematics. I presume the Faculty will change "Mathematics"
e
to "Faculty of Scienc" and will ensure an appropriate notation is made
in the Graduate Calendar. (cf. Chemistry entry, 1974-75, p. 127).
SKT/ sh
?
cl.
C
SIMON FRASER UNIVERSITY
.
?
New Graduate Course Pronosal rorm
CALENDAR INFORNAT ION:
Department: ?
Mathematics
?
Course Number: 601
Title:
Trends and Developments in Mathematics, i.
Description:
An investigation of the fundamental concepts and techniques of the
calculus and modern algebra,with stress on the algorithmic aspects of these areas
of Mathematics.
Credit Hours:
?
5
?
Vector:
?
Prerequisite(s) if an
y
:
Permission
ENROLLMENT AND SCHEDULING:
Estimated Enrollment: ?
15 ?
When will the course first be offered:
Fall, 1975
How often will the course be offered:
Onceeverytwoyears.
JUSTIFICATION:
The course is needed as the Mathematics Department's contribution to the Gradu te
40
Program in Educational Practice (Mathematics Education) to be offered by the
Faculty of Education. Itisa key part ofa program desiqpedto improve the
level of mathematics teaching in the Junior and Senior Secondary schools in
this province.
RESOURCES:
Which Faculty member will normally teach the course:
Drs.Alspach,Berggreri, Gerber, 1-larrop and
Thomson.
What are the budgetary implications of mountin
g
the course: ?
Will
need $5,000to pay a
post-doctoral fellowtoteachacourse _that would have been taught bth
faculty member assignedtothiscourse.
Are there
sufficient Library resources
?
(annend
details):
?
See attachment.
Appended:,
a) ?
Outline of the Course
b) ?
An indication of the comnetence
of the Faculty member to
give the course.
c) ?
Library resources
-
Approved:
Departmental Graduate Studies Comxnitt
?
:.
_
1J
)AL
I
i iT '
-
Date:
•2
'
k
_-
Faculty Graduate Studies Committee:
_
Date:____________
Faculty:
_
Date:_______________
Senate
Graduate Studies Committee:
___Date:
Senate:
_______________________________
Library Resources
The existing holdings in Mathematics books are more than adequate
for this course. However, the student will be encouraged to find papers which
develop further the topics in the course, both at a level which would be
useful to him/her and at a level which would be accessible to his/her future
students. Consequently, it is important to note that the library subscribes to
such journals as:
(1)
The Mathematics Teacher
(2)
Mathematical Gazette
(3)
The Monthly, of the Mathematical Association of America
(4)
Vector, a publication of the B.C. Association of Mathematics Teachers
(5)
Scientific American
All of these regularly publish papers which would serve as supplementary
material at a level appropriate to this course.
Competence of Proposed Faculty
The mathematical material included in the course is such as
could be taught by any competent mathematician. Of more Importance is the
individual's concern for, and knowledge of, problems of mathematics education.
Several members of the Proposed Faculty have spoken at length, in both
formal and informal settings, with mathematics teachers in the Province and
with specialists in mathematics education. All of the Proposed Faculty have
been actively involved for more than a year in discussions with Professors
Trivett and Dawson of the Education Faculty on both the approach and content
of this course. In addition, some of those whose names are listed have
published results of their research into problems of mathematics education.
.
0
MATHEMATICS 601
TRENDS AND DEVELOPMENTS IN MATH. I
A. Algorithmic Approaches
I. General study of algorithms
a.
Flowcharting
b.
Efficiency of algorithms
II. Examples of algorithms
B. Calculus
I. Concepts of the calculus
a.
The Real Numbers - order and completeness
b.
Functions
c.
Limits
1.
Convergence of sequences and series
2.
limf(x)
3.
Derivatives
1 4
. Integrals
II. Applications of the calculus
a.
Physical Sciences
b.
Biological Sciences
c.
Social Sciences
C. Algebra
I. Algebra as an extension of High School algebra
a. Groups
1.
Permutation Groups and Counting
2.
Symmetry
b. Rings
1.
Rings in number theory
2.
Polynomial Rings
-2-
: ?
C. (continued)
I. c. Fields
1.
The fields of High School algebra
2.
Constructing other fields
3.
Symmetry, groups of fields
II. Impossibility of certain geometric constructions
•
?
III. Algorithmic aspects of algebra
S
SIt0N FRASER UNIVERSITY
New Graduate Course
Pro
p
osal
form
CALENDAR INFORMATION:
Department: ?
Mathematics
?
-
? Course Number: 602
Title:
Trends and Deve1opents in Mathematics, II.
-
-
Description:
Thebasicconceptsandtechniquesoflinearalgebraandstatistics,with
an emphasis on their applications. A consideration of the axiomatic approach to
Mathematics_as_ exem
p
lified _
by_ different t yp
es ofgeometry.
Credit Hours:
?
-
?
5 ?
Vector:
5-0-0
?
Prerequisite(s) if an
y : _
Permission
ENROLLMENT
AND.SCHEDULING:
Estimated Enrollment:
?
15 ?
When will the course first he offered:
Fall, 1976
How often will the course be offered:
Onceeverytwoyears.
JUSTIFICATION:
•
The course _isneededas __the Mathematics Department's contribution to the Graduate
Program in Educational Practice (Mathematics Education) to be offered by the Faculty
of Education. It is a key part of a program designed to improve the level of
mathematics teaching in the Junior and Senior Secondary schoOls in this
province.
F::;oUrcI:S:
Which Faculty member will normally teach the course:
Drs_ Aispach,Berggren,-Gerber,Harrop and
Thomson
What are the budgetary implications of mountin
g
the course:
?
Will
need $5,000to_pay
a post—doctoral fellow to teach a course that would have been taught by the
faculty member assigned to this course.
Are there sufficient Library resources (annend details):
Seeattachment.
Appended:, a) Outline of the Course
b)
An indication of the com
p
etence of the Facult
y
member to
g ive the course.
c)
Library resources
Approved: Departmental Graduate Studies Committee.
?
JJ-&)—'
-
_flate: \
-
Faculty Graduate Studies Committee:
?
Date:_________
.
?
Faculty:
?
Date:_______
Senate Graduate Studies Committee:
?
__Date:__________
Sonatas
?
Datel______________
Competence of Proposed Faculty
The mathematical material included in the course is such as
could be taught by any competent mathematician. Of more importance is the
individual's concern for, and knowledge of, problems of mathematics education.
Several members of the Proposed Faculty have spoken at length, in both
formal and informal settings, with mathematics teachers in the Province and
with specialists in mathematics education. All of the Proposed Faculty have
been actively involved fore more than a year in discussions with Professors
Trivett and Dawson of the Education Faculty on both the approach and content
of this course. In addition, some of those whose names are listed have
published results of their research into problems of mathematics education..
is
Library Resources
The existing holdings in Mathematicsbooks are more than adequate
for this course. However, the student will be encouraged to find papers which
develop further the topics in the course, both at a level which would be
useful to him/her and. at a level which would be accessible to his/her future
students. Consequently, it is important to note that the library subscribes to
such journals.as:
(1)
The Mathematics Teacher
(2)
Mathematical Gazette
(3)
The Monthly, of the Mathematical Association of America
(4)
Vector, a publication of the B.C. Association of Mathematics Teachers
(5)
Scientific American
All of these regularly publish papers which would serve as supplementary
material at a level appropriate to this course.
MATHEMATICS 602
TRENDS AND DEVELOPMENTS IN MATH II
A. Linear Algebra and Matrix Theory
I. Systems of Liner Equations
II. Vector Spaces
a.
Linear Operators and Linear Functionals
b.
Derivative and Integral
as Linear Operators
III. Applications of Linear Algebra
a.
Game Theory
b.
Linear Programming
B. Statistics and Probability
I.
Descriptive Statistics
II.
Probability
•
?
III. Theory of Inferential Statistics
IV. Applications
ai Experimental Design
b. Sample Survey Design
C.
Quality Control
C. Geometry
I. Reasons for Axiomatics and the
Evolution of the Method
II. Description of the Method
III. Examples of Axiom Systems
a.
Plane Euclidean Geometry
b.
Finite Geometries
c.
Projective Geometry
IV. Consistency.
and Independence of Axiom Systems
-
S..
V
I.
•1
APPENDI
t
B
.
Trends and Dev lopments
in:
Mathematics Education
t
•..T
The number for
this
course
Education ?
,
Trends -
Developments in Mathematics Education I
.
is yet to be
Nonethelss., it is anticipated that at a minimum the co:c !i
?
?
/
?
include the following topics:
A. Affective and
1
Cognitive Factors in Learning a:-.atics
I. Self Concept and School Achievement
I. Confluent Educati n as it pertains to ma:::-::tics
education
I]1. Psychology of Learning Mathematics for t.o v
• '
child/for the adolescent
IV.
Subordination of
Teaching
to Learning
B. Problems in Remedial Work
I.
Principle of Multiple Embodiment
II. Analysis of
Learner Difficulties in aritherc'..c
and algebraic operationals/number systems/co-:
C. Strategies to Develop and
Meet Curriculum Des;grs
I.
Coals and Objectives foi Mathematics Teaching
II.
Strategies for Teaching Mathematics
I.
?
?
ative Evaluation in Mathc.atcs
t
III.
Teaching
Formative and Sunm
IV.
Analysis of Mathematics Curriculum
V.
Research Design
Again,
the number for the course Education -,
Trcr
and Developments in Mathematics Education II is yet to o?
?
.• ?
mined. The following content outline is
provided, however, o
that one can gain a perspective of
the minimum content to c
considered in the course.
0..
?
A
Strategies to Devel p and MeetCurricuu
?
e;ig
Can extension of th topic ini-ted in
Edc.t.:o
B. Importance of error'
^'
in learning mathematics
I. Computational Error
11. Self-correction
III. Algebraic error
IV.
Measurement and estimation
V.
Personal perception
VI.
Individual schema: assimilation and
accoro:ijc:,
C. Physical Aids and Manipulative Materials
for
Mathematics
• I.
Role and organization of mathematics 1::
II. Physical Aids and Manipulative Materia1
a)
Couners
b) Attribute blocks
•
?
c) Coloured rods
d) Multi.base blocks
?
•
e) Ceoboards, pegboard
s
f) Geometric models
g) Mathematical games
•
The two extended
essays
required for the
Graduate
in atheatics Education will conform to the outline
for c:':::LI
essays contained in paper Ed GS 8
and
other such reguiatic•.s
which may from time to time be involved by'the Universi::..
In addition, one of the extended essays must
have
emphasis
on the mathematicswhile the other
must focus
c the
pedagogy
çf mathematics teaching. In the former case, the
major supervisor shall be a member of the Mathematics
Depart-
ment with the second member of the Supervisory
Committee corninz
from the Faculty of Education. In the latter case, the major
supervisor
shall be from
thel
Faculty of
Education with
the
second member of the Supervisory Committee being from the
athemattcs Departmento
.,
The optional coarse
provided
during the 76-3
son:
may be either an education course or a mathematics
CC :.
list of approved optional courses is provided below.
date .must have written approval of his senior
.
supervisc 5ef:rc
registering for an optional, such approval to be
file
"
' with
the Director ol Graduate Studies, Faculty of
Education, no less
than two weeks prior to the comencement of the
courso.
Courses may be added to or 'deleted from this list only
1j
with the
approval of
the Graduate Studies Committee o.'
:
Faculty of Education acting on the recommendation of
the Prcran
Coordinator.
EDUCATION COURSES
?
MATHEMATICS COURSES
Education - ?
Mathematics -
Education - ?
Mathematics -
Education - ?
Mathematics -
Education ?
Mathematics
-
Education -
? Mathematics -
Be;ause of the vriati n'
,
in the number of credit hours
granted for mathematis courss, itinay be necessary
for a
student to take two inathematis courses in order to obtin the
3.
requre S semester hour credit.'
*
cMATHEMATICS 601
TRENDS AND DEVELOPMENTS IN MATH. I
'. AlgorittfliC Approaches
I. General study of algorithms
a.
Tlovcharting
b.
Efficiency of algorithms
It. '
Examples of algorithms
3. Calculuø ?
.
1. Limits and Continuity
S
II. Derivatives
III. Integrals
IV. Al
g
9 rithma
in
theCa1cUiU5
C. Algebra
? .
I. Algebra as an extension of high achool algebra
a.
Groups
b.
Rings
c.)Fields
d. Polynomial Rings
II. Impossibility of certain geometric constructions
IlL. Algoithmic aspec
ts
of algebra
7
I
MATHEMATICS 602
L)
TRENDS AND DEVELOPMENTS IN MATH IT
:1 ?
.••
• ?
/
A.
?
Linear Algebra and Matrix Theory
/
I.
?
S y
stems
of
linear equations
II. ?
Other
uses
for
linear algebra
B. ?
StatiatLs and Probability
0
I• ?
Des
cirt
ptiv
e
Statistics
U.
?
Probability ?
.
III. ?
Theoiçy of Inferentia]1.Statieti4.
IV.
?
Applcations
a. ?
Experimental Design
o-.
b. ?
$arnple Survey Design
. ?
c.
?
cuality Control
C.
?
Geometry
a__.
?
- - ?
• ?
-.
?
-
?
-
?
-
?
-.
zeasuus or Axiomatics and me evo
l
u
t
ion of the
method
It. Description of the method
III. Examples of Axiom Systems
a.
Plane Euclidean Geometry
b.
Finite Ceomet1eg
c.
Projective Geometry
IV. Consistency and Independence of
Axiorn
Systems
