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Recommendations for Early Childhood, Elementary
Education, and Special Education Majors Department of Mathematics 12 March, 2009 Since January 2009, the General
Curriculum MTEL examination has a significantly expanded Mathematics subtest
(40 questions) which will be scored separately and must be passed for students
to pass the examination. The
Mathematical Foundations courses that have been in place here at Westfield
State College are entirely compatible with the new "Guidelines for the
Preparation of Elementary Teachers" that accompanied this change in MTEL. (Available online at http://www.doe.mass.edu/mtel/MathGuidance.pdf.) Indeed, we are one of the very few
Massachusetts colleges that are not scrambling to completely revamp their
mathematics content offerings for future elementary teachers in response to
these new changes. We are grateful to all those who
continue to provide invaluable advising, wonderful support and appropriate
course registration of our pre-service elementary teachers. We are happy to share this updated
version of our recommendations.
They are unchanged other than the recommendation on the course Math 360:
"Current Trends in Mathematics Education: Regional NCTM Conference in Boston"
and introducing Volker Ecke as the person coordinating elementary education in
our department. For Early Childhood, Elementary
Education, and Special Education majors, our department recommends the
following coursework in mathematics: 1)
Math 150 (Foundations: Mathematical Reasoning) as a first
mathematics course taken during the student's first year. This is a core course. It is required for Early Childhood,
Elementary Education, and Special Education majors. 2)
A second mathematics core course which is chosen from among the following: a)
Math 251 (Foundations: Geometry). b)
Math 252 (Foundations: Probability and Statistics). c)
Math 253 (Foundations: Number Systems).
These courses can be taken in any
order following Math 150. While
other mathematics core courses may be appropriate on rare occasions, these
courses are recommended. This
recommendation reflects changes in requirements and core status from the past. Please note that Math 110 and Math
111 are not recommended. 3)
As many of the Foundations courses that a student can fit
into their program. a)
From the outset of their development, Math 150, Math 251, Math
252, and Math 253 have been compatible with both the Massachusetts
Curriculum Frameworks and the National Council of Teachers of Mathematics Standards
for School Mathematics. They
are designed precisely to provide the necessary mathematical preparation for
pre-service teachers in a context that nurtures their interest in teaching
mathematics. b)
The courses Math 251, Math 252, and Math 253 are the only
mathematics courses that satisfy the Mathematics/Science elective listed under
"Additional Arts and Sciences Coursework"listed on p. 99 of the Bulletin. c)
We realize that not all education students can take four
mathematics courses. However, to
have comprehensive coverage of the content strands of the Massachusetts
Curriculum Frameworks students must take Math 150, Math 251, Math 252, and
Math 253. d)
Students must take Math 150, Math 251, Math 252, and Math 253
to have coverage of all of the areas that make up the mathematics portion of
the Massachusetts Tests for Educator Licensure (MTEL). 4) Another
mathematics offering: Math 360:
Regional NCTM Conference in Boston, MA Students enrolled in this course
will attend the National Council of Teachers of Mathematics Regional Conference
in Boston, MA (October 21-23, 2009) and will prepare logs, portfolios and
presentations related to sessions at the conference. More information about these
courses can be found at the URL http://www.wsc.ma.edu/math/courses.asp Questions, comments, concerns,
and/or suggestions are appreciated.
Please direct all such matters to Volker Ecke at vecke@wsc.ma.edu or x5348. Detailed advising sheets for Math 150, 251, 252, 253, 352 Math 150 (Revised:
2/23/06)
Foundations:
Mathematical Reasoning Advising This core course is a requirement for Early Childhood, Elementary
Education, and Special
Education majors and
should be taken early in their program (first or second year). This is a mathematics subject matter
course which covers the patterns, relations, and algebra strands of the
Massachusetts Curriculum Frameworks in mathematics at the collegiate
level. To meet Massachusetts
teacher licensure requirements, students are also required to take MATH
352. To have comprehensive
coverage of the content strands in Mathematics, students must take Math 251, 252, and Math 253. Math 150 is inappropriate for students who are not interested in
Elementary Mathematics Education.
Students who are just looking to satisfy the Mathematics Core
Requirement and have not specific requirement or recommendation for their
major, Math 110 and/or Math 111 may be more appropriate choices. Course
Description An introductory course. Topics include: finding, analyzing, and
describing patterns; sets and classification; functions and relations;
inductive and deductive reasoning; problem solving; and logic. Students will develop a conceptual
understanding of the course material in a learning environment that models the
pedagogical foundations of the Massachusetts Curriculum Frameworks for
Mathematics and the National Council of Teachers of Mathematics (NCTM)
Standards. Pedagogy Part of the course objective is to
introduce students to some of the teaching pedagogy outlined by the NCTM. Following the NCTM Standards, the
course is designed to educate students to become active participants (rather than passive observers) in
mathematical thinking, and to encourage them to educate their future students
in the same spirit. This may be
done using some or all of the following approaches: o
Small group work o
Emphasis on student verbal explanation
of problem-solving processes rather than just providing answers. Verbally explaining or defending
solutions can help develop students' mathematical thinking, as well as
articulative skill. o
Increasing students'
self-reliance on checking solutions leads
to deeper mathematical thinking.
They have to think about whether or not their answers make sense; they
have to think about the problem further to devise a way to check the solution;
and their understanding and thinking about the problem will be deepened. If the professor simply says, "That's
right" or "That's wrong," thinking about the problem will immediately cease.
o
The Constructivist
approach to learning is emphasized: students discover and build
mathematical concepts themselves, rather than just memorizing them without
really understanding. According to schema
learning theory, knowledge is acquired in greater depth and is more efficiently
retained if it can be connected with the learner's pre-existing knowledge. It cannot be assumed that learners will
make the connections without help.
The connections of new material to other knowledge structures must be
made; and in keeping with the self-reliance issue raised earlier, the connections
should be made by the students themselves whenever possible. o
Using manipulatives as a tool for understanding mathematical concepts and for
solving problems. o
Developing different
problem-solving strategies (estimating, drawing a diagram,
discovering patterns, constructing a table, etc.) that are applicable to a wide
variety of situations. Other
objectives vary from instructor to instructor. There is a real concern that many students preparing to be
elementary school teachers lack basic arithmetic skills that they need to teach
their students. This issue is
frequently addressed in the "plus" sections of MA 150. Another concern is that the attitude
they as teachers have about mathematics is likely to carry over into their own
classroom; keeping a journal is one way of helping students deal with this
issue. Course Objectives Required
topics in MA 150 include: o
Problem solving techniques o
Patterns o
Sets and classification o
Functions and relations o
Inductive and deductive
reasoning o
Logic Instructional Objectives Upon
completion of the course, students will be able to: o
Appropriately select and
apply different problem-solving techniques o
Clearly articulate the
problem-solving method(s) used o Utilize mathematical and logical reasoning o Construct
simple proofs o Use
basic set theory to describe different
types of sets and their relationships o
Use functions to describe and solve applied problems o
Describe mathematical
patterns and incorporate them in problem-solving o
Describe the difference
between deductive and inductive reasoning, including the strengths and limits
of each Resources o
Bassarear, T. Mathematics for Elementary School
Teachers, 3rd Ed., Houghton-Mifflin Co.
o
Bennett and Nelson. Mathematics for Elementary Teachers,
6th Ed., McGraw Hill Publishing; ISBN: 0-072-53298-X + supplements &
manipulative kit. It is strongly recommended that
anyone teaching the course for the first time read one or more of the following three books: o
Ohanian, S. Garbage Pizza, Patchwork Quilts, and
Math Magic, W. H. Freeman and Co., 1992. o
Schifter, Deborah (ed.). Reconstructing Mathematics Education,
Teachers College Press, 1993. o
Ma, Liping. Knowing and Teaching Elementary
Mathematics, Lawrence Erlbaum Associates, Inc., 1999. The following videotape resources
are available from the math department: o
Teaching Math: a Video
Library, K-4, Annenberg/CPB Mathematical Science Collection, WGBH, 1995. ( A
collection of 26 tapes and 11 DVDs) o
Challenge in the Classroom,
Mathematical Association of America (no date given). o
Mathematics: Making the
Connection, NCTM, 1991. o
Discovery Workshop, NCTM,
1991. o
Using Numbers: Real Data in
the Classroom, Dale Seymour Productions, 1990. o
Learning Games, Frog
Publications, 1997. Math 251 (Revised:
3/12/09) Foundations: Geometry Advising This course is a suggested course for Early
Childhood, Elementary
Education, and Liberal
Studies majors. This is a mathematics content course
which covers the geometry strand of the Massachusetts Curriculum Frameworks in
Mathematics at a collegiate level. To meet Massachusetts teacher licensure requirements,
students are required to take Math 150 and Math 352. To have comprehensive
coverage of the content strands in mathematics, students must take Math 251, Math 252, and Math 253 as
well. These three courses can be taken in any order after successful completion
of Math 150. Math 251, Math 252, and Math 253 are the
only mathematics courses that can be used to fulfill the "upper level"
requirement for Early Childhood and Elementary Education majors. Course description: An
introductory course on geometry and measurement. Topics will include: Euclidean geometry, characteristics and
properties of 2- and 3-dimensional shapes, topology, symmetry and
transformational geometry, the development of measure, and the derivation of
measurement formulae. Students
will develop a conceptual understanding of the course material in a learning
environment that models the pedagogical foundations of the Massachusetts
Curriculum Frameworks for Mathematics and the NCTM Standards. Prerequisite: Math 150 or equivalent. Course Objectives: Upon completion of this course students will have learned to:
Pedagogy One of the course objectives is to
introduce students to some of the teaching pedagogy outlined by the NCTM.
Following the NCTM Standards, the course is designed to educate students to
become active participants (rather than
passive observers) in the mathematical experience, and to encourage them to
educate their future students in the same spirit. This may be done using some or all of the following
approaches: o
Using geometry-based manipulatives and technology as tools for understanding mathematical concepts, solving problems,
and preparing them to employ these manipulatives effectively in their
classrooms in the future. These
manipulatives should include several of the following: unit cubes, geoboards, pattern blocks,
regular polygon templates, tangrams, geometric algebra blocks, models of the
conic sections, Legos, Tangles, flexagons, Zome geometry, origami and
paper-folding, geometric solids, conic section models, and geostrips. Appropriate technology may
include: scientific calculators,
Geometer's Sketchpad, Cabri Geometry, Tesselmania, Logo, CAD programs, and
choices from the wealth of interactive Java scripts that enable explorations of
geometry in real time on the Internet; o
Small group work; o
Emphasis on student verbal explanation
of problem-solving processes rather than just providing answers; verbally
explaining or defending solutions can help develop students' mathematical
thinking, as well as articulation skills; o
Increasing students'
self-reliance on checking solutions leads
to deeper mathematical thinking.
They have to think about whether or not their answers make sense. They also have to think about the
problem further to devise a way to check the solution. As a result their understanding and
thinking about the problem will be deepened. If the professor simply says, "That's right" or "That's
wrong," thinking about the problem will immediately cease; o
The Constructivist
approach to learning is emphasized: students discover and build
mathematical concepts themselves, rather than just memorizing them without
really understanding. According to schema learning theory, knowledge is
acquired in greater depth and is more efficiently retained if it can be
connected with the learner's pre-existing knowledge. It cannot be assumed that learners will make the connections
without help. The connections of
new material to other knowledge structures must be made, and in keeping with
the self-reliance issue raised earlier, the connections should be made by the
students themselves whenever possible; o
Developing different
problem-solving strategies (estimating,
drawing a diagram, discovering patterns, constructing a table, etc.) that are
applicable to a wide variety of situations. Appropriate Texts Michael Serra, Discovering Geometry: An Investigative Approach,
Key Curriculum Press, 2003. David Gay, Geometry by Discovery,
John Wiley & Sons, 1998. Phares G. O'Daffer and Stanley R. Clemens, Geometry: An
Investigative Approach, Addison-Wesley Publishing Company, 1992. L. Christine Kinsey and Teresa E. Moore, Symmetry, Shape and
Space: An Introduction to
Mathematics Through Geometry, Key
Curriculum Press, 2001. Math 252 (Revised:
3/12/09) Foundations: Probability
and Statistics Advising This course is a
suggested course for Early Childhood, Elementary Education, and Liberal Studies majors. This is a
mathematics content course which covers the probability and statistics strand
of the Massachusetts Curriculum Frameworks in Mathematics at a collegiate
level. To meet Massachusetts teacher licensure requirements, students are
required to take Math 150 and Math 352. To have comprehensive coverage of the
content strands in mathematics, students must take Math 251, Math 252, and Math 253 as
well. These three courses can be taken in any order after successful completion
of Math 150. Math 251, Math
252, and Math 253 are the only mathematics courses that can be used to fulfill
the "upper level" requirement for Early Childhood and Elementary Education
majors. Course
description: The study of the foundations of Probability and Statistics.
Topics will include understanding, constructing, and computing data graphs and
numerical summary measures; probability models; and statistical inference.
Students will develop a conceptual understanding of the course material in a
learning environment that models the pedagogical foundations of the
Massachusetts Curriculum Frameworks for Mathematics and the NCTM
Standards. Prerequisite: Math 150
or equivalent Course
Objectives: Upon
completion of this course students will have learned about: 1. bar
graphs/histograms. 2. circle graphs (pie charts). 3. mean, median, mode. 4. stem-and-leaf displays. 5. standard deviation. 6. box plots. 7. line plots. 8. randomness. 9. probability models. 10. probabilities
of equally likely outcomes. 11. probabilities
of events. 12. product
tables. 13. tree
diagrams. 14. statistical
inference: confidence intervals and/or hypothesis testing. 15. (optional) simple linear regression. Pedagogy One of the course objectives is to
introduce students to some of the teaching pedagogy outlined by the NCTM.
Following the NCTM Standards, the course is designed to educate students to
become active participants (rather than
passive observers) in the mathematical experience, and to encourage them to
educate their future students in the same spirit. This may be done using some or all of the following
activities: M&M Bar Graphs Coin
Flip (3 flips) "Fox in Sox"
line plots Real
Words (tree diagram activity) Horse Race
(exploratory game) "Pokemon"
(geometric probability distribution) Sum of Dice Roll Missing
Monsters (attribute activity) Minimum of Dice
Roll Math 253 (Revised:
3/12/09) Foundations: Number
Systems Advising: This course is a suggested course for Early
Childhood, Elementary
Education, and Liberal
Studies majors. This is a mathematics content course
which covers the number systems strand of the Massachusetts Curriculum
Frameworks in Mathematics at a collegiate level. To meet Massachusetts teacher licensure requirements,
students are required to take Math 150 and Math 352. To have comprehensive
coverage of the content strands in mathematics, students must take Math 251, Math 252, and Math 253 as
well. These three courses can be taken in any order after successful completion
of Math 150. Math 251, Math 252, and Math 253 are the
only mathematics courses that can be used to fulfill the "upper level"
requirement for Early Childhood and Elementary Education majors. Course description: An
introductory course on number systems.
Topics include the development and properties of various number systems
(such as integers, rational, real and complex numbers), as well as operations
and different representations in these number systems (e.g. in bases other than
10). Students will develop a conceptual understanding of the course material in
a learning environment that models the pedagogical foundations of the
Massachusetts Curriculum Frameworks for Mathematics and the NCTM Standards. Prerequisite: Math 150 or equivalent. Course Objectives: Upon completion of this course students will have learned:
Pedagogy One of the course objectives is to
introduce students to some of the teaching pedagogy outlined by the NCTM.
Following the NCTM Standards, the course is designed to educate students to
become active participants (rather than
passive observers) in the mathematical experience, and to encourage them to
educate their future students in the same spirit. This may be done using some or all of the following approaches:
o
Small group work; o
Emphasis on student verbal explanation
of problem-solving processes rather than just providing answers; verbally
explaining or defending solutions can help develop students' mathematical
thinking, as well as articulation skills; o
Increasing students'
self-reliance on checking solutions leads
to deeper mathematical thinking.
They have to think about whether or not their answers make sense. They also have to think about the problem
further to devise a way to check the solution. As a result their understanding and thinking about the
problem will be deepened. If the
professor simply says, "That's right" or "That's wrong," thinking about the
problem will immediately cease; o
The Constructivist
approach to learning is emphasized: students discover and build
mathematical concepts themselves, rather than just memorizing them without
really understanding. According to schema learning theory, knowledge is
acquired in greater depth and is more efficiently retained if it can be connected
with the learner's pre-existing knowledge. It cannot be assumed that learners will make the connections
without help. The connections of
new material to other knowledge structures must be made, and in keeping with
the self-reliance issue raised earlier, the connections should be made by the
students themselves whenever possible; o
Developing different
problem-solving strategies (estimating,
drawing a diagram, discovering patterns, constructing a table, etc.) that are
applicable to a wide variety of situations. Math 352 (Revised:
3/12/09) Foundations of Teaching
Mathematics: PreK-6 Advising: This course is a suggested course for Early
Childhood, Elementary
Education, and Liberal
Studies majors. This is a mathematics methods course. To
meet Massachusetts teacher licensure requirements, students are required to
take Math 150 and MATH 352. To have comprehensive coverage of the content
strands in mathematics, students must take Math 251, Math 252, and Math 253 as well. These three
courses can be taken in any order after successful completion of Math 150. Math 251, Math 252, and Math 253 are the
only mathematics courses that can be used to fulfill the "upper level"
requirement for Early Childhood and Elementary Education majors. Course description: Designed to introduce the prospective early
childhood, elementary, and special education school teacher to the
teaching of mathematics. An activity-based format will be used to
create a learning environment that fosters an exploration of the
processes of mathematics. Emphasis will be placed on the role and use
of manipulatives in a laboratory setting that encourages the
development of fundamental concepts in mathematics. Topics may
include: the inductive and deductive processes, measurement, graphing,
cognitive development theory, the learning cycle, discussion of
innovative projects, state and national frameworks, techniques for
assessment, number and arithmetic operations, patterns, variables,
modeling and geometry. Three contact hours per week, including
substantial laboratory/activity time. Prerequisites: Math 150 and one
of the Math 25x
mathematics subject matter courses, or permission of
instructor
Course Objectives: Upon successful completion of this course students will have gained: 1) An understanding of current trends in mathematics education
policy and goals. 2) An understanding of learning theory and practices that
promote mathematics literacy. 3) An awareness of the variety of curricular approaches
available to elementary mathematics educators, including inquiry, discovery,
and interdisciplinary curricula. 4) An ability to design mathematics lessons and units that are
developmentally appropriate and sensitive to the needs, values, and interests
of a diverse group of students. 5) An ability to construct assessment plans that are
compatible with teaching goals and methods and that allow for multiple ways of
representing knowledge. 6) An ability to use multimedia technologies to support
meaningful learning. 7) An understanding of the role of reflection in professional
development and lifelong learning. 8) An awareness of organizations and resources that serve the
professional development of elementary mathematics teachers. Potential Textbook: Elementary and Middle School
Mathematics—Teaching Developmentally, John
A. Van De Walle, 7th edition, Pearson Allyn and Bacon. Potential Topics: - Understand different learning styles. - Comparing different teaching styles. - Inquiry-based Learning in Mathematics. - Planning in The Problem-Based Classroom. (Chapter 5) - Building Assessment into Mathematics Instruction.
(Chapter 6) - Using Technology in Mathematics Instruction. (Chapter
8) - Using Manipulatives in Mathematics Instruction. - Memorizing versus Understanding, e.g. for the
multiplication facts using memorization only versus understanding the use of
the distributive property. - Differentiated Instruction in the Mathematics
Classroom. - Teaching Mathematics in the Era of the NCTM Standards
and the Massachusetts Curriculum Frameworks, e.g. Content Areas investigated by
Grade Level and Teaching Methods. (Parts of Chapters 1, 9 - 23) o Number
Sense (9-14) o Algebra
and Fractions (15-18) o Geometry
and Measurement (19-21) o Probability
and Statistics (22, 23) | Mathematics Links | Resources | Cool Mathematics Links | Careers in Mathematics | | WSC Writers Guide | Accuplacer Exam | Contact | Home | |
