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Recommendations for Early Childhood, Elementary
Education, and Special Education Majors Department of Mathematics September 2008 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 consists of Math 251 (Foundations: Geometry), Math 252 (Foundations: Probability and Statistics), or Math 253 (Foundations: Number Systems). 3) As many of the Foundations courses that a student can fit into their program. a) Math 150, Math 251, Math 252, and Math 253 were designed by Prof. Warren Hill while he was the chair of the committee writing the mathematics section of the Massachusetts Curriculum Frameworks. We have tried to keep these courses parallel to both the Massachusetts Curriculum Frameworks and the National Council of Teachers of Mathematics Standards so they 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 "upper level" mathematics/science elective. c) We realize that not all education 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. Detailed course and advising information about these courses is attached. Copies of these documents can be found at www.wsc.ma.edu/math/educationadvising.asp This site will be updated when changes are made. Questions, comments, concerns, and/or suggestions are appreciated. Please direct all such matters to Julian Fleron at jfleron@wsc.ma.edu or X5716. Math 150
Foundations:
Mathematical Reasoning
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: *
Small group
work *
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. *
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. *
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. *
Using
manipulatives as a tool
for understanding mathematical concepts and for solving problems. *
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: *
Problem
solving techniques *
Patterns *
Sets and
classification *
Functions
and relations *
Inductive
and deductive reasoning *
Logic Instructional Objectives Upon completion of the course, students will be able to: *
Appropriately
select and apply different problem-solving techniques *
Clearly
articulate the problem-solving method(s) used *
Utilize
mathematical and logical reasoning *
Construct simple proofs *
Use basic set theory to
describe different types of sets
and their relationships *
Use functions to describe and solve
applied problems *
Describe
mathematical patterns and incorporate them in problem-solving *
Describe the
difference between deductive and inductive reasoning, including the strengths
and limits of each Texts/Resources Bassarear, T. Mathematics for Elementary School Teachers, 3rd Ed.,
Houghton-Mifflin Co. ISBN:0-6-1805-111-2. 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:) Ohanian,
S. Garbage Pizza, Patchwork
Quilts, and Math Magic, W> H> Freeman and Co., 1992. Schifter,
Deborah (ed.). Reconstructing
Mathematics Education, Teachers College Press, 1993. Ma,
Liping. Knowing and Teaching
Elementary Mathematics, Lawrence Erlbaum Associates, Inc., 1999. (The
following videotape resources are available from the math department:) Teaching
Math: a Video Library, K-4, Annenberg/CPB Mathematical Science Collection,
WGBH, 1995. ( A collection of 26 tapes.) Challenge
in the Classroom, Mathematical Association of America (no date given). Mathematics:
Making the Connection, NCTM, 1991. Discovery
Workshop, NCTM, 1991. Using
Numbers: Real Data in the Classroom, Dale Seymour Productions, 1990. Learning
Games, Frog Publications, 1997. Math 251 (Revised:
10/4/05) 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 IDIS 260. 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. Presently Math 251 is a core course. Catalog 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:
*
Small group work; *
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; *
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; *
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; *
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:
10/4/05) 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 IDIS 260. 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. Math 252 is a core course. Catalog
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&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:
10/04/05) 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 IDIS 360. 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. Presently Math 253 is a core course. Catalog 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: Small group work; 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; 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; 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; Developing different problem-solving strategies (estimating, drawing a diagram, discovering patterns, constructing a table, etc.) that are applicable to a wide variety of situations. | Mathematics Links | Resources | Cool Mathematics Links | Careers in Mathematics | | WSC Writers Guide | Accuplacer Exam | Contact | Home | |