Division of Education
Fall 2012
Course Prefix and Number: EDUC 313
Course Title: Introduction to Mathematics
Credits: Three Semester Hours
Instructor: Dr. Betty Dickson
Classroom: AC233
Class Time: 1:00 – 2:20 pm
Office Location: AC 217
Office Hours: M 10:00 -2:00; T 11:00-1:00; W 9:00- 12:00; R, 12:00- 1:00 or by
appointments.
Telephone Number: (501) 370-5237
E-Mail: bdickson@philander.edu
Textbook:
Van De Walle, J.A. (2009). Elementary and Middle School Mathematics:
Teaching Developmentally. (7th ed.). Boston: Allyn & Bacon.
PROGRAM GUIDELINES
Conceptual Framework (CF):
The theme of the conceptual framework for the program is “The Teacher as the FORCE in the
Teaching/ Learning Process.” The framework’s five underlying principles are: Facilitator,
Organizer, Reflector, Collaborator, and Energizer. Each principle is aligned with Pathwise’s four
domains, Arkansas Standards, NAEYC Standards, and AMLE Standards.
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Pathwise Domain:
Domain A: Organizing Content Knowledge for Student Learning
Domain B: Creating an Environment for Student Learning
Domain C: Teaching for Student Learning
Domain D: Teacher Professionalism
NAEYC Standards:
Standard 1.0 Child Development and Learning
Standard 2.0 Family and Community Relationship
Standard 3.0 Assessment
Standard 4.0 Curriculum Development and Implementation
Standard 5.0 Professionalism
AMLE Standards:
Standard 1. Young Adolescent Development.
Standard 2. Middle Level Philosophy.
Standard 3. Middle Level Curriculum and Assessment.
Standard 4. Middle Level Teaching Fields.
Standard 5. Middle Level Instruction and Assessment.
Standard 6. Family and Community Involvement.
Standard 7. Middle Level Professional Roles.
Arkansas Licensure Standards
1. The teacher understands the central concepts, tools of inquiry, and structures of the
discipline(s) he or she teaches.
2. The teacher plans curriculum appropriate to the students, to the content, and to course
objectives.
3. The teacher plans instruction based on human growth and development, learning
theory, and the needs of students.
4. The teacher exhibits human relations skills, which support the development of human
potential.
5. The teacher works collaboratively with school colleagues, parents/guardians, and the
community to support students’ learning.
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COURSE DESCRIPTION:
An introduction to mathematics instruction for prospective teachers. The course covers
two broad areas: (a) foundations of mathematics education that all effective teachers
should have, and (b) topics found in the K to 8 mathematics curriculum.
COURSE OBJECTIVES
Unit One: Foundations for Teaching Mathematics in a Constructivist Environment
At the end of the course, the student will be able to:
1.
Identify and discuss the “reform movement” in school mathematics by analyzing specific
content of Principles and Standards for School Mathematics. (CF 3; Pathwise A, C; NAEYC
2.F, 3.A; AMLE 1.3; Arkansas Standards 1) Assessment – Examinations 1, 3, Lesson Plan,
Reflection, Quizzes, Lesson Plan, In –Class Exercises .
2.
Explain and demonstrate what it means to do mathematics. (CF 1, 2; Pathwise A, C; NAEYC
2.F, 3.F; AMLE 3.1; Arkansas Standards 1, 2, 3) Assessment – – Examinations 1, 3, Lesson Plan,
Reflection, Quizzes, Lesson Plan, In –Class Exercises .
3.
Relate the constructivist view of learning to the teaching of mathematics. (CF 1, 2;
Pathwise A, C; NAEYC 3; AMLE 2, 3 5; Arkansas Standards 1, 2, 3) Assessment – – Examinations
1, 3, Lesson Plan, Reflection, Quizzes, Lesson Plan, In –Class Exercises
4.
.
Demonstrate teaching problem solving using the three-part lesson format. (CF 1; Pathwise
C; NAEYC 1, 2, 4.D; AMLE 5; Arkansas Standards 2, 3). Assessment – – Examinations 1, 3, Lesson
Plan, Reflection, Quizzes, Lesson Plan, In –Class Exercise; Problem Solving .
5.
Develop lessons based on the three-part lesson structure designed to address the ranges of
abilities in a diverse classroom. (CF 1, 2, 3, 4; Pathwise A, B, C; NAEYC 1.D, 2.F, 3.A: AMLE
3.1, 3.2, 3.3; Arkansas Standards 2, 3) Assessment – – Examinations 1, 3, Lesson Plan, Reflection,
Quizzes, Lesson Plan, In –Class Exercises .
6.
Correlate integrated assessment with instruction. (CF 1, 2, 3; Pathwise C; NAEYC 4; AMLE
5; Arkansas Standards 1, 2, 3) Assessment – – Examinations 1, 3, Lesson Plan, Reflection, Quizzes,
Lesson Plan, In –Class Exercises .
7.
Devise methods for teaching mathematics equitably for all students. (CF 1, 2 5; Pathwise A,
B, C; NAEYC 3.A; AMLE 1, 5;; Arkansas Standards 1 - 5) Assessment – – Examinations 1, 3,
Lesson Plan, Reflection, Quizzes, Lesson Plan, In –Class Exercises .
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8.
Design activities to assist children to develop a collection of number relationships. (CF 1,
2; Pathwise A, C; NAEYC 2.F; AMLE 3, 5; Arkansas Standards 1, 2, 3) Assessment ––
Examinations 2, 3, Lesson Plan, Reflection, Quizzes, Lesson Plan, In –Class Exercises, Problem
Solving
9.
.
Identify and demonstrate different approaches to developing operation meaning. (CF 1, 2;
Pathwise A, C; NAEYC 2.F; AMLE 3, 5; Arkansas Standards 1, 2, 3) Assessment –– Examinations 2, 3,
Lesson Plan, Reflection, Quizzes, Lesson Plan, Problem Solving, In –Class Exercises .
10.
Demonstrate how to assist children to develop whole-number place-value concepts. (CF 1
,2; Pathwise A, C; NAEYC 2.F; AMLE 3, 5; Arkansas Standards 1, 2, 3) Assessment – – Examinations 12, 3,
Lesson Plan, Reflection, Quizzes, Lesson Plan, In –Class Exercises .
11.
Assist children to use invented strategies for whole-number computation. (CF 1, 2, 5;
Pathwise A, B, C; NAEYC 2.F, 3.A; AMLE 1, 3, 5; Arkansas Standards 1, 2, 3) Assessment – Examinations
2, 3, Lesson Plan, Reflection, Quizzes, Lesson Plan, Problem Solving, In –Class Exercises .
12.
Develop an understanding of algebraic thinking as it relates to the K to 8 level. (CF 1, 2, 5;
Pathwise A, B, C; NAEYC 2.F, 3.A; AMLE 1, 3, 5; Arkansas Standards 1, 2, 3). Assessment – –
Examinations 2, 3, Lesson Plan, Reflection, Quizzes, Lesson Plan, Problem Solving,In –Class Exercises .
13. Understand the relationship between fractions and decimal and percent concepts and how
to teach these concepts at the K to 8 level. (CF 1, 2, 5; Pathwise A, C; NAEYC 2.F; AMLE 3, 5; Arkansas
Standards 1, 2, 3). Assessment – – Examinations 2, 3, Lesson Plan, Reflection, Quizzes, Lesson Plan, In –Class Exercises.
14. Apply the van Hiele Theory to geometry instruction. (CF 1, 2, 3; Pathwise A, C; NAYEC 2.F;
AMLE 3; Arkansas Standards 1, 2, 3) Assessment –– Examinations 2, 3, Reflection, Learning Center,
Quizzes, In –Class Exercises .
DISPOSITIONS: Upon completion of this course, candidates will be able to:
1.
Demonstrate a sense of caring. (CF: 1.1.1, 1 1.2, 3.3.3, 5.5.3; NAEYC: 5B; AMLE: 7
Domain: B1, B2, D1, D2; Arkansas Standards 4, 5)
2.
Demonstrate how to establish rapport with children. (CF: 1.1.1, 1.1.2, 3.3.3, 5.5.3;
NAEYC: 5B; AMLE: 7; Domains: B2, D2; Arkansas Standards 4, 5)
3.
Demonstrate a sense of efficacy. (CF: 1.1.1, 1.1.2, 3.3.3, 5.5.3; NAEYC: 5B Domain: B1,
B2, D1, D2; Arkansas Standards 4, 5)
4.
demonstrate how to model a positive attitude towards children.(CF: 1.1.1;1.1.2,
3.3.35.5.3; NAEYC:,5B; AMLE 7; Domain: B1,B2,D1,D; Arkansas Standards 4, 5)
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TECHNOLOGY: Upon completion of this course, candidates will be able to:
1.
understand how to use technology to enhance learning. (CF: 2.2.8, 3.3.6; NAEYC:
2C, 4B, 4C, 4D; AMLE: 3, 5; Domain: A4, D3; Arkansas Standards 1, 2, 3)
2.
understand how to use technology to locate, evaluate, and collect information
from a variety of sources. (CF: 2.2.8, 3.3.6; NAEYC: 2C, 4B, 4C, 4D; NMSA: 3, 5;
Domain: A4, D3; Arkansas Standards 1, 2, 3)
3.
understand how to select and use a variety of software for teaching mathematics.
(CF: 2.2.8, 3.3.6; NAEYC: 2C, 4B, 4C, 4D; NMSA: 3, 5; Domain: A4 D3 4.7; Arkansas
Assignments:
1. Three (3) written exams will be given through out this semester to assess the
attainment of information and materials covered in this class. Examinations will
cover lecture, readings from the textbook and assigned readings of
professional journals. The format will include multiple choice questions,
questions, and essay questions. Make-up exams with not be given without a documented
excuse.
2.
Each student will develop a Math Learning Center. Refer to Common Core
Standards.
3.
Each student will submit a reflection for selected classes.
4.
Each student will write a lesson plan using the format provided by the instructor.
5.
Student will work in groups of 2-3 and introduce a problem solving strategy and
provide a handout.
6.
Pop –quizzes and in-class exercises will be given throughout the semester.
If you miss a pop quiz or in class exercise, you may not recover those points.
7.
If you are absent or late arriving to class, three points will be deducted from your
class attendance points for each absence or tardiness.
 Three (3 @ 100 points each) Written Exams
 Math Learning Center
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300 points
100 points





Class Reflection
Lesson Plan
Problem Solving Strategy
Pop quizzes and in class exercises
Class Attendance
100 points
25 points
50 points
100 points
93 points (approximately)
Expectations:
1.
Class attendance, participation, punctuality, preparation, and interaction are
essential for your success in this class.
2.
Assignments are due at the beginning of each class period. Ten points will be
deducted for each day the assignment is late.
3.
Academic integrity is expected.
4.
All assignments must be typed.
5.
Children, food, drinks, chewing gum, cellular phones, nor beepers to class.
Grading Policy:
90-100
80- 89
70- 79
60- 69
50- 0
A
B
C
D
F
Course Outline:
Foundations for Teaching Mathematics in a Constructivist Environment
Week 1
Teaching mathematics in the Era of the NCTM Standards
a.
Principles and Standards for School Mathematics
b.
The Professional Standards for Teaching Mathematics
c.
The Assessment Standards for School Mathematics
d.
Influences and Pressures on Reform
Week 2
Exploring What It Means to Do Mathematics
e.
Traditional Views and New Approaches
f.
Mathematics as a Science of Pattern and Order
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g.
The Role of the Teacher
Week 3& 4
Teaching Through Problem Solving
h.
Teaching Through Problem Solving
i.
The Before, During, and After Model
j.
Finding Problems
k.
Teaching About Problem Solving
l.
Planning a Problem-Based Lesson
m.
Diversity in the Classroom
n.
Planning for ELL
o.
Drill and Practice
p.
The Traditional Textbook
Week 5
Building Assessment Into Instruction
q.
The Assessment Standards
r.
Assessment Tasks and Problem-Based Instructional Tasks
s.
Rubrics
t.
Gathering Data
u.
High Stakes Testing
v.
Grading
 Examination 1
Week 6
Teaching Mathematics Equitably to All Children
w.
The Classroom Teacher and Special Children
x.
Specific Types of Special Needs
Week 7
Using Technology to Teach Mathematics
y.
Calculators in Mathematics Instruction
z.
Computers in Mathematics Instruction
Week 8
aa.
Instructional Software
bb.
Guidelines for Selecting and Using Software
Developing Early Number Concepts and Number Sense
a.
From Counting to Number Sense
b.
Developing a Collection of Number Relationships
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c.
d.
e.

Week 9
Week 10
Extensions to Numbers up to 20
Connections to the World
The Mental Math Connection
Lesson Plan
Developing Meanings for the Operations
f.
Additive and Multiplicative Structures
g.
Teaching the Meaning of the Operations
h.
Addition and Subtraction Issues
i.
Multiplication and Division Issues
j.
Issues Across All Operations
Whole-Number Place-Value Development
k.
Early Development of Base-Ten and Place-Value Concepts
l.
Patterns and Relationships
m.
Working with Money
n.
Number Sense and Large Numbers
 Examination 2
Week 11
Strategies for Whole-Number Computation
o.
Invented Strategies
p.
General Suggestions for Developing Invented Strategies
q.
How Will You Deal With the Traditional Algorithms?
r.
Addition, Subtraction
s.
Mental Addition and Subtraction
t.
Traditional + and – Algorithms
u.
Multiplication, Division
 Math Learning Center
Week 12
Algebraic Thinking
v.
Generalizations and Symbolisms
w.
Making Structure Explicit
x.
Patterns
y.
Functions and Representations of Functions
z.
Sources of Functional Relationships for the Classroom
aa.
Generalizations About Functions
Week 13 &14 Decimal and Percent Concepts and Decimal Computation
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bb.
cc.
dd.
ee.
ff.
gg.

Week 15
Decimals: An Alternative Symbol System for Base-Ten
Fractions
Characterization of the Decimal Point
Familiar Fraction/Decimal Equivalents
Percents Are Another Name for Hundredths
Percent Problems
Decimal Computation
Problem Solving Strategy
Geometric Thinking and Geometric Concepts
hh.
The Development of Geometric Thinking
ii.
Learning About Shapes and Properties
jj.
Learning About Transformations
kk.
Learning About Location
ll.
Learning About Visualization
mm. Assessment of Geometric Goals
 Final Examination
TEACHING STRATEGIES










Lecture
Discovery Learning
Discussion
Small Group activities
Cooperative Learning
Demonstration Modeling
Simulation
Technology/Media Presentation
Problem Solving
Multiple Intelligence Strategies
BIBLIOGRAPHY
Brandy, T. (1999). “So what?” Teaching children what matters in math.
Portsmouth, NH: Heinemann.
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Ferrini-Mundy, J. (2000). The standards movement in mathematics education :
Reflections and hopes. In M.J. Burke (Ed.), Learning mathematics for a new
century (pp. 37-50). Reston: VA: National Council of Teachers of Mathematics.
Fosnot, C. T., & Dolk, M. (2001). Young mathematicians at work: Constructing
number sense, addition, and subtraction. Portsmouth, NH: Heinemann.
Gavin, M. K., Sinelli, A. M., & St. Marie, J. (2001). Navigating through
geometry in grades 3-5. Reston, VA: National Council for Teachers of
Mathematics.
Griffin, S., (2003). Laying the foundation for computational fluency in early
childhood. Teaching Children Mathematics, 9, 306-309.
Irwin, K. C. (2001). Using everyday knowledge of decimals to enhance
understanding. Journal for Research in Mathematics Education, 4, 399-420.
Kari, A. R., & Anderson, C. B., (2003). Opportunities to develop place value
through student dialogue. Teaching Children Mathematics, 10, 78-82.
Mann, R. L. (2004). Balancing act: The truth behind the equals sign. Teaching
Children Mathematics, 11, 65-69.
Mokros, J., Russell, S. J., & Economopoulos, K. (1995). Beyond arithmetic:
Changing mathematics in the elementary classroom. Palo
Alto, CA: Dale
Seymour Publications.
Reeves, C. A., & Reeves, R. (2003). Encouraging students to think about how
to think! Mathematics Teaching in the Middle School, 8, 374-377.
Reys, R.E., & Reys, B. J. (1983). Guide to using estimation skills and Strategies
(GUESS) Boxes I & II. Palo Alto, CA: Dale Seymour.
Stenmark, J. K., & Bush, W. S. (Eds.). (2001). Mathematics assessment: A
practical handbook for grades 3-5. Reston, VA: National Council of Teachers of
Mathematics.
Students With Disabilities Policy:
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This is the policy of Philander Smith College to accommodate students with disabilities pursuant
to federal and state laws; as well as the College’s commitment to equal opportunity for all
students. Any student with a disability who needs accommodations, for example, in setting
placement, arrangements for examinations, or class location, etc. should contact the Integrated
Council Center to complete a registration form.
www.nctm.org/standards
www.ablongman.com/vandewalle6e
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