Springfield Technical Community College
School of Mathematics, Sciences, and Engineering Transfer
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Mathematics
Mathematical Reasoning
MATH 126
3 Credits
ALGB-093 or ALGB-097 (C- or better) or placement at
college-level on math placement test.
Problem Solving Approach to Mathematics for Elementary
School Teachers, A (11th Edition)
Authors: Billstein, Libeskind and Lott
ISBN: 0321570553
Course Description
The goal of this course is to give students the content base and
problem solving skills necessary to teach elementary school
mathematics as defined by the Massachusetts State Frameworks and
the National Council of Teachers of Mathematics. Explorations of
mathematics reasoning and problem solving. Topics will cover two
of the strands from the Massachusetts State Frameworks. 1) Number
Systems 2) Patterns, Functions and Algebra.
Instructional Objectives
The student must be able to:
1. Understand place value
2. Understand models of whole number arithmetic
3. Understand arithmetic underlying a word problem
4. Demonstrate an understanding of mathematical algorithms for whole number
arithmetic
5. Perform the four basic operations of whole numbers using various algorithms
6. Demonstrate knowledge of problem solving techniques.
7. Demonstrate knowledge of various numeration systems other than the HinduArabic system.
8. Demonstrate knowledge of prime and composite numbers and their relation to
greatest common factors and least common multiples.
9. Understand the Fundamental Theorem of Arithmetic
10. Demonstrate knowledge of the four basic operations of fractions using
various algorithms.
11. Demonstrate knowledge of the four basic operations of decimals using
various algorithms
12. Demonstrate knowledge of rates, ratios, and percent.
13. Demonstrate knowledge of the four basic operations of integers using various
algorithms
14. Demonstrate knowledge of the real number system
Teaching Procedures
This course is divided into four (4) modules. Each module is correlated with a specific
set of chapters in the text. The teaching methodology employed in this course
emphasizes the lecture approach and encourages student participation. Course Compass
is required and the text is optional. Please note that we will not be in the computer lab
for our class.
Attendance
Attendance is required. A student having three absences risks withdrawal from this
course. A student absent from class bears full responsibility for all subject and
procedural information discussed in class, including any changes in exam dates and
assignments.
Testing and Grading
There will be a total of 8 Homework Assignments, 4 Tests and 1 Final Exam. The final
grade will be based 40% on the Homework Assignments, 40% on the Test average and
20% on the Final Exam. Any exam not taken will be counted as a 0. If you will miss a
test, you must contact your instructor within 24 hours to schedule a make-up.
If at any time during the semester there is any evidence of academic dishonesty or
collusion by students on an exam or quiz, the Dean of Students and other relevant
college authorities will be notified, and students involved may be dismissed from the
course with an automatic grade of F.
STCC Policy on disruptive behavior
Behavior, which disrupts the establishment or maintenance of the learning environment,
may result in the student causing the behavior to be excluded from the classroom by the
instructor. The student may be subject to further punitive action by the Dean of
Students. Late arrival and early departure from class is considered disruptive behavior.
Students are expected to arrive on time for class, and to seek permission from the
instructor if they need to leave class early.
Individual Help
The instructor will meet with students during scheduled office hours. To insure the
availability of the instructor, please make an appointment. The Tutor Center in the Math
Department (through Room 425) is open from 8:00AM to 3:00PM Monday through
Friday. Students may drop in at any time to work with student tutors. Professional
tutors are available in the Student Success Center by appointment.
Special Needs
Students with special needs that require accommodations must contact the Office of
Disability Services for processing of the necessary documentation, and then speak to the
instructor.
Expectations
Students are expected to conduct themselves in a manner that is consistent with the
policies outlined in the College Catalog (pgs. 67-80). Respect and consideration for
others contribute to a positive environment for learning in the classroom. Both faculty
and students should encourage CIVILITY by speaking and listening respectfully to
others. In addition, actions that interrupt the learning process should be avoided. For
example, pagers, beepers, and chiming watches should be turned off.
Disclaimer
The instructor reserves the right to change topics covered or the order in which they are
covered as well as designated test dates at their discretion, after notifying the class in
advance.
Course Topics
Module 1
Chapter 3: Whole Numbers and Their Operations
Addition and Subtraction of Whole Numbers
Algorithms for Whole Number Addition and Subtraction
Multiplication and Division of Whole Numbers
Algorithms for Whole Number Multiplication and Division
Mental Mathematics and Estimation for Whole Number Operations
Chapter 4: Algebraic Thinking
Divisibility
Prime and Composite Numbers
Greatest Common Divisor and Least Common Multiple
Test 1 based on Chapter 3 and 4
Module 2
Chapter 5: Integers and Number Theory
Integers and their Operations of Addition and Subtraction
Multiplication and Division of Integers
Chapter 6: Rational Numbers as Fractions
The Set of Rational Numbers
Addition, Subtraction, and Estimation with Rational Numbers
Multiplication and Division of Rational Numbers
Ratios, Proportions and Proportional Reasoning
Test 2 based on Chapter 5 and 6
Module 3
Chapter 1: An Introduction to Problem Solving
Mathematics and Problem Solving
Exploration with Patterns
Reasoning and Logic: An Introduction
Chapter 2: Numeration Systems and Sets
Numeration Systems
Describing Sets
Other Set Operations and Their Properties
Test 3 based on Chapter 1 and 2
Module 4
Chapter 7: Decimals and Real Numbers
Introduction to Decimals
Operations on Decimals
Nonterminating Decimals
Percents and Interest
Chapter 8: Proportional Reasoning, Percents and Applications
Real Numbers
Variables
Equations
Functions
Equations in a Cartesian Coordinate System
Test 4 based on Chapter 7 and 8
Final Exam – Cumulative based on Chapters 1-8