Core Course Review Documentation
Foundational Component Area: MATHEMATICS
Component Area Option? No
Proposed Course: Math 1233 (College Algebra)
Credit Hours: 3
Proposed by: MSU Mathematics Department
Date: September 2012
Please document how the proposed course meets each of the following requirements. (You
may provide a written explanation or copy and paste the appropriate information from the
syllabus.)
Content:
Courses in this category focus on quantitative literacy in logic, patterns, and
relationships.
This course will focus mainly on the following topics:
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Linear Functions with applications to real world problems
Quadratic Functions with applications to optimization problems
Polynomial Functions and Equations and related theory (e.g. Division Algorithm)
Solving Polynomial Equations and Inequalities
Rational Functions and related theory (e.g. Asymptotes)
Solving of Rational Equations and Inequalities
Exponential Functions with applications to growth and decay problems
Logarithmic Functions and related theory to exponential equations
Solving Exponential and Logarithmic Equations
SKILLS: Courses involve the understanding of key mathematical concepts and the application of
appropriate quantitative tools to everyday experience.
Universal Problem Solving Goal:
Students will further their development of problem solving and logical reasoning skills through
the investigation of real world situations, including model creation. This universal goal will be
infused throughout the College Algebra curriculum, as seen within the objectives following goals
1 through 3 below.
Goal 1: Functions and Equations
College Algebra will strengthen students’ mastery of algebraic and quantitative techniques
necessary for problem solving and mathematical modeling in the study of other disciplines.
Objectives: Students will demonstrate
A. An understanding of the concepts of function and rate of change;
B. The ability to effectively use multiple perspectives (symbolic, numeric, graphic, and
verbal) to explore elementary functions such as linear, exponential, power, polynomial,
logarithmic, rational, and radical functions as appropriate;
C. The ability to recognize and use standard transformations such as translations, reflections
and dilations with graphs of elementary functions;
D. The ability to apply a variety of equations to model real world situations, by choosing an
appropriate method, developing a suitable equation, and solving accurately;
Goal 2: Communication
College Algebra will improve students’ ability to communicate mathematical ideas clearly in
oral and written form.
Objectives: Students will demonstrate
A. The ability to build and interpret models using multiple perspectives (symbolic, numeric,
graphic, and verbal) and predict results;
B. The ability to communicate processes and solutions orally and in writing;
C. The ability to make quantitative and algebraic arguments;
D. The ability to read and interpret information presented in various forms.
Goal 3: Technology
College Algebra will develop students’ ability to use technology appropriately for understanding
and doing mathematics.
Objectives: Students will demonstrate
A. An understanding of syntax and order of operation in the use of technology as a tool in
problem solving and exploration;
B. The ability to use technology to find necessary values of a function, such as maximums,
minimums, roots, and intersections.
Relating to Assessment:
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Daily Homework assignments based on exercises from the textbook or electronic
supplements to the textbook
Experiential learning assisted by the use of graphing calculators
Preparation for and review of the above activities by in-class interaction with the
instructor
Each of these types of activities links directly to the assessment of core objectives. The assessment
instrument will primarily be comprised of problems for the student to solve that are similar to the
assigned daily homework. Some of the assessment items will call for the use of graphing
calculators. In-class interaction with the instructor will provide the student feedback regarding the
ability to solve problems in the assessment instrument.
ASSESSMENT OF CORE OBJECTIVES: Assessments should be authentic, intentional and
direct. The following three Core Objectives must be addressed in each course approved to fulfill this
category requirement:
Critical Thinking Skills - to include creative thinking, innovation, inquiry, and analysis, evaluation
and synthesis of information
Communication Skills - to include effective development, interpretation and expression of ideas
through written, oral, and visual communication
Empirical and Quantitative Skills - to include the manipulation and analysis of numerical data or
observable facts resulting in informed conclusions
Over the course of the semester the student is asked to solve various types of problems. In
each instance the student must decide on an appropriate solution technique, implement the
technique as accurately as possible, and formulate a conclusion. Samples of student’s work
from embedded exam questions will be used in the assessment of critical thinking,
communications skills and empirical and quantitative skills.
Critical thinking will be assessed with an imbedded question on an hourly exam related to
rational functions. Students will be asked to identify all asymptotes of the graph of a
specific rational function, any holes in the graph, and to determine the zeros of the function.
Students will also be asked to graph the rational function. In addition to instruction that
faculty give students during class to help them understand the various features of the
graph of a rational function and how to determine those features from the rational
expression that defines the function , a guided inquiry activity will be provided to students
to help them further develop their understanding of oblique asymptotes. The activity will
also provide the student an opportunity to extend their knowledge of oblique asymptotes
of rational functions to non-linear asymptotes for this class of functions. See Attachment 2
for the rubric for assessing this core objective.
The assessment problems used to assess communication skills will be comprised of
problems on a comprehensive final exam. Some of the problems used to assess this core
objective involve solving a variety of equation types (e.g. rational, absolute value, radical,
quadratic, exponential, logarithmic), as well as solving related inequalities. See Attachment
3 for the rubric for assessing this core objective.
Empirical and Quantitative skills will be assessed with imbedded questions on two hourly
exams. One imbedded question on the hourly exam that includes quadratic functions will
be designed to assess students understanding of how functions are used to model the
motion of a projectile and how algebraic and graphic techniques can be used to answer a
variety of questions about the flight of the projectile. A second imbedded question on an
hourly exam that includes applications of linear equations will include an applied problem
in which the principle of Conservation of Mass is used to solve a mixture problem. See
Attachment 4 for the rubric for assessing this core objective.
ADDITIONAL INFORMATION: Provide any additional information supporting course
inclusion in the core (optional).
Assessment rubrics are taken from the AAC&U Value Rubrics.
PLEASE ATTACH THE FOLLOWING
1.
2.
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4.
Syllabus
Assessment for Critical Thinking Skills
Assessment for Communication Skills
Assessment for Empirical & Quantitative Skills
Attachment 1 Sample course syllabus
Prerequisite: Math 1003 (Intermediate Algebra) with a grade of “C” or better, math THEA score of 270,
math Accuplacer score of 90, or satisfactory score on placement exam.
Textbook:
A Graphical Approach to College Algebra, 5th Edition, by Hornsby, Lial, Rockswold
Calculator:
A graphing calculator is required for this course.
Objective:
This course is designed to be a comprehensive course in the study of algebra for students
planning to take additional mathematics.
Homework: Homework assignments will be given daily. It is your responsibility to attempt all assigned
problems and to come to class prepared to discuss the material. Also, daily homework quizzes may be
instituted at the discretion of the instructor.
Attendance: You are expected to attend class, to arrive on time, and to remain in class until dismissed.
Obviously, the only way to accomplish the work required is to be present, both physically and mentally, at
every class meeting. Students may be dropped by the instructor for excessive absences unless there are
extenuating circumstances which are promptly communicated. Please refer to the university’s official class
attendance policy before deciding to discontinue attending class.
Additional Assistance: Please contact your instructor for extra help during this course. Math help sessions
are offered by the math department in room Bolin 101 every afternoon.
Grading: There will be unit tests, a final exam, and a daily grade which will be generated from the daily
assignments as well as any in-class quizzes. The final course grade will be determined by the earned
percentage of total possible points.
Earned % of Total Points Course Grade
90 - 100
A
80 - 89
B
70 - 79
C
60 - 69
D
Below 60
F
The outline below shows sections and topics to be covered from the textbook:
1.1
1.2
1.3
1.4
1.5
1.6
2.1
2.2
2.3
2.4
2.5
2.6
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
4.1
4.2
4.3
4.4
4.5
5.1
5.2
5.3
5.4
5.5
5.6
Real Numbers and the Rectangular Coordinate System
Introduction to Relations and Functions
Linear Functions
Equations of Lines and Linear Models
Linear equations and Inequalities
Applications of Linear Functions
Graphs of Basic Functions and Relations; Symmetry
Vertical and Horizontal Shifts of Graphs
Stretching, Shrinking, and Reflecting Graphs
Absolute Value Functions
Piecewise-Defined Functions
Operations and Composition
Complex Numbers
Quadratic Functions and Graphs
Quadratic Equations and Inequalities
Further Applications of Quadratic Functions and Models
Higher-Degree Polynomial Functions and Graphs
Topics in the Theory of Polynomial Functions (I)
Topics in the Theory of Polynomial Functions (II)
Polynomial Equations and Inequalities; Further Applications and Models
Rational Functions and Graphs
More on Rational Functions and Graphs
Rational Equations, Inequalities, Models, and Applications
Functions Defined by Powers and Roots
Equations Inequalities, and Applications Involving Root Functions
Inverse Functions
Exponential Functions
Logarithms and Their Properties
Logarithmic Functions
Exponential and Logarithmic Equations and Inequalities
Further Applications and Modeling with Exponential and Logarithmic Functions
Attachment 2: Assessment for Critical Thinking Skills
An assessment of student competency would be based on the following rubric:
Evidence
Explanation of
issues
Conclusion and
related outcomes
Capstone
4
Milestones
3-2
Benchmark
1
Solution technique
chosen is among the
best possible for the
problem
A sequence of
mathematical steps
leading toward the
solution is performed
without error
Solution technique chosen will work but is not
among the best possible choices
Conclusion is clearly
expressed and is
logically connected to
previous work
Conclusion is ambiguous or does not take all
appropriate information into account
A solution technique
is chosen without
consideration of the
details of the problem
The chosen sequence
of mathematical steps
is performed with
multiple errors or
does not lead towards
a correct conclusion
Conclusion, even if
correct, is not
supported with any
argument
A sequence of mathematical steps leading
toward the solution is performed but the work
is not complete or has one to two
mathematical errors
Attachment 3: Assessment for Communication Skills
An assessment of student competency would be based on the following rubric:
Capstone
4
Content
Development
Genre and
Disciplinary
Conventions
Control of Syntax
and Mechanics
Uses appropriate, relevant,
and compelling content to
illustrate mastery of the
subject, conveying the
writer's understanding, and
shaping the whole work.
Demonstrates detailed
attention to and successful
execution of a wide range of
conventions particular to a
specific discipline and/or
writing task (s) including
organization, content,
presentation, formatting,
and stylistic choices.
Work skillfully
communicates meaning
with clarity and fluency, and
is virtually error-free
Milestones
3-2
Benchmark
1
Uses appropriate, relevant, and
compelling content to explore ideas
within the context of the discipline and
shape the whole work.
Uses appropriate and
relevant content to
develop simple ideas
in some parts of the
work.
Follows expectations appropriate to a
specific discipline and/or writing
task(s) for basic organization, content,
and presentation.
Attempts to use a
consistent system for
basic organization
and presentation.
Work generally conveys meaning to
readers. There are relatively few errors
Work sometimes
impedes meaning
because of errors in
usage
Attachment 4: Assessment for Empirical and Quantitative Skills
An assessment of student competency would be based on the following rubric:
Capstone
4
Milestones
3-2
Benchmark
1
Representation
Skillfully converts
relevant information into
an insightful
mathematical portrayal in
a way that contributes to
a further or deeper
understanding.
Completes conversion of information
but resulting mathematical portrayal
is only partially appropriate or
accurate.
Calculation
Calculations attempted
are essentially all
successful and sufficiently
comprehensive to solve
the problem.
Uses the quantitative
analysis of data as the
basis for deep and
thoughtful judgments,
drawing insightful,
carefully qualified
conclusions from this
work.
Calculations attempted are either
unsuccessful or
represent only a portion of the
calculations required to
comprehensively solve the problem.
Uses the quantitative analysis of data
as the basis for workmanlike
(without inspiration or nuance,
ordinary) judgments, drawing
plausible conclusions from this work.
Completes
conversion of
information but
resulting
mathematical
portrayal is
inappropriate or
inaccurate.
Calculations are
attempted but are
both unsuccessful
and are not
comprehensive.
Uses the quantitative
analysis of data as
the basis for
tentative, basic
judgments, although
is hesitant or
uncertain about
drawing conclusions
from this work.
Application/Analysis