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Math Competency
Purpose:
• Develop critical and analytical thinking skills Engage students in
sound mathematical thinking and reasoning.
• Enhance and reinforce students’ understanding of concepts through the
use of technology when appropriate.
EX: graphing calculators, computers, software such as MyMathLab,
students’ response system, etc.
• Develop mathematical fluency to improve written and verbal
communication.
• Analyze the structure of real world problems and plan solutions, and
solve the problem using appropriate tools.
EX: Use functions to model real world applications.
• Explore multiple representation of topics (graphical, numerical ,
symbolic, verbal)
Why:
• Prerequisite for calculus and precalculus
• Have not learned, a review of topics of high school
• Prerequisite for other programs such as science, nursing
• To satisfy state requirements and accreditation, for graduation in some
programs
• Gateway course for higher mathematics and sciences
FUTURE NOTE:
course should be more rigorous (more depth, not more topics?)
Population:
• Students who need the future sequences for prerequisites.
EX: Math, science, engineering, business, accounting majors.
Part of sequence: Yes
General education course: Yes (get clarification)
21^{st} century redefinition:
• As students enter college more prepared, this class in 10 – 15 years
might have fewer sections.
• Emphasis more depth, might be too many topics right now.
• Change in ways of teaching (more handson, activities based,
collaboration, cooperation, technological (with
more on line sources , interaction could go beyond meeting times of the class),
• More abstract and formal coverage
• Focus on concepts rather than just rote skills
• Higher expectation of students knowing well their foundational and
arithmetic skills rather than promoting a total dependency on calculators
Course Content:
• The basic content of this course focuses on functions:
definition of functions
domain and range
function notation
types of functions (EX: linear, quadratic, exponential, absolute value,
logarithmic, power with rational exponents, piecewised defined functions)
transformations
 graphs and their properties (EX: extrema, symmetry, even/odd, etc.)
solving nonlinear inequalities graphically
intersection of graphs (non linear of 2 variables )
 difference quotients
real world applications (EX: average rate of change)
 operations including composition
inverse functions
piecewise defined linear & nonlinear functions (evaluate and graphing)
asymptotes
 exponential and logarithmic functions including applications of interest
(graph, properties,
domain, range, solve simple exponential and logarithmic equations )
EX: ln x = 3, e^{kt} = 45
• Coordinate geometry
 circles (equations, completing the squares , distance, midpoint)
Suggested Delivery and methodologies:
• students should graph by hand and use the
calculator
• More focus on analyzing graphs over making graphs
Side Notes:
• Use classroom set of calculator to prevent
cheating.
• Students don’t get much about functions before college algebra. Students
should demonstrate applications of math more heavily than previous course (such
as Intermediate algebra)
• In the future, maybe create an alternative, less rigorous college
algebra course for students who do not go on!
• Consult with chemistry on depth of logarithmic functions and properties
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