# 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 pre-calculus

• 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 hands-on, 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, piece-wised defined functions)

-transformations

- graphs and their properties (**EX:** extrema, symmetry, even/odd, etc.)

- solving non -linear 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

-piece-wise defined linear & non-linear 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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