 # College Algebra Core Competencies Assessment 2007-2008: Area II Courses

 State Competencies (Learning Outcomes Being Measured) Assessment Procedures Course Name and NMCCN (Process/Instrument named or described – rubric attached) Assessment Results How Results Will Be Used To Make Improvements (Optional) Recommendations/Goals/ Priorities 1. Students will graph functions Students should: a. Sketch the graphs of linear, higher-order polynomial, rational, absolute value, exponential, logarithmic, and radical functions. b. Sketch a graph using point plotting and analysis techniques, including basic transformations of functions such as horizontal and vertical shifts, reflections, stretches, and compressions. c. Determine the vertex, axis of symmetry, maximum or minimum, and intercepts of a quadratic equation. The course objectives are distributed to instructors and students at the beginning of each semester. At the end of the semester, students are given a comprehensive final exam correlated to the objectives. A benchmark of 70% is used to determine whether a competency has been met.Nine objectives were measured for this competency. In Spring 2008, the average mastery of this competency was 63%.Students scored well above the benchmark on two of the objectives : Sketching absolute value and quadratic functions using transformation techniques. Students scored slightly below the benchmark on four objectives covering material on sketching polynomial functions of degree 3 or higher, sketching radical and exponential functions using transformation techniques, and determining the radius and center of a circle by completing the square. Students scored well below the benchmark on the remaining three objectives covering material on sketching rational functions, sketching logarithmic functions using transformation techniques, and determining the vertex, axis of symmetry, intercepts and max/min of a quadratic function. Results of the assessment will be discussed with each faculty member who teaches College Algebra. More time, effort and supplementary material will be devoted to quadratic, rational and logarithmic functions. Additionally, more material will be developed that can be used as review after the concepts have been completed. More practice material will be developed on sketching functions with basic transformations. Some College Algebra faculty will utilize out of class testing in the Testing Center in order to use class time more effectively.The main priority for 2008-2009 will be to improve student’s understanding of and ability to determine the vertex, axis of symmetry, intercepts and max/min of a quadratic function since the quadratic function in general is a fundamental objective of College Algebra. 2. Students will solve various kinds of equations. Students should: a. Solve quadratic equations using factoring , completing the squares , the square root method , and quadratic formula. b. Solve exponential and logarithmic equations. c. Solve systems of two or three linear equations . Four objectives were measured for this competency following the format above. In Spring 2008, the average mastery on this competency was 65%. Students scored above the benchmark on solving quadratic equations using techniques stated in the competency. Students scored slightly below the benchmark on solving exponential equations and solving a system of three linear equations. Students fell well below the benchmark on solving logarithmic equations. Supplementary material, both study guides and worksheets, will be developed for solving logarithmic equations. Material to review systems of equations will be distributed later in the semester as a review to this objective. Some College Algebra faculty will utilize out of class testing in the Testing Center in order to use class time more effectively. 3. Students will demonstrate the use of function notation and perform operations on functions . Students should: a. Find the value of a function for a given domain value b. Add, subtract , multiply, divide and compose functions. c. Determine the inverse of a function. d. Compute the difference quotient for a function. e. Correctly use function notation and vocabulary related to functions, i.e. domain, range, independent variable, of, even symmetry, etc. Eight objectives were measured for this competency following the format above. In Spring 2008, the average mastery of this competency was 63%. Students scored above the benchmark on performing operations on functions, including finding the composite of two functions and determining the domain and range of a function. Students met the benchmark on computing the difference quotient and were slightly below the benchmark on determining algebraically if a function was odd or even. Performance was well below the benchmark for determining if a function was one to one and finding the inverse of a function. The inverse function concept will be discussed in more detail and more material will be developed for student practice. The problem on the assessment instrument on finding the inverse of a function will be changed from finding the inverse of a rational function to finding the inverse of a linear function. Some College Algebra faculty will utilize out of class testing in the Testing Center in order to use class time more effectively. 4. Students will model/ solve real -world problems. Students should: a. Use and understand slope as a rate of change. b. Use equations and systems of equations to solve application problems. c. Apply knowledge of functions to solve specific application problems. d. Solve compound interest problems. e. Solve application problems involving maximization or minimization of a quadratic function. f. Solve exponential growth and decay problems. End – Area II - Algebra Seven objectives were measured for this competency following the format above. In Spring 20008, the average mastery of this competency was 60%. Students scored above the benchmark on two objectives: Solving an application problem using a system of equations and applying the knowledge of functions to solve an application problem. Students were slightly below the benchmark on solving an application problem involving the max/min of a quadratic function. Performance was well below the benchmark on four of the seven objectives: Understanding slope as a rate of change and solving applied problems involving variation, compound interest and exponential growth or decay. More supplemental material will be developed for the objectives that are below the benchmark Some College Algebra faculty will utilize out of class testing in the Testing Center in order to use class time more effectively.
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