From:Mt. San Jacinto College Math Department

to:all Math INstructors

from:Mt. San Jacinto college Math Department

subject:Math 105 SLo’s

date:January18, 2011

Purpose: The purpose of this document is to clearly state the expected Student Learning Outcomes (SLO) for the College Algebra course (Math 105). In it you will find the list of expected outcomes, examples of the assessment problems used to measure the outcomes, the rubric used to evaluate student performance, and lists of descriptions of specific types of major and minor errors associated with each outcome.

SLO Summary: The purpose of havingCollege Algebra SLO’S is to formally articulate some of the more critical skills that are to be acquired by College Algebra students and to evaluate the extent to which those students have acquired those skills. This information will be utilized by the Math Department to design more effective course outlines and objectives and, where indicated,by instructors to improve their teaching techniques. A detailed formulationof the evaluation process is provided and will serve to effect a more uniformassigning of grades among math instructors. Analysis of assessment results will produce information that will aid all three outcome levels within the institution: SLO’S, DLO’S, and ILO’S.

First, at the course level (SLO level), each instructor will gatherand track student performance data in the specific areas deemed most critical to a truly successful completion of the College Algebra course. This will assist each instructor in evaluatinghis or her students. Valuable information will be collected that can be used to adjust, if necessary,an instructor’s pedagogy of the specific areas being measured. Although grades are the final assessment tool, measuring the degree to which a student has acquired specific critical skills will allow instructors to identify potential problem areas in the course and in some cases a lack of preparation on the parts of some students. It is currently possible for a student to complete College Algebra by having acquired sufficiently many general course skills but still be lacking some key skills, thereby resulting in a relatively high probability that the student will not be successful in a subsequent math course for which College Algebra is a prerequisite. That is unacceptable and should be remedied in part by SLO tracking and analysis of the data.

Second, at the department level (DLO level), examining results from all sections of a given course will allow the department to evaluate the effectiveness of the course as a whole. There are specific skills that a student who completesCollegeAlgebra should have in order for that student to have a reasonable chance to be successful in future math courses. Modifications to course outlines and curriculum content can be made more meaningfully once SLO data has been collected and student weaknesses have been identified. Student performances of each SLO will be analyzed at the end of each semester or each academic year to determine if any adjustments need be made to the material being measured or its presentation. This will be an ongoing and evolving assessment process that can be used to identify student performance levels, both general and specific, on the most critical skills to be acquired from the course.

Third, at the college level (ILO level), the data collected will make it fairly simple to demonstrate the extent to which the math program is being effective. This data will provide information that will reveal the degree to which individual students are experiencingsuccess. This information will indicate the Math Department’s commitment to meeting its goals and obligations and should have positive budget related benefits. It can also be used in the joint hiring process to justify the possible need for additional fulltime math instructors.

All measurements takenby individual instructors of College Algebra will be combined at the department level to bring about any necessary modifications of the course outline and will be utilized to improve the effectiveness of the teaching of those SLO topicson which students do not generally perform well. Each instructor will takehis or her own measurements, following the prescription contain in this document, and can use the results to improve his or her own teaching of the more critical skills. The measuring and tracking of SLO’S is not intended to be used to humiliate, chastise, or even embarrass instructors. Instead, those activities are simply intended to be the means by which the department can improve the effectiveness of its courses and the teaching methodologies of its members. They are also intended to make coverage and emphasis of critical topics more uniform among math instructors.

The assessment tools listed in this document will be amended and adjusted by the department as the need arises. Also, the rubric designed for the evaluation of student work is intended to be used for this course only. Each math coursehas or will have a rubricthat has been tailored just for it.

Assessment: Each outcome will be assessed by two problemson a test or quiz, two problems on the final exam, or one problem on a test or quiz and a different problem on the final exam. Each SLO description contains a generic form that should be adhered to when formulating assessment problems. Following those descriptions are sample assessment problems. Each assessmentproblem is tied to one or more of the objectives in the course outline of record and is designed for students to demonstrate the extent to which they have acquired an individualskill or multiple skills within a single problem.

Tracking and Analyzing: At the end of the semester each instructor will track results (scores) for each of the assessment problems and will forward those results along with corresponding final course gradesto the faculty member responsible for managing the College Algebra SLO results. The results for all of the College Algebrasections will be combined and a final summary will be sent out to all faculty members for their comments and input. Once all of the data has been analyzed it will be used to evaluate student performance on the whole. If it is discovered that students generally didnot perform at an acceptable level, action plans can be put into place to adjust the program or the instructing in order to attain the goal. Those adjustments will result from faculty workshops and roundtable discussions on how to improve the effectiveness of the teaching of those critical areas being measured. This will allow for an across the board sharing of ideas and techniques that can be used to improve the overall effectiveness of the math program.

Student Learning Outcomes for Math 105

Student Learning Outcome #1:
Graphing Rational Functions / The student will demonstrate an ability to graph a rational function of them form, where P1 and P2 are polynomial functions with integral coefficients and which have degree at most three. The degree of P2 must be positive. f must have at least a horizontal or an oblique asymptote and can have at most two vertical asymptotes. f may or may not contain a removable discontinuity.
Student Learning Outcome #2:
Finding the Inverse of a
One-to-One Function / The student should be able to formulate the inverse of a one-to-one function f that has any of the following forms: 1) , where m and b are rational and m is not 0, 2) , where h and k are integers, 3) (or x < 0), where a and b are integers and a is not 0, 4) (or x > h), where h and k are integers and a is a nonzero integer,
5) (or x < h), where h and k are integers, 6)(or x < h), where h and k are integers andk is not 0. The student should also be able to state the domain of.
Student Learning Outcome #3:
Transforming graphs by Stretching, Compressing, Reflecting, and Translating / The student should demonstrate the ability tograph a function of the form 1) , where a, b, h, and k are integers and a is not 0, or 2) , where a, b and k are integers and neither a nor b is 0, by viewing the graph as a combination of stretches, compressions , reflections, and translations of the graph of The function f should be of one of the following forms:
1) , 2), 3), 4),
5)
Student Learning Outcome #4:
Finding a Composition
of Two Functions / The student should demonstrate the ability to formulate the compositionor, given that the two functions f and g individually have any of the following forms: 1), where m and b are integers and m is not 0, 2) , where a, b, and c are integers and a is not 0, 3) , where h and k are integers, 4) , where h and k are integers and k is not 0,
5), where h is an integer, 6), where h and k are integers, 7), where a and k are integers and a is not 0. Have the student state the domain of theformulated composition.

Math 105 SLO Sample Questions

Student Learning Outcome #1: Have students graph one from eachcategory. Students should be

required to show asymptotes, intercepts, and discontinuities.

Student Learning Outcome #2: Have students find the inverses of one function from each category.

A.

B.

Student Learning Outcome #3: Have studentsworkone problem from each category.

1. Graph by viewing it as a transformation

of the graph of. State what the individual impacts

of the negative sign and the 1 are on the graph of.

Graph by viewing it as a transformation of the graph of. State what the individual impacts of the negative sign and the 1 are on the graph of.

Graph by viewing it as a transformation of the graph of. State what the individual impacts of the negative sign and the 1 are on the graph of.

1. Graphby viewing it as a

transformation of the graph of. State what the

individualimpacts of the 3, -1, and 2 are on the graph

of.

Graphby viewing it as a

transformation of the graph of. State what the

individual impacts of the negative sign in front of the

radical, the negative sign in front of the x, and the -3 are

on the graph of.

Graphby viewing it as a transformation

of the graph of. State what the individual

impacts of the -2 and the +2 are on the graph of.

Note that the -2 contains two separate affects. Mention

each.

Student Learning Outcome #4: Have students work one problem from each category.

1. Given thatand,find

and state its domain.

Given thatand, find

and state its domain.

Given thatand, find

and state its domain.

B. Given thatand,find

and state its domain.

Given thatand,

findand state its domain.

Given thatand , find

and state its domain.

Math 105 SLO Rubric

N/A / Student not present when SLO was administered.
0 / No attempt at solving the problem (student in class but left answer blank) or the attempt reflected a complete lack of understanding of what an appropriate solution should look like or an appropriate graph should contain.
1 / Student demonstratessome understanding of the instructions but the execution contained multiple major errors or the graph is missing multiple major features. The answer produced may or may not be appropriate for the problem.
2 / Student demonstrates some understanding of the instructions but the execution contained one major error or the graph is missing one major feature. The answer produced is appropriate for the problem.
3 / Student demonstrates a complete understanding of the instructions. The execution contains multiple minor errorsbut no major error or the graph is missing multiple minor features. The answer produced is appropriate for the problem.
4 / Student demonstrates a complete understanding of the instructions. The execution contains at most one minor error but no major errors or the graph is missing at most one minor feature. The answer produced is appropriate for the problem.

The lists of major and minor errors shown below are by no means exhaustive. They contain some of the more common errors made by College Algebra students and are intended as guidelines only. Any attempt to generate an exhaustive list of major and minor errors for would be futile.

Descriptions of Some Common ErrorsAssociated with Math105 SLO’S

Student Learning Outcome #1: Graphing Rational Functions

Major Errors: 1) Student’s graph indicates fewer asymptotes than there should be.

2) Student’s graph indicates more asymptotes than there should be.

3) Student’s graph indicates an incorrect type of asymptote. Perhaps

the graph shows an oblique asymptote when one doesn’t exist.

4) Student’s graph contains asymptotes that are always mutually

exclusive. That is, the graph shows two horizontal asymptotes, two

oblique asymptotes, or one horizontal and one oblique.

5) Student’s graph of f fails to approach an indicated asymptote

asymptotically. In other words, the indicated asymptote doesn’t

appear to be behaving as such.

6) Student’s graph isn’t even a function.

7)Student’s graph of f is shown to approach a correct asymptote

from an incorrect direction.

8)Student’s graph intersects a vertical asymptote.

9)Student miscopies the original problem in such a way that the flavor of the problem is destroyed.

Minor Errors: 1) Student’s graph fails to cross an asymptote where it should.

2) Student’s graph crosses a non-vertical asymptote where it shouldn’t.

3) Student’s graph shows an incorrect intercept.

4) Student’s graph is missing an intercept.

5) Student’s graph indicates asymptotes as solid lines.

6) Student’s graph does not use arrows to indicate continuation.

7) Student’s graph indicates a correct asymptote but the function

doesn’t “hug” the asymptote tightly. In other words, closeness is

not well reflected.

8) Student miscopies the original problem in such a way that the

“flavor” of the problem is preserved.

Student Learning Outcome #2: Finding the Inverse of a One-to-One Function

Major Errors: 1) Student produces an inverse that isn’t even a function.

2) Student produces an inverse that has an incorrect domain. Often

this is due to the student’s failure to state the domain when the

implied domain is not satisfactory.

3) Student cannot produce an inverse due to an inability to

perform the algebra necessary to isolate the new “y” or the

original “x.”

4) Student produces an inverse by using incorrect algebraic

techniques. The algebra being used is not legitimate.

5) Student miscopies the original function in such a way that the

“flavor” of the original function is destroyed

Minor Errors: 1) Student makes a sign error while solving for the new “y.”.

2) Student makes an arithmetic error while solving for thenew “y.”

3) Student states the domain of the inverse using correct numbers

but incorrectinequality symbols or uses interval notation

incorrectly.

4) Student miscopies the original function but in such a way that the

“flavor” of the original function is preserved.

Student Learning Outcome #3: Transforming Graphs by Stretching, Compressing,

Reflecting and Translating

Major Errors: 1) Student’s graph is missing a type of transformation that the actual

graph contains.

2) Student’s graph contains a type of transformation that the actual

graph lacks.

3) Student’s graph isn’t even a transformation of the correct basic

function. For example, a student’s graph looks like a

transformationofwhen it should be a transformation

of.

4) Student’s graph indicates a transformation with an incorrect

orientation. For example, what should have been a horizontal

translation is indicated as a vertical translation, or what should

have been a y-axis reflection is indicated as an x-axis reflection.

5) Student miscopies the given function in a such a way that one

or more transformations was omitted or the flavor of the

function was destroyed, meaning that the basic function to

which the given function was related has been altered.

Minor Errors: 1) Student’s graph indicates that one of stretching or compressing

hasbeen mistaken for the other, but the mistaken transformation

at least has the correct orientation (horizontal or vertical).

2) Student’s graph indicates a translation that has a correct

orientation and magnitude but an incorrect direction.

3) Student’s graph indicates that two transformations were

individually performed correctly but performed in an incorrect

order.

4) Student miscopies the given function in such a way that a

transformation was altered but the same type is still present and

the basic function to which the given function is related has not

been altered.

Student Learning Outcome #4: Finding a Composition of Two Functions

Major Errors: 1) Student findswhen asked to find.

2) Student cannot perform the algebra necessary to simplify f(g(x)).

3) Student misinterprets composition as product.

4) Student miscopies one or both of f and g in such a way that the

resulting composition is not the same type of function as the intended composition.

5) Student erroneously excludes from the domain ofthose

values of x that are not in the domain of f

6) Student states a domain forthat is not a subset of the domain

of g.

Minor Errors: 1) Student makes an arithmetic or sign error during the process of

simplifying f(g(x)).

2) Student miscopies one or both of f and g in such a way that the

resulting composition is the same type of function as the actual

composition and has the same domain.

3) Student misstates the domain of in such a way that it is and

should be aproper subset of the domain of g but is also a proper

subset or superset of the intended domain.