# Assessment Plan 2014

# CALIFORNIA STATE UNIVERSITY, CHICO ANNUAL PROGRAM ASSESSMENT REPORT

BS, Department of Mathematics and Statistics (4 Options: Applied, Pure, Education, Statistics)

Date: 8/13/14

# I. Assessment of Student Learning Outcomes

**Name and Contact Information of Program Assessment Coordinator: Thomas Mattman**

**Department of Mathematics and Statistics, zip 0525 898-4102**

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**Goal Statements and Student Learning Outcomes**

**[General Content] Graduates are proficient in performing basic operations on fundamental mathematical objects and have a working knowledge of the mathematical ideas and theories behind these operations.**

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GC1 Demonstrate basic skills and conceptual understanding of differential, integral, and multivariable calculus.

GC2 Demonstrate basic skills and conceptual understanding as relating to fundamental mathematical objects introduced in our degree core, such as, sets, functions, equations, vectors, and matrices.

GC3 Demonstrate more technical skills and more in-depth and broader conceptual understanding in core mathematical areas (such as, analysis, geometry/topology, algebra, applied math, statistics), relevant to their option in the major.

# [Critical Thinking/Problem Solving] Graduates use critical thinking and problem solving skills to analyze and solve mathematical & Statistical problems.

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PS Interpret and translate problems into appropriate mathematical language; then solve problems by applying appropriate strategies and interpreting the results.

# [Communication] Graduates communicate mathematics effectively in a manner appropriate to career goals and the mathematical maturity of the audience.

Com1 Demonstrate the ability to effectively and accurately write on mathematical topics relevant to their mathematics option and appropriate to their audience.

Com2 Demonstrate the ability to effectively and accurately speak on mathematical topics relevant to their mathematics option and appropriate to their audience.

# [Proof Proficiency] Graduates have a basic proficiency in the comprehension and application of proofs.

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PP Students can read mathematical proofs, extract the key ideas used in the proof, and convey the logic behind the proof; they can also write their own rigorous and logically correct proofs.

# [Technology] Graduates know how to use technology tools (e.g., graphing calculators, computer algebra systems) appropriate to the context of the problem.

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Tech Students use technology to manipulate mathematical objects (e.g., functions equations, data sets, etc.), to conduct mathematical explorations, to model problem scenarios, and to analyze mathematical objects.

# [Life-long Learner] Graduates are aware of the important role of mathematics and have the interest and ability to be independent learners and practitioners.

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LL1 Students demonstrate the ability to apply mathematics and statistics to new contexts (e.g., in other classes, the workplace, graduate school, or classes they teach).

LL2 Students recognize and appreciate the role that mathematics can play in their futures and in society in general.

# Course Alignment Matrix:

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See attached Excel Spreadsheet (Appendix B)

# 4. Learning Outcome(s) Assessed in AY 2013-14 (Year 7 of Assessment Plan)

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Com1-I, GC1-IP, CG3-IP, PS-IP, Tech-I, LL1-I, LL2-M

# 5. Assessment Methodology Used

We assessed the SLOs at the level of mastery (I, P, M, for Introductory, Progressing, Mastery) indicated above by embedding assessment items in final exams for Math 120, 121, 220, and 361 as well as in an exit survey for graduating seniors. As far as possible, we used assessment items similar to those in Year 1 or 2 of our assessment plan. Aside from Math 361, these courses are taught by multiple instructors who contributed to developing the instruments and agreed to make them common to their respective exams. Instructors also contributed to constructing rubrics that we applied to determine performance at the Exemplary, Proficient, Acceptable, and Unacceptable levels. Together with the department chair, Rick Ford, we simplified the exit survey to focus on the two Life-Long learner SLOs (LL1 and LL2). By e-mail, the chair invited all graduating math majors to complete this on-line survey.

In appendix A we collect assessment items, rubrics, raw scores and sorted data for all class assessments and the exit survey. Student work is available upon request. When possible, we used the rubrics of Year 1 and 2 as a guide, updating as needed. Rubrics for new items follow the same general style with descriptions of performance at the Exemplary, Proficient, Acceptable, and Unacceptable levels.

# 6. Assessment Results

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Student Learning Outcome |
Where sample is from (sample size) |
Measure |
% Exemplary + Proficient by item |

Com1-I |
MATH 120 (18) |
Embedded Exam Problem 6 |
77 |

Com1-I |
MATH 121 (3) |
Embedded Exam Item 3 |
0 |

GC1-I |
MATH 120 (18) |
Embedded Exam Problem 7 |
61 |

GC1-IP |
MATH 121 (3) |
Embedded Exam Item 1 |
67 |

GC1-IP |
MATH 121 (3) |
Embedded Exam Item 4 |
0 |

GC1-P |
MATH 220 (18) |
Embedded Exam item |
50 |

GC3-IP |
MATH 361 (9) |
Embedded Exam Item 1 |
56 |

PS-I |
MATH 120 (18) |
Embedded Exam Problem 11 |
23 |

PS-I |
MATH 120 (18) |
Embedded Exam Problem 12 |
34 |

PS-P |
MATH 121 (3) |
Embedded Exam Item 2 |
67 |

PS-P |
MATH 220 (18) |
Embedded Exam item |
6 |

Tech-I |
MATH 120 (18) |
Embedded Exam Problem 13 |
34 |

Tech-I |
MATH 121 (3) |
Embedded Exam Item 2 |
67 |

LL1-I |
Exit Survey (17) |
Survey Item 2 |
94 |

LL2-P |
Exit Survey (17) |
Survey Item 1 |
88 |

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**Analysis / Interpretation of Results**

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Results/Analysis/Interpretation

**Math 120: **Math 120 (First semester calculus) is required of all majors and also serves as a service course for students in the sciences and engineering. The focus is the derivative and its applications. We selected the Fall 2013 semester course for assessment of all our majors. There were several instructors who together prepared a common final exam with assessment items embedded. Eighteen majors took the final exam that semester. Raw data for our analysis is available in Appendix A.

Problem 6: This item asks students to use the definition to find the derivative of 7/x. Seventy-eight percent of the majors scored at the Exemplary or Proficient level. This is what we should expect of our majors for this type of question.

Problem 7: This item asks students to find the derivative at a point of a curve defined implicitly. Although this should be straightforward, students often find it challenging to correctly use the chain rule in this setting. Sixty-one percent of our majors were Proficient or better.

Problem 11: Students need to optimize the cost of fencing given a fixed area to enclose where the cost of fencing varies. Word problems continue to be a weak point, not only for majors, but for all students in Math 120. The results of 23 percent Exemplary or Proficient bear this out.

Problem 12: The “falling ladder” is the archetypal related rates problem and we wish students would come out of first semester calculus with a better understanding of this type of problem. Only 34 percent of our majors met the Proficient or Exemplary level on this word problem.

Problem 13: Students were asked to compute a simple Riemann sum using the midpoint rule. This also should be a very simple calculation. This topic comes at the end of the course, so some instructors may have rushed through it, or students may not even have been attending. Still, 34 percent Proficient or Exemplary among our majors is disappointing.

Aside from the SLO PS at the introductory level (assessed by Problems 11 and 12), each of the problems was directed at a different SLO: Problem 6 – Com1-I; Problem 7 – GC1-I; Problem 13 – Tech – I.

**Math 121: **Math 121 (Second semester calculus) is required of all majors and also serves as a service course for students in the sciences and engineering. The focus is the integral and its applications. We selected the Fall 2013 semester course for assessment of all our majors. There were three instructors who together prepared items common to their final exams. Three majors took the final exam that semester.

Raw data for our analysis is available in Appendix A. Due to the small data set, the results may be more representative of the students in question rather than math majors as a whole.

Item 1: We ask for a simple integration by substitution. This is the most elementary or integration techniques. Two of the three majors were able to execute the task at Exemplary or Proficient level.

Item 2: We ask students to interpret a computer-generated figure in order to set up an integral for a volume of rotation. This should be elementary, but like anything slightly less than routine, is quite challenging for our students (majors or not). That two of three majors completed this at Exemplary or Proficient level is a pleasant surprise.

Item 3: Is a conceptual problem that asks students a meta-question about the manipulation and use of power series. That none of the three majors rose to the Proficient level (let alone Exemplary) is very disappointing.

Item 4: We have students perform various basic manipulations of vector calculus. This topic typically comes at the end of the semester and may be given short shrift by instructors pressed for time or students who may no longer be attending. Still that all three majors performed at an Unacceptable level is surely unacceptable.

Items 1 and 4 addressed the SLO GC1 at the introductory or progressing level; Item 2, the SLOs PS-I and Tech-I; and Item 3 the SLO Com-I.

**Math 220: **Math 220 (Third semester calculus) is required of all majors and also serves as a service course for students in the sciences and engineering. The focus is on calculus in two or more dimensions. We selected the Fall 2013 semester course for assessment of all our majors. There were two instructors who together prepared items common to their final exams. Eighteen majors took the final exam that semester. Raw data for our analysis is available in Appendix A. There were two items assessed, however the two instructors used different numbering systems on their exams (and slightly different wordings!). Below, we refer to the numbering in Appendix A.

Item 1: We ask students to calculate four quantities derived from the equation of a space curve: the tangent, normal, binormal, and curvature. This is a straightforward calculation so it is unfortunate that only half of the majors were able to perform at the Exemplary or Proficient level.

Item 2: Students must convert an integral written in Cartesian coordinates into polar. This is a very standard technique that can bring a difficult integral into a more manageable form. Only one of the eighteen majors managed Proficient performance. The remainder were Unacceptable, which is, again, an appropriate word here.

Item 1 addressed the SLO GC1 and Item 2 the SLO PS, both at the progressing level. Due to an error in the SLO matrix, the SLO Com2 was not assessed in this round.

**Math 361: **Math 361 (Boundary Value Problems and Partial Differential Equations) is required of all majors in the applied option. Occasionally, students in other options or majors (e.g., physics or engineering) take this course. We selected the Fall 2013 semester course for assessment of all our applied math majors. There was a single instructor who helped prepare an item embedded on the final exam. All nine students in the course were majors and took the final. Raw data for our analysis is available in Appendix A.

The embedded item asks students to solve a Sturm-Liouville system and assesses the SLO GC3 at the introductory or progressing level. The problem and rubric seek to measure a geometric understanding of the eigenvalues and eigenfunctions. This is a challenging problem, but central to the course content. Fifty-six percent of the majors performed at the Proficient or Exemplary level.

**Exit Survey: **We invited graduating math majors to complete an on-line survey and eighteen did. The chair, Rick Ford, assisted in revising the instrument so that it focused on the LL1 and LL2 SLOs. Raw data for our analysis is available in Appendix A.

Item 1 asked about students’ awareness of the role of math in life and society and assessed the SLO LL2 at the progressing level. Eighty-eight percent of the respondents were at the Exemplary or Proficient level.

Item 2 asked students about their plans for the coming year and assessed SLO LL1 at the introductory level. Ninety-four percent were at the Proficient or Exemplary level.

# 8. Planned Program Improvement Actions Resulting from Outcomes:

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No program improvements are planned for Math 120, 121, 220, or 361 as a result of the SLO assessment.

# 9. Planned Revision of Measures or Metrics:

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For the most part, there are no planned revisions for the measures or metrics for any of our course assessments. An exception is Math 220 where there was no assessment of the Com2 SLO. This will be assessed the next time we return to Math 220 in five years. In addition, only three math majors took Math 121 in the fall semester this year. In future, it will be better to collect data in the spring for this course as that is the “normal” time to take it for the large majority of our majors.

The Exit Survey needs some revision as, in several places, students are asked to “circle” a more detailed or descriptive answer. However, this was not implemented on the on-line survey. In addition, we need to develop an alumni questionnaire so that we can follow up on SLO LL2 next year. We expect it will be very similar to the current exit survey.

# 10. Planned Revisions to Program Objectives or Learning Outcomes (if applicable)

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No changes made or planned.

# 11. Changes to Assessment Schedule (if applicable)

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Following a suggestion from last year’s committee, we will assess LL2 in a two year process. In Year 4 of the assessment plan, we will evaluate LL2 at the progressing level using an item from the exit survey. In Year 5, we will follow up with the same students to gauge how their understanding of this SLO has changed, if at all. In this way, all SLOs will be assessed within the five-year plan. However, as we only conducted the exit survey for the first time this year, we will, exceptionally, conduct an alumni questionnaire next year in order to complete our first five-year cycle.

# 12. Information for Next Year

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What learning outcome(s) are you examining next year and who will be the contact person?

2014-2015 will be Year 2 of a new Assessment schedule. In year two we collect data from Math 230, 260, 305, 350, and 351. The SLOs that will be assessed from these classes are:

230 —Tech at the Progressing and Mastery level.

260 — PS at the Mastery level

305 and 350 —GC2 at all three levels (Introductory, Progressing, and Mastery) 351 – PS at the Mastery level

Also, to follow up on the Exit Survey first administered this year, Alumni Questionaire—LL2 at the Mastery levels

The contact people will be Vladimir Rosenhaus and Rick Ford, and an as-yet- unnamed (apprentice) Assessment Committee member.

# II. Appendices (please include any of the following that are applicable to your program)

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**Assessment Data Summaries (Test items, Rubrics, Raw Data)****Assessment Schedule and Course Alignment Matrix**

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**Please submit completed reports electronically to your college assessment representative.**