# Annual Program Assessment Report 2016

# CALIFORNIA STATE UNIVERSITY, CHICO ANNUAL PROGRAM ASSESSMENT REPORT

BS, Department of Mathematics and Statistics

(4 Options: Applied Mathematics, Pure Mathematics, Mathematics Education, Statistics)

Date: 09/19/2016

# I. Assessment of Student Learning Outcomes

**Name and Contact Information of Program Assessment Coordinator: Colette Calmelet**

**Department of Mathematics and Statistics Holt 212, phone 898-6895. ****ccalmelet@csuchico.edu**

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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)

# 4. Learning Outcome(s) Assessed in AY 2015-16 (Year 9 of Assessment Plan)

PP-IPM, PS-M, GC1-PM, GC3-IPM, Com1-M, Com2-M

# 5. Assessment Methodology Used

We assessed the SLO’s at the level of mastery (I, P, M, for Introductory, Progressing, Mastery) indicated above by embedding assessment items in tests and final exams for Math 235 (S16), Math 330 (S16), Math 420 (S16), Math 449 (S16). As far as possible, we used assessment items similar to those in Year 3 of our assessment plan. Math 235 courses were taught by two instructors who contributed to developing the instruments and agreed to make them common to their respective exams. All instructors also contributed to constructing rubrics that we applied to determine performance at the Exemplary, Proficient, Acceptable, and Unacceptable levels.

In appendix we collect assessment items, rubrics, raw scores and sorted data for all class assessments. When possible, we used the rubrics of Year 3 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 (SLO) |
Where sample is from (sample size) |
Measure |
% Exemplary + Proficient by item |

COM1-P |
MATH 330 (29) |
Embedded Test Problem 1 |
86 |

COM1-M |
MATH 420 (4) |
Embedded Test Problem 2 |
75 |

PP-I |
MATH 235 (12) |
Embedded Test Problem 2 |
8 |

PP-I |
MATH 330 (29) |
Embedded Test Problem 2 |
86 |

PP-I |
MATH 330 (29) |
Embedded Test Problem 3 |
31 |

PP-M |
MATH 420 (7) |
Embedded Test Problem 3 |
43 |

GC1-P |
MATH 235 (12) |
Embedded Test Problem 1a Embedded Test Problem 1b |
92 83 |

GC1-M |
MATH 420 (8) |
Embedded Test Problem 1 |
63 |

GC3-I |
MATH 235 (12) |
Embedded Test Problem 3 |
67 |

GC3-P |
MATH 235 (12) |
Embedded Test Problem 3 |
67 |

GC3-M |
MATH 449 (22) |
Embedded Test Problem 1 |
45 |

GC3-M |
MATH 449 (22) |
Embedded Test Problem 2 |
64 |

PS-M |
MATH 235 (12) |
Embedded Test Problem 4ab |
50 |

PS-M |
MATH 235 (12) |
Embedded Test Problem 4cd |
42 |

PS-M |
MATH 235 (12) |
Embedded Test Problem 4e |
25 |

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**Analysis / Interpretation of Results**

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**Spring 2016 Assessment**

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**Math 235**: Math 235 is an important course and therefore is multi-section. It is a core course for all math options. Math 235 is also attended by non-Math majors for Economics, Computer Science and Civil Engineering students in order to fulfill a math requirement in their respective major.

The SLOs that are being measured are: GC1-P, GC3-IP, PP-I, PS-M

**COM1:**Demonstrate the ability to effectively and accurately write on mathematical topics relevant to their mathematics option and appropriate to their audience.**GC1**-‐P: Demonstrate basic skills and conceptual understanding of differential, integral, and multivariable calculus and fundamantal mathematical objects introduced in our degree core, such as, sets, functions, equations, vectors, and matrices.**GC3**-‐IP: Demonstrate more technical skills and more indepth and broader conceptual understanding in core mathematical areas (such as, analysis, geometry/topology, algebra, applied math, statistics), relevant to their option.**PP-‐I:**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.**PS-‐**M: Interpret and translate problems into appropriate mathematical language; then solve problems by applying appropriate strategies and interpreting the results.

**GC1 **is being assessed at the *Progressing Level*, **GC3 **is being assessed at the Introductory and Progressing levels, **PP **at the *Introductory Level, *and PS at *Mastery level.*

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**Problem 1a**: This is a multiple choice question asking to verify whether a given matrix is the inverse of another given matrix. The following steps were evaluated:

- whether they used one of the correct methods either by row reduction of multiplying both matrices and verify if the product is the identity matrix.
- whether their calculations are correct.

Most students were able to solve this problem. 92% of the students got full points for this problem and only 8% failed.

**Problem 1b**: This question involved the application of the inverse matrix to solve a non- homogeneous system. For this problem a majority of students received full credit (83%) and a minority of them obtained no credit (7%).

**Problem 2**: This question was more theoretical and therefore more challenging. It was applied to the definition of eigenvalues of a matrix, and required additional skills in proof writing. Evaluations were based on the following criteria:

- whether or not the correct definition of eigenvalues is used
- whether or not the matrix multiplication properties are used

- whether the matrix product was considered and whether the proof was completed.

The majority of students scored poorly, 58% of the students missed completely the question, 33% attempted to solve it and only 9% answered correctly.

**Problem 3**: This problem was related to the concept of linear independence of some given vectors and was graded according to the following criteria:

- whether or not the vectors formed a matrix
- whether or not some rows are identical
- whether the row reduction method is used
- whether the correct definition of linear independence was made.

These problems are generally harder for students due to the fact that linear independence is a difficult mathematical concept requiring a certain level of understanding from students. However a majority of students 66% had this problem right, while 25% obtained partial results and 9% of students did not answer the question.

**Problem 4: **This problem required a complete understanding of the row reduction method as well as the full interpretation of the outcomes. This problem tested the students on an important part of the course related to the solutions of linear systems and their applications. The criteria used to grade this problem were:

- whether or not the students answered partially to questions a, b and d
- whether the students answered correctly to questions c and e.

50% of the students had no mistakes on questions a and b, 42% of them had correct answers for questions c and d, and a minority of the students 25% replied correctly for question e. We observe also that a minority of students 16% missed all questions.

**MATH 330: **Math 330 is another core course in our program. It is also a required course for all our majors and is taught in both semesters. Students learn mainly how to read and write mathematical proofs, this course is necessary particularly for our general math and education majors.

The SLOs that are being measured are:

**COM1-P:**Demonstrate the ability to effectively and accurately write on mathematical topics relevant to their mathematics option and appropriate to their audience.**PP-IP:**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.

**COM1-P***Progressing Level*and**PP-IP**at the

*Introductory and Progressing Levels.*

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# Problem 1- COM1-P

This problem deals with properties of a given relation. Students were expected to demonstrate their ability to understand the properties of a relation and show how to apply these properties using a given directed graph.

Most students were able to handle very well this question: 86% of the majors scored correctly.

# Problem 2 - COM1-P and PP-I

In this problem student were asked to prove that the sum of two odd integers is even. This was an easy question which was answered correctly by most of the students of the class 93%, and 62% of the students reached the perfect score.

# Problem 3 - COM1-P and PP-I

Students were offered a problem on the theory of sets and more precisely on the property of intersection and union of sets. Students were expected to prove an important identity in set theory. One of the difficulty of the problem was to write the formal and complete proof.

A minority of students 10% were able to solve this problem entirely, 31% of the students answered exemplary or proficiently, and a majority of them 66% were able to prove the identity partially.

**MATH 420. **This course is required for all our options and is considered difficult by our students due to the presence of abstract concepts. The course requires adequate knowledge in analysis and good skills on proof writing.

The SLOs that are being measured are:

- GC1-M: At mastery Level, demonstrate basic skills and conceptual understanding of differential, integral, and multivariable calculus and fundamantal mathematical objects introduced in our degree core, such as, sets, functions, equations, vectors, and matrices.
- COM1-M: At mastery level, demonstrate the ability to effectively and accurately write on mathematical topics relevant to their mathematics option and appropriate to their audience.
- PP-M: At mastery level, 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.

# Problem 1 – GC1-M

Application of the notion of limits and the use of proofs in the evaluation of limits. This is a theoretical question based on Calculus I topics.

Results: 50% of the students obtained perfect a score as they were able to give a complete and correct proof. Most students were able to solve this problem adequately: 75%, and only 25% had unsatisfactory answers.

# Problem 2 – COM1-M

This problem is an application of the properties of convergent sequences, which requires understanding of the concept of convergence and requires good skills in proof writing.

Results: Most students were able to solve this problem correctly: 75% of the majors scored at the Exemplary and Proficiency level.

# Problem 3 – PP-M

This problem requires understanding of sequences and series. The difficulty of this question lies on the common confusion made by students between sequences and series. This is also an abstract problem requiring good proof writing skills.

Results: 43% of the students were able to solve this problem correctly. 37.5% of the students provided exemplary or proficient answers.

**MATH 449. **This course is a core course required for all math majors. Math 449 is considered difficult by our students due to its theoretical and abstract contents. The course requires an extensive knowledge on proofs and basic knowledge of modern algebra.

The SLOs that are being measured are:

GC3-M: At mastery level, demonstrate more technical skills and more indepth and broader conceptual understanding in core mathematical areas (such as, analysis, geometry/topology, algebra, applied math, statistics), relevant to their option.

# Problem 1- GC3-M

This challenging problem requires knowledge of the structure of group and its application to a particular set.

Result: 45% of the students gave exemplary or proficient answers.

# Problem 2 - GC3-M

This problem requires the understanding of the definition of generators as well as some computational skills.

Result: 64% of the students gave exemplary or proficient answers.

# 8. Planned Program Improvement Actions Resulting from Outcomes:

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No program improvements are planned for Math 235, 330, 420, or 449 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.

# 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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No changes made or planned.

# 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?

2016-2017 will be Year 4 of a new Assessment schedule. In year 4 we collect data from Math 337/346, Math 341, Math 342 and Math 435/437. The SLOs that will be assessed from these classes are:

GC3 at the Introductory, Progressing, and Mastery levels for Education and General majors.

Exit surveys will be conducted for LL1-I and LL2-P.

The contact persons are Kevin McGown (Assessment Coordinator), Rick Ford (Department Chair), and Sergei Fomin (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)**

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**Assessment Schedule and Course Alignment Matrix**

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