Core Curriculum Assessment Report For

Core Classes In the

Department of Mathematics and Statistics June 2011

Committee Members

Kathleen Gustafson (Chair) Jill Faudre

Tony Rickard Latrice Laughlin

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Outline I. Introduction II. Methodology III. Discussion of specific courses IV. Conclusions & recommendations V. Data Collected

I. Introduction The Department of Mathematics and Statistics (DMS) has completed its review of the core mathematics courses for 2011. A special committee, formed for the purpose of assessing the mathematics core, met in May 2011 to gather the data presented in this report. The DMS currently offers eight core courses, of which four were reviewed by the committee. The personnel resources of the committee made it difficult to include more courses and at the same time have an equitable allocation of assessment duties. The core mathematics curriculum was designed in order that students will achieve “advanced literacy in mathematics.” The description of the Core Curriculum as in The UAF Baccalaureate Experience: The Philosophy asserts that “advanced literacy in mathematics implies a solid grasp of quantitative reasoning and appreciation of mathematical applications. Most important is acquiring the knowledge necessary for informed judgement on the uses of mathematical and statistical interpretations confronting us in everyday life.” Our assessment of the core mathematics courses will address this goal. Each core class is unique and will address mathematical literacy in a unique way.

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II. Methodology Our methodology was driven by three documents. The first is the philosophy of the core (as stated in the introduction). The second is the Core Curriculum Review Process for Core Classes in the Mathematical Sciences which outlines a basic approach that focuses on syllabi and final exams in each course. The third is the assessment report on the core mathematics courses completed in May 2009. The 2009 report assessed all core math courses except Math 107 and 200. The courses reviewed in this assessment are Math 107, 200, 262 and 272. Below is a table displaying all the core MATH courses and when they were assessed (STAT 200 is also a core course offered by the Department of Mathematics and Statistics and is assessed in a separate report developed by the DMS statistics faculty):

Exams were sampled from one or more of the Fall 2009 through Spring 2011 semesters. Each final exam was reviewed in light of the desired outcomes for the course. There are three expected learning outcomes common to each of the courses. 1. Students master problem-solving skills. 2. Students learn to manipulate abstract symbols 3. Students learn a broad spectrum of mathematical applications. The third outcome concerns content related objectives that are unique to each individual course. Thus, this outcome will be split into several specific concepts listed under the separate courses. In addition, a fourth criterion is added for Math 107. 4. Students have mastered the prerequisite material for the course. While this fourth outcome does not directly address student outcomes for the core courses, it does address the problem of incorrect student placement, which has been recognized as a problem for our courses. Our method for assessment is as follows: A random sample of exams from each course is chosen, or where possible, all exams are reviewed. For each section of exams, one or more problems that represented each outcome are chosen and the student’s response is given a rating of 0 to 4, with 4 being highest. We then summarize these scores to arrive at estimates of student performance in each area. This summary is given at the end of the report.

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III. Discussion of Specific Courses Math 103X Concepts and Contemporary Applications of Mathematics Introduction The content of Math 103 is chosen in an attempt to make a more relevant and meaningful mathematics course for a student majoring in a non-technical field. As a core course, it is expected that the enrollment will include most majors in the liberal arts, the fine arts, and other disciplines where analytical skills such as Calculus have not traditionally played an important part. With emphasis on management science, statistics and data management, and social choice and decision-making, the topics covered in Math 103 are a good representation of the logical and computational needs of a modern college graduate. This course is viewed as a terminal mathematics course. As a result, it is not the aim of the Department of Mathematics and Statistics to create a rigidly standardized syllabus. Our current textbook contains more material than can be discussed in one semester and therefore the instructors retain some flexibility in choosing topics to cover. Presently, the syllabus consists of some mandatory chapters and several optional chapters. Observations from 2011 Assessment For reasons stated in the introduction, we did not review Math 103 for this Assessment Report.

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Math 107- Functions for Calculus Introduction The primary goal of this course is to prepare students to take Calculus, although it also prepares students for STAT 200 and MATH 205 and 206, and is a terminal course for some. It covers a wide range of topics such as algebra, operations on functions, graphing, logarithms and exponential functions. Because of the large number of topics covered, the syllabus for this course is fairly rigid. This fixed syllabus is our way to ensure that the course meets the spirit of the Core. In addition, the departmental assessment committee plans to review final exams periodically to ensure students are learning material in sufficient depth. Actions taken Mandatory placement was implemented and has been in effect for this course since Fall 08. It was felt that this implementation would increase the success rate of Math 107 students by only allowing those students who have the necessary algebra and other prerequisite skills necessary for succeeding in precalculus into the course. Also, a line of communication has been established between the UAF mathematics department and both the Center for Distance Education (CDE) and the College of Rural Alaska (CRCD) to ensure that we are able to collect final exams for assessment purposes. Results of actions taken Mandatory placement: This assessment did not attempt to measure the impact of mandatory placement although it is the general opinion of the committee that the new policy is better. Collection of final exams from CDE and CRCD: We were finally successful in retrieving the necessary exams from both sources. Observations from 2011 Assessment The committee assessed the four criteria listed under section II on methodology. Outcome 3 was split into the following objectives specific to Math 107. a) Understanding the nature of functions b) Solving equations c) Graphing basic functions (polynomial, rational, exponential, and logarithmic functions, and functions containing radicals) d) Understanding the properties of exponential and logarithmic functions We reviewed the finals with the following results. As in both the 2005 and 2007 reports, the highest outcomes were manipulating abstract symbols, solving equations, and prerequisite material. Added to the relative strengths this time is exponents and logarithms. The weakest areas were mastering problem solving skills, the nature of functions and graphing basic functions. As a whole, the Math 107 performance was lower than we would like in all areas, and lower than the scores from last assessment.

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For the first time we had success in getting exams from the College of Rural. We received 22 exams from the Northwest Campus. In general, students did well. However, it was noted by the reviewer that the students were allowed to use notes and a calculator which is not the usual case in the UAF campus or CDE courses. From the Center for Distance Education, we received all final exams for the paper-based course (3 total), but none from the online version of the course. The instructor of the online course keeps the exams rather than having them filed at the CDE office, and was not available to give them to us.

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Math 161- Algebra for Business and Economics Introduction The primary goal of this course is to prepare students to take Calculus for Business and Economics. It covers a wide range of topics such as algebra, graphing, logarithms and exponential functions, mathematics of finance, and linear algebra. Because of the large number of topics that must be covered the syllabus for this course is fairly rigid. This fixed syllabus is our way to ensure that the course meets the spirit of the Core. Math 161 is a business counterpart to Math 107, and final exams are reviewed periodically by the departmental assessment committee to ensure students are learning material in sufficient depth. Observations from 2011 Assessment For reasons stated in the introduction, we did not review Math 161 for this Assessment Report.

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Math 262 - Calculus for Business and Economics Introduction Math 262X is a one-semester calculus for the business major. This course must cover a lot of ground and the syllabus is fairly rigid. Individual instructors are required to adhere to the syllabus and hence the syllabus is our main tool in assuring that the course meets the spirit of the Core. To further assure this, the department periodically reviews the final examinations to ensure material is covered in sufficient depth and to assure that the students develop competence in the subject matter. Observations from 2011 Assessment The committee assessed the three criteria listed under section II on methodology. Outcome 3 was split into the following objectives specific to Math 262. 3a) Limits and continuity 3b) Differentiation and integration – calculations 3c) Maximization/minimization problems 3d) Analysis of functions of one variable and their graphs 3e) Applications of integration and differentiation 3f) Partial derivatives We reviewed the finals with the following results. Student outcomes were high in outcome 3a (limits and continuity) and 3c (max/min problems), both improvements over the last assessment. In all other outcomes, scores were lower than last assessment with the weakest area being outcome 3d, analyzing functions. Outcome 1, problem solving, is also very low scoring. This is a very typical situation. Word problems are often the most difficult problems on a final and are used to differentiate between the A and B students.

Several things are noted by the reviewer. First, one instructor’s final exams did not contain any problem pertaining to outcome 3c, max/min problems (thus the highlighted 47 in the chart above). This makes it hard to conclude anything about the improvement from last assessment (80% versus 64% in total score percentage). This matter needs to be addressed with the instructor. Second, one set of exams did not meet the expectations of the department. The exam consisted of 18 problems pertaining almost entirely to outcomes 3a, 3b and 3f. The only problem that could be considered an “application problem” was overly simple (“find the marginal revenue”), and the only “analyzing of functions” was a problem that asked the student to find intervals where the function is

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increasing/decreasing. The exam had no real applications as they apply to business or economics, there was no graphing or analysis of functions past the last problem mentioned and no area problems. Also, the 18 problems were scored out of 1 point each, but the scores on the exams were out of 15.

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Math 272X - Calculus for the Life Sciences Introduction Math 272X is a one-semester calculus for majors in the life sciences. This course must cover a lot of ground and the syllabus is fairly rigid. Individual instructors are required to adhere to the syllabus and hence the syllabus is our main tool in assuring that the course meets the spirit of the Core. To further assure this, the department shall periodically review the final examinations to ensure that the material was covered in sufficient depth and to assure that the students developed competence in the subject matter. Observations from 2011 Assessment The committee assessed the four criteria listed under section II on methodology. Outcome 3 was split into the following objectives specific to Math 272. 3a) Limits and continuity 3b) Differentiation and integration – calculations 3c) Maximization/minimization problems 3d) Analysis of functions of one variable and their graphs 3e) Applications of integrals and derivatives 3f) Differentiation and integration – concepts

-knowing how derivatives and integrals are related to graphs -having the ability to discern whether differentiation or integration is involved -understanding how a derivative and an integral relates to the original function

We reviewed the finals with the following results. Overall scores were very good. Student outcomes were best in the areas limits and continuity, manipulating abstract symbols, and analyzing functions. The weakest area was problem solving, which is typical. Overall, the scores are noticeably higher than in 2007. It should be noted that only one section of this course is offered each fall, so only 2 sections totaling 13 exams were reviewed. Also, the same person assessed Math 272 this time as did in 2007, and the same instructor has taught this course since Fall of 2004, so the differences in the two sets of scores are most likely due to the particular students in the courses, and perhaps some improvement in instruction.

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Math 200X - Calculus I Introduction Math 200 is the first course in a three-semester calculus sequence for the physical sciences. The course covers a lot of ground and the syllabus is fairly rigid. Individual instructors are required to adhere to the syllabus, which is our main tool in assuring that the course meets the spirit of the Core. To further assure this, the department shall periodically review the final examinations to ensure the material was covered in sufficient depth and to assure that the students developed competence in the subject matter. Observations from 2011 Assessment The committee assessed the four criteria listed under section II on methodology. Item 3 was split into the following objectives specific to Math 200. a) limits and continuity b) differentiation and integration c) maximization/minimization problems d) analysis of functions of one variable and their graphs e) applications of integrals and derivatives Student outcomes were pretty good overall. Over half of the exams selected ranked 3 or 4 in all outcomes. In three categories, over 75% of the exams selected ranked as 3 or 4. The best areas were differentiation, manipulating abstract symbols, and limits with 78%, 77% and 76% respectively scoring at the 3 or 4 level. Outcomes 1, 3c and 3e are the lowest scoring outcomes. However, it should be noted that these outcomes are usually best assessed through word problems which are typically the hardest types of problems for students to master. Scores are significantly higher than they were the last time Math 200 was assessed in 2007. As always, the difference in scores for these two reports could be due to (1) the individual reviewer and (2) the types of problems chosen to represent the individual outcomes.

Math 200 Scores

Outcome 4 3 2 1 0

# of exams

average out of

4

total score

%

% at 3 or

4

1 Problem solving skills 35 12 12 12 17 88 2.4 60.2 53.4

2 Manipulate abstract symbols 37 33 9 7 2 88 3.1 77.3 79.5

3a Limits & continuity 36 31 13 5 3 88 3.0 76.1 76.1

3b Differentiation /integration 39 29 11 8 1 88 3.1 77.6 77.3

3c Maximization/Minimization 31 12 19 15 5 82 2.6 64.9 52.4

3d Analysis of functions & their graphs 40 14 13 11 4 82 2.9 72.9 65.9

3e Applications of integrals & derivatives 32 11 11 11 17 82 2.4 59.1 52.4

Averages 2.8 69.7 65.3 The last three categories have fewer exams reviewed because there were some final exams that contained no questions on these topics. Specifically, there were final exams in which there was

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not a single application of the derivative or integral. There were final exams without a single question about extrema in any form. There were final exams that asked no questions about graphs of functions or analysis of functions beyond merely asking for the derivative of a given function. The reviewer also comments that there was a huge variation in difficulty of exams. For example, there were exams that consisted of evaluating limits, finding derivatives, and evaluating integrals only. And exams for which over 50% of the points were challenging applied problems. In the former, nearly all papers scored 4. In the latter, all six papers scored 1 or less for applications. Math 201X - Calculus II Introduction Math 201 is the second course in a three-semester calculus sequence for the physical sciences. The course covers a lot of ground and the syllabus is fairly rigid. Individual instructors are required to adhere to these syllabi and hence the syllabi are our main tool in assuring that the course meets the spirit of the Core. To further assure this, the department shall periodically review the final examinations to ensure the material was covered in sufficient depth and to assure that the students developed competence in the subject matter. Observations from 2011 Assessment For reasons stated in the introduction, we did not review Math 201 for this Assessment Report. Math 202 - Calculus III Introduction Math 202 is the third course in a three-semester calculus sequence for the physical sciences. The course must cover a lot of ground and the syllabus is fairly rigid. Individual instructors are required to adhere to these syllabi and hence the syllabi are our main tool in assuring that the course meets the spirit of the Core. To further assure this, the department shall periodically review the final examinations to ensure the material was covered in sufficient depth and to assure that the students developed competence in the subject matter. Observations from 2011 Assessment For reasons stated in the introduction, we did not review Math 202 for this Assessment Report.

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IV Conclusions The problem of incorrect student placement has been greatly improved since establishing a mandatory placement system in Fall 2008. Unfortunately, it is not really possible to determine whether or not mandatory placement has improved student success because it is very likely that most students who did not have the necessary skills to succeed in the core classes in the first place dropped out of the course before final exams were ever given. Regardless of this, we believe that mandatory placement is a necessary measure and though having an appropriate standardized test score or receiving an appropriate grade in a precursor course does not always guarantee having an appropriate level of prerequisite knowledge or preparedness, it is at least a start. For the first time we were successful in collecting most exams from the College of Rural Alaska and the Center for Distance Education. The only comment of note was by the reviewer of the Math 107 exams from the Northwest Campus of Rural Alaska. She comments that the students were allowed to use notes and a calculator on their final exams, whereas these items were not allowed on the UAF campus exams. This is an issue that should be discussed. Our current method of data collection should be reviewed and possibly revised. The problems on the final exams are, naturally, written with a focus on representing the material covered in class and are deliberately varied in difficulty to produce an accurate overall analysis of student knowledge. They are not necessarily designed to evaluate or isolate the areas or skills targeted in assessment. This makes it difficult to produce an accurate comparison of student performance even within a particular course. It was suggested that we might abandon the strategy of assessing eight or nine different outcomes for every course every two years and instead focus on one or two problematic areas in each class. These problematic areas would be relatively easy to identify given the data from the past five assessments. Thus, while it would not be reasonable to expect all instructors for a particular course to include on their finals eight problems designed for assessment, incorporating a single medium-difficulty problem from one or two problematic areas is feasible. This would also focus instructors on these weak areas of the curriculum. This would have the additional advantage of making assessment across several semesters, including summer terms, a realistic amount of work. And again, as stated in the last assessment, we need to make sure that all core math course instructors are aware of the assessment process and what is expected on final exams.

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Recommendations from 2011 Assessment 1. Discuss the possibility of putting a person in charge of the following in order to ensure the future success of the assessment process. A. Collecting final exams B. Informing all core instructors of their responsibility in the assessment process C. Distributing a clear, specific syllabus to each core course instructor in order to maintain consistency between sections and to ensure a smooth transition between sequential classes. D. Communicate to all core course instructors what is expected on final exams. E. Establish a communication system with both the Center for Distance Learning and the College of Rural Alaska 2. Discuss the following possible changes to our method of data collection. A. Reevaluate our outcome criteria. B. Use more than one exam problem to represent each chosen outcome. C. Assign more than one reviewer to assess each course.

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Outcome Data for 2011 Assessment We must caution the reader not to infer comparisons between courses based on these numbers since each course was reviewed by a different committee member. It is valid to compare the average scores within courses and this is what we have done.

Math 107 111 exams assessed 2011 TOTALS Scores

Outcome 4 3 2 1 0

# of exams

average out of

4

total score

%

% at 3 or 4

1 Problem solving skills 11 24 29 34 13 111 1.9 47 32

2 Manipulate abstract symbols 16 32 38 18 7 111 2.3 57 43

3a Nature of functions 6 24 41 23 17 111 1.8 45 27

3b Solving equations 12 37 41 11 10 111 2.3 57 44

3c Graphing basic functions 10 19 38 32 12 111 1.8 46 26

3d Exponents & logarithms 13 32 32 24 10 111 2.1 53 41

4 Prerequisites 11 41 33 14 12 111 2.2 56 47

Averages 2.1 52 37 Math 200 88 exams assessed 2011 TOTALS Scores

Outcome 4 3 2 1 0

# of exams

average out of

4

total score

%

% at 3 or

4

1 Problem solving skills 35 12 12 12 17 88 2.4 60.2 53.4

2 Manipulate abstract symbols 37 33 9 7 2 88 3.1 77.3 79.5

3a Limits & continuity 36 31 13 5 3 88 3.0 76.1 76.1

3b Differentiation /integration 39 29 11 8 1 88 3.1 77.6 77.3

3c Maximization/Minimization 31 12 19 15 5 82 2.6 64.9 52.4

3d Analysis of functions & their graphs 40 14 13 11 4 82 2.9 72.9 65.9

3e Applications of integrals & derivatives 32 11 11 11 17 82 2.4 59.1 52.4

Averages 2.8 69.7 65.3

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Math 262 80 of 80 exams assessed

2011 TOTALS Scores

Outcome 4 3 2 1 0

# of exams

avg out of 4

total score

%

% at 3 or 4

1 Problem Solving 19 23 16 4 18 80 2.3 57 53

2 Manipulate Abstract Symbols 13 21 27 18 1 80 2.3 58 43

3a Limits and Continuity 35 34 9 2 0 80 3.3 82 86

3b Differentiation/Integration 8 30 26 16 0 80 2.4 59 48

3c Max/Min problem 26 8 10 3 47 3.2 80 72

3d Analyzing Functions 13 22 18 14 13 80 2.1 53 44

3e Applications of Der. And Int. 24 23 18 12 3 80 2.7 67 59

3f Partial Derivatives 21 29 21 7 2 80 2.8 69 63

Averages 2.6 66 58

Math 272 13 of 13 exams assessed 2011 TOTALS Scores

Outcome 4 3 2 1 0

# of exams

average out of

4

total score

%

% at 3 or 4

1 Problem Solving 6 1 2 2 2 13 2.5 63.5 53.8

2 Manipulate Abstract Symbols 9 3 0 1 0 13 3.5 88.5 92.3

3a Limits and Continuity 12 1 0 0 0 13 3.9 98.1 100.0

3b Differentiation and Integration 3 7 2 1 0 13 2.9 73.1 76.9

3c Max/Min problem 5 6 1 0 1 13 3.1 76.9 84.6

3d Analyzing Functions 7 4 2 0 0 13 3.4 84.6 84.6

3e Applications of y' and integration 7 2 1 2 1 13 2.9 73.1 69.2

3f Concepts of y' and integration 5 5 3 0 0 13 3.2 78.8 76.9

4 Prerequisites 9 3 1 0 0 13 3.6 90.4 92.3

Averages 3.2 80.8 81.2

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Comparison of last assessment vs 2011 Outcome Scores We must caution the reader not to infer too much from these comparisons since different committee members may have done the reviews in the different years.

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