MAT175 Calculus I has a uniform departmental syllabus and a uniform departmental final (updated in Fall 2013). The uniform syllabus gives a precise scheduling of each topic. The course outcomes and the major outcomes incorporated into this course are assessed on the uniform final exam.
MAT175 is a required course for all math majors and is also required for a number of other science majors. It has a corequisite, MAT155, with the same objectives that will be assessed in conjunction with this course.
MAT175 Course Outcomes [assessed using the problems in the brackets]:
1. Evaluate limits (as part of Departmental Objectives in Mathematics a,b and e)
[assessed with problems 6-9 on the uniform final exam]
2. Prove basic theorems using limits of the difference equation (as part of a,b and f)
[assessed with problem 10 on the uniform final exam]
3. Differentiate functions using key theorems (as part of a,b & e)
[assessed with problems 1-5 and 19 on the uniform final exam]
4. Find the tangent line to a given graph at a given point (as part of a,b and e)
[assessed with problems 3-4 on the uniform final exam]
5. Solve maximum and minimum problems using differentiation (as part of a,b,c and e)
[assessed with problems 13, 14, 16 on the uniform final exam]
6. Solve related rates problems (as part of a,b and c)
[assessed with problem 11 on the uniform final exam]
7. Apply methods of calculus to curve sketching (as part of a,b)
[assessed with problems 12, 13, 14 on the uniform final exam]
8. Antidifferentiation, Riemann Sums, and Fundamental Theorem of Calculus (as part of a,b, and e)
[assessed with problems 15, 17, 18, 20 on the uniform final exam]
Math Major Outcomes incorporated into MAT175 [assessed using problems in the brackets]:
A. Perform numeric and symbolic computations
[assessed with all problems on the uniform final exam]
B. Construct and apply symbolic and graphical representations of functions
[assessed with problems 3, 4, 12 & 14 on the uniform final exam]
C. Model real-life problems mathematically
[assessed with problems 11, 15, & 16 on the uniform final exam]
E. State and apply mathematical definitions and theorems
[assessed with problems 6, 9, 10, 15, 17 on the uniform final exam]
F. Prove fundamental theorems
[assessed with problem 10 on the uniform final exam]
Fall 2016 Assessment Report for MAT 175:
The data used for assessment may be found here. It should be noted that only 4 of the 8 sections of MAT 175 submitted data. This unfortunate situation will hopefully be avoided in the future by the implementation of more frequent reminders leading up to the final exam.
The Course Outcomes (CO) data show that CO 5 had the lowest percentage of student success (52%), with COs 7, 6, 8, and 4 not much better. COs 5 through 8 are typically where students struggle the most, especially as they are more difficult and are covered in the latter half of the course (note that performance in all sections was about the same), but the poor performance on CO 4 is surprising. Looking at the data for questions 3 and 4 of the uniform final (which determine the percentage for CO 4), it seems that the issue may be traced back to the unusual results from Sections II and IV, which one would like to think must be extreme outliers. It is possible that these results are not as bad as they seem, since it could be that many students earned substantial partial credit for questions 3 and 4 (the instructors are asked to report only the number of students that earn full credit for each question). However, it is also possible that the instructors of sections II and IV did not sufficiently cover the topics in question. It may be worth implementing some kind of mechanism for reminding instructors of their responsibility to achieve all COs. On a happier note, the percentage of student success in COs 1 through 3 were much better: 77%, 91%, and 71%, respectively. Traditionally, success in CO 2 is quite difficult for students because it is assessed by question 10 on the uniform final, which requires a student to be competent in using algebra, functional notation, and taking limits. These are all topics addressed in previous courses, so seeing a high percentage in CO 2 is especially encouraging since it is either some indication that math preparation is improving or that our instructors are doing an outstanding job (or both).
The Math Major Outcomes (MMO) data show that MMO C had the lowest percentage of student success (59%), which is quite typical since it is assessed by questions 11, 15, 16 of the uniform final, which are all word problems. There was not a lot of variation among the different sections, except for in MMO B where sections I, II, III, and IV achieved 77%, 45%, 64%, and 66%, respectively. Again the unusually poor results from section II seem to be the most significant factor. If our goal is to be at or above 70% in all MMOs, then we have met that goal in MMOs E and F, and were close in MMO A. We would also be close in MMO B if the outlier data from section II were removed. It is clear then that MMO C should be the focus of any actions taken as a result of this assessment.
The following suggestions will be brought to the attention of the Educational Policy Committee of the Math Department:
1. More reminders to instructors about meeting Course Objectives and completing Tally Sheets.
2. Put Tally Sheets online to simplify data collection.
3. Consider how to address the poor performance in MMO C (word problems).
4. Clarify Tally Sheet grading policy.
Outcomes Prior to Fall 2016:
MAT175 Course Outcomes [assessed using the problems in the brackets]:
1. Evaluate limits (as part of Departmental Objectives in Mathematics a,b and e)
[assessed with problems 7-9 & 14 on the uniform final exam]
2. Prove basic theorems using limits of the difference equation (as part of a,b and f)
[assessed with problem 10 on the uniform final exam]
3. Differentiate algebraic and trigonometric functions using key theorems (as part of a,b & e)
[assessed with problems 1-6 on the uniform final exam]
4. Find the tangent line to a given graph at a given point (as part of a,b and e)
[assessed with problems 3-4 on the uniform final exam]
5. Solve maximum and minimum problems using differentiation (as part of a,b,c and e)
[assessed with problems 15-16 on the uniform final exam]
6. Solve related rates problems (as part of a,b and c)
[assessed with problem 11 on the uniform final exam]
7. Apply methods of calculus to curve sketching (as part of a,b)
[assessed with problems 12, 15 & 16 on the uniform final exam]
Math Major Outcomes incorporated into MAT175 [assessed using problems in the brackets]:
A. Perform numeric and symbolic computations
[assessed with all problems on the uniform final exam]
B. Construct and apply symbolic and graphical representations of functions
[assessed with problems 3, 4, 12 & 14 on the uniform final exam]
C. Model real-life problems mathematically
[assessed with problems 11 & 13 on the uniform final exam]
E. State and apply mathematical definitions and theorems
[assessed with problems 5, 6, 7, 9, 14 & 15 on the uniform final exam]
F. Prove fundamental theorems
[assessed with problem 10 on the uniform final exam]
Fall 2013 Assessment Plan for MAT 175:
MAT175 Calculus I has a uniform departmental syllabus and a uniform departmental final. The uniform syllabus gives a precise scheduling of each topic. The course outcomes and the major outcomes incorporated into this course will be assessed with the uniform final exam.
Due to the realignment of Calculus courses across the CUNY campuses, there has been a major change in our Calculus I syllabus. As a consequence we will assess MAT175 in Spring 2014 with a new uniform syllabus and a new uniform final.
Fall 2011 Assessment Report for MAT 175:
MAT175 Calculus I has a uniform departmental syllabus and a uniform departmental final (starting in Spring 2011). The uniform syllabus gives a precise scheduling of each topic. The course outcomes and the major outcomes incorporated into this course are assessed on the uniform final exam.
Originally the plan was to assess this course in Spring 2011 however due to faculty illness and injury and staff shortage we were only able to design the uniform final in Spring 2011. It was implemented in Fall 2011. Adjuncts were asked to voluntarily submit the data for their sections in Spring 2012. The data was analyzed in the Summer of 2012.
Observations before data analysis: The instructors were asked to submit data listing the numbers of students who passed their section and the numbers of passing students who scored each problem correctly. This data was entered into a spreadsheet by staff in the assessment office. Percentages of passing students scoring each problem correctly and achieving each goal correctly was then computed using the spreadsheet by the mathematics department assessment ambassador. Three sections had instructors who incorrectly submitted their data as they has over 100% of students scoring some problems correctly. Thus they must have reported total students scoring each problem correctly rather than only passing students. As it turns out all instructors submitted percent of students who scored each problem correctly (perfectly) rather than percent of passing students. This makes the data less useful for the purposes of our department as we are concerned about the preparation of students for subsequent courses. It is not uncommon for a student to need to take calculus twice before passing. It is a very challenging course. However it is essential that students who pass the class are prepared for subsequent courses in mathematics and science that require Calculus I as a prerequisite.
The data spreadsheet complete with analysis. On the far right the percentage of students achieving each goal is recorded. This percentage is sometimes over 100% because it is the number of students scoring the problem correctly divided by the number of students who passed the course. One of the sections did not report student performance on problem 16 which leads to no entry in some outcome assessment points for that section.
Conclusions: The different sections of the course had widely disparate performance on the various course objectives.
In "Section D" of the class only 13% of the students met Course Objective 5 and while this is a difficult type of problem, other sections had 85% of students achieving this objective. The same section of the course had poor performance in 4 other Course Objectives as well and astoundingly high performance on the first course objective. While we are not allowed to use this data to determine the hiring of adjunct faculty, this raises deep concern about this particular section of the class. It is clear the professor spent too much time on the first topic in the course and then rushed through or even skipped subsequent topics. Only 12 students passed in that section of the course. So now we move on to examine the performance of the students in the other 6 sections of the course (which had a total of 97 passing students). Immediately one sees that the other two sections (C and F) with exceptionally high performance on the first course outcome (over 90%) had low scores on the second course outcome (57% and 40%). Luckily they bounced back up to high performance on the third course outcome. One of these sections has students scoring over 80% on the rest of the course outcomes.
To perform a fair assessment of the overall performance of students in this course we have provided a final row in which the total students of all sections were taken. Due to the fact that Section F did not report performance on Question 16 we have added an additional final row with totals not including that section to compute outcomes which were assessed using Question 16. Over 75% of students achieved Course Outcomes I, III and VII. These three outcomes are the nuts and bolts of calculus. Outcome IV, which is also a standard basic calculus topic, had 72% performance. With knowledge of these outcomes, students are prepared for subsequent courses. Note that Calculus II requires a C in Calculus I, in hopes that 100% of students progressing to Calculus II have mastered these outcomes. We are proposing a winter session 1 credit Calculus problems class to help students who have passed Calculus I improve their abilities to these levels. The other three outcomes are more difficult for students. Outcome II concerns proving and this is often the first course in which a student is asked to write a proof. It is expected that students will develop this ability over a few years. Nevertheless 57% of students achieved this outcome. Outcomes V and VI had 65% and 70% of students performing well on the exam. These two outcomes concern applied topics which involve many steps. One cannot perform well on applications without already mastering the nuts and bolts. It is common for students to repeat Calculus I, taking their first semester to learn the basic outcomes and then a second semester to master these applied outcomes. We hope that our proposed 1 credit winter session course, will allow more students to succeed in Calculus I without needing to take the course twice.
We now turn to the Major Outcomes. One must keep in mind that Calculus I is the first course in the Mathematics Major and the overwhelming majority students will major in other subjects. Even math majors will develop their performance on these outcomes over a few years. Nevertheless students performed quite well on Major Outcome E (79%) which involves the statement and application of mathematical theorems. It is good to see this as students going on to other majors without taking subsequent mathematics courses can use this ability to read a math textbook and learn math as needed on the side. Not surprisingly the poorest performance was 59% on Major Outcome F which involves proving mathematical theorems. This skill will be introduced slowly over a series of courses and then become the central focus of the final two required courses in the mathematics major: Modern Algebra and Analysis. Overall the performance on the Math Major Outcomes was satisfactory considering this is the first course in the major even if every student were to continue on towards becoming a math major. Regardless of a students performance on the major outcomes, if a student enjoys mathematics and has performed well in this class (B or up), we would encourage that student to complete a mathematics major. The other skills will be developed over time.
Action Taken by the Department (September 2012):
The Educational Policy Committee has decided to create a winter session 1 credit Calculus problems course for students who have passed Calculus I but have not mastered the prerequisite skills for Calculus II. Students may take the class to achieve the C necessary to take Calculus II. Other students may just wish to take this problem session class to improve their skills to perfection. We also decided to adapt the uniform department syllabus to include a third in class exam. The new syllabus is at the top of this page.