MAT176
MAT176 is a required course for all math majors and is also required for a number of other science majors. It has a corequisite, MAT156, with the same objectives that will be assessed in conjunction with this course.
MAT176 Course Outcomes [assessed using the problems in the brackets]:
1. Find antiderivatives and integrals (as part of Departmental Objectives in Mathematics a,b & e)
[assessed with questions 1,2,5 of the uniform final]
2. Solve physical and geometric problems (a, b, c & e)
[assessed with questions 3,4 of the uniform final]
3. State and Apply the Fundamental Theorem of Calculus and the Definition of Riemann Sums (b & e)
[assessed with question 2,5 on the uniform final]
4. Compute Taylor series and verify convergence of power series (a & b)
[assessed with questions 7,8,9,10,11,12 of the uniform final]
Math Major Outcomes incorporated into MAT176 [assessed using problems in the brackets]:
A. Perform numeric and symbolic computations
[assessed with questions 1,2,5 of the uniform final]
B. Construct and apply symbolic and graphical representations of functions
[assessed with questions 3,4 of the uniform final]
E. State and apply mathematical definitions and theorems
[assessed with questions 2,7,8,9,10,11,12 of the uniform final]
Spring 2019 Assessment Report for MAT 176:
The data referred to can be found here. The percentage of students that passed the course was about 86%, which is above the target pass rate of 80%. In 2 of the 4 sections the pass rate was over 90%, so it may be appropriate to revise the target pass rate up to 90%. For each question on the final exam, the percentage of students earning full credit for that question was calculated. On 7 of the 12 questions more than 50% (and as high as 70% on question #5) of the students earned full credit. A target of 60% for all questions would be ambitious; in this case 60% or more was achieved on only 3 of the 12 questions. Questions #2, 4, 9, 10, 12 had percentages below 50%, and questions #10, 12 had percentages of 37% and 30%. Recent (January 2020) changes to the uniform final exam may improve these percentages in the future.
Spring 2017 Assessment Report for MAT 176:
The data used for assessment may be found here.
The Course Outcomes (CO) data shows that CO 4 had the lowest percentage (48%) of student success. This result is not surprising as the material on Taylor series is difficult and covered towards the end of the course. Three of the four sections were below or well below 50%, so the problem is a general one. The data for COs 1-3 is more satisfactory, with success rates of 64%, 75%, and 66%, respectively.
The Math Major Outcomes (MMO) data were similar to that of the CO data. At 49%, the MMO E percentage was well below that of MMOs A and B. Again the poor performance occurred in three of the four sections. Since the MMO E percentage is determined by essentially the same questions on the final exam as that of CO 4, the similarity is not surprising.
The following suggestions will be made to the Educational Policy Committee of the Math Department:
1. Update Course Outcomes to reflect the current state of MAT 176.
2. Put Tally Sheets online and clarify Tally Sheet grading policy.
3. Update sample final exam (question 2 was switched to MAT 175 final exam).
4. Consider how to address the poor performance on CO 4 (series questions).
Outcomes Prior to Fall 2016:
MAT176 Course Outcomes [assessed using the problems in the brackets]:
1. Find antiderivatives and integrals (as part of Departmental Objectives in Mathematics a,b & e)
2. Solve physical and geometric problems (a, b, c & e)
3. State and Apply the Fundamental Theorem of Calculus and the Definition of Riemann Sums (b & e)
4. Compute Taylor series and verify convergence of power series (a & b)
Math Major Outcomes incorporated into MAT176 [assessed using problems in the brackets]:
A. Perform numeric and symbolic computations
B. Construct and apply symbolic and graphical representations of functions
C. Model real-life problems mathematically
E. State and apply mathematical definitions and theorems
MAT176 will be assessed in Fall 2011 with a uniform final exam. This was postponed to Spring 2012 due to staff shortage.
MAT176 data has been collected in Spring 2012.
Observations before data analysis: Two sections of the class have had their data submitted. The data was submitted in the form of numbers of students completing each problem correctly rather than numbers of passing students performing each problem correctly. Naturally this needs to be taken into account when assessing the class. Another concern is that major outcome C was not assessed on this final, although it is assessed in many other courses in the major.
Data and Analysis: Spreadsheet with data (percents of students scoring each problem correctly for the two sections and the totals of the pair of sections), and analysis (averaging the percents of students to obtain a score for each outcome and then further dividing the score by percentage of passing students in the final row under each outcome).
Analysis: The students performed best in Course Outcome 3, which is somewhat surprising because this is a difficult concept. However it may indicate that students had more difficulty with the computation intensive questions assessing the other course outcomes. Their performance on Course Outcome 1 could be improved, and it is particularly surprising how poorly the students on the very first basic question on the exam. They definitely need to practice more problems and be pushed to do more homework. The performance on Course Outcome 2 which involves understanding regions in Euclidean space and well as three dimensional geometry had the lowest performance. They did better than expected in Course Outcome 4, which is the last topic of the course and not even covered in second semester calculus at many universities. Overall, it is a serious concern that students did not perform better in Course Outcome 1 as this can seriously affect their ability to apply Calculus II correctly in future courses. The students must practice more!
Calculus II is only the second course in the math major. We did not assess Major Outcome C in this course, but it will be assessed in subsequent courses so that is not a concern. The students did fairly well on Major Outcome E, especially for students so early in the program. They did poorly on Major Outcome B, as expected at this early stage. This Major Outcome is reinforced in subsequent courses and the students improve slowly over time. It is a serious concern that the students performed so poorly on Major Outcome A, as this can hinder their ability to perform successfully in subsequent courses in the major. It should be noted that not all students in Calculus II are future math majors. We only admit those with higher grades into the subsequent courses of the major.
Recommendations: The students need to be pushed to do more repetitive rote calculation practice. We should add more problems assessing these basic calculations separately. We might consider removing problems from the exam which were not really part of the course outcomes so that students can focus more of their energy and time on the other problems.
Departmental Response: So far the department's Educational Policy Committee has already proposed a short winter session course designed to be taken by students between Calculus I and Calculus II to review and practice what they have learned.