MAT172 Precalculus has a uniform departmental syllabus and a uniform final. 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. MAT172 was last assessed in Fall 2010 and will be assessed again in Spring 2013.
The overwhelming majority of students in MAT172 are neither math majors nor intend to be math majors. However, this is the second course in the sequence leading towards the courses required for the major and it covers crucial major outcomes. The majority of math majors begin mathematics at the precalculus level or higher and many transfer in having completed all the introductory courses at another college.
MAT172 Course Outcomes:
1. Graph linear, polynomial, trigonometric, exponential, and logarithmic equations (a,b)
2. Identify equations for given graphs (a,b, & e)
3. Work with functions: inverting, composing, multiplying and dividing functions (a,b,e)
4. Represent and solve real-world problems requiring optimization of quadratic functions (a,b,c)
5. Use the unit circle to determine the values of trigonometric functions (b,e)
6. State and apply trigonometric identities (b,e)
7. Represent and solve real-world problems involving exponential growth and decay (b,c)
Math Major Outcomes incorporated into MAT172:
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
Fall 2018 Assessment of MAT172:
The data referred to may be found here. The percentage of students that passed the course was about 82%, which is above the target pass rate of 80%. The target success rate of 70% was surpassed on 7 of the 17 questions, and a success rate of more than 60% was achieved on all but 3 of the questions, namely questions #14 (40%), 16 (56%), 17 (52%). The percentages for #14, #16, #17 were higher (67%, 76%, 71%) in the following semester, so the fall 2018 numbers may not indicate a serious issue. We will continue to monitor the situation.
Spring 2013 Assessment of MAT172:
Plan: (January 2013) MAT172 was assessed in Spring 2013 using a uniform final. The instructors were asked tally the number of passing students scoring perfectly on each problem in the uniform final exam. Four sections reported their tallies. Two of the sections reported on all students rather than passing students. The data and analysis is available on a single spreadsheet. Due to the inconsistent reporting, totals were taken and individual sections of the class are not being compared to one another as was done in the past. Nevertheless we can compare different course and major outcomes to one another.
The students performed well on Course Outcomes 1 and 3 (graphing and working with functions). This material is introduced at the beginning of the course and is given plenty of time. There is serious concern regarding student performance on Course Outcome 6 (using trigonometric identities). This topic is covered too quickly. It is also problematic that College Algebra has so little trigonometry on its final, so that this subject is almost entirely new to some of the students taking precalculus. On a positive note, students performed better on Course Outcome 5 (Unit Circle Trigonometry) and on Course Outcomes 4 and 7 (concerning real world problems). In Fall 2010 students performed very poorly on these course outcomes and the syllabus was adjusted in response to this concern. It appears the adjustments have helped considerably.
Although MAT172 is not part of the math major and very few students taking this course continue on to become math majors, it does cover Major Outcomes A, B C and E. The students performed quite well on the first two of these outcomes, particularly graphing, which sets them up with a solid foundation to start the major if they choose to major in mathematics.
Fall 2010 Assessment of MAT 172:
Plan: (May 2010) MAT172 data will be collected in Fall 2010. All classes were given a uniform final exam and scores for each problem were recorded for each student by each section's instructors. Those instructors who followed the uniform syllabus closely submitted their student's scores for assessment, so that we could determine the success of the official syllabus' schedule. Some instructors neglected to follow the syllabus and their students reported that they had skipped some topics altogether. Students are still required to learn all material on the syllabus by reading the textbook and tutoring regardless of the actions of their instructor. Nevertheless we felt we should not assess the effectiveness of the department's course based on instructors who had not followed the syllabus. The assessment ambassador, Dr. Sormani, will be given these scores sometime in February 2011.
Observations before data analysis: (Feb 2011) Only three instructors volunteered to submit data. We were not given funding to pay adjuncts for compiling their data into spreadsheets and greatly appreciate the three who volunteered to do so. The three sections being reviewed will be referred to as Sections A, B and C. Although the sections were assessed identically and there is a uniform syllabus, we keep the data separate to compare with the instructor's responses to the questionnaires concerning exactly how they personally altered the course.
Data and Analysis: (Feb-May 2011) The first set of columns in the following spreadsheets were submitted by the instructors including course grades, effort marks on a scale of 1-5 and scores on each problem on the uniform final for each student that passed their class. We then added columns on the right computing scores for each of the course outcomes and each of the major outcomes for each student. The formula used to compile these scores, the maximum score, the good score and the passing score for each outcome is given in the next few rows of that column. At the bottom of each column we indicate the percent of students failing to meet the outcome and the percent of students performing well on the outcome.
Section A : spreadsheet and instructor's questionnaire
Section B : spreadsheet and instructor's questionnaire
Section C : spreadsheet and instructor's questionnaire
The following spreadsheet combines the information regarding the percent of students performing well and the percent of students failing to meet each outcome. We also plan to include information from the instructors' questionnaires here:
Precalculus Analysis of Sections A, B & C: spreadsheet
Conclusions:
It should be immediately noted that student performance varied wildly from section to section on the Course Objectives. Clearly some instructors emphasized certain course objectives more than others. Course Objectives 2 & 5 need to be examined more closely. While the Section B instructor never submitted the questionnaire, it is clear from student performance in this subject that this instructor taught some outcomes so thoroughly that 100% of students passed those outcomes and then other outcomes must have been ignored as the percent of students performing well was very low.
Other instructors submitted their questionnaires. The one instructor who said his students had completed the official departmental project on the unit circle had 83% of students perform well on that topic (Outcome 5), while the other sections had fewer than that percentage of students even passing on that topic.
On the whole students performed well on the Major Objectives addressed in MAT172. On average, over half the students performed well on Major Objectives A, B & E and it is not surprising that on average only 40% performed well on Major Objective C on real life problems as applications are difficult. Student success in Major Objective C varied wildly from one section to another so this must be examined more deeply. On average fewer than 16% of students failed at each of these major objectives which is quite exceptional so the overall course design seems to be addressing the major objectives well.
The two sections whose instructors mentioned their students had completed the departmental projects on applications had higher performance from their students on major outcome C (50% and 73% performing well as opposed to 0% performing well with the other instructor).
The questionnaires revealed concerns by the instructors regarding the poor preparation of their students and the quantity of material covered in this class. However, they seemed less concerned about skipping topics essential to calculus. This may be a result of the fact that the instructors are adjuncts (high school teachers) and are not viewing precalculus as a preliminary course but rather as an advanced course. We may need to work harder to convince these adjuncts to follow the syllabus even if it leaves some students behind, and to assign all the difficult projects the department has designed to train students. Adjuncts are often concerned about student evaluations and will be "nice" allowing students to skip subjects on the departmental syllabus. Sadly, we don't have enough full time faculty to teach this class although in the past, when the syllabi and projects were first developed, we always ensured that 1-2 sections were taught by professors each semester.
It is a serious concern that in some sections 90% of students are failing to meet Course Outcome 2 (graphing) while in another section 70% are failing to meet Course Outcome 5 (unit circle trig). This sort of inconsistency makes it difficult for Calculus instructors to review for their students. Perhaps a uniform final is not enough to determine who passes the class. We may need to require that students pass separate subsections of the final. This is being proposed to the EPC.
Time: This was 7 hours data and spreadsheet formula entry by a faculty member plus 2 hours each of volunteer time by the adjunct instructors completing data entry and questionnaires. 2 hours were spent on analysis and conclusions by the assessment ambassador.