MAT104 College Algebra 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.
The overwhelming majority of students in MAT104 are neither math majors nor intend to be math majors. However, this is the first 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.
MAT104 Course Outcomes [assessed using the problems in the brackets]:
1. Graph lines and parabolas [2, 7, 13]
2. Solve linear equations/inequalities in one variable [1, 2]
3. Factor, add, subtract, multiply and divide polynomials [3, 6, 8, 9, 10, 15]
4. Evaluate functions or expressions and apply the quadratic formula [7, 12, 13]
5. Manipulate formulas involving radicals, exponentials and logs [4, 5, 11]
6. Compute lengths and angles in triangles using trigonometric functions [14]
Math Major Outcomes incorporated into MAT104 [assessed using problems in the brackets]:
A. Perform numeric and symbolic computations [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]
B. Construct and apply symbolic and graphical representations of functions [2, 7, 11, 12, 13, 14]
C. Model real-life problems mathematically [5, 14]
Fall 2012 Assessment Plan and Report for MAT 104:
In the Fall 2012 we assessed MAT 104 using the same measures and techniques as in Spring 2010. That is, the course was assessed using a uniform departmental syllabus and a uniform final for all sections of MAT 104 in Fall 2012.
MAT104 data was collected in Fall 2012 and it was analyzed in Summer 2012. A spreadsheet with the data and analysis may be found here. There was exceptionally different performance by students in different sections however in all sections there was poorer performance in Course Outcome 4 which is essential to future classes. In two sections (which had low pass rates below 60%) the performance on Outcome 4 was below 50%. In other sections the performance on this outcome was below 60%. Course Outcome 1 failed to have good performance in
in three sections and this needs to be addressed. It appears students have very little practice graphing. On a positive note, the performance on some outcomes were over 75% this assessment year, and so we recorded this on our spreadsheet. Two of the sections had such very good performance on Outcomes 2,3,5, A and C. Most sections had very good performance on 5 and C. The students seem to have mastered their applications! This is very important as MAT104 is a prerequisite for many courses in the sciences, social sciences and business.
Spring 2010 Assessment Report for MAT 104:
A uniform departmental syllabus and a uniform final were used for all sections of MAT 104 in Spring 2010.
MAT104 data was collected in Spring 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 during the week of 9/22/2010-9/29/2010.
Observations before data analysis (9/20/2010): This uniform final does not actually explicitly require students to graph a line or a parabola on graph paper making it difficult to assess Course Objective 1 and Major Outcome A. Course Objective 2 is only assessed on 2 problems (although one may observe that students should have achieved this objective before entering MAT104 as this is tested on the placement exam). Course Objective 6 is tested only on one question which happens to be an applied question [14] and thus pure knowledge of triangles is not thoroughly tested. Major Outcome C is not adequately assessed as the only questions related to applied math involve advanced techniques (exponentials and trigonometry) and there are no applied problems related to linear techniques. In other words, assessment of Major Outcome C may be negatively affected by students having difficulty with advanced topics in the course and not the modeling of real-life problems.
The data is available as a spreadsheet (11/4/2010): This data comes from the seven sections whose instructors volunteered to contribute to the assessment process. Each instructor provided information as to how closely he or she followed the uniform syllabus. There were three different approaches reported: following the uniform syllabus closely, skipping a particular trigonometry lesson and skipping 3 lessons including the particular trig lesson. Each section submitted the total number of students taking the final exam and the number of students who completed each problem perfectly on the uniform final exam. The percentage of students scoring each problem correctly from each section and from each of the three approaches to the courses was recorded. Course and Major outcomes were also assessed with a percentage of students scoring problems related to that outcome correctly for each section and for each of the three approaches. 60% was viewed as acceptable (considering the scores had to be perfect) and below 50% was viewed as unacceptable. Standard deviations for each problem and each course and major outcome were found for the three approaches to the course. Every problem and outcome was commented upon in the grid.
Preliminary observations as related to the data (significantly more detailed observations are on the chart):
I. In the future instructors should be asked how many students taking the final completed homework and how many attended the freely available tutoring. If more than 50% of students are engaged in these activities then one can start expecting a higher percentage of students to score each problem correctly. Note that the one approach to teaching which skipped three lessons and provided additional in class review led to high percentages of students completing problems 1, 5, 6, 8 and 12 correctly on the uniform final. However the skipped lessons did not significantly improve any of the course outcomes and lead to very low performance on Course Objective 6. If students can be encouraged to attend the free review sessions and tutoring, lessons need not be skipped in class and the entire course may be completed.
II. The trigonometry lessons skipped by many of the instructors were lessons near the end of the course. Perhaps by reordering the course, placing lessons essential to the outcomes earlier in the semester, less instructors will end up skipping lessons crucial to Course Objective 6. As mentioned before data analysis, it is essential to
test this outcome with more than one question: there should be a question on pure trigonometry and a separate question on trigonometry with an application. With two
questions on this important topic (which is a prerequisite to precalculus and to physics), more instructors may emphasize this topic.
III. As mentioned before data analysis the final exam does not adequately assess Major Outcome C. Students should have an exponential problem and or a linear problem written in an applied manner. Students performed reasonably well on this outcome as it is currently assessed.
IV. There was significant variation between instructors and in the performance of students with the same instructor in different sections. Students may place into MAT104 in a variety of ways and some students may be new to the university. The uniform syllabus is meant as a guide to keep the instructors on track and push the students to keep up with a college level course. Instructors observed that evening students have less time for homework and that Freshman are less likely to acknowledge that they are having difficulty with the course until it is too late.
The Educational Policy Committee of the Department of Mathematics and Computer Science will be given a copy of this report and will determine the best way to act upon this information in Spring 2011.
Time: This report took 8 hours of data entry and analysis plus 1 hour each for each of 6 adjunct volunteers,