Trinity Washington University
Math 101 and Math 101s Summary Report: Fall 2009 Semester
[Revised with added longitudinal data, June 2010]
J. Sheridan (M.Ed.)
M. Whitty (M.A.T.)
Trinity Washington University
June 19, 2010 [Amended Version]
Introduction
The Fall 2009 semester brought several changes to the administration of Trinity’s developmental mathematics courses [Table 1]. Class sizes were decreased, eBooks were adopted, and a new math specialist was hired. Also, while meaningful post-testing of the developmental math cohort did not exist in previous years, post-tests were successfully administered to 55% of students still attending class at the end of the semester. These scores enabled us to refine the math placement benchmarks used in the College of Arts and Science.
Table 1: Comparison of Fall Math 101/101s Administration 2008 – 2009
| | Fall 2008 | Fall 2009 |
|Instructors |Whitty, Gibbons, Luse | Whitty, Sheridan |
|Cohort size | 161 | 176 |
|Number of sections | 7 | 9 |
|Avg. class size | 23 | 20 |
|Teaching platform |Introductory Algebra by |Introductory Algebra by |
| |Lial/Hornsby/McGinnis, hardcopy |Lial/Hornsby/McGinnis, eBook + |
| |textbook only |MyMathLab |
|% of cohort post-tested | 28% | 55% |
In August of 2009, Joe Sheridan was hired to replace Ariel Gibbons as math specialist. Joe brought with him extensive experience with MyMathLab, the online instruction and resource delivery system purchased during the Spring 2008 semester. MyMathLab, a product developed by Pearson Education, is advertised as a tool that will increase retention rates, improve pass rates, reduce resource demands, and lower student costs. Its core qualities of flexibility, time-efficiency, security, instant feedback, and accountability are especially well suited for underserved populations.
Despite the changes to the administration of Trinity’s developmental math curriculum, student retention and success rates dropped [Table 2]. Possible reasons for this include: 1) Consistent standards for instruction and assessment were put in place, thus improving the validity of student grades; 2) At-risk students were advised proactively this semester through a more formalized early alert system. This resulted in a greater number of students withdrawing from courses than in previous years. [Appendix A: Longitudinal Data 2008-09]
Of the 41 students who withdrew from Math 101 this semester, 38 had failing grades due to low attendance. Class attendance continued to be our greatest challenge. The use of cell phones during class continues to be a concern as well. We plan to address these challenges through stricter attendance and cell phone policies in the future.
While an overall success rate of 51% does not sound good, it should be remembered what this is a measure of; 51% of the students who were enrolled in Math 101 at the beginning of the semester succeeded in the course and were able to move on to their next math course. More promising statistics related to this cohort include the success rate of students who stayed in the course through the final exam (77% passed with a C- or higher) and post-test improvement by all students who passed the course (average score improvement was +57%).
Table 2: Comparison of Fall Semester Math 101/101s Outcomes 2008 – 2009
|Student Outcomes |Fall 2008 |Fall 2009 |
|Overall success rate |65% |51% |
|Success rate among students still enrolled in course at end of semester (all A,| | |
|B, C and F’s) |73% |67% |
|Success rate among students who took the final exam |unknown |77% |
|Completion rate (took the final exam) |unknown |66% |
| | | |
|Withdraw/abandon/fail rate |35% |49% |
|Withdraw/abandon rate |unknown |34% |
|Withdraw rate |11% |23% |
| | | |
|Average Accuplacer score improvement |unknown |57% |
Characterizing our Entrants
The number of students in the Math 101/101s cohort increased by 9% from 2008 to 2009. Two additional sections of Math 101s were added to the fall course schedule in an attempt to reduce class sizes at the developmental level. Our goal was to cap the development courses at 18 students instead of 25. The nine sections filled quickly, resulting in an average class size of 20, which was still an improvement over the average class size of 23 the prior year. The two math specialists were each assigned four sections of Math 101 for the semester. Martha taught the ninth section as an overload.
Accuplacer pre-test scores were easily obtained for 116 of the new students who were placed into the eight sections of Math 101s in the fall of 2009. The average arithmetic placement score for these 116 students is 32.6. The average elementary algebra placement score for these students is 30. The average scores for new students in the fall of 2008 were similar [Table 3].
Table 3: Average Pre-test Scores for Incoming Freshmen, Fall 2008 and Fall 2009
| Average Accuplacer Score (20 – 120 point scale) | Fall 2008 | Fall 2009 |
| Arithmetic pre-test score | 34.2 | 32.6 |
| Elementary algebra pre-test score | 32.4 | 30.0 |
The lowest possible score on either of these tests is 20 and the highest possible score on either test is 120. Therefore, a score of 30 on the elementary algebra test means only 10% of the elementary algebra questions were answered correctly. And, a score of 32 means that the average Math 101s student was able to answer only 12% of the arithmetic questions correctly [Chart 1].
Chart 1: Average Placement Scores for First-Year Students Placed in
Math 101S for the Fall 2009 Semester (N = 116 students)
[pic]
Content/Pedagogy
Practice and repetition are important in any skills-based course. In past semesters, practice problems were assigned out of a textbook to do outside of class as homework. Answers to odd-numbered problems were available in the back of the book. If a student had trouble with a problem, they had to wait until the next class to get help. This semester, with the introduction of MyMathLab, students were able to do the homework problems online and receive immediate feedback regarding their solutions. When a correct answer is submitted in MyMathLab, students receive an immediate response such as Fantastic! or Outstanding! If an incorrect answer is submitted, MyMathLab gives a hint as to where the mistake lies. The student has two more chances to solve the problem and still receive credit for a correct answer. After three unsuccessful tries, the student is shown the correct answer and given a similar problem to try. The process then starts again, with three more attempts accompanied by helpful hints. We chose not to set time limits on homework assignments to encourage students to spend extra time trying, and retrying, homework problems until they got them right.
Another advantage of MyMathLab is that it provides a rich set of support utilities for each homework problem. On the side of each homework screen are tabs labeled Help Me Solve This, View an Example, Textbook, Video, Animation, and Ask My Instructor. When a student clicks on Video, they are shown a video of an instructor teaching the concept on a blackboard. When they click on Textbook, they are taken to the page of the textbook where the concept is covered. When they click on Ask My Instructor, an email window pops up which is pre-addressed to the instructor and references the homework problem in question.
MyMathLab provides students with the tools they need to assess their progress outside of class. This, in turn, empowers them to take charge of their own learning. Students at all levels can benefit from the immediate feedback that MyMathLab provides.
Outcomes: Grades
A total of 176 students entered either Math 101 or Math 101s at the beginning of the semester. 153 students were enrolled in eight sections of Math 101 with supplementary instruction (Math 101s) and 23 were enrolled in one section of Math 101 without supplementary instruction (Math 101). Math 101 without lab is a hangover from previous years when the lab and lecture portions of Math 101 were separate entities. In previous years, students got separate grades for their labs and their lectures and it occasionally happened that students would pass their 1-credit lab, yet fail their 3-credit lecture. Unfortunately, this led to the most-at-risk students repeating the Math 101 lecture without the benefit of supplementary instruction. In other words, the students who most needed an extra hour of instruction and practice, were excused from such sessions. As a result, this cohort suffered, as evidenced by the higher withdraw and fail rates [Table 4].
Table 4: Withdraw and Fail Rates for Math 101 and Math 101s During the Fall 2009 Semester
| |Math 101s (N = 153) |Math 101 (N = 23) |
|Withdraw rate (just W’s) | 21% | 39% |
|Fail rate (includes all F’s and W’s) | 48% | 57% |
It is for this reason the math specialists are recommending Math 101 be dropped from the curriculum in CAS. All students who place into developmental mathematics at Trinity should be required to attend the supplementary instruction sessions offered by Math 101s.
The distribution of grades for the entire Math 101/101s cohort is shown in Chart 2 below. During the Fall 2009 semester, the lowest passing grade for Math 101/101s was set at 68%, which is a C-. Any score below this constitutes failure. The grade of D is not given since Math 101 and Math 101s are skills-based courses that require mastery for success. Students must truly understand and be able to apply the concepts taught in Math 101 before they can move on to the next course in their mathematics sequence. [See Appendix B for more detailed grade distribution data.]
[pic]
*The nomenclature F(A) represents students who failed the course by abandonment.
These are students who remained enrolled in the course but did not take the final exam.
Outcomes: Post-test Results
Accuplacer post-tests were administered to 86 students on Friday, December 4th. In the weeks prior to the test, it was explained to students that participation in the post-testing process was not required and would have no bearing on semester grades. The average arithmetic score for the 86 students who took the post-test was 53.4. The average score on the elementary algebra portion of the test for the same students was 47.6. This accounts for a 35.5% improvement on the arithmetic test and a 53.5% improvement on the elementary algebra test [Table 5].
Table 5: Average Scores for Math 101/101s Students Who Took Both the Pre- and Post-Assessments on Accuplacer in the Fall 2009 semester (N = 86 students)
| | Pre-test score | Post-test score | Change |
|Arithmetic Test | 39.4 | 53.4 | + 35.5 % |
|Elem. Algebra Test | 31.0 | 47.6 | + 53.5 % |
When the scores of students who failed Math 101 are removed from the post-testing cohort, 64 students remain who both passed the course and took the post-test. The arithmetic average increases to 56.6 and the elementary algebra average increases to 49.9, a 56.8% and a 57.4% improvement, respectively [Table 6].
Table 6: Average Scores for Math 101/101s Students Who Took the Accuplacer
Post-assessment and Passed the Course (N = 64 students)
| | Pre-test score | Post-test score | Change |
|Arithmetic Test | 36.1 | 56.6 | + 56.8 % |
|Elem. Algebra Test | 31.7 | 49.9 | + 57.4 % |
Charts 3A and 3B show the average pre- and post-test scores of Math 101 students according to their final grade in the course. Part 3A shows the scores on the Arithmetic portion of the test and Part 3B shows the scores on the Elementary Algebra portion. As would be expected, the better a student did in the course, the higher their post-test score tended to be. Interestingly, there was no appreciable difference in pre-test averages among the different grading cohorts. In other words, small differences in scores at such low placement levels are not good indicators of success in a skills-based course such as Math 101. [See Appendix C for more information on the math placement cut scores used in the College of Arts at Science at Trinity.
Chart 3A: Pre- and Post-test Scores on Accuplacer Arithmetic Test
for Each Grade Category in Math 101/101s [N = 64]
Chart 3B: Pre- and Post-test Scores on Accuplacer Elementary Algebra Test
for Each Grade Category in Math 101/101s [N = 64]
Factors that Affect Outcomes: Attendance and Homework
The attendance policies for Math 101 and Math 101s are clearly stated in the course syllabi. In a skills-based course such as Math 101, missing class can seriously affect the student’s ability to master the material. In order to move students from their current math aptitude levels to the levels required for Math 109 (Foundations of Mathematics), or Math 102 (Intermediate Algebra), the instructors have to move from topic to topic at a fairly rapid pace. Only by doing so, can students reach the required level of understanding for the next math course. Students who miss class without finding out what was covered, or without attempting the assigned homework, are invariably frustrated by their inability to understand the topic being covered on their return to class. Only very motivated students who seek extra help (via office hours, tutoring or computer help) are able to miss class and pass the course [Table 7].
Table 7: Attendance in Math 101s: (N = 87 students)
|Attendance |Number of students |Number passed |Pass rate |
|0 – 5 absences |43 |31 |72% |
|6 – 10 absences |24 |11 |46% |
|> 10 absences |20 | 5 |25% |
| Total |87 |47 |54% |
Homework is also an important component of learning in Math 101. Student success typically increases as students do more math problems on their own. Through the problem sets assigned each day, students are finally able to use the concepts taught in class and make them a part of their intuition. Therefore, homework completion rates have a direct positive correlation with pass rates in Math 101, as would be expected [Chart 4].
Chart 4: Homework Completion Rates vs. Pass Rates for All Math 101/101s Students Who
Received Grades Other Than W in Fall 2009 (N = 135)
[pic]
Conclusions/Recommendations
1.) Now that Math 101s is a 4-credit course which includes a 1-credit supplementary instruction session, we see no need to continue a Math 101 course that does not include supplementary instruction. All students who place into Math 101 can benefit from supplementary instruction.
2.) While the Accuplacer cut scores established in 2008 served well as a first approximation, we have now adjusted them to better serve our student population. The Arithmetic cut score is being lowered from 70 to 60, and the Elementary Algebra cut score is being raised from 40 to 50. [Appendix C: Establishment and Adjustment of Cut Scores]
3.) To help underprepared students prepare for Math 101 at Trinity, a summer workshop could be offered. Many community colleges offer this option to help motivated students move through the developmental curriculum more quickly. The workshops normally consist of approximately 20 hours of intensive pre-algebra or arithmetic review and are scheduled shortly before the semester begins. After taking the workshop, students are given the opportunity to retake the placement test, possibly enabling them to place into a higher-level math course.
4.) Since absenteeism affects underprepared students so adversely, we recommend more stringent and more consistently enforced attendance policies in all developmental courses.
5.) Since Accuplacer benchmarks occasionally need to be adjusted to better serve our students, we oppose the posting of benchmarks in course catalog descriptions (see below).
MATH 101 - Introductory Algebra / Lecture / 1
Provides students with an intensive review of high school algebra. Topics include a review of basic arithmetic operations, the real number system, algebraic expression and exponents with basic rules of algebra, linear equations and inequalities with applications, and graphs of equations and inequalities. Recommended for students who need a review of high school algebra before fulfilling the general education or Core math requirement. Formerly MAT 103A Intermediate Algebra. This course may not be taken as pass/fail by students in the School of Professional Studies, and CAS students must earn a C or higher in order to pass the course. A weekly laboratory meeting supplements instruction for this course. 3 credits. Prerequisite: School of Professional Studies: Grade of C or higher in MATH 100 OR score of 110 or higher in Arithmetic portion, but 108 or lower in Elementary Algebra portion of Accuplacer test.
Appendix A: Longitudinal Data – Fall 2008 vs. Fall 2009
Chart 5 shows a comparison of student grades in Math 101/101s for the Fall 2008 and Fall 2009 semesters. The instructors for the Fall 2008 semester were Whitty (3 sections), Gibbons (3 sections), and Luse (1 section). Instructors for the Fall 2009 semester were Whitty (5 sections) and Sheridan (4 sections).
[pic]
The biggest outcome difference between the two cohorts is the 128% increase in the number of students who withdrew from the course (from 18 withdrawals in 2008 to 41 withdrawals in 2009). One factor that contributed to this increase was the concerted effort made by the Dean’s Office to advise at-risk students before the withdraw deadline. This effort was more organized than in previous years, with students and their advisors acting more quickly and consistently on teacher recommendations.
Appendix B: Grade Distribution Data
The largest class had 24 students and the smallest class had 15 students. Pass rates in the classes range from a low of 31.8% to a high of 72% [Table IV]. The final grade counts and pass rates per teacher were similar [Table V].
Table IV: Math 101/Math 101s Grades by Section, Fall 2009 (N = 176)
| |Math101s(5) |Math101s(6) |Math101s(7) |Math101s(8) |Math101s(LC) |
|A’s |2 |3 |1 |2 |2 |
|B's |5 |1 |3 |2 |6 |
|C's |3 |2 |4 |6 |5 |
|F's |1 |4 |2 |2 |4 |
|F's (A) |2 |1 |2 |3 |0 |
|W's |6 |5 |3 |4 |1 |
|Total |19 |16 |15 |19 |18 |
|Pass% |0.526 |0.375 |0.533 |0.526 |0.72 |
| | | | | | |
| | | | | | |
| |Math101s(1) |Math101s(2) |Math101s(3) |Math101(1) | |
|A's |3 |1 |2 |2 | |
|B's |1 |4 |9 |7 | |
|C's |3 |7 |3 |1 | |
|F's |7 |3 |2 |2 | |
|F's (A) |2 |5 |1 |2 | |
|W's |6 |4 |3 |9 | |
|Total |22 |24 |20 |23 | |
|Pass% |0.318 |0.5 |0.7 |0.435 | |
* F (A) = failure by abandonment
| |Whitty |Sheridan |
|A's |10 |8 |
|B's |17 |21 |
|C's |20 |14 |
|F's |13 |14 |
|F's (A) |8 |10 |
|W's |19 |22 |
|Total |87 |89 |
|Pass% |54% |48% |
Table V: Math 101/101s Grades
by Teacher - Fall 2009
(N = 176)
Appendix C: Establishment and Adjustment of Cut Scores
The College of Arts and Science first began using Accuplacer for pre-assessment of incoming students in the spring of 2008. The tests are administered online through a platform called Accuplacer, which is administered by The College Board. Unfortunately, the Accuplacer tests do not come with prescribed or suggested cut scores (benchmarks) since mathematics course titles differ from one institution to another, even when the course content is the same.
For example, Basic Mathematics at UDC is called Arithmetic at Northern Virginia Community College; Introductory Algebra at Trinity is called Elementary Algebra at Montgomery College, and Foundations of Mathematics at Trinity is called Survey of Mathematics at Prince George’s Community College. Because of this lack of guidance from The College Board, the testing coordinator (Laura Irwin) asked the math specialist (Martha Whitty) to analyze the three tests available on Accuplacer and determine how best to use them at Trinity for placement into remedial vs. college-level mathematics courses. The mathematics content on each test is summarized in Table I.
Table I: Summary of Content on Accuplacer Math Tests
| Test name | Topics covered | No. of questions |Min score |Max score |
|Arithmetic |Whole numbers and fractions | ≈ 6 | | |
| |Decimals and percents | ≈ 6 | 20 | 120 |
| |Problem solving | ≈ 5 | | |
| | | | | |
|Elementary Algebra |Signed numbers and rationals | ≈ 2 | | |
| |Algebraic expressions | ≈ 6 | 20 | 120 |
| |Equations and inequalities | ≈ 4 | | |
| | | | | |
|College-level Math |Algebraic operations | 4 | | |
| |Equations and inequalities | 3 | | |
| |Coordinate geometry | 3 | 20 | 120 |
| |Functions | 4 | | |
| |Trigonometry | 4 | | |
| |Applications | 2 | | |
The method used to establish the first cut scores was to take the test repeatedly, assuming different student skill levels. It was determined that a combination of two tests would be necessary to accurately categorize students for math placement into remedial vs. entry-level college mathematics. The Arithmetic test would be given first, immediately followed by the Elementary Algebra test. The cut scores established in Spring 2008 are summarized in Table II.
Table II: Math 101s, Math 101, and Math 109 Accuplacer Cut Scores
(Set by M. Whitty in April 2008)
| Course Placement | Combined Scores |
| Math 101s | 69 or lower on Arithmetic AND ≤ 40 on Algebra |
| Math 101 | 70 or higher on Arithmetic AND ≤ 40 on Algebra |
| Math 109 | 70 or higher on Arithmetic AND > 40 on Algebra |
At the completion of the Fall 2009 semester, the existing cut scores were reexamined for validity. All freshman Accuplacer scores were analyzed, even those of students who placed into higher-level math courses. The pre- and post-assessment scores, combined with semester outcomes in all entry-level math courses, indicated an adjustment was necessary. After examining possible scenarios, the following adjustments were agreed upon: the arithmetic benchmark would be lowered from 70 to 60, and the elementary algebra benchmark would be raised from 40 to 50. This meant that any student who scored below a 60 on the arithmetic test AND below a 50 on the algebra test would place into Math 101s. Any student who scored a 60 or above on the arithmetic test AND a 50 or above on the algebra test would place directly into Math 109.
If these adjusted cut scores had been in place for the Fall 2009 semester, the overall effect on class sizes would have been minimal. 13 extra students would have been added to the Math 101 cohort, increasing the cohort size to 189. This is still a manageable size when distributed across nine sections [Table III].
Table III: Estimated Effect of Adjusting Math Benchmarks for Math 101s and Math 109
| |Number of students who placed into |Number of students who would place into|
| |course under current benchmarks |course under new benchmarks (60/50) |
| |(70/40) | |
|Math 101 Placement, Fall 09 | 176 | 189 |
|Math 109 Placement, Fall 09 | 28 | 41 |
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