MS 050 Conceptual Approach Fall 1996: Follow-Up Report III
Where the alumni are now in their post-MS 050 mathematics program at the College of Micronesia-FSM.
17 Feb 98
Dana Lee Ling
Title III Math/Science Software Specialist College of Micronesia-FSM
This is the third report in a series of follow-up reports of 95 students who were in MS 050 PreAlgebra in the Fall of 1996 at the College of MicronesiaFSM. The first report found that the Conceptual Approach did not significantly affect the rate of success for students in MS 050 PreAlgebra. The second report found a strong positive impact on student success in the subsequent course, MS 098 Transition to Algebra. This third report finds that very few of the original group students who passed MS 050 and MS 098 were able to then pass MS 100 College Algebra. MS 100 is the second course after MS 050. Thirty-five of the original 95 students passed both MS 050 and MS 098 on the first attempt. Of thirty who then went on to take MS 100, only seven students passed on the first attempt. Only one student in fourteen of the original Fall 96 MS 050 students has successfully completed the first three math courses in the math sequence at the College. A mapping of students through the courses is provided in the report.
The experimental Conceptual Approach curriculum, which had such a positive impact on the success rate for students in MS 098, apparently had no impact two courses downstream. Fifteen Conceptual Approach alumni of the original 35 in the group entered MS 100 without repeating any prior course. Of these fifteen students only two students obtained an A, B, or C necessary for promotion to the next course.
The 60 extant curriculum students, essentially a control group, also had fifteen students enter MS 100 without repeating any prior course. Although the extant curriculum group was roughly twice as large as the experimental section, the course supplied an equal number of students into MS 100. Of the fifteen extant curriculum students only five passed MS 100. The numbers involved are too small to attach significance in the difference between the two who passed MS 100 from the Conceptual Approach and the five who passed from the Extant Curriculum.
Other findings include the confirmation that most students repeat a math course at least once during their time at the College, and the finding that students who promote themselves after failing the prerequisite course usually do not succeed in the subsequent course. Of note is that some students repeat the course that they have just passed. One student has taken and passed MS 050 three times. By the third time the student took the course the course had been renumbered MS 095. The student possibly mistook the higher number for a higher level of course. The charts further below were generated from data from the Office of Admissions and Records BETTYbase Microsoft Access database.
The charts use the following abbreviations:
The charts use the following abbreviations.
ms098: Developmental Mathematics.
ms098: Transition to Algebra.
ms100: College Algebra.
ms101: College Algebra and Trigonometry.
P : Promoted (A, B, or C)
R : Repeated (D, F, or W)
NFR : No further record. This does not necessarily mean the student has left school, although this is likely to be true for students who had no further record beyond MS 050 in the Fall of 1996.
Legend: 35: The number of students entering the course | P-ms050-R: The course | | 20 (0) 15:
Twenty students received an A, B, or C and were eligible for promotion. Fifteen students received a D, E, or F and were expected to repeat the course. Some students, for unknown reasons, passed a course and then opted to repeat the course. Although some students who have not earned promotion improperly opt to take the next higher course, not all cases that appear to be improper promotion are actually an improper promotion. The database does not have all the state campus grades in the database. If there is a number in parentheses, then that is the number of students currently in that course. Thus:
| 9 P-ms100-R 1 (7) 1 | |
Indicates that 9 people entered MS 100, 1 was promoted, 7 are currently in MS 100, and 1 will be repeating the course. Note that the diagram makes no reference to real time. In the above example the seven students are currently in the course, the other two students have taken the course in a prior term. None of the (7) students would include the 1 who needs to repeat the course, the 9 students are nine different students. The one who needs to repeat would be shown as entering MS 100 in the next tier down the chart. Not all branches were completely mapped. The chart is read as a flow chart from top to bottom.
Conceptual Approach students: 35 P-ms050 Conceptual Approach-R 20 15 | | ______________| ______|____________ 1 19 4 9 2 NFR P--ms098-----------R NFR P-ms050-R P-098-R 16 3 3 6* 2 | | | ___________| |____ |____________ 1 15 3 1 2 P-ms098-R P-ms100-R P-ms098-R P-ms098-R NFR 1 2 13 1 2 1 | | | | | __________| |______________| ___| |____ 1 1 5 9 2 1 NFR P-ms101-R NFR P-ms100-R P-ms098-R P-ms100-R 1 1 (7) 1 (1) 1 (1) | P-ms098-R (1) 6* ____________________| 1 1 4 P-ms050-R P-ms098-R NFR 1 1 Extant Curriculum students: 60 P-ms050 Extant Curriculum-R 40 20 ___________________|____________ ______|____________ 1 1 1 35 4 15 1 NFR P-ms050-R P-ms100-R P-ms098-R NFR P-ms050-R P-098-R 1 1 19 16 7 8 1 | | | | ____________| |________________________ 1 1 3 15 10 4 1 1 P-ms095 P-ms101 NFR P-ms100-R P-ms098-R NFR P-ms100 ms101 1 1 5 (1) 9 4* (2) 4 | | _________| |________ 3 2 2 7 NFR P-ms101-R NFR P-ms100-R (1) 1 (5) 2 | P-ms101-R (1) 4* |_______ 3 1 P-ms100-R NFR (2) 1
Any effect that the MS 050 Conceptual Approach had is difficult to document a year later in the second course downstream. The sample size is too small, however, to make any definitive conclusions at this time. More importantly, very few students proceed along the "intended" or hoped for path through math at the College. Of 95 students who entered MS 050 in the Fall of 1996, only seven would pass MS 050 and go on to pass MS 098 and MS 100 without repeating any of the three course. That is a "throughput" of 7%. The inverse is one in fourteen students succeeds in math at the College from MS 050 through to MS 100. By next summer I would anticipate that fewer than seven will have made it through the sequence without a single repeat.
Previously the commonly held belief in the math department was that half of all students pass a given math course. That rate was low enough to cause pursuit of a Title III Strengthening Institutions section for mathematics education at the College. The reality is a higher rate of actual decay over time: if half repeated each class then 48 should have entered MS 098, 24 should have entered MS 100, and 12 should have passed MS 100. The above charts show 60 entered MS 098, 35 entered MS 100, and 7 passed. Overall the decay rate exceeded 50% and the largest percentage loss occurred in MS 100.
Losses: MS 050 to MS 098: 35 of 95 lost: 37% MS 098 to MS 100: 25 of 60 lost: 42% MS 100 to MS 101: 28 of 35 lost: 80%
The course sequencing is not thought at this point to be a significant cause of the loss rates. The courses have been carefully redesigned and now progress sequentially at a steady pace through the material, as opposed to the leaps and gaps of the past. The students need more support and assistance in order to experience success in the math sequence. The department Chair has suggested increasing the contact hours per week in class as one approach as this has been shown to improve student success in math at the College. The hope is that this paper will stimulate further discussion and generate thought on new ideas and ways to bring mathematical comprehension to our students. Further comments on possible remedies are included at the end of the MS 098 report below.
Where the alumni are now in their post MS 098 mathematics program at the College of
18 Feb 98
Dana Lee Ling, Title III Math/Science Software Specialist
College of Micronesia-FSM
Students in all sections of MS 098 Transition to Algebra in the Spring of 1997 experienced difficulty in MS 100 College Algebra at the College of Micronesia-FSM. Due to the small sample sizes involved, the time lag between MS 098 and MS 100, and the number of variables, no statistically sound conclusions can be made as to whether one approach in MS 098 was more helpful to students in MS 100.
Attached further below are diagrams that depict what happened in subsequent math courses to students who were in MS 098 in the Spring of 1997. In the original study the students were in four groups. The text below describing the four groups comes from the original study report:
To assess the effectiveness of different computerassisted instructional approaches, 98 students in MS 098 Transition to Algebra at the College of MicronesiaFSM national campus were randomly assigned to one of four groups of students. The students in the study were all Micronesian. Micronesians are a Pacific island group of peoples. For all of the students in the class, English is a second language. The 98 students speak languages from one of four major language groups in Micronesia, Chuukese, Kosraen, Pohnpeian, and Yapese.
All four groups used the same textbook series in Houghton Mifflins Introductory Algebra series by Aufmann et al. The four groups were:
Group Long Name Description Software n Ctrl Control No computer use None 23 Opt Optional Optional Computer Use outside Algebra 30 of class. Tutor Int Internal Use of computers during class Algebra 21 time with optional use of Tutor computers outside of class Ext External Use of computers is assigned Algebra 24 and occurs primarily outside of Tutor and regular class time MathView
The Control group had no access to computers. The Control group was taught outside of the computer laboratory using a more traditional lecture based format. The Control group classroom, like all non-computer classrooms at the College, is not air-conditioned.
The Optional group had the option of coming to the computer laboratory outside of class to use drill and practice algebra software. Attendance during open laboratory times was purely voluntary. The instructor encouraged students to come to the laboratory to use the Algorithmic Algebra Tutor software. The class itself was held in the air-conditioned computer laboratory, thus the students were well aware of the existence of the laboratory and the computers.
The Internal group used the computers on a daily basis inside of class. The instructor allowed, with guidance, students to proceed at their own pace through the drill and practice Algorithmic Algebra Tutor software package. The Internal group also had available the option of coming to computer laboratory during open laboratory times.
The External group was exposed to both the Algorithmic Algebra Tutor and to MathView software. The External group was required to complete external assignments in the computer laboratory and the students were also allowed to come into the computer laboratory to use math software during open laboratory times.
Students who did not complete either the pre-test or the post-test were not included in the pre-test/post-test study statistics. These students were included in the computer use hours study.
The diagrams chart how many students were promoted or repeated and what courses they took next. See the report above on MS 050 for details on how to read the charts.
The MS 098 branches are only mapped to the next course, it is too soon to develop an accurate picture from a "deeper" map.
Control group: 28 P-ms098-R 18 10 __________________| |______________________ 1 3 14 5 2 3 P-ms101 NFR P-ms100-R P-ms098-R NFR ms100-R 1 1 (2) 11 2 (1) 2 3 Optional group: 49 P-ms098-R 19 30 __________________| |______________________ 1 2 16 17 12 1 P-ms095 NFR P-ms100-R P-ms098-R NFR ms100-R (1) 4 (2) 10 10 (1) 7 1 Internal group: 27 P-ms098-R 14 13 ___________________| |______________ 1 2 11 9 4 ms098-R NFR P-ms100-R P-ms098-R NFR 1 11 1 8 External group: 29 P-ms098-R 12 17 ___________| |_______________________________ 2 10 6 9 1 1 NFR P-ms100-R P-ms100-R NFR ms100-R ms101 3 7 3 3 1 (1)
Although no conclusion can be made statistically, there is also no evidence that external usage model that was adopted for MS 098 in the Summer of 1997 is harmful to the students. The external group put 12 of 29 (41%) into MS 100 and 30% (3 of 29 = 10%)of those made it through MS 100 on the first try. In rank order of throughput this is the highest throughout on a "first try" basis:
Throughput MS 100 External: 3/29 = 10% Optional: 4/49 = 08% Control: 1/28 = 03% Internal: 0/27 = 00%
The small success rates prevent significance from being attached (a change in success of one student would change the values significantly), but the argument can be made that the External approach did not harm the students in the group in their academic progress.
A separate study of MS 050 Fall 1996 alumni showed that only seven of ninety-five students passed MS 050, MS 098, and MS 100 on the first try. The greatest difficulty for students in attaining success is in MS 100.
The success of an experimental curriculum in MS 050 PreAlgebra referred to here as the Conceptual Approach was confirmation of the premise that the students know a lot of scattered and half-remembered factoids about mathematics. MS 050 and MS 098 have the rates of success that they enjoy because the students are rebuilding previously existing knowledge. MS 100 is the first course for many students that is not a review course. Many students have been able to brush up on rusty knowledge and survive MS 050 and MS 098 without a significant effort. MS 100 pushes the students to the College level for the first time.
The MS 050 and MS 098 courses use a Houghton Mifflin text, currently Aufmann's Introduction to Algebra with Basic Math 2nd Edition. The MS 100 text is Houghton Mifflin's Larson and Hostetler Algebra and Trigonometry 4th edition. The texts were chosen as they closely mirrored the course outlines. The course outlines had previously been worked on and revised to provide a better sequential flow of topics. There is no significant gap or leap in mathematical knowledge between courses.
MS 100 College Algebra is a standard College level algebra course. The course is used and accepted on transfer to other regional institutions. The solution is not to reduce the scope or sequence of MS 100 but to find combinations of techniques and student support services that will increase student success in MS 100.
The greatest impact on student success in mathematics to date has been contact hours. Increasing the contact hours to five hours a week has yielded dramatic improvements over three hours a week in studies done in 1996 - 1997 at the College.
Direct student support in the form of regular and intense academic counseling and assistance could be another potential avenue to explore. Class sizes, however, would have to come down from their present 25 to 30 student size to under 20 students per class in order to permit faculty time to work individually with students. This would in turn require more faculty members and more classroom space to handle the smaller but more numerous math sections.
Tuesday, June 06, 2000
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