A Study of Math 811 Outcomes Draft 6/23/98

A Study of Math 811 Outcomes, 1995-97

Bob Hasson
Department of Mathematics
College of San Mateo

Contents

1  Introduction
2  How many units did Math 811 students earn?
    2.1  The outcomes by term
    2.2  The cumulative outcomes over the study period
    2.3  The data tables
3  How many semesters did students enroll?
    3.1  Discussion
    3.2  Is there leakage?
    3.3  The data tables
4  What is a reasonable criterion for success in Math 811?
5  How many Math 811 students were successful?
6  How many Math 811 students went on to take Beginning Algebra?
    6.1  Discussion
    6.2  The data tables

1  Introduction

Math 811 came into being as a self-paced, self-study course in Arithmetic and Pre-Algebra in 1981. Seventeen years have passed. The purpose of this paper is to document and analyse the recent student outcomes in Math 811 to the extent that such an analysis can be done using the records in the district's data base.

The enrollment of Math 811 is open entry, which means students may enroll in the course at any time during the semester. Students study pretty much on their own, but help is available on request from both the teacher of record and from Math Lab personnel (especially Carol O'Connor). Students may earn anywhere from 0 to 4 units spread over as many semesters as they wish. Completion of 3 units is considered to be completion of the course. the fourth unit is considered to be extra enrichment work.

The questions to be answered in this document are the following:

  1. How many units did Math 811 students earn?
  2. How many semesters did they enroll in doing it?
  3. What is a reasonable criterion for ``success'' in Math 811?
  4. How many Math 811 students were successful?
  5. How many Math 811 students went on to take Beginning Algebra?
  6. How well did Math 811 students do in Beginning algebra?

The information that is the basis of this study covers the following academic terms: Fall 95, Spring 96, Summer 96, Fall 96, Spring 97, Summer 97, and Fall 97.

I should note that the only source of information for this study is the district's data base. This study is prone to the shortcomings of any observational quantitative study in that it shows outcome patterns but does not in itself explain the causal mechanisms involved. However, the patterns revealed may be suggestive. The prudent researcher will seek to corroborate the conclusions reached here using other sources of information. In particular it would be useful to interview a number of Math 811 students to establish their reasons for entry or exit from the course, their attitudes and reactions to the course, and their study patterns.

2  How many units did Math 811 students earn?

I answer this question in two ways. First I look at the outcomes for the 7 disjoint terms in the study. Then I look at the cumulative unit totals over the 7 terms of the study.

2.1  The outcomes by term

Tables 1 through 7 (see section 2.3) break down the number of units earned by students in each of the terms of the study. Things to notice are:

  1. The preponderant outcome in sections during the regular academic year was 0 units earned . The percentage of students who earned zero units varied from term to term between 55.7% and 72.1%. Conversely the percentage of students who earned at least one unit varied between 27.9% and 44.3%. See Tables 1 through 7.

  2. Those students who enroll in Math 811 during the Summer seemed to do much better. (But the totals involved are much smaller.) For the two summers observed the percentages earning 0 units were 40.6% and 27.3%. The percentages of students earning at leat 1 unit were 59.4% and 72.7%. See Tables 1 through 7.

  3. The percentage of students who earned 3 units (all in the same academic term) varied between 8.4% and 15%. It didn't matter much whether the term is Summer or not. See Tables 1 through 7.

  4. The Spring enrollment was significantly smaller than the Fall enrollment. The Summer enrollment was quite small - only one section. See Tables 1 through 7.

2.2  The cumulative outcomes over the study period

The total of number of units earned over the course of the study by each student was calculated.

Things to notice are:

  1. Most students who enrolled in Math 811 during the study period earned no units at all. This percentage was 57%. See Table 8.
  2. The percentage of students who ``finished the course'', that is earned 3 units, was 18.4%.

2.3  The data tables

Table 1: Fall 95
Units 0 1 2 3
n 182 44 27 41 294
% 61.9 15.0 9.2 14.0 100

Table 2: Spring 96
Units 0 1 2 3
n 108 28 29 29 194
% 55.7 14.4 15.0 15.0 100

Table 3: Summer 96
Units 0 1 2 3
n 13 13 4 2 32
% 40.6 40.6 12.5 6.3 100

Table 4: Fall 96
Units 0 1 2 3
n 138 33 31 28 230
% 60 14.4 13.5 12.2 100

Table 5: Spring 97
Units 0 1 2 3
n 102 30 19 14 165
% 61.8 18.2 11.5 8.5 100

Table 6: Summer 97
Units 0 1 2 3
n 9 14 6 4 33
% 27.3 42.4 18.2 12.1 100

Table 7: Fall 97
Units 0 1 2 3
n 163 33 11 19 226
% 72.1 14.6 4.9 8.4 100

Table 8: Cumulative units earned
Eventual
Units 0 1 2 3 4
n 525 118 110 170 3 926
% 56.7 12.7 11.9 18.4 0.3 100

3  How many semesters did students enroll?

3.1  Discussion

This question seems to be best explored by cross tabulating by eventual units earned and the number of semesters needed to earn them. The resulting data tables may be found in section 3.3.

Things to note are:

  1. With the exception of those students who earned 4 units, the distribution of the number of semesters enrolled was not strikingly different among the 0 units, 1 units, 2 units, and 3 units groups. See Table 10.
  2. In all groups (except the very small group of students who earned 4 units) the great majority of students enrolled for only one semester. See Table 10.
  3. 47.4% of all the students who enrolled during the period of the study earned no units at all and were gone after one semester. No other combination of units earned and number of semesters remotely approaches this percentage. See Table 10.

3.2  Is there leakage?

First a discussion of the leakage problem is needed.

In the first semester of the study (Fall 95), it is unknown how many students were continuing from previous semesters, and therefore there is some uncertainty about how many units students eventually earned. Similarly, in the last semester of the study (Fall 97), it is unknown how many students continued in semesters following. Again there is some uncertainty about how many units these students eventually earned. One could say that the ultimate results for these students have ``leaked'' beyond the bounds of the study.

To check the problem of leakage before the initial semester of the study (Fall 95), I took the students of the last semester of the study (Fall 97) and counted how many units they earned in Math 811 before that last semester. This should give some indication of the extent of the leakage before the initial semester.

Table 12 tabulates units earned in Fall 97 against units earned before Fall 97 (through the first semester of the study). Table 13 shows the corresponding row percentages. One can see that few of the students (9.7%) who enrolled in Fall 97 earned any units at all before Fall 97.

Table 14 tabulates units earned in Fall 95 against units earned after Fall 95 (through the last semester of the study). Table 15 shows the corresponding row percentages. Here the percentage of students who earned units after Fall 95 is 13.6%, again not a high percentage.

I conclude that the leakage problem exists but is minimal. The previous figures on eventual units earned should perhaps be a bit higher, but certainly not much higher.

3.3  The data tables

Table 9: Eventual units by Semesters, raw numbers
Eventual Semesters
units 1 2 3 4
0 442 69 14 0 525
1 86 25 6 1 118
2 73 22 11 4 110
3 133 25 10 2 170
4 0 2 1 0 3
734 143 42 7 926

Table 10: Eventual units by Semesters, row percentages
Eventual Semesters
units 1 2 3 4
0 84.2 13.1 2.7 0 100%
1 72.9 21.2 5.1 0.9 100%
2 66.4 20.0 10.0 3.6 100%
3 78.2 14.7 5.9 1.2 100%
4 0 67.7 33.3 0 100%

Table 11: Eventual units by Semesters, percent of the total
Eventual Semesters
units 1 2 3 4
0 47.4 7.5 1.5 0 56.7
1 9.3 2.7 0.6 0.1 12.7
2 7.9 2.4 1.2 0.4 12.9
3 14.4 2.7 1.1 0.2 18.4
4 0 0.2 0.1 0 0.3
73.3 15.5 4.5 0.6 100%

Table 12: Units earned by Fall 97 students before Fall 97
Units earned
Units earned before Fall 97
Fall 97 0 1 2
0 149 7 7 163
1 26 4 3 33
2 10 1 0 11
3 19 0 0 19
204 12 10 226

Table 13: Units earned by Fall 97 students before Fall 97,
row percents
Units earned
Units earned before Fall 97
Fall 97 0 1 2
0 91.4 4.3 4.3 100
1 78.8 12.1 9.1 100
2 90.9 9.1 0 100
3 100 0 0 100
90.3 5.3 4.4 100

Table 14: Units earned by Fall 95 students after Fall 95
Units earned
Units earned after Fall 95
Fall 95 0 1 2 3
0 158 10 9 5 182
1 32 8 3 1 44
2 23 4 0 0 27
3 41 0 0 0 41
254 22 12 6 294

Table 15: Units earned by Fall 95 students after Fall 95,
row percents
Units earned
Units earned after Fall 95
Fall 95 0 1 2 3
0 86.8 5.5 4.9 2.7 100
1 72.7 18.2 6.8 2.3 100
2 85.2 14.8 0 0 100
3 100 0 0 0 100
86.4 7.5 4.1 2.0 100

4  What is a reasonable criterion for success in Math 811?

There is no absolute answer to this question. So I will instead present two possible views,

  1. One can think of Math 811 as a 3-unit course in Arithmetic/Pre-Algebra. In this case, 3 units signifies completion of the course and certification of readiness for Beginning Algebra, while less than than 3 units does not.

  2. One might argue that, for students with very low levels of basic skills, even earning a total of one unit may be considered a success. Also, It appears that at least some students drop out of Math 811 because they have decided they are already prepared for Algebra. (Few of these succeed in Algebra, however.)

For the purposes of this study I will take the first view while recognizing that others may take the second view.

5  How many Math 811 students were successful?

Here I define success as earning 3 units in Math 811. Referring back to Table 8 one can see that the percentage of students who earned 3 or 4 units was 18.7%.

Because of leakage this figure should be revised upwards a bit, but not very much. So by the stated criterion, fewer than one fifth of students are successful.

6  How many Math 811 students went on to take Beginning Algebra?

6.1  Discussion

Tables 16 and 17 track Math 811 students in Math 111 and Math 110.

Things to notice are:

  1. 16.1% of the 926 students in this study attempted Beginning Algebra. 11.1% of all students attempted Math 111 while 5.0% attempted Math 110. See Tables 16, 17, and 18.

  2. 8.1% of the 926 students in this study attempted Beginning Algebra and succeeded (grade of A, B, or C).

  3. Among the students who earned 3 or 4 units in Math 811, 46.8% attempted Beginning Algebra and succeeded.

  4. 30 students earned less than 3 units in Math 811 yet still succeeded in Beginning Algebra.

6.2  The data tables

Table 16: Math 811 units earned by Math 111 grade
Math 111 grade
Math 811 Units A B C D F W
0 0 0 3 0 2 11 16
1 0 2 5 0 0 7 14
2 2 3 8 0 2 8 23
3 12 10 12 0 2 17 53
14 15 28 0 6 43 106

Table 17: Math 811 units earned by Math 110 grade
Math 110 grade
Math 811 Units A B C D F W
0 0 1 3 0 1 4 9
1 1 0 0 0 0 1 2
2 1 0 1 0 0 2 4
3 2 4 7 0 3 11 27
4 0 0 0 0 0 1 1
4 5 11 0 4 19 43

Table 18: Math 811 units earned by
Beginning Algebra success
% attempting and
Math 811 units % attempting succeeding at
earned n Beginning Algebra Beginning Algebra
0 or 1 643 6.4 2.3
2 110 24.6 13.6
3 or 4 173 46.8 27.2
All students 926 16.1 8.3

File translated from TEX by TTH, version 2.25.
On 16 Mar 2000, 18:39.