A total of 214 students initially qualified by using the software for ten hours or more -- 35 third graders, 35 fourth graders, 75 fifth graders, and 69 sixth graders. No special data or time logs were required of the teachers. However, at the end of the study they provided the following data for each student: name, id number, starting date, estimated number of times used per week, estimated minutes of use per time. From this information it was possible to create the estimated number of minutes used for each student. Three students who used the software for 9 hours and 45 minutes were included in the test group. One of these also qualified as a home user.

Students were allowed to take the software home for installation on their home computers. Seven of them took it home and never or rarely used it. However, fifteen students used the software for 5 hours or more, the standard we established for the home use group. With data on only 15 students presently available no attempt was made to see if home use improved final performance. We intend to combine the home use group from the current algebra study with these 15 and perform the statistical analysis then.

Methodology

Data on the test subjects were provided in the following proportions: School A (Elementary) - 29 students , School C (Middle) - 69 students, and School B (Elementary) - 116. They were a diverse group of schools. School A - Elementary is a small school located in an industrial blue collar area near the airport. It probably has the least affluent group of students of the three schools. This may be ascertained from the relatively large percentage of students who were on free or reduced cost lunch -- an index of the economic status of its students. It is about evenly divided racially. School B - Elementary is a communications skills magnet school located in a relatively affluent section of the city and has the fewest of its students receiving free or reduced cost lunches. White students form the predominant racial group here. The reverse is true at School C - Middle. The latter forms a middle ground economically between the other two schools.

School	% White/td>	% Black	% getting free lunch (economic status)
School A Elementary	47%	49%	65%
School B Elementary	47%	39%	23%
School C Middle	41%	50%	49%

This large, urban school district in North Carolina has almost 100,000 students. Overall 42% of these are black while 50% are white. As may be viewed from the North Carolina and national 1996 SAT mathematics scores below, this is double the ratio of black students statewide and almost four times the national percentage.

	North Carolina Average Score	%	United States Average Score	%
All students	486	100	508	100
American Indian	440	2	477	1
Asian American	534	2	558	9
Black	415	20	422	11
White	506	73	523	69
Other	483	2	472	11

Source: Department of Public Instruction, Raleigh, North Carolina

Each school had its own method of using the software. The approach of School A Elementary was probably the most innovative. Several teachers indicated they were computer phobic. They would allow their students participate in the study if they did not have to use the computer themselves. Therefore, all the test subjects were taught by the technology teacher in the computer lab. The software was used before school began. Students were told to come to the lab as soon as their parent or the bus dropped them off at school. The time missed was play time outside. Since participation was on a completely voluntary basis, the first week only ten students showed up to use the software. Word got out that it fun to learn on your own this way. The second week about twenty students came to use FUNdamentallyMATH. Eventually more than sixty students participated to one degree or another. Twenty-nine (29) pupils qualified as test subjects by the ten hour rule. The primary use of the software was during pre-school time but some teachers allowed those students who could work at the computer completely on their own to use it during classroom time as well. School A test subjects tended to use the software for 20 minutes three or four days a week.

The principal at School C Middle school placed 18 computers on tables along the walls inside one teacher's classroom. Different classes of students were taught by this teacher throughout the day. The test subjects here tended to use the software 2 or 3 times a week for 20 or 30 minutes a session depending on the teacher's assessment of the needs of the child.

Although there was a computer lab with about 50 computers at School B Elementary School, it was rarely used for the study. Instead each teacher had a few computers in their classroom. The teachers would work together to share each others computers when they were idle. The manner and extent of computer use was quite varied. Some teachers provided their students with only a minimally acceptable ten hours of computerized instruction. Others provided several times that amount.

The test group from all three schools combined averaged 23 hours of computerized instruction for each student during the school year.

Scores generated by the computer program showing a student's progress mastering a particular mathematics technique were for the teacher only and were not used for the statistical evaluation. Instead only the scores on the North Carolina statewide end of grade examinations in mathematics were used. Every child in the state in grades 3 through 8 must take this exam. Data was collected on the pre-test, the 1997 end of grade exam, and the 1998 end of grade exam (post-test) for students in grades 4 through 6. The third grade students take a statewide exam early in that year to establish a baseline for the student's progress. This was the students' pre-test. The third grade end of grade exam in 1998 was the post-test.

North Carolina statewide end of course examinations are also given in algebra I, geometry, and algebra II. The current test group studying algebra will be evaluated via the statewide algebra I end of course exam.

The control group was picked after the 1998 end of grade exams were given, as the requirements of the research project were a very low priority task for the district's research staff. Moreover, we did not know who would remain in the test group at yearend. It would have been needlessly time consuming to have picked control subjects for many students who did not continue with the study. However, every effort was made to keep the selection of control subjects unbiased. The first step was to compile a list of students who had been exposed to the software for amounts of time less than ten hours. Any student on that list was not permitted to be a control. The 1997 end of grade score (i.e., the pre-test) was recorded for each of the 214 test subjects. It was then discovered that fourteen of these students had moved into the school district after the pre-test was given. Since no pre-test data was available to the Research Department, these students had to be dropped from the study. This left 200 students who used the software. 200 control subjects were selected. Each control subject had to mirror the test subject. A considerable effort was made to keep the use of the software as the only difference. Every control subject needed to have the same grade, same gender, and same race as his or her counterpart test subject. A control subject was also required to have a raw score on the pre-test within two points of that of its corresponding test subject. At this point the number of control subjects equaled the number of test subjects. However, each group would soon be reduced further. Students to serve as control subjects had been found based on the pre-test results only. Now the 1998 scores were accessed. One test subject was now found to have moved from the school district. The test group was reduced to 199. A large number, 37, of the control subjects selected were discovered to have not taken the post-test. Presumably this was due to their moving from the district. The control group was reduced to 163. Ninety-one of the control subjects came from the three schools already in the study, but 72 control subjects did not. Since the selection process was totally random, the two groups -- test and control -- could now be compared.


Results

The statistics provided by the Research Department were analyzed using SPSS statistical software. Numerous comparisons were conducted. T-tests were used due to that type of test's ability to compare two completely independent groups against each other. The entire test and entire control groups were first examined against each other. The information was then broken down by grade for comparisons of each grade's test group versus that grade's control group. Ethnic comparisons were made. The progress of the entire group of black test students was compared with that of all the white test students. Black students were also compared to the black control group grade by grade. Only two of these t-tests could meet the rigorous standards of proof required for a classroom experiment, the 95% confidence level. Both of these concerned the performance of African-American students and did produce very important results:

1. Among black students, fourth graders in the test group had significantly higher scores than those in the control group. The difference in the 1998 scores is statistically significant at the 90% level; this means there is only a 9.9% probability that these results could occur randomly.

4th Grade Black Students - 1998 Score

	No. of Students	Mean	Standard Error of the Mean
Control Group	8	143.38	4.04
Test Group	13	151.92	2.96

The data for black students in grades 3, 4, 5, and 6 is provided below. Multiply the number in the significance column by 100 to find the probability in percentage terms that the event described was due to chance.

All sections of the software have been tested over and over again with students by its developer. He reports being repeatedly surprised at the speed and clarity with which students using FUNdamentallyMATH tended to learn two subject areas. The two topics are multiplication and Euclidean Geometry. Multiplication is a fourth grade topic. It is very possible that these two subjects are learned more easily at the computer than in the traditional way. The computer's capacity to instantly provide graphic illustrations of a multiplication sequence as well as to drill the student with infinite patience make it an ideal tool to use to learn this math operation.

T-Test 1998 Score Blacks Only Group Statistics

Grade	Type	N	Mean	Std. Deviation	Std. Error of the Mean
3	Control	18	140.44	10.49	2.47
	Test	17	140.18	10.89	2.64
4	Control	8	143.38	11.43	4.04
	Test	13	151.92	10.68	2.96
5	Control	17	156.94	9.85	2.39
	Test	27	156.44	9.09	1.75
6	Control	23	154.09	7.74	1.61
	Test	25	156.24	11.30	2.26

Independent Samples Test

Grade		t	df	Sig. (2-tailed)	Mean Diff.
3	Equal variance assumed	0.074	33	0.941	0.27
	Equal variance not assumed	0.074	32.698	0.941	0.27
4	Equal variance assumed	-1.735	19	0.099	-8.55
	Equal variance not assumed	-1.706	14.163	0.11	-8.55
5	Equal variance assumed	0.171	42	0.865	0.50
	Equal variance not assumed	0.168	32.084	0.868	0.50
6	Equal variance assumed	-0.764	46	0.449	-2.15
	Equal variance not assumed	-0.775	42.632	0.442	-2.15

Levene's Test for Equality of Variances

Grade		F	Sig.
3	Equal variance assumed	0.062	0.806
4	Equal variance assumed	0.159	0.695
5	Equal variance assumed	0.238	0.628
6	Equal variance assumed	2.249	0.141

The ability of FUNdamentallyMATH to teach all fourth grade math topics (including multiplication) is outlined even more dramatically when we examine just the difference between the pre-test and the post-test scores. The test group of fourth grade black students had an almost one-half point lower average score on the 1997 pre-test (i.e., on the starting level) than that of the fourth grade black control group. As you can see from the charts below, the variability of this test group's 1998 performance was very much smaller than that of the control. When viewed in terms of their relative improvements, the t-test of the fourth grade black students enhanced performance was significant at an amazing 99.9% confidence level.


T-Test 1998 Score minus the 1997 Score Blacks Only Group Statistics

Grade	Type	N	Mean	Std. Deviation	Std. Error of the Mean
3	Control	18	3.6111	6.3998	1.5084
	Test	17	4.4118	7.922	1.9214
4	Control	8	2	7.329	2.5912
	Test	13	11	3.6056	1
5	Control	17	8.2353	5.379	1.3048
	Test	27	8.2222	4.7744	0.9188
6	Control	23	3.2174	6.3886	1.3321
	Test	25	4.52	6.29	1.2585

Independent Samples Test

Grade		t	df	Sig. (2-tailed)	Mean Diff.
3	Equal variance assumed	-0.33	33	0.744	-0.8007
	Equal var. not assumed	-0.3283	0.792	0.745	-0.8007
4	Equal variance assumed	-3.785	19	0.001	-9
	Equal var. not assumed	-3.24	9.122	0.01	-9
5	Equal variance assumed	0.008	42	0.993	0.0131
	Equal var. not assumed	0.008	31.098	0.994	0.0131
6	Equal variance assumed	-0.711	46	0.481	-1.3026
	Equal var. not assumed	-0.711	45.541	0.481	-1.3026

If one were to characterize by grade level the main difficulty most students experience in learning math, the grade and problem might be associated as follows:

Grade Level	Main Instructional Difficulty
4	Learning Multiplication
5	Learning Long Division
6	Transition to middle school combined with a poor background in math fundamentals

Consider for a moment the possibility that the very same students who showed such progress in learning multiplication also used the software to learn long division in the fifth grade. Most of the difficulty students have learning long division stems from their lack of knowledge of the multiplication algorithm and / or the multiplication tables. Once the latter are mastered, the capacity to provide instant graphic examples and patient drill might now speed knowledge of long division. The experience of being successful two years in a row could lead to less anxiety and difficulty adjusting to middle school. Based on the fourth grade data and the highly significant data that follows below, we believe a longitudinal study is now an imperative.

2. A t-test revealed the capacity of the computerized instruction to prevent the constant widening of the gap in performance between the white and black students. The test to see "Did Blacks Improve More Than Whites" for all 4 grades (3 through 6) showed a negative relationship in the control group. In other words, among students who did not use the software, there was a significant difference in the improvement of scores, when whites and blacks are compared. Improvement in the post-test scores was much lower among blacks, with a 99.8% certainty that this difference was not due to chance. On the other hand, in the test group, the improvement in scores among black students was actually greater than among white students (although this difference was not statistically significant).

Without the software we are certain to have a constant slippage -- a widening of the gap between the performance of the two groups. With the software this does not occur.


T-Test Did Blacks Improve More Than Whites?
1998 - 1997 Group Statistics

Type	Ethnic Background	N	Mean	Std. Dev.	Std. Error
Control	Black	66	4.4697	6.5309	0.8039
	White	82	7.6585	6.0394	0.6669
Test	Black	82	6.7439	6.2988	0.6956
	White	100	6.18	5.8316	0.5832

Independent Samples Test 1998 - 1997

Type	t	df	Sig. (2-tailed)	Mean Diff.
Control
Equal variance assumed	-3.079	146	0.002	-3.1888
Equal variance not assumed	-3.053	134.238	0.003	-3.1888
Test
Equal variance assumed	0.626	180	0.532	0.5639
Equal variance not assumed	0.621	167.271	0.535	0.5639

Levene's Test for Equality of Variances

Grade	F	Sig.
Control - Equal variance assumed	0.006	0.938
Test - Equal variance assumed	1.623	0.204

The typical performance of African-American students (i.e., the control group) is even worse when one considers the distribution of skill levels in the study. The state of North Carolina mandates that schools use the end of grade exams to classify students into 4 skill level groups. In this way the state can track how well under-performing groups of students are doing. A translation of these levels into clear English might be as follows:

Level 1 - severely educationally impaired; far below grade; insufficient performance
Level 2 - modestly below grade; inconsistent performance
Level 3 - performing at grade level
Level 4 - performing above grade.

The definitions provided by the state are italicized.


There were very few Level 1 students in the study. Therefore, the chart below combines students in Levels 1 and 2 into one "Below Grade" category. It represents the student distribution on the pre-test.

Control Group	Below Grade	At Grade Level	Above Grade	No.
Black	27	27	12	66
White	10	22	50	82
Test Group	Below Grade	At Grade Level	Above Grade	No.*
Black	30	32	20	82
White	2	40	58	100

* The entire test group also included 10 Asian students, 6 Hispanic students, and 1 American Indian.

One would normally expect students in the Below Grade group to demonstrate a larger improvement than those in the above grade. It is very difficult for a student who is ranked in the 96th percentile, for example, to demonstrate considerable advancement. Compare that with the opportunity for students at the 35th percentile to make a major advance.

Based on this expectation both the principal investigator (Professor Frank Brown) and the software developer (Howard Diamond) propose the following hypothesis:

Now that it has been shown that a particular type of computerized instruction can break the normal deterioration in the math skills of black students vis-a-vis those of white students, we tend to believe that another study which has the same students use this software for three to five consecutive years will show the average gap in relative performance narrow significantly or even disappear.

Further Comments

The following is a chart of the test group of fourth grade black students - the group which demonstrated outstanding improvement. The chart is sorted by math level.


The students are equally divided between below grade, on grade, and above grade categories. Judging from their percentile ranks three of the four students classified as below grade maintained approximately the same fourth grade percentile rank standing while one made a substantial improvement. All of the other students made substantial improvement -- if an improvement from 96th percentile to 99th may be called substantial.

There is an unusually high percentage of students who used the software at home for 5 hours or more. 23% of these students qualified as home users while only 7.5% of the entire test group did. Another interesting fact is that the students from School A Elementary appear to have done as well as those from School B Elementary. This implies is that voluntary use before school was just as effective as classroom computer assisted training.

Several other items of general interest should be noted:

1. The principal investigator sought to have the test group use only FUNdamentallyMATH as their sole exposure to mathematics software. However, all of the students in the third through fifth grades were exposed to another company's math software package. Both the control group and the test group used this software. Only the test group used FUNdamentallyMATH. Therefore, we believe the differences in performance between the test and control groups were due to the use of FUNdamentallyMATH.

2. The data which tracked the improvement in score (i.e., 1998 minus 1997) for Level 1 students -- far below grade students -- indicated an F test significant at the 90% confidence level.

Level 1 (all races) 1998 - 1997

	Number	Mean	Std. Dev.	Std. Error of Mean
Control	7	-3.5714	4.0766	1.5408
Test	5	1.8000	8.1670	3.6524

Levene's Test for Equality of Variances

F	Signif.
4.153	.069

The considerably more rigorous T-test indicated that the difference in improvement between the Test and Control Groups of 5.3714 had a significance statistic of .161 -- or a 16.1% probability of being due to chance. Given the small numbers involved as well as the considerable variability as evidenced by the standard deviation and standard error, we suspect that one or more test group students did remarkably well. No conclusion should be based on the result of one or two students. However, it is something that suggests that another similar study with a considerably larger number of students selected from this group should be conducted.

3. The 1998 score of the combined group of white and black test subjects was tested to see if there was a correlation with estimated time of use. 182 students' scores had a positive but very small correlation with time of use. The Pearson Correlation was .161 and was significant at the 95% confidence level (i.e., a 3% probability of being due to chance). Although the relationship achieved an important level of significance, we believe the degree of correlation is too low to suggest an important relationship. Rather it appears the a high minimum level of use is probably more meaningful. Since the entire test group averaged 23 hours of use, and the fourth grade black students who did exceptionally well averaged 27 hours of school use, we tend to believe that any educator planning to use the software should plan for at least a minimum of 20 hours during the school year.

Time of home use may be very important for Level 4, i.e., advanced students. There was no statistically significant difference between the Level 4 test and Level 4 control students


1999 Report of the Research Project
FUNdamentallyMATH: Computer Assisted Instruction In Mathematics
by Professor Frank Brown

General Background of the Study's Second Year

The 1998-99 school year, the second year of the two year project, involved an examination of the ability of FUNdamentallyMATH software to improve students' algebra skills. Two mathematics teachers at Middle School D used the software with their eighth grade pupils.

FUNdamentallyMATH is a DOS program that will work with virtually any IBM compatible computer ever made -- from the early "286's" to the modern "Pentiums". All it requires is the ability to show color and a central processing unit with at least a 640K memory capacity, extremely modest requirements by modern standards. However, it will not work on a network. (A more modern, multimedia version that will network is being developed. It should be available for the 2000-2001 school year.) Middle School D has over 300 computers all of which are networked. Because the school's network protocol made it difficult to take a computer temporarily off-line, Chip Publications Inc., the developer of FUNdamentallyMATH, provided 18 used "386" computers which were setup as stand alone computers. They were placed in a classroom in the eighth grade math wing very near the participating teachers' classrooms.

The 1998-99 school year began with Middle School D entering its new facility. It's enrollment of 1045 students is rather large for a middle school. Each grade level has its own section of the school. Middle School D is located on a large tract of land which also contains an elementary school and a high school. The three schools are located in close proximity to enable a student to remain on essentially the same campus from Kindergarten through 12th grade.

Middle School D is a Workplace Magnet School. Space is allocated so that one-third of its students come from families who are employed nearby, one-third of the students must live in the area, and the last third are sent from satellite areas wishing to contribute minority students to this very modern facility. Because of the last condition, Middle School D has an unusually high percentage of African-American students for a school located in a relatively affluent section of the city. It is only two miles from Elementary School B. The racial balance at all of the four schools participating in the study is shown below.

School	% White	% Black	% getting free lunch (economic status)
School A - Elementary	47%	49%	65%
School B - Elementary	47%	39%	23%
School C - Middle	41%	50%	49%
School D - Middle	38%	55%	39%

Methodology

The two teachers sent their classes to work with the software one day a week for 45 minutes at a time. Students used it for approximately 17 hours from mid-Nov. through mid-April stopping one month before the state exam. Occasionally some students would work on the software in groups of twos and threes. These small groups would be sent to the math computer lab to work on material just covered in class. Typically there would be a student question, an explanation from the teacher, and then further reinforcement of the explanation by sending small groups of students to use specific sections of the software.

Students in the algebra study were exposed to only FUNdamentallyMATH software and their textbooks. Although the teachers were provided with copies of the software to be given to students for home use, neither of the teachers had any students use the software at home. Perhaps they thought it was undemocratic to allow extra time on the software for students fortunate enough to have a home computer.

Both teachers had their students follow a similar curriculum. Students were directed by the teachers to use the sections of the software beginning with the 7NUMBERS file in the first directory (basic skills directory) and continue up to and including the next to last word problem file in the algebra directory, the @WRDPRB8 file. A few advanced files such as the logarithm file and the introduction to matrices were avoided. The entire FUNdamentallyMATH curriculum is outlined on the next page.

The pre-test - used mainly to select appropriate control subjects - was the North Carolina end of 7th grade examination. Each control subject had to have the same sex, race, and grade as its matching test subject. The difference between the test subject and its corresponding control subject's pre-test raw scores was kept as small as possible. It was usually zero or only one point.

The post-test was the NC Algebra 1 examination. The test group was composed of 54 students. Seven (7) of these students moved to the district after the pre-test was given. Forty-seven (47) control subjects were picked to correspond to the test subjects for whom the pre-test data was available. One control remains for a student who moved from the district before the Algebra 1 statewide exam was given. Roughly 40% of all students involved were ranked "on-grade" (level 3) and the rest "above grade" (level 4).

Results

The raw score results for the entire test group, all 54 students who used the software during the school year, is highly significant. The t-statistic is 2.839 -- significant at the 99.5% confidence level. In plainer terms, there is a 1 in 200 chance that the result shown below is due to chance.

Percentile rankings in this report are statewide figures. The number of students taking this examination in May of 1998, the last date for which data is presently published, was 83,124. One is forced to conclude that a jump of 17 percentile ranks is an enormous improvement vis-a-vis other students.

	N	Algebra Raw Score	Percentile
Entire Test Group	54	58.70	62.28
Entire Control Group	47	53.53	45.11

Algebra t-test for Equality of Means (Control vs. Test)

t	df	Significance (2 tailed)	Mean difference
-2.839	99	.005	-5.17

Multiply the number in the significance column by 100 to find the probability in percentage terms that the event described was due to chance.

The data reveals not only a significant improvement in performance but a dramatic reduction in the skewness when the test group is compared to the control.

T-Test 1999 Algebra Score Group Statistics

Type	N	Mean	Std. Deviation	Std. Error of the Mean
Control	47	53.53	10.38	1.51
Test	54	58.70	7.89	1.07

The data also was tested for significance (i.e., test versus control) in terms of ethnic subgroups as well as for gender as a factor. The results were significant at the 95% confidence level for Black students and Female students. A case could also be made that the Male only test was significant, since it came so close at the 94.5% confidence level. Had we been using a table in a book instead of the more accurate SPSS software, it would have exceeded the 95% mark. (See the footnote at the end of the report.)

T-Test 1999 Algebra Score Blacks Only Statistics

Type	N	Mean	Std. Deviation	Std. Error of the Mean
Control	15	51.27	10.39	2.68
Test	16	59.06	6.17	1.54

Algebra t-test for Equality of Means - Blacks Only (Control vs. Test)

t	df	Significance (2 tailed)	Mean difference
-2.560	29	.016	-7.80

What is so exciting about the performance of the African-American test group students is that it confirms the ability of the software demonstrated in the first year of the research project to aid these students. Moreover, while the control group of Black students performed the worst, the Black test group had the highest scores.

Test Group	N	Algebra Raw Score	Percentile
Black	16	59.06	64.19
White	31	58.45	61.19
Control Group	N	Algebra Raw Score	Percentile
Black	15	51.27	39.27
White	29	54.59	47.87

Females represented another group that demonstrated a significant improvement from the use of FUNdamentallyMATH.

T-Test 1999 Algebra Score Females Only Statistics

Type	N	Mean	Std. Deviation	Std. Error of the Mean
Control	25	52.96	10.26	2.05
Test	32	57.81	7.27	1.29

Algebra t-test for Equality of Means (Control vs. Test)

tcdf	Significance (2 tailed)	Mean difference
-2.089	55	.041	-4.85

Although the females in the test group continued to lag the males within the test group, their enhanced performance from computer assisted instruction helped them to outperform the males in the control group.

	N	Algebra Raw Score	Percentile
Females - Test Group	32	57.81	58.97
Males - Control Group	22	54.18	49.68
Males - Test Group	22	60.00	67.09

The data for Males only (test group versus control) is also significant, if one will permit a significance level of .055 (i.e., the 94.5% confidence level) to be called significant.*

One unanticipated benefit from using the software was that it dramatically improved the African-American test subjects' general knowledge of mathematics. All of the students had to take the North Carolina statewide end of eighth grade examination. The improved performance of the Black test subjects on the end of grade examination was significant.

T-Test 1999 End of 8th Grade Score Blacks Only Statistics

Type	N	Mean	Std. Deviation	Std. Error of the Mean
Control	15	174.07	7.89	2.04
Test	17	179.82	6.18	1.50

Algebra t-test for Equality of Means (Control vs. Test)

t	df	Significance (2 tailed)	Mean difference
-2.313	30	.028	-5.76

One test subject took the end of grade examination but not the algebra test. Perhaps this student was ill when the latter test was given.

The African-American test subjects general knowledge of mathematics appears to be helped so much by the computer that we may maintain it enabled them to catch up to their white classmates.

End of 8th Grade Exam - Summary Table

	N pre-test	Pre-test	N post-test	Post-test	Gain
Black - control	15	172.73	15	174.07	1.34
Black - test subjects	15	173.53	17	179.82	6.29
White - control	29	175.31	29	179.28	3.97
White - test subjects	29	175.66	31	178.97	3.33

Once more (as it was with the elementary school students the year earlier) the improvement within the control group is inverted from what we would expect. The White control students show a substantially higher ability on the pre-test and, yet, gain more than the Black control students. In fact the difference in improvement, i.e., the 1999 end of grade score minus the 1998 end of grade score, is significant at the 95% confidence level, if a t-statistic at the 94.3% can be viewed as significant. It would have reached the 95% level had a table in a book been used to analyze the results.*

The software appears to have been even more beneficial to the African-American middle school students than to the African-American elementary school students who participated the year before. The black students in grades 3 through 6 who were exposed to FUNdamentallyMATH improved as much as the white students. However, their ability to perform mathematical tasks still lagged that of the white students. The black middle school test subjects outperformed all other groups. Since there was no statistically significant difference between their 1999 end of 8th grade exams (i.e., the post-test) and that of the white students, we can state that the two groups were now equal. The black students have caught up!


Conclusions

All students can benefit from the use of software such as FUNdamentallyMATH as an adjunct to their study of algebra. African-American students seem to benefit the most. These students are able to catch up to their white classmates through the review of previously taught material which was a prelude to studying algebra. One strategy to aid African-American students suggested by the research project would be to use software such as FUNdamentallyMATH for 15 to 20 minutes a day in elementary school and expand this to one whole period one day a week in middle school. The gap between white and black students would first be kept from growing. In middle school the gap may be closed.

Just why African-American students benefit the most is still a mystery. However, here are some possible reasons:

1, The attendance rate is lower and absenteeism is greater for this ethnic group. Without a resource for catching up one can easily become lost in math class. FUNdamentallyMATH's comprehensive nature allows the students to teach themselves material they have missed.

2, The study habit of individualized, self-paced instruction leading to self-taught knowledge may be acquired through computer use. Pride in educational attainment is reinforced.

3, Experience with prejudice may cause these students to come to school with an unhealthy attitude toward the white power structure or anyone else in authority. The computer is non-judgmental and extraordinarily patient.

* Were we using a table in a book instead of the more accurate SPSS software, the statistic would appear to have reached the 95% confidence level. Tables in books usually stop showing t-statistics beyond 30 degrees of freedom. Instead they tend to list the level of 1.95996 as the 95% confidence amount for all degrees of freedom beyond 30 because there is so little change in the 95% threshold at higher number of degrees. The Male only t-statistic was -1.976, higher than that shown in tables. The t-statistic for the relative increase (1999 end of grade minus 1998 end of grade) of the White control group versus the Black control group was 1.95813, an almost identical number to the level in tables.

Professor Frank Brown (Principal Investigator)
112 Peabody Hall, CB # 3500
University of North Carolina
Chapel Hill, NC 27599-3500
919-962-2522