THE IMPACT OF HOMESCHOOLING ON MATH EDUCATION
A study of homeschooled children in northeastern Illinois showed that the children scored better than the national norms. Low math computation subset scores lowered total math scores (Frost, 1988). Tennessee children are tested in specified grades from second through eighth. Most homeschoolers scored significantly higher than both their public school counterparts and national norms, but math scores showed the least advantage (Long, 1987; personal communication, Tennessee Department of Education, December 13, 1989). Washington homeschoolers scored between the 65th to the 68th percentile over a fouryear period. The lowest subtest level was in math computation, about 9 percentile points below national averages (Wartes, 1989, p. 1216; Wartes, 1990, p. 23). Tipton reported that in West Virginia, “Means for homeschooled children equalled or exceeded those of publicschooled children in most sections.” The only mention of lower scores was in ninthgrade math computation, concepts, and total math (Tipton, 1991a, p. 5051, 7475; Tipton, 1991b). Generally, homeschoolers are scoring above national norms in math, but math scores tend to be lower than other testing areas, with computation one of the lowest scores in the subtests.
According to Benjamin Bloom, professor of education at the University of Chicago, the home has the greatest impact upon the child’s learning of reading, vocabulary, and problem solving. The least impacted areas are spelling and arithmetic computation (Bloom, 1981, p. 11). Bloom’s comments were made before homeschooling became popular. Subsequent test results of homeschoolers substantiate his statement.
Commenting on an article by Ray (1988) in which he mentioned the relatively low math computation scores among homeschoolers, Duffy (1989, p. 38), a curriculum specialist, said that his comments “stirred up a hornet’s nest” as publishers sought to promote their computation skills programs. Bloom’s indication of the home’s small influence upon math computation skills, publishers efforts to enhance homeschool curriculum, and research showing lower homeschool math computation scores indicate that further research is necessary in this area. Homeschool parents need to know what factors may help their students to succeed in math.
Only one other study is known to have analyzed influences on math scores in the homeschool. Richman, Girten and Snyder (1992) gathered data among Pennsylvania homeschoolers in the third through eighth grades. There is a great need for further research on what influences math scores.
Method
The study took place in the first half of 1994. Surveys were distributed within a 15mile radius of Longview, Washington, which included communities in Oregon. Both states require homeschool students to be tested each year. Homeschool families involved in the study had to meet the following criteria: (1) the student had been homeschooled for at least the complete school year for which the test was given, (2) the student had been administered a nationallynormed standardized test including subtests of math computation and application, and (3) the student was in the third grade or above for the year tested. Washington does not require testing until after age seven, so the first and second grades were eliminated. Nearly all test results were from 1992 or 1993.
Of the homeschooling families which met the above criteria, 14 refused to participate (since they were too busy or thought the study was too personal in nature), 4 could not find tests, 2 didn’t return calls and 45 families participated. This resulted in a return rate of 69.2%. There were 77 useable surveys and test results. Twentynine of the students were from Oregon and 48 were from Washington. Students took the following tests: California Achievement Test – 69 students, Stanford Achievement Test – 6 students, Iowa Test of Basic Skills – 2 students.
The mean scores in total math and total battery for these 77 students were at the 68.3 national percentile and the 74.4 percentile, respectively. The total language average was 73.8; total reading was 78.4.
Results
Years of Schooling
There was no significant relationship between the entire math scores of the homeschooled student and the number of years the student was home educated, was in public school or was in private school.
Grade Level
The null hypothesis stated that the grade level has no relationship to entire math scores of home schooled students. The Pearson’s r was significant at the .05 probability level (Table 1). The relationship was of a negative nature. In other words, the higher grades had lower computation math scores.
Pearson’s r: Grade Level and Math Scores 


N 
r 
Slope 
ztest 
Null 
Computation 
74 
.195 
.003 
1.664 
M<M^{0} , p < .05 
Application 
75 
.010 
.000 
.086 
retained 
Total Math 
75 
.082 
.001 
.707 
retained 
Table 1. Relationship between grade level and test scores.
Richman, Girten, and Snyder (1992, p. 10) discovered that homeschool students in Pennsylvania tended to score higher in the upper grades than in the lower grades. Both the Pennsylvania study (Richman, Girten, & Snyder, 1992, p. 11) and this study showed a dramatic increase in total math scores from third grade to fourth grade, as did a study by Wartes (1990, p. 3). Thirdgrade scores in the Pennsylvania and Wartes studies may have been lower because formal studies were not required until age eight and many third grade students had not been tested before (Richman, Girten, & Snyder, 1992, p. 15.). After seventh grade there was some decline in math application scores in this present study. In Ray’s (1990, p. 30) study there appeared to be a decrease in total math scores after ninth grade. Wartes’ (1990, p. 3) showed a slight decline in total math from fourth grade to eighth (no scores are listed after eighth grade). But there was no drop in computation scores in Wartes’ (1989, p. 3637) study. The decline of math computation scores in this study could have been from a deemphasis on math instruction after a certain level.
Gender
Biserial: Boys and Girls 


N 
r 
S.D. 
ztest 
Null 
Computation 
74 
.212 
25.784 
1.811 
M>M^{0}, p < .05 
Application 
75 
.345 
23.770 
2.968 
M¹M^{0, <}, p < .01; M>M^{0}, p < .01 
Total Math 
75 
.304 
24.082 
2.619 
M¹M^{0}, p < .01; M>M^{0}, P < .01 
Table 2. Relationship between boys’ and girls’ test scores.
Wartes (1990, p. 5) did not find a significant difference between the genders in total math. He did find a significant difference of girls outscoring boys in language and boys outscoring girls in science. In this study, thirdgrade girls had the lowest scores (47.1 percentile total math average). Thirdgrade boys had the highest (88.2 percentile total math average). It is generally accepted that boys mature slower than girls behaviorally, socially, and academically. This research has revealed that boys were ahead of girls in math in the elementary grades. That significant advantage disappeared during the teen years.
Hours Spent on Math
The null hypothesis stated that the amount of time spent on math has no significant effect on entire math scores of homeschooled students. Parents indicated on an interval scale of halfhour increments the time the student spent on math. In the correlation of time spent on math and entire math scores, a Pearson’s r test was run. The coefficient for math computation and total math was significant at the .05 probability level (Table 3). There was a significant relationship between more time spent on math study and higher computation and total math scores.
Pearson’s r: Hours and Math Scores 


N 
r 
Slope 
ztest 
Null 
Computation 
74 
.212 
.001 
1.814 
M>M^{0}, p < .05 
Application 
75 
.175 
.001 
1.505 
retained 
Total Math 
75 
.197 
.001 
1.693 
M>M^{0}, p < .05 
Table 3. Relationship between number of hours of math study and test scores.
The Richman, Girten, and Snyder (1992, p. 14) study did not find any significance between the amount of time spent on math and entire math scores. In this study, the difference between 1 hour and 1.5 or more hours is not significant using the ztest. There was a significant relationship between spending less than 1 hour on math and lower computation and total math scores.
Puzzles
The null hypothesis stated that enjoyment of finding solutions to puzzles has no relationship to entire math scores of homeschooled students. Students were asked to rate puzzles on a graphic rating scale from 1 (enjoyable) to 9 (frustrating). In the correlation of enjoyment of puzzles and entire math scores, a Pearson’s r was run. The coefficient for math application was significant at the .05 probability level (Table 4). Homeschooled students who enjoy finding solutions to puzzles have higher math application scores than those who are frustrated with puzzles.
Pearson’s r: Puzzles and Math Scores 


N 
r 
Slope 
ztest 
Null 
Computation 
74 
.092 
.001 
.789 
Retained 
Application 
74 
.240 
.003 
2.047 
M¹M^{0} , p <.05; M<M^{0}, p < .05 
Total Math 
74 
.186 
.002 
1.593 
Retained 
Table 4. Relationship between homeschool students’ enjoyment of puzzles and test scores.
Mortensen Math
Mortensen Math is a supplementary, manipulative curriculum. This survey asked the parent, “Does the student understand Mortensen Math?” No support was found for an effect of Mortensen Math upon math scores among the fifteen students who understood it. This finding disagreed with a study conducted by Richman, Girten, & Snyder (1992, p. 13) which found the use of Mortensen Math as statistically significant in math application when seventeen students used it as a supplementary math activity (t = 2.87, p < .01, df = 161).
Curriculum
Four categories of curricula were used in this study: Saxon Math, A Beka, secular classroom math texts, and other texts (nearly all were from Christian publishers). When a ztest was run between any curriculum and the secular classroom texts, a significant decline for most total math scores was found for those who used the secular classroom math texts. There was no significant difference in entire math scores between the curricula of Saxon, A Beka, and other (which included Bob Jones and A Beka video). In the Richman, Girten, and Snyder (1992, p. 11) study, math texts were ranked by students’ percentile scores: Saxon (91), school district’s textbooks (80), A Beka (77), Bob Jones (77) and other programs (65).
Several parents in this study who used secular classroom texts appeared to have changed math textbooks frequently. The type of curriculum used over many years may be significant and needs to be studied further.
Method of Study
The null hypothesis stated that there is no significant relationship between the type of instructional method used for math and entire math scores of hometaught students. The ztest was used to compare resulting test scores of tutoring by an adult and studying material on their own. The null was rejected at least at the .05 confidence level in all areas of math (Table 5). Homeschooled students whose primary understanding of math comes from studying the material on their own had higher entire math scores.
Ztest 
Self Study 49 
Tutoring 19 
Null 
Computation 
68.90 
53.16 
t= 2.27; M¹M^{0}, p <.05, M>M^{0}, p <.05 
Application 
73.73 
57.37 
t= 2.62; M¹M^{0}, p <.05, M>M^{0}, p <.01 
Total Math 
73.08 
54.68 
t= 2.92; M¹M^{0}, p <.05, M>M^{0}, p < .01 
Table 5. Relationship between method of study and test scores.
Several reasons for higher scores for selfstudy are possible: parenttutors may not understand the math being taught; tutored students may be more passive learners, because the parent is always there to answer questions; students learning the material on their own proceed with lesson exercises as the lesson is adequately understood.
Computer Programming Experience
There was no significant relationship in this study between the ability of 19 hometaught students to program a computer and their entire math scores. In the study conducted by Richman, Girten, and Snyder (1992, 1314) it was found that the ability to program a computer was related to higher math achievement scores. The 16 students who had the ability to program had significantly higher scores in computation (t = 2.83, p < .01, df = 161), in application (t = 3.96, p < .001, df = 161) and in total math (t = 3.72, p < .001, df = 161).
Enjoyment of Math
The null hypothesis stated that enjoyment of math has no significance upon the entire math scores of homeschooled students. Using a graphic rating scale of 1 to 9, students rated themselves as enjoying math (1) to being bored with math (9). The Pearson’s r revealed that homeschool students who enjoy math have significantly higher application and total math scores (Table 6).
This study did not answer whether the enjoyment of math caused the higher math scores, or whether those who have a better understanding of math application therefore enjoy math more.
Pearson’s r: Enjoyment of Math and Math Scores 


N 
r 
Slope 
ztest 
Null 
Computation 
74 
.140 
.002 
1.192 
Retained 
Application 
74 
.260 
.003 
2.220 
M¹M^{0}, p < .05; M<M^{0}, p < .05 
Total Math 
74 
.226 
.003 
1.933 
M<M^{0}, p < .05 
Table 6. Relationship between enjoyment of math and test scores.
Perceived Difficulty of Math
The null hypothesis stated that among homeschool students, there is no significant relationship between math being hard and entire math scores. Students were asked on a graphic rating scale of 1 to 9 to rate math as being easy (1) to being hard (9). The Pearson’s r for math computation, application, and total math was significant at the .01 probability level (Table 7). For homeschooled students, there is a significant relationship between math being easy and higher entire math scores.
Pearson’s r: Difficulty of Math and Math Scores 


N 
r 
Slope 
ztest 
Null 
Computation 
74 
.402 
.005 
3.433 
M¹M^{0}, p < .01; M<M^{0}, p < .01 
Application 
74 
.430 
.005 
3.671 
M¹M^{0}, p < .01; M<M^{0}, p < .01 
Total Math 
74 
.437 
.005 
3.732 
M¹M^{0}, p < .01; M<M^{0}, p < .01 
Table 7. Relationship between perceived difficulty of math and test scores.
The Richman, Girten, and Snyder (1992, p. 14) study asked the parents, on a scale of 1 to 7, “How well do you think this child likes math (as compared to other subjects)?” Their findings showed no significance. The results may have differed if the question was asked of the students.
Parent Overseer
There was no significant relationship between entire math scores and which parent oversaw the math program. Only 10 of the 75 parent math overseers were fathers.
Checking of Math Answers
There was no significant relationship between the entire math scores and whether the parent or the child checks the math answers.
Discussion of Incorrect Problems
The null hypothesis stated that there is no significant relationship between discussion of incorrect problems by the parent and the child and the entire math scores of the hometaught student. In the correlation of whether the parent discusses incorrect problems and the entire math scores, a biserial was run. The coefficient for math computation was significant at the .05 probability level (Table 8). There is a significant corresponding relationship between discussion of incorrect problems by the parent and the child and higher computation scores of the hometaught student.
Biserial: Discussion of Incorrect Problems and Math Score 


N 
r 
S.D. 
ztest 
Null 
Computation 
74 
.229 
25.784 
1.957 
M>M^{0}, p <.05 
Application 
75 
.032 
23.770 
.271 
Retained 
Total Math 
75 
.112 
24.082 
.963 
Retained 
Table 8. Relationship between discussion of incorrect math problems and test scores.
Fathers’ Educational Level
The null hypothesis stated that there is no significant relationship between the educational background of the father and the entire math scores of the hometaught student. The Pearson’s r significant for math application at the .01 probability level and at .05 probability level for total math (Table 9). There is a direct correlation between homeschool students who have fathers with a higher level of schooling and higher application and total math scores.
Pearson’s r: Fathers’ Educational Level and Math Scores 


N 
r 
Slope 
ztest 
Null 
Computation 
74 
.000 
.000 
.004 
Retained 
Application 
75 
.354 
.003 
3.045 
M¹M^{0}, p < .01; M>M^{0}, p < .01 
Total Math 
75 
.201 
.002 
1.726 
M>M^{0}, p < .05 
Table 9. Relationship between fathers’ educational level and children’s test scores.
Mothers’ Educational Level
The null hypothesis stated that there is no significant relationship between the educational background of the mother and the entire math scores of the hometaught student. The Pearson’s r was significant at the .05 probability level (Table 10). The relationship was inverse. Homeschool students who had mothers with a higher level of schooling had lower computation scores than those whose mothers had a lower level of schooling.
Pearson’s r: Mothers’ Educational Level and Math Scores 


N 
r 
Slope 
ztest 
Null 
Computation 
74 
.214 
.002 
1.830 
M<M^{0}, p < .05 
Application 
75 
.060 
.000 
.518 
Retained 
Total Math 
75 
.065 
.001 
.558 
Retained 
Table 10. Relationship between mothers’ educational level and children’s test scores.
When parents were asked in the Richman, Girten, and Snyder (1992, p. 14) study, “What is the highest number of years of ‘formal education’ completed by the parents [sic] who is supervisor of the home education program?” no significant difference was found in the students’ entire math scores. When both parents’ educational backgrounds were considered in this study, there was no significant difference in entire math scores. The differences were evident when grouped separately according to mothers and fathers. Why mothers with higher educational levels in this study had children with lower computation scores is unknown.
Parents’ Math Background
The null hypothesis stated that there is no significant relationship between the math background of the father and the entire math scores of the hometaught student. The Pearson’s r was significant at the .05 probability level (Table 11). There is a direct correlation between homeschool students who have fathers with a higher level of math background and higher math application scores.
There was no significant relationship between the mother’s math background and the student’s math scores.
Parents’ Math Seminar Attendance
The null hypothesis stated that there is no significant relationship between the number of math seminars attended by the mother and the entire math scores of the hometaught student. The Pearson’s r was significant at the .05 probability level (Table 12). The relationship was inverse. Homeschool students had lower computation scores if their mothers had attended math seminars compared to students whose mothers who had not attended.
Pearson’s r: Fathers’ Math Background and Math Scores 


N 
r 
Slope 
ztest 
Null 
Computation 
74 
.087 
.001 
.742 
Retained 
Application 
75 
.245 
.003 
2.107 
M¹M^{0}, p < .05; M>M^{0}, p < .05 
Total Math 
75 
.176 
.002 
1.518 
Retained 
Table 11. Relationship between fathers’ math background and children’s test scores.
Pearson’s r: Mothers’ Math Seminar Attendance and Math Scores 


N 
r 
Slope 
ztest 
Null 
Computation 
74 
.240 
.001 
2.053 
M¹M^{0}, p < .05; M<M^{0}, p < .05 
Application 
75 
.073 
.000 
.628 
Retained 
Total Math 
75 
.186 
.000 
1.601 
Retained 
Table 12. Relationship between mothers’ math seminar attendance and test scores.
There was no significant relationship between the number of math seminars attended by the father and the student’s entire math scores. Richman, Girten, and Snyder (1992, p. 1011) discovered stronger math application scores (r = .17, p < .05) and total math scores (r = .17, p < .05) in relation to the number of seminars attended by both parents. It may be that families in this study who were concerned about previous low math scores attended math seminars. Even if the seminars helped, they may not have been enough to bring scores up to the level of the other students in the study. Only 10 mothers in this study reported attending seminars as opposed to 50 parents in the Richman, Girten, and Snyder study. It may be that math seminars were more available to homeschoolers in Pennsylvania, whereas only the “desperate” in this study made special attempts to attend math seminars.
Support Group Involvement
The null hypothesis stated that there is no significant relationship between involvement in a homeschool support group by the parentteacher and the entire math scores of the hometaught student. The biserial coefficient for math computation was significant at the .05 probability level (Table 13). The relationship was of a negative nature. There is a significant corresponding relationship between involvement in a home school support group by the parentteacher and higher computation scores of the hometaught student.
Biserial: Support Group Involvement and Math Scores 


N 
r 
S.D. 
ztest 
Null 
Computation 
74 
.265 
25.784 
2.265 
M¹M^{0}, p < .05; M<M^{0}, p < .05 
Application 
75 
.059 
23.770 
.505 
Retained 
Total Math 
75 
.189 
24.082 
1.628 
Retained 
Table 13. Relationship between support group involvement and test scores.
Richman, Girten, and Snyder (1992, p. 15) commented about a previous Pennsylvania study, stating that those who are connected to a support network “appear to score higher . . . in math.” The rationale given was that “these support groups often have local meetings which focus upon educational topics. They also organize regional seminars and a large statewide conference [with] many helpful workshops.” A reason for lower scores in this study may be the type of individuals drawn to the local support groups. Parents who feel a need to tutor their students in math (an indicator of lower scores in this study) may desire the assistance of likeminded individuals and gravitate to a support group. Another reason could be a lack of math training provided by the local support groups.
Discussion
Richman, Girten, and, Snyder (1992, p. 15) made note of a positive correlation between achievement and independence in math study as the student moved into the higher grades. This correlation may be seen in this study in the students who scored higher in math and who also studied math lessons on their own.
One of the issues of debate in the public school system has been that teachers give preferential treatment to boys over girls. The advantage boys have in math in the lower grades, as replicated in this study, may be more an indication of gender traits than the result of preferential treatment. Stereotyping of gender by some parents (e.g., “boys need math more than girls”) may give preferential treatment to boys, but homeschool parents probably consider math important for both genders of elementary school age. Test scores indicate that homeschoooled girls of latter elementary age do not lack adequate math instruction. Gender issues should be reevaluated.
Bentzen (1963, p. 98) wrote, “Unless our educational system groups children on the basis of their maturational readiness for learning, we may unwittingly be putting boys at a grave disadvantage.” Personnel (Ilg & Ames, 1978, p. 6) at the Gesell Institute recommended starting boys in formal education a full year after girls. If readiness is a factor for academic preparedness, this study might suggest starting girls in math later than boys while starting boys in other subjects later than girls. This is a touchy issue, since either gender may feel slighted if held back. The issue warrants further study.
Students who enjoyed math and found it easy did better than the other students in this study. In a conventional school, a math instructor has to teach to the majority of the class members. Bright students might be bored, and slow learners may feel frustrated. In the homeschool environment it is possible to tailor the program to the individual student. The challenge for parents is to make the lessons easy enough to avoid frustration and enjoyable enough to avoid boredom. Making math easy and enjoyable may be linked to the avoidance of certain curriculum, the joy of self discovery (learning the material on their own), the father’s modeling through higher education and math knowledge, and a sufficient amount of time spent on math study.
References
Bloom, Benjamin (1981). All our children learning: A primer for parents, teachers, and other educators. New York: McGraw Hill.
Duffy, Cathy (1989, April/May). News you can use. The Teaching Home, pp. 3739.
Frost, Eugene Albert (1988). A descriptive study of the academic achievement of selected elementary schoolaged children educated at home in five Illinois counties. Dissertation Abstracts International, 48(1), 1589A.
Ilg, Frances L., Louise Bates Ames, Jacqueline Haines, & Clyde Gillespie (1978). School readiness: behavior tests used at the Gesell Institute (4th ed.). New York: Harper & Row, Publishers.
Long, Betty W. (1987, February 10). Personal correspondence to Mike Farris of the Home School Legal Defense Association, Paeonian Springs, Va.
Ray, Brian D. (1986). A comparison of home schooling and conventional schooling: With a focus on learner outcomes. A paper presented as part of Ph.D. requirements at Oregon State University. Available from National Home Education Research Institute, 5000 Deer Park Dr. SE, Salem OR 97301‑9330.
Ray, Brian D. (1988, August/September). Research report: Washington state homeschool testing. The Teaching Home, p. 57.
Ray, Brian D. (1990). A nationwide study of home education: Family characteristics, legal matters, and student achievement. Salem, OR.: National Home Education Research Institute.
Ray, Brian D. (1992). Marching to the beat of their own drum: A profile of home education research. Paeonian Springs, VA: Home School Legal Defense Association. Available from the National Home Education Research Institute, 5000 Deer Park Dr. S.E., Salem OR 97301.
Richman, Howard B. & Susan Richman (1988, September 14). Legalization of home schools Should proceed. Education Week, p. 32.
Richman, Howard B., Girten, William, & Snyder, Jay (1992). Math: What works well at home. Home School Researcher, 8, 919.
The Teaching Home. (1991, April/May). Study of home education, p. 35.
Tipton, Mark (1991a). An analysis of achievement test scores of West Virginia homeschooled children. Unpublished master’s thesis, Antioch University.
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