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This paper is in response to a request to determine if there is a significant difference in math test scores that can be attributed to methods of instruction and teaching assignments at Harmony Creek Middle School based on ethnicity, socioeconomic status and ethnicity. Test scores for all students grouped by teacher, gender, ethnicity and socioeconomic status as determined by the eligibility of the student to qualify for free or reduced price lunch. An Analysis of Variance test (ANOVA) was performed on each data subset and when significant differences were found a post hoc analysis using a simple t-test assuming equal variances was used to evaluate the presence of any significant difference in the mean test scores in math that may be attributed to the method of instruction and other listed factors.
Do gender, ethnicity, socioeconomic status, method of instruction and teacher assignments significantly affect math scores at Harmony Creek Middle School?
Harmony Creek Middle School administration has become concerned with math test score over the past several years and has examined the structure of the program in an effort to address the situation. Professional development activities for the three teachers' currently teaching math classes have been provided and a restructuring of the teaching methodology has been proposed as a possible solution to the problem. At present two of the math teachers use a standards based instructional method with the third teacher using a more traditional method. This paper will attempt to address the different teaching methods along with gender, ethnicity, and socioeconomic status and in what manner these factors apparently affect the math scores within the school. It should be noted that this research is very limited in nature and further research is called for in this subject. It should also be noted that with the limited data available and with the methods of compiling the statistics that there are possible errors within the conclusions. An analysis of data covering several years would possibly be a better indicator of the identified issues and could produce different results.
At present there is some favor to standardize the teaching methods within the school to provide more consistent instruction of the math program. Differing opinions as to efficiency of traditional teaching methods versus standards based instruction exist. Opinions to the concept of grouping students by ethnicity and by abilities within ethnic groups are also a subject of some contention to the staff.
Studies seem to suggest that a standards based classroom helps children to gain a better grasp of math and helps the student to become a better critical thinker. Traditional methods of teaching may produce better procedural skills but seems to do little to help students become better problem solvers. Grouping students by ethnicity and by abilities has also been shown to produce very few positive effects and tend to actually increase gaps in knowledge and skills. Assigning students to teachers of the same race have not been shown to have a significant effect on test scores.
This paper will study the test scores of all math students at Harmony Creek Middle School according to race, gender, and socioeconomic status. Methods of instruction will also be examined to attempt to determine if traditional instructional methods or standards based methods are more effective. It is hypothesized that there is no significant difference in math scores for students based on gender, socioeconomic status or ethnicity. The hypothesis is also that there is no relationship between teacher assignment and test scores based on ethnicity.
Review of literature
Past studies have theorized that grouped students should on average do better and individually should do at least as well. It is also theorized that a status order could lead to increased competition within the group, harder work by individuals and to higher results for the group as a whole (Hoffer, 1992). Other factors would appear to have some bearing on grouping though as it is often thought that teachers relegated to lower group classes would have lower levels of job satisfaction and that the effort of these teachers would decline. The grouping of students by ability or ethnic grouping may also result in unequal allocation of resources, the education of blacks, for instance, would often not receive the same quality resources and concerns as the education of whites (Harris, 2008).
Students in higher grouped classes are more likely to be taught by more skilled and motivated teachers who would provide more engaging instruction. Lower grouped classes would tend to focus on basic skills, test preparation and rote learning (Worthy, 2010). Since lower grouped classes would move more slowly and cover less material the gap in content covered would steadily increase. It is often put forth that able students are held back by slower ones when all the students work together in the same class (Goodlad's 1984).
To compare the efficiency of the methods of instruction this project used the ANOVA test to compare scores between the students and the three teachers in an effort to determine if the Direct Instruction method or the Standards based Instruction yielded higher scores. A t-test: two sample assuming equal variances was used as a post hoc analysis when the ANOVA test indicated that there were significant differences in the research data subsets. Assuming a random assignment of students to the three teachers this research should yield results that will allow for a determination to be made as to the Method of Instruction that would insure the highest math scores for the students. A 95% confidence level was used to tabulate the results of this research.
The dataset contains scores from 216 students. Students were assigned to classes apparently without regard to ethnicity, ability, gender or socioeconomic status as each class contained students representing each factor. 71 students were taught by Ms. Ruger using a Direct Instruction or traditional method of instruction. 145 students were taught by Ms. Smith and Ms. Wesson who both employ a Standards Based method of instruction. The analysis of the data was used to find if there was a direct tie between the Method of Instruction and the math scores. A t-test: two sample assuming equal variances was used to compare the scores for the Direct and the Standards based instructional methods.
The data was also used to compare the test scores by factors of ethnicity, gender and socioeconomic status being taught using direct instructional method versus Standards based instruction methods. A t-test: two sample assuming equal variances was used here also for comparison of the scores.
Results and Analysis
71 students were assigned to Ms. Ruger (direct instruction method). 69 students were assigned to Ms. Smith and 76 to Ms. Wesson (standards based method). Students taught using the direct method had a mean score of 55.2 and the mean for students in standards based classes was 70.17. The calculated t Stat for this comparison was 6.94 and the critical value was 1.97. The t Stat being much larger than the critical value allows for the rejection of the null hypothesis and allows us to assume that there is a significant difference in the effectiveness of the two methods of instruction with the Standards based method resulting in higher math scores.
Male students make up 56% of the population for this research. 39 males were assigned to direct instruction classrooms and 81 were assigned to classes using a standards based method. The mean for direct instruction students (male) was 53.30 and the mean for standards based students (male) was 68.20. A t Test gave us a calculated t Stat of 5.13 and a t critical value of 1.98. Because the t Stat is larger than the t Critical we can reject the null hypothesis and find that there is a significant difference of the scores of male students in direct instruction classrooms and those taught in standards based classroom with the direct instruction method yielding higher scores.
Female students make up 44% of the population. 32 females were assigned to classrooms using a direct instruction method and 64 were assigned to standards based method classes. The mean for females taught using the direct instruction method was 57.65. The mean for females taught using the standards based method was 72.65. A calculated t Stat of 4.78 and a t Critical value of 1.98 would allow for the rejection of the null hypothesis as the t Stat is larger than the t Critical value. Rejecting the null in this instance would allow us to determine that the math scores of females taught using the standards based instruction method were higher than those of females taught using the direct instruction method.
Asian students make up 24% of the population of students. The number of Asian students taught under the direct instruction method was 17 and the number of Asian students taught under the standards based method was 36. A t Test: two tailed assuming equal variances resulted in a mean of 53.70 for Asian students assigned to teachers using a direct instruction method and 71.36 for those Asian students assigned to teachers using standards based methods. A calculated t Stat of 3.76 and a t Critical value of 2.00. The value of the t Stat being larger that the t Critical value allows for the rejection of the null hypothesis and leads to the conclusion that within the Asian subpopulation those students taught using the standards based method of instruction scored higher in math than those Asian students taught using the direct instruction method.
Black students represent 24% of the group. The number of black students taught using the direct instruction method is 18 and the number of black students taught under the standards based method is 34. The mean for Black students assigned to teachers using the direct instruction method was 55.22 and 72.06 for those Black students assigned to teachers using standards based methods. A t Test of this subpopulation resulted in a calculated t Stat of 3.82 and a t Critical value of 2.00. As the value of the t Stat is larger than the t Critical value the null hypothesis is rejected and a conclusion that the standards based teaching method results in higher math scores for the black students in this population is reached.
Hispanic students account for 31% of the population of this group. The number of Hispanic students taught using the direct instruction method was 25 and the Hispanic students assigned to standards based classrooms numbered 41. A t Test of the Hispanic subpopulation resulted in a mean of 55.64 for Hispanic students assigned to teachers using direct instruction and a mean of 70.41 for those assigned to teachers employing standards based teaching methods. A calculated t Stat of 3.90 and a t Critical value of 1.99 was observed for this subpopulation. As the t Stat is larger than the value of t Critical the null hypothesis is rejected and it is concluded that Hispanic students achieve higher math scores when taught using a standards based method.
White students account for the remaining 21% of the population. 11 students of this subpopulation are assigned to teachers using a direct instruction method and 34 to teachers employing standards based methodology. A t Test resulted in mean of 56.90 for white students under a direct instruction method and a mean of 66.73 for white students taught using standards based method. A calculated t Stat of 2.06 and a t Critical value of 2.01 allow for the rejection of the null and the conclusion that white students taught using standards based teaching methods achieved higher math scores during the period studied.
35 students in this group receiving free or reduced price lunches were assigned to teachers using a direct instruction method. 69 students received free or reduced price lunches and were assigned to teachers using standards based teaching methods. The calculated mean for this subpopulation taught under direct instruction was 56.17. The mean for the students receiving free or reduced price lunches taught under standards based instruction was 71.02. A calculated t Stat of 5.10 and a t Critical value of 1.98 allow for the rejection of the null hypothesis and allows for the determination that students receiving free or reduced price lunches achieve higher math scores when taught using standards based methods.
36 students who did not receive free or reduced price lunches were assigned to teachers using a direct instruction method. 76 students who did not receive free or reduced price lunches were assigned to teachers who used standards based instruction methods. The mean score for students who paid full price for lunches and were taught using direct instruction was 54.38% and the mean score for students paying full price and assigned to teachers who use standards based methods was 69.39. A calculated t Stat of 4.75 and a t Critical value of 1.98 allow for the rejection of the null hypothesis and further allow for the conclusion that students who did not receive reduced price or free lunches and were taught using the standards based instruction method scored achieved higher math scores than the students who did not receive reduced price or free lunches and were assigned to teachers using a direct instruction teaching method.
The results of this study would seem to make a clear suggestion that Standards Based Instruction should improve math test scores at the Harmony Creek Middle School. In nearly every category there existed a significant difference in scores between students taught using a Standards Based method and those taught using a Direct Instruction method. This trend appears across all of factors that were examined and would appear to follow the trends noted in other research that does exist. As Thompson (2009) noted Standards Based practices were found to be significant contributors to students math achievement and that virtually none of the observed non-SBI practiced were found to be a significant contributor to student achievement by gender or ethnic grouping.
For the purpose of this research a committee was formed to assist in the evaluation of the research results and in the determination of the more effective instructional means. Committee members consist of 3 active or former middle school teachers who are familiar with the type of research to be evaluated, the instructional methods and with the demographics of the community, two community members who are active in their support of the school and a faculty member of the local community college. All members were chosen because of their involvement in both the community and local schools. All of the committee members have some background in education, business, and finance or in the legal field.
Harmony Creek Middle School will need to purchase 71 textbooks at a cost of $100 each to implement the change to a standards based instructional method in all math classes. The total cost of the textbooks will be $7100. The committee feels that the expense of purchasing new textbooks that will be needed to implement a school wide policy of a standards based teaching method is justified as there should be a marked improvement in math scores which should result in an improved atmosphere throughout the school and the community.
Implementing changes to the math curriculum should increase scores which will help to boost the morale of both students and faculty. An increase in math scores will also tend to increase support from the community as its members soon see that Harmony Creek Middle School is not content to maintain the status quo and is willing to take steps to improve the education of the students and in the improvement of the community. The vision statement of Harmony Creek Middle school proclaims that:
We believe that each of our students, our faculty and our community is unique.
We believe that each of our students, our faculty, and our community deserve the opportunity to achieve their full potential.
We believe that each person is responsible for their own actions and the consequences of those actions.
We believe that diversity strengthens individuals and the community.
We believe that learning in an essential and lifelong process.
To these ends this committee feels that we must enforce this vision statement with action and do all that is possible to further education, diversity and opportunity within our schools. We also feel that one method to accomplish this goal is the implementation of a Standards Based Instructional method in math classes at Harmony Creek Middle School.