Pretests were administered in each class during one class period (see Appendix A for the sixth grade pretest and Appendix B for the seventh grade pretest). The pretest consisted of ten grade-level word problems which were based on concepts the students had already been taught during the school year.
Pretest data were entered into an Excel spreadsheet in which student names were listed in the first column. Each pretest item number was listed across the top of the spreadsheet, and for each student, the number “1” was placed in the item cell for a correct answer, and a “0” was placed for an incorrect answer. The final column returned the number of items each student answered correctly. These numbers were transferred to a separate spreadsheet which calculated the average number of correct answers for each grade level. A similar procedure was used to record posttest data.
Data for All Students.
As shown in Table 2, the mean pretest score for sixth grade students (n=61) was 5.38. Scores ranged from 0 correct answers (three students) to 10 correct answers (two students), with a median score of 5.5. The mean score for seventh grade students (n=41) was 3.88. Scores for this group ranged from 0 correct answers (4 students) to 9 correct answers (three students), with a median core of 4. See Figure 4.1 for the distribution of pretest scores.
Table 2
Mean Pretest Scores for All Students
Grade Participants (n) Pretest Mean Standard Deviation Standard Error
Median Mode Range
6 68 5.38 2.61 0.32 5.5 7 10
Figure 4.1. Distribution of Pretest Scores for All Students.
Posttests were administered after five weeks of instruction and practice sessions using the PIES strategy (see Appendix C and D for posttests for each grade, and Appendix E and F for practice problems). Students who were absent from school when the pretest was administered were given the posttest, but their scores were not included in the research data.
The posttests were not administered in one class period, due to several factors. First, the amount of time it took students to complete the problems on the posttest was longer than the time it took for the pretest, possibly because they were applying the steps of the PIES strategy.
Second, the school district had missed several days of school due to inclement weather, so teachers were behind schedule on presenting new material that would be assessed on the spring formative assessment and could not devote an entire class period for posttest administration. Finally, the seventh grade classes had a regular unit test scheduled for the week prior to the PIES posttest that had to be moved to the Monday on which the posttest was planned.
In the sixth grade classes, the teacher made time at the beginning of class for students to finish their pretests, and they were able to finish them in three separate class sessions. Because seventh grade students had a unit test and a formative test during the week the posttest was
planned, they were only allotted twenty-to-thirty minutes a day to complete the posttest. For several seventh grade students, it took five days to complete the posttest.
As shown in Table 3, the mean posttest score for sixth grade students (n=68) was 6.57. Posttest scores for sixth grade students ranged from 1 correct answer (one student) to 10 correct answers (two students), with a median score of 7. The mean posttest score for seventh grade students (n=41) was 5.20. Scores ranged from 0 correct answers (two students) to 9 correct answers (two students). See Figure 4.2 for the distribution of posttest scores.
Table 3
Mean Posttest Scores for All Students
Grade Participants (n) Posttest Mean Standard Deviation Standard Error
Median Mode Range
6 68 6.57 2.08 0.25 7 8 9
7 41 5.20 2.28 0.36 5 5 9
Figure 4.2. Distribution of Posttest Scores for All Students.
Both groups showed improvement from pretest to posttest. A paired sample t-test was performed to determine whether there was a statistically significant difference between pretest and posttest means.
As shown in Table 4, among sixth grade participants in the study, there was a significant difference between pretest and posttest scores (t (68) = 4.944, p<.001). Similarly, there was a significant difference between pretest and posttest mean scores for seventh graders (t (41) = 3.861, p<.001). Therefore, the data support the hypothesis, which was that students in inclusive middle school mathematics classes who learn to use the PIES mnemonic word problem strategy will demonstrate improvement from pretest to posttest measures of word problem solving performance.
Table 4
Comparison of Means and Paired Sample t-Test Results – All Students Grade Participants (n) Pretest Mean Posttest Mean t Stat t Critical two-tail P(T<=t) two-tail 6 68 5.38 6.57 4.944 1.996 0.0000 7 41 3.88 5.20 3.861 2.021 0.0002
Data for Students with Disabilities (SWD)
Separate data analysis, identical to analysis for all participants, was conducted for participating students with disabilities to determine whether the same results would be observed for this subgroup.
As shown in Table 5, the pretest mean score for sixth grade SWD (n=21) was 3.95. Scores for this group ranged from 0 correct answers (two students) to 8 correct answers (one student), with a median score of 4. The mean score for seventh grade SWD (n=13) was 2.54. Scores ranged from 0 correct answers (three students) to 7 correct answers (two students), with a median score of 2. The distribution of pretest scores for SWD is shown in Figure 4.3.
Table 5
Mean Pretest Scores - SWD
Grade Participants (n) Pretest Mean Standard Deviation Standard Error
Median Mode Range
6 21 3.95 2.45 0.54 4 3 8
7 13 2.54 2.53 0.70 2 2 7
Figure 4.3. Distribution of Pretest Scores – SWD.
As shown in Table 6, the posttest mean score for sixth grade SWD (n=21) was 5.81, with a median score of 6. Scores ranged from 1 correct answer (one student) to 10 correct answers (one student). The mean posttest score for seventh grade SWD was 3.62, with a median score of 4. Scores ranged from 0 correct answers (two students) to 7 correct answers (one student). The distribution of posttest scores is shown in Figure 4.4.
Table 6
Mean Posttest Scores - SWD Grade Participants (n) Posttest Mean Standard Deviation Standard Error
Median Mode Range
6 21 5.81 2.52 0.55 6 8 9
Figure 4.4. Distribution of Posttest Scores – SWD.
Again, both groups showed improvement from pretest to posttest. A paired sample t- test was performed to determine whether there was a statistically significant difference between pretest and posttest measures for this subgroup. As shown in Table 7, there was a significant different between pretest and posttest mean scores for sixth grade participants (t (21) = 4.468, p<.001). However, there was no significant difference between pretest and posttest mean scores for seventh grade students (t (13) = 1.783, p=0.999). Because of the mixed results, it is difficult to draw a conclusion about the effectiveness of the PIES strategy with students who have disabilities. These results are discussed in Chapter 5.
Table 7
Comparison of Means and Paired Sample t-Test Results – SWD
Grade Participants (n) Pretest Mean Posttest Mean t Stat t Critical two-tail P(T<=t) two-tail 6 21 3.95 5.81 4.4677 2.08596 0.0002 7 13 2.54 3.62 1.7828 2.17881 0.0999