Inequalities (as proposed by the Georgia Department of Education). To ensure
consistency in grading on the posttest, the students recorded their answers on a Scantron sheet, which was read and scored electronically. The teacher of both groups examined the Scantron sheets to account for any possible grading errors due to poor erasures. The teacher of each group provided the scores to the researcher.
IMMS administration. At the end of Unit 7, the IMMS was administered online via Survey Monkey to participants in both groups in a safe, nonthreatening environment in their math classrooms. As discussed earlier, survey results were not obtained from 16 participants due to technical difficulties during the administration of the survey. It was impossible for the teacher to tell which students‘ survey responses were not actually submitted. To ensure that a student‘s responses were not counted twice, the teacher did not have any students resubmit their responses.
indicated that the use of ―electronic data collection in quantitative research is popular‖ (p. 159) and ―provides an easy, quick form of data collection‖ (p. 159). The researcher believed that using the anonymity of an online survey format helped prevent
apprehension by the participants and may have encouraged honesty (Ary, Jacobs, Razavieh, & Sorensen, 2006; Whelan, 2008). A paper version of the survey was available to anyone who chose to complete this type of survey rather than the online version. Care was taken by the teachers to make certain that students knew this was a research project specifically relating to CPS use and that their participation and responses were not detrimental to them in any way. To reduce possible bias, the researcher did not have access to the students during the survey. A copy of the online survey was included for review by the Liberty University Institutional Review Board (See Appendix O). Data Analysis
This study investigated the effect of CPS-based math instruction with or without PI on the achievement and motivation of eighth grade students. Parametric tests utilized are discussed in this section.
Analysis of student achievement data. An analysis of covariance (ANCOVA) was conducted to see if there was a difference in the Unit 7 mean posttest scores of students who received CPS with PI and students who received CPS without PI. In order for the results of the ANCOVA to be utilized and the results considered generalized to the population of interests, several assumptions were verified using appropriate statistical analyses: reliability of the covariate, linearity, homogeneity of regression, normality, and homogeneity of variance. An ANCOVA has the ability to determine if the means
adjusting for differences in group size. This was appropriate since there were 16 more students in the treatment group than in the control group (Green & Salkind, 2008). Additionally, an ANCOVA is appropriate when groups are deemed to be nonequivalent due to lack of randomization in the selection process. A covariate, 2010 ITBS Math Total scores, was used to adjust for differences between the groups on prior math achievement. According to Gay and Airasian (2003), ―Analysis of covariance adjusts scores on a dependent variable for initial differences on some other variable related to performance on the dependent‖ (p. 343). The means and standard deviations of the Unit 7 Posttest for the treatment group and the control group were calculated. The effect size was calculated using the Eta squared statistic and interpreted based on Cohen‘s d (1988).
Analysis of student motivation data. Data were collected from the IMMS to measure student motivation. The IMMS consists of four subscales (attention, relevance, confidence, and satisfaction) that have been determined in previous research to be
correlated (Gabrielle, 2003; Keller, 2010b). Thus, a correlation matrix for each of the four subscales of the IMMS was created prior to conducting the MANOVA. Because the subscales were correlated, MANOVA was determined to be the appropriate statistical method for this research setting (Green & Salkind, 2008; Tabachnick & Fidell, 2008). The MANOVA tested whether there was a difference between the IMMS scores of students who received CPS with PI and students who received CPS without PI in terms of the linear combination of the four motivation subscales. Follow up testing was
completed in order to determine which components of motivation might be significantly different between the treatment group and the control group. Since the means of two
series of independent sample t-tests (Green & Salkind, 2008; Indiana University, 2006). In order for the results of the t-tests to be utilized and generalized to the population of interests, several assumptions were verified using appropriate statistical analyses: multivariate normality, independence of units, homogeneity of variance matrices, linearity, singularity, and multicollinearity. Independent sample t-tests were then conducted to determine if the differences in the mean scores on each of the IMMS subscales for the two groups were significant or if the differences were due to sampling error.
Summary
This research was conducted in a public eighth grade middle school in rural northeast Georgia during one four-week unit of math study. During the course of this math unit, students in both the treatment group and the control group received CPS-based math instruction. However, only the treatment group received PI in addition to the CPS- based math instruction. At the end of the unit, student posttest scores were collected and analyzed using an ANCOVA. Additionally, at the end of the treatment all students completed a validated online survey, the IMMS, in order to measure motivation in regards to CPS-based instruction with and without PI. The IMMS scores were analyzed using a MANOVA and multiple independent sample t-tests. The results of the study are presented in the following chapter.