Because the students were assigned to the three conditions in the order their teacher brought them, the preliminary analyses were necessary to be applied to see if there was any difference on the measurements among three groups prior to the treatment.
As shown in Table 2, 3×2 MANOVA was run to examine the estimation accuracy (Percentage of Absolute Error), regression coefficient R2, Slope and base 10 score at pretest. No significant gender differences (p= .81) were found on PAE, R2, slope and base-10 scores at pretest. For male group, PAE = 15. 75, R2 = .57, Slope = .53, base 10 score = 2.68. For the female group, PAE = 18. 31, R2 = .46, Slope = .43, base 10 score = 2.73. Either group differences (p = .18) were found on at pretest on PAE, R2, slope and base 10 scores at pretest. For blocks group, PAE = 17. 54, R2 = .44, Slope = .50, base 10 score = 2.69. For bundles group, PAE = 13. 00, R2 = .61, Slope = .57, base 10 score = 2.61. For control group, PAE = 20. 60, R2 = .46, Slope = .39, base 10 score = 2.51. The participants in the three groups (i.e., blocks, bundles and control groups) were still in the logarithmic representations that were lower than the index R2 of linear representation at pretest respectively: In the blocks group, Rlin2 < Rlog2, (0.52 vs. 0.79). In bundles group Rlin2 < Rlog2, (0.48 vs. 0.73) and control group Rlin2 < Rlog2, (0.43 vs. 0.62). All of the students across the three groups were found logarithmic dominant in pretest. Therefore none of the students was screened out. All the 58 participants went on to the posttest.
The preliminary analysis indicates that there were no gender or group differences among the participants on estimation accuracy (Percentage of Absolute ...
... middle of paper ...
...onsidered as covariate for the outcomes of Slope in the further analysis. No further planned comparison or post-hoc test was conducted. The results were tested using the multivariate criterion of Wilks’ Lambda (Λ) for each dependent variable of time condition and age.
The results provided converging evidence that overall estimation improved over time, Wilks’ λ = .97, F(4, 52) = 3.39, p < .05, ŋ2 = .29. The instructional intervention effect is significant, for the group differences of condition, Wilks’ λ = .87, F(8, 104) = 5.92, p < .05, ŋ2 = .19. There was also found interaction effect of time* condition, Wilks’ λ = .87, F(8, 104) = 5.41, p < .05, ŋ2p = .18.
The test of between-subject use the results of Greenhouse-Geisser. Among each dependent variable measure, mean PAE improved over time, F(1, 55) = 3.17, p <.001, ŋ2 = .17. No interaction effect was found.
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