Comparing Five Methods of Teaching Percents: A Statistical Analysis, Study notes of Teaching method

Download Comparing Five Methods of Teaching Percents: A Statistical Analysis and more Study notes Teaching method in PDF only on Docsity! EDUCATIONAL STATISTICS II (EDRM 711) Report #22: Model In this report I will analyze the data from a study of five different ways to teach the concept of percents. Students of four different mathematical ability levels were chosen to participate in the study. Students within an ability level were randomly assigned to five conditions. Percents were taught differently within each condition. The five methods used to teach percents were a) the three-cases method, b) the equation method, c) the formula method, d) the unitary analysis method, and e) the proportions method. (See Parker and Leinhardt, 1995, for a description of these methods.) At the end of the instruction, all students were administered a twenty-point test on percents. The following line graph illustrates the means for the five conditions on the percents test. For this graph, and the analyses that follow, method 1 is the three cases method, 2 is the equation method, 3 is the formula method, 4 is the unitary method, and 5 is the proportions method. METHOD 54321 Es tim at ed M ar gi na l M ea ns 16 15 14 13 12 11 10 9 The three cases method appears to be the worst; the proportions method appears to be the best. The mean difference between these two methods is 5.25 points, which is over a full standard deviation difference. Statistics 4 9.75 4.79 4 13.25 4.27 4 12.75 3.86 4 12.00 4.69 4 15.00 4.69 Three Cases Equation Formula Unitary Proportions Valid N Mean Std. Deviation The omnibus test of mean differences is statistically significant (P < .001). This means that true differences exist between the methods. Tests of Within-Subjects Effects Measure: MEASURE_1 58.700 4 14.675 27.092 .000 6.500 12 .542 Source METHOD Error(METHOD) Type III Sum of Squares df Mean Square F Sig. The size of the differences can be estimated with 95% simultaneous confidence intervals. The following table shows that the only differences we can be certain of are comparisons with the three-cases method. More specifically, we know that the equation method, the unitary method, and the proportions method all yield higher achievement on the percents test than the three-cases method. We cannot conclusively ascertain that any one of these methods is better than the others, though the proportions method does show the most promise based upon sample results. This method results in a mean gain of at least 3.4 points when compared to the three-cases method. (Note: A valid confidence interval cannot be constructed to compare the unitary and proportions methods since the difference scores were all the same.)