The Most Appropriate Way of Educating Elementary Age Children in Mathematics - Coursework Example

A study to determine the most appropriate way of educating elementary age children in mathematics al affiliation: Introduction The main aim of the study is determining the most appropriate way of educating elementary age children in mathematics. Specifically, it is believed that 5th grade girls performance is higher in small class sizes and on the other hand for boys, they do better in larger classes. A pilot program was arranged through school district whereby some of the classes had to be reduced before the mathematical competency assessment was undertaken. The variables included in the data set include Gender: male (M) or female (f), Classroom: small (1), more than 10 children (medium; 2), between 11 and 19 children large (3), 20 or more children, Score: final score on competency assessment Perform exploratory data analysis on all variables in the data set. Research Hypothesis Girls could perform better than boys in classrooms that have fewer students Exploratory data analysis on all data set variables was undertaken as indicated in the next section Gender Case Processing Summary Gender Cases Valid Missing Total N Percent N Percent N Percent Math-scores Male 30 100.0% 0 0.0% 30 100.0% Female 30 100.0% 0 0.0% 30 100.0% Case Summariesa Participant Classroom size Math-scores 1 1 10 or less 93.00 2 2 10 or less 96.00 3 3 10 or less 92.00 4 4 10 or less 95.00 5 5 10 or less 89.00 6 6 10 or less 87.00 7 7 10 or less 93.00 8 8 10 or less 99.00 9 9 10 or less 92.00 10 10 10 or less 91.00 11 11 11-19 90.00 12 12 11-19 86.00 13 13 11-19 87.00 14 14 11-19 92.00 15 15 11-19 90.00 16 16 11-19 93.00 17 17 11-19 87.00 18 18 11-19 92.00 19 19 11-19 91.00 20 20 11-19 89.00 21 21 20 or more 90.00 22 22 20 or more 91.00 23 23 20 or more 98.00 24 24 20 or more 93.00 25 25 20 or more 94.00 26 26 20 or more 92.00 27 27 20 or more 90.00 28 28 20 or more 89.00 29 29 20 or more 88.00 30 30 20 or more 87.00 31 31 10 or less 95.00 32 32 10 or less 98.00 33 33 10 or less 92.00 34 34 10 or less 90.00 35 35 10 or less 88.00 40 40 10 or less 98.00 41 41 11-19 89.00 42 42 11-19 92.00 43 43 11-19 92.00 44 44 11-19 95.00 45 45 11-19 85.00 46 46 11-19 82.00 47 47 11-19 85.00 48 48 11-19 86.00 49 49 11-19 90.00 50 50 11-19 89.00 51 51 20 or more 76.00 52 52 20 or more 72.00 53 53 20 or more 79.00 54 54 20 or more 81.00 55 55 20 or more 82.00 56 56 20 or more 79.00 57 57 20 or more 74.00 58 58 20 or more 82.00 59 59 20 or more 86.00 60 60 20 or more 81.00 Total N 60 60 60 a. Limited to first 100 cases. Descriptives Gender Statistic Std. Error Math-scores Male Mean 91.2000 .58408 95% Confidence Interval for Mean Lower Bound 90.0054 Upper Bound 92.3946 5% Trimmed Mean 91.0556 Median 91.0000 Variance 10.234 Std. Deviation 3.19914 Minimum 86.00 Maximum 99.00 Range 13.00 Interquartile Range 4.00 Skewness .557 .427 Kurtosis .244 .833 Female Mean 87.1667 1.32707 95% Confidence Interval for Mean Lower Bound 84.4525 Upper Bound 89.8808 Median 88.5000 Variance 52.833 Std. Deviation 7.26865 Minimum 72.00 Maximum 98.00 Range 26.00 Interquartile Range 10.50 Skewness -.272 .427 Tests of Normality(normal distribution) Gender Statistic df Sig. Statistic df Sig. Math-scores Male .120 30 .200* .957 30 .259 Female .100 30 .200* .965 30 .402 *. This is a lower bound of the true significance. a. Lilliefors Significance Correction Math-scores Histograms Box Plot for math-score Classroom size Case Processing Summary Classroom size Cases Valid Missing Total N Percent N Percent N Percent Math-scores 10 or less 20 100.0% 0 0.0% 20 100.0% 11-19 20 100.0% 0 0.0% 20 100.0% 20 or more 20 100.0% 0 0.0% 20 100.0% Descriptives Classroom size Statistic Std. Error Math-scores 10 or less Mean 93.2500 .81394 95% Confidence Interval for Mean Lower Bound 91.5464 Upper Bound 94.9536 5% Trimmed Mean 93.2778 Median 93.0000 Variance 13.250 Std. Deviation 3.64005 Minimum 87.00 Maximum 99.00 Range 12.00 Interquartile Range 6.50 Skewness .002 .512 Kurtosis -1.080 .992 11-19 Mean 89.1000 .72873 95% Confidence Interval for Mean Lower Bound 87.5747 Upper Bound 90.6253 5% Trimmed Mean 89.1667 Median 89.5000 Variance 10.621 Std. Deviation 3.25900 Minimum 82.00 Maximum 95.00 Range 13.00 Interquartile Range 5.75 Skewness -.342 .512 Kurtosis -.292 .992 20 or more Mean 85.2000 1.59868 95% Confidence Interval for Mean Lower Bound 81.8539 Upper Bound 88.5461 5% Trimmed Mean 85.2222 Median 86.5000 Variance 51.116 Std. Deviation 7.14953 Minimum 72.00 Maximum 98.00 Range 26.00 Interquartile Range 11.25 Skewness -.177 .512 Kurtosis -.824 .992 Tests of Normality(Normal distribution) Classroom size Statistic df Sig. Statistic df Sig. Math-scores 10 or less .127 20 .200* .952 20 .401 11-19 .138 20 .200* .969 20 .724 20 or more .123 20 .200* .971 20 .768 *. This is a lower bound of the true significance. a. Lilliefors Significance Correction Math-scores Histograms Box Plot Descriptive or Exploratory data analysis interpretation Basing on descriptive statistics, it is observed that under gender males has a higher math mean score (91%) than females (87%).This is clearly indicated in the box plot. Under classroom size, it is clearly evident that the smaller the classroom size is the high the math mean score. For instance, math mean score for 10 or less classroom size,11-19 classroom size and 20 or more class room size include 93,89 and 85 respectively. It is also observed that the median (91%) and mean (91%) under gender math mean score is same. This clearly proves that the data is normally distributed (Dey 1993). Similarly, under classroom size, math mean score (93) and median (93) is also seen to be the same and this implies that the data is normally distributed Descriptive statistics table for the sample Table. Descriptive statistics N Minimum Maximum Mean Std. Deviation Gender 60 1 2 1.50 .504 Classroom size 60 1 3 2.00 .823 Math-scores 60 72.00 99.00 89.1833 5.92750 Valid N (listwise) 60 Factorial ANOVA The factorial ANOVA was performed using the data set provided Univariate Analysis of Variance Between-Subjects Factors Value Label N Gender 1 Male 30 2 Female 30 Classroom size 1 10 or less 20 2 11-19 20 3 20 or more 20 Dependent Variable: Math-scores Source Type III Sum of Squares df Mean Square F Sig. Corrected Model 1381.483a 5 276.297 21.576 .000 Intercept 477220.017 1 477220.017 37266.639 .000 Gender 244.017 1 244.017 19.056 .000 Classroom 648.233 2 324.117 25.311 .000 Gender * Classroom 489.233 2 244.617 19.102 .000 Error 691.500 54 12.806 Total 479293.000 60 Corrected Total 2072.983 59 a. R Squared = .666 (Adjusted R Squared = .636) Profile Plots To determine if there is a main effect of gender, post hoc tests can be used if applicable. In this case, basing on the results, it is observed that, for classroom sizes, the p values are 0.00.This therefore means that the effect of classroom size on math mean score is statistically significant. It can be concluded that the math mean score for 10 or less, 11-19 and 20 class room sizes are not the same. Post hoc is normally used to determine which variables have differences in cases where the test statistics such as ANOVA can’t really determine which variables are different. This can happen when we have more than two variables, whereby there could be a difference between any of these variables. In this case, it’s not known which variables have the differences. For our case, the variables are two (male and female) and we already know that the mean score is not the same between the two groups. Therefore, there is no need of doing post hoc test To determine if there is a main effect of classroom size, post hoc tests can be used if applicable as well (Field 2013). In this case, basing on the results, according to the table above, it is observed that for gender main effect, the p values are 0.00.This therefore means that the effect of gender is statistically significant. It can be concluded that the math mean score for males and females are not the same. Post hoc will not be useful in interaction effect interpretation since we already have interaction plot which plays the same role. In this case, it is observed that the means score for 10-19 and 10 or less classroom size is the same but that of 20 or more classroom size is seen to be different from either of them. To determine if there is any interaction the two variables, ANOVA was used as below and post hoc tests was as well used to describe the differences observed as indicated below Descriptives Math-scores N Mean Std. Deviation Std. Error 95% Confidence Interval for Mean Minimum Maximum Lower Bound Upper Bound 10 or less 20 93.2500 3.64005 .81394 91.5464 94.9536 87.00 99.00 11-19 20 89.1000 3.25900 .72873 87.5747 90.6253 82.00 95.00 20 or more 20 85.2000 7.14953 1.59868 81.8539 88.5461 72.00 98.00 Total 60 89.1833 5.92750 .76524 87.6521 90.7146 72.00 99.00 ANOVA Math-scores Sum of Squares df Mean Square F Sig. Between Groups 648.233 2 324.117 12.967 .000 Within Groups 1424.750 57 24.996 Total 2072.983 59 Post Hoc Tests Multiple Comparisons Dependent Variable: Math-scores Tukey HSD (I) Classroom size (J) Classroom size Mean Difference (I-J) Std. Error Sig. 95% Confidence Interval Lower Bound Upper Bound 10 or less 11-19 4.15000* 1.58100 .029 .3455 7.9545 20 or more 8.05000* 1.58100 .000 4.2455 11.8545 11-19 10 or less -4.15000* 1.58100 .029 -7.9545 -.3455 20 or more 3.90000* 1.58100 .043 .0955 7.7045 20 or more 10 or less -8.05000* 1.58100 .000 -11.8545 -4.2455 11-19 -3.90000* 1.58100 .043 -7.7045 -.0955 *. The mean difference is significant at the 0.05 level. After running one way ANOVA, it is observed that the p value is less than 0.05.This implies that the means between the groups are not equal. Therefore, we need to run post hoc test to determine which variables have different mean scores between them. Basing on post hoc test, it is observed that the mean scores between all the groups are not the same since the p value for all of them is less than 0.05. To determine if there is support for the hypothesis that girls could perform better than boys in classrooms that have fewer students, interaction plot was constructed. In this case, it is observed that there is support for the research hypothesis. Basing on interaction plot below (estimated marginal means of math-scores); it is clearly evident that the mean score of smaller class size (10 or less) drops towards females or girls. It is clearly evident that as the mean score for the class size of 20 and more approaches towards females it drops drastically. On the other hand, the mean scores remain almost constant for small size classes (11-19 and 10 or less).Also according to interaction plot above, the mean score is seen to rise from the side of boys to girls above 90 for 10 or less class size. Therefore, this proves that girls perform better in small class size than boys and also in big size classes girls perform poorly than boys. Conclusion In conclusion, it is observed that girls perform better than boys in fewer number classrooms than boys. On the other hand boys perform better than girls in classroom with big number than girls. In this regard, the research hypothesis was accepted; that is, girls could perform better than boys in classrooms that have fewer students or boys could perform better than girls in classrooms with many students. This information could be used to set up a program that is most effective and most appropriate in educating elementary age children in mathematics. References Field, A. (2013). Discovering statistics using IBM SPSS Statistics Dey,I. (1993). Quantitative Data Analysis. A User-friendly Guide for Social Scientists. London, New York: Routledge, 43(2), 45-61. Read More