Mathematical Thinking - Essay Example

Running Head: Mathematical Thinking Mathematical thinking Assignment 1 Institution name: Course title: Date: Question 1. Description of the sample Students In the sample it is realized that the number of students involved in the exercise totals to 576. These students come from different schools which are geographically located in different locations. Of the 576 students male students count up to 279. This translates to 48.4 % of the total sample. Female students on the other part count to 297 translating to 51.6 percent of the total sample. It can be noted that this sample is uniformly distributed between gender variables. Table 1.0 showing total number of students who participated n the study as well as their gender frequencies Figure 1.0 pie chart showing gender participation in the all the schools. The gender representation is shown by the pie chart above where 48.44% of the male and 51.56% of the female are participated as respondents. Descriptive statistics showing students location The same stdnts are geographicaly drawn from three school locations. These locationsa are Urban, Suburban and rural. These form 100% of the sample locations since no missing location was encountered. In the analyis it was found that the location that had the highest sample number was rural with contribution of more than 50% of the total population sample. Urban followed with 176 students translating to 30.6% while the suburban had 111 students translating to 19.3% of the total population sample. From Fig. 2.0 a pie chart showing number of students per school location Question 2 Descriptive table showing respondent on mathematical proof Table 2.0 The above table shows the mean standard deviation, variance and skewness of the all the six scale of mathematical thinking Question 3 Performance in male and female There is no much difference in the performance of male and female students in the mathematical thinking classes. However it was realized that female students tend to have better skills in logical relations compared to male students. Female students in this scale performed better than male students, this is translated to the higher mean of 8.0323 compared to males’ mean of 9.2626.Female student’s also depicted mastery of generalization skills better than male students with an upper margin of 0.3278. This is also realized in the induction scale with females indicating slight upper margin of 0.013. In the other scales of use of symbols and generalization, male students depicted a slight better performance than female students. From the analysis it can be concluded that female students have a higher achievement ratio in total mathematics compared to that of male students. Female students depicted a total achievement mean of 28.507 while male depicting a total achievement mean of 25.496. it can be generalized that female students are better in mathematics classes as compared to male students Question four Differences in schools In overall performance suburban schools indicate higher performance index than the urban or rural schools. Compared to urban schools in generalization, suburban has a higher mean of 8.5275 compared to Urban 7.1936. This translates to a difference of 1.3339 in mean. In can therefore it can be inferred that suburban students tend to generalize better than urban students. In other scales like induction, deduction, use of symbols and logical relations suburban schools also display a higher skill level evidenced by the higher mean displayed compared to the urban students. In total mathematics achievement, suburban still indicate a high achievement with a mean of 28.298 as compared to urban 25.544. Suburban students can therefore be assumed to be doing better as compared to other students in other schools. The mean deviation in all scales of urban schools is also higher than that of sub urban schools. This indicates the extreme cases that are likely to be encountered in the urban schools. However as indicated by the deviation of suburban schools, there is an indication that most students perform averagely as compared to other students in other locations. Question five Effects of gender on generalization Univariate Analysis of Variance Acording to the above analysis it can be noted that in total generalization, male students in rural environment have a higer mean as compared to those in urban and suburban schools . In female students there is a difference however with students in suburban displaying higher mean than those in rural and urban areas. The highest female mean in this case is 9.5547 while the higest male mean is 8.1533. in total female studenst in all areasperfom better than male students. This infers that gender has some influence on generalization. From the above data it can also be infered that students in suburban areas perform better than those in rural areas and urban areas. Urban schools indicated low generalization mean index of the three locations. Location therefore determine the students generalization score/skills. The line graph above shows the mean of male students and female students. From the graph it can be notted that most female students indicate high mean values in urban and rural establishment. Male students however indicate low mean values. This realization can be used to conlcude that gender has a role in generalization perfomance of students. The data above hower dose not explain the low performance of female students in urban areas. The significant values of separate gender and location affect on generalization strongly indicates no reason at all as to reject the hypothesis that they both affect the outcome. It is therefore drawn from the analysis that gender and location separately affect the outcome of generalization scores amongst students. From the above test the significant value of joint gender and location is exactly 0.05. this value depicts some evidence of location and gender having some effect on generalization performance FOR INDUCTION Univariate Analysis of Variance In induction gender also is seen as a contributing factor. Male students perform better in total as compared to female students. In urban areas male students indicated a mean of 7.6884 against that of female at 7.1202. this is also seen in suburban areas with male students indicating a high mean of 9.1182 and females indicating a mea of 7.2222. From the analysis it a conclusion can be drawn to the effect that male student perform better in induction as compared to female students The line graph below depicts a visual picture of the same. The significant values of separate gender (0.552) and location (0.0266) affect induction strongly since the values are greater than 0.05.They indicates no reason at all as to reject the hypothesis that they both affect the outcome. It is therefore drawn from the analysis that gender and location separately affect the outcome of induction scores amongst students. QUESTION SIX INTERESTING ASPECT OF DATA IN THIS FILE From this data we can realize that performance in total mathematics thinking in rural areas is higher than in most of the other areas. Consider the graph below for induction at different schools. It is to be realized that male students as well as female students display high mean values as compared to other locations. The same trend also applies to generalization. The line graph below also indicate that in rural areas students tend o have higher generalization abilities as compared to other locations. References Achen, Christopher H. (1982). Interpreting and using regression. Series: Quantitative Applications in the Social Sciences, No. 29. Thousand Oaks, CA: Sage Publications. Argrous, G. (2011) 3rd edition. Statistics for research. London, Sage Berry, William D. (1993). Understanding Regression Assumptions. Series: Quantitative Applications in the Social Sciences, No. 92. Thousand Oaks, CA: Sage Publications. Coakes, S. & Ong, C. SPSS: analysis without anguish version 18.0 for windows. John Wiley & Sons. Diekhoff, G.M (1996).Basic statistics for the social and behavioral sciences. Upper Saddle River, N.J., Prentice Hall Hardy, Melissa A. (1993). Regression with dummy variables. Thousand Oaks, CA: Sage Publications. Series: Quantitative Applications in the Social Sciences, No. 93. Read More