Object in Math: Estimating the Length and Weight - Essay Example

Is a more able of mathematics better at estimating the length and weight of an object than a less able student? I have always wondered whether it was due to natural ability or diligent work that one was placed in a higher academic group than another. I have used the idea of estimation in terms of length and weight of an object to determine natural mathematical ability. In this investigation I wanted to find a method of examining people’s natural ability in estimating, and assess whether those people in the higher mathematic sets do have a greater natural grasp of the subject than those in the lower mathematics set. I therefore randomly chose 20 students from both higher and lower math classes (10 from higher and 10 from lower) to estimate the length (in centimeters) and weight (in grams) of a pen. I decided to specify the units of measurement because some students, such as those from Britain or USA, also use the imperial system of measurement. I have restricted the population of students to girls in my school as it has been proven in the past that the two sexes do have different spatial abilities. Therefore I believe that using boys could have an effect on the results by adding the additional variable. The pen has a length of 14.5cm and a weight of 12 grams. Hypothesis I believe that people who are in the higher mathematics sets will be more able to guess the length and weight of an object with more accuracy than those in the lower sets. This investigation will examine the innate aptitudes of people: abilities that are not usually learned from a textbook. In addition, I believe that those who are better at guessing the weight will, in general, be better at guessing the length. I also believe that the estimates of length will be more accurate than the estimates of the weight. Data Table 1 High Level Set Participant Wt. Gms. Abs Error Lng. Cms Abs Error 1 6 6 10 4.5 2 5 7 10 4.5 3 9 3 12.5 2 4 13 1 11 3.5 5 8 4 8 6.5 6 7 5 10 4.5 7 6.5 5.5 11 3.5 8 11 1 13 1.5 9 11 1 9.5 5 10 4.5 7.5 12 2.5 Mean 4.1 3.8 Table 2 Studies Level Set Participant Wt. Gms. Abs Error Lng. Cms. Abs Error 1 4 8 10 4.5 2 2 10 8 6.5 3 14 2 13 1.5 4 10 2 15 0.5 5 9.5 2.5 5 9.5 6 7 5 9 5.5 7 10 2 14 0.5 8 2 10 13 1.5 9 6 6 8 6.5 10 5 7 7 7.5 Mean 5.45 4.4 Analysis The data was analyzed by viewing several graphical aspects. The groups were compared using the percentage of error on length and weight. An additional chart was created to analyze overall error and predict the trend for a larger sample. Figure 1 indicates the weight error expressed in percetage. It shows both higher and studies level groups. As can be seen, the higher level group was consistently more accurate than the studies level group. The mean error (from data tables) for the higher level group was 4.1 grams, while the studies level group had a mean error of 5.45 grams. Figure 2 illustrates the length error expressed as a percentage. The estimation of length shows that the higher level set was more consistent, but the studies group had 4 samples that were as good or better than any of the higher set. However, the overall mean for the higher set was lower with a mean error of 3.8 cm., while the studies set had a mean error of 4.4 cm. Figure 3 is a scatter plot that shows the overall accuracy of the participants. It also includes a trend line to predict the results that correlate length accuracy to weight accuracy. . As the chart indicates, the overall accuracy of the higher level set was more consistent and more accurate than the studies set. In addition, it indicates that the greater the weight error, the greater the length error was for the studies set. However, the flat line for the higher set did not show the same correlation. Figure 4 illustrates the same data as Figure 3 with the axis reversed. Once again we see the trendline of weight error for the higher set running well below the error of the studies set. In addition, it shows that the data for the higher set is more tightly grouped than the studies set. Evaluation The hypothesis that the higher level set would be more accurate at estimating has proven true. This demonstrates that there is an innate ability that contributes to a student’s math skills. The exception of the 4 students in the studies set that guessed the length more accurately may be due to the small sample set and may not bear out in a larger experiment. The fact that the higher level students were more consistent (maximum to minimum range) further indicates a common characteristic among this set. There was no significant correlation between the accuracy of the weight and the accuracy of length for the higher group as indicated by the flatness of the trendline in Figure 3 and 4. There was a slight correlation for the studies group as shown by the rising trendline in Figures 3 and 4. This may be due to the few students in the group who were at a higher level than their peers. Overall, however, the ability to guess length does not indicate an ability to guess weight for either set. However, the hypothesis that the length would be more accurate than the weight has been shown to be true for both sets as indicated in Figures 1 and 2. Conclusion The experiment has indicated that students who have a natural ability to estimate spatial parameters have more ability at mathematics. In addition, students are better at estimating the length, which is visible, than they are at estimating weight. Due to the small sample size and the concentrated environment of the participants, the results cannot be generalized for a larger population. The results of the experiment are interesting and indicate a need for further research. Additional experiments need to be conducted that would involve a larger sample size and a widespread group of participants. In addition, other controls would need to be in place to determine the validity of the data. Read More