# statistics

By AnjieTangie
Sep 28, 2014
1130 Words

TITLE:

To determine whether standard 3 students of San Fernando Boys’ Government School perform better in Mathematics than Mental Mathematics

STATEMENT OF TASK

Mathematics is a very important subject taught in all schools. Mental mathematics compliments the regular mathematics and therefore both are tested in primary schools. Mathematics is the written application of operation. It teaches students to think clearly, reason well and strategize effectively. Mental Mathematics is the ability to utilise mathematical skills to solve problems mentally. The marks scored by pupils generate statistics which are used by teachers to analyse a student’s performance and development of theories to explain the differences in performance.

The Standard 3 class is where the transition from junior to senior level occurs where teachers expect the transference of concrete to abstract thinking would have occurred.

A common theory by many primary school teachers is ‘Students perform better in Mathematics than Mental math. Mental math is something that has to be developed and involves critical thinking. Mental math requires quick thinking and the student must solve the problem in their minds whereas in regular mathematics, the problem can be solved visually. Therefore, teachers should take these factors into consideration while testing and marking students in these areas.’

In this study, the statistics of 30 students of a standard 3 class of San Fernando Boys’ Government School will be analysed to determine the truth of this theory.

DATA COLLECTION METHODS

Mathematics and mental mathematics marks of term 1 of the class of 2013 were obtained from a Standard 3 teacher of San Fernando Boys’ Government School. The marks were divided into the form:

Mathematics Marks, x

Mental Mathematics marks, y

DATA PRESENTATION AND ANALYSIS

Sample number

Marks earned (x)

x²

1

70

4900

2

86

7396

3

49

2401

4

66

4356

5

94

8836

6

68

4624

7

92

8464

8

96

9216

9

76

5776

10

71

5041

11

83

6889

12

59

3481

13

65

4225

14

98

9604

15

80

6400

16

68

4624

17

72

5184

18

85

7225

19

100

10000

20

69

4761

21

61

3721

22

80

6400

23

87

7569

24

95

9025

25

63

3969

=1933

=154087

Table 1: Sample data of marks earned by students in Mathematics examinations

Sample Number

Marks Earned (y)

y²

1

40

1600

2

93

8649

3

26

676

4

53

2809

5

100

10000

6

46

2116

7

93

8649

8

86

7396

9

39

1521

10

46

2116

11

74

5476

12

60

3600

13

40

1600

14

86

7396

15

66

4356

16

45

2025

17

61

3721

18

87

7569

19

48

2304

20

55

3025

21

75

5625

22

62

3844

23

24

576

24

60

3600

25

33

1089

=1498

=101338

Table 2 of marks earned by students in Mental Mathematics

Calculation of Measures of Spread (mean, variance and standard deviation) of mathematics and mental mathematics marks.

Mean =

=

=77.32

Variance S² =

=

=185.098

Standard Deviation S =

=

=13.61

Mean =

=

= 59.92

Variance S² =

=

=463.11

Standard S =

Deviation =

=21.52

STEM AND LEAF DIAGRAM

Mathematics

Mental Mathematics

9

9

9 8 8 6 5 3 1

6 2 1 0

7 6 5 3 0 0

8 6 5 4 2

0

0

1

2

3

4

5

6

7

8

9

10

4 6

3 9

0 0 5 6 6 8

3 5

0 0 1 2 6

4 5

6 6 7

3 3

0

Key: 9 4 represents 49 marks

Key: 5 3 represents 53 marks

Figure 1: Stem and leaf diagram of marks earned in Mathematics and Mental Mathematics

Calculation of the median Q1, Q3, inter-quartile range, maximum and minimum values of mathematics and mental mathematics

Mathematics

Mental Mathematics

Lower Quartile Q1 =th term

=

=6.5th term

=

=67 marks

Median Q2 =th term

=

=13th term

=76 marks

Upper Quartile Q3 =th term

=

=19.5th term

=

=89.5 marks

Inter-quartile =Q3-Q1

Range =89.5-67

=22.5

Maximum value = 100marks

Minimum value =49marks

Lower Quartile Q1 =th term

=

=6.5th term

=

=42.5 marks

Median Q2 =th term

=

=13th term

=60 marks

Upper Quartile Q3 =th term

=

=19.5th term

=

=80.5 marks

Inter-quartile =Q3-Q1

=80.5-42.5

=38

Maximum value =100

Minimum value =24

BOX AND WHISKER DIAGRAM

Figure 2 of a stem and leaf diagram of mathematics and mental mathematics marks

Figure 3 of a bar graph representing marks earned in mathematics Modal Class: 61-70 marks

Figure 4 of a bar graph representing marks earned in mental mathematics Modal Class: 31-40, 41-50, 51-60 marks

DISCUSSION OF FINDINGS

The data collected of marks earned by a standard 3 class in mathematics and mental mathematics was statistically analysed and conclusion about trends were made.

Measures of central tendency were calculated for both mathematics marks and mental mathematics marks. It was found that students tend to perform better in mathematics than mental mathematics as the mean of marks earned in mathematics (77.32) was higher than that of mental mathematics (59.92).

The modal classes were also determined from the bar graphs. The modal class of marks earned in mathematics (61-70) were also higher than the modal classes of mental mathematics which had three different modal classes (31-40, 41-50, 51-60). This also helps to prove the theory that students perform better in mathematics than mental mathematics is true.

The measures of spread of both subjects were also calculated. Both the variance and standard deviation of mathematics: 185.098 and 13.61 respectively were lower than that of those of mental mathematics: 493.11 and 21.52 respectively. The variance and standard deviation marks calculated for mental mathematics were much higher than mathematics which shows that the marks for mental mathematics were spread over a larger range of values and also shows more consistency in mathematics scores than mental mathematics.

The lower quartile, median, upper quartile, inter-quartile range, maximum and minimum marks were determined from the stem and leaf diagram which helped for easy analysis of data. The median for marks earned in mathematics (76) were higher than the marks earned in mental mathematics (60). This indicates a better performance in mathematics than mental mathematics. From the box and whisker diagram (figure 2), the mathematics marks are more positively skewed that the mental mathematics marks which is almost symmetrical. Also, from the comparative bar charts, the mental mathematics marks are more negatively skewed than the mental mathematics marks. This enforces the theory that students perform better in mathematics than mental mathematics marks.

From these statistics, it is proven that students of San Fernando Boys’ Government perform better in Mathematics than Mental Mathematics. Therefore, statistics can be generated at other primary schools throughout Trinidad to determine whether students of other schools follow the same trend that students score higher marks in Mathematics than Mental Mathematics and results can be compared.

To determine whether standard 3 students of San Fernando Boys’ Government School perform better in Mathematics than Mental Mathematics

STATEMENT OF TASK

Mathematics is a very important subject taught in all schools. Mental mathematics compliments the regular mathematics and therefore both are tested in primary schools. Mathematics is the written application of operation. It teaches students to think clearly, reason well and strategize effectively. Mental Mathematics is the ability to utilise mathematical skills to solve problems mentally. The marks scored by pupils generate statistics which are used by teachers to analyse a student’s performance and development of theories to explain the differences in performance.

The Standard 3 class is where the transition from junior to senior level occurs where teachers expect the transference of concrete to abstract thinking would have occurred.

A common theory by many primary school teachers is ‘Students perform better in Mathematics than Mental math. Mental math is something that has to be developed and involves critical thinking. Mental math requires quick thinking and the student must solve the problem in their minds whereas in regular mathematics, the problem can be solved visually. Therefore, teachers should take these factors into consideration while testing and marking students in these areas.’

In this study, the statistics of 30 students of a standard 3 class of San Fernando Boys’ Government School will be analysed to determine the truth of this theory.

DATA COLLECTION METHODS

Mathematics and mental mathematics marks of term 1 of the class of 2013 were obtained from a Standard 3 teacher of San Fernando Boys’ Government School. The marks were divided into the form:

Mathematics Marks, x

Mental Mathematics marks, y

DATA PRESENTATION AND ANALYSIS

Sample number

Marks earned (x)

x²

1

70

4900

2

86

7396

3

49

2401

4

66

4356

5

94

8836

6

68

4624

7

92

8464

8

96

9216

9

76

5776

10

71

5041

11

83

6889

12

59

3481

13

65

4225

14

98

9604

15

80

6400

16

68

4624

17

72

5184

18

85

7225

19

100

10000

20

69

4761

21

61

3721

22

80

6400

23

87

7569

24

95

9025

25

63

3969

=1933

=154087

Table 1: Sample data of marks earned by students in Mathematics examinations

Sample Number

Marks Earned (y)

y²

1

40

1600

2

93

8649

3

26

676

4

53

2809

5

100

10000

6

46

2116

7

93

8649

8

86

7396

9

39

1521

10

46

2116

11

74

5476

12

60

3600

13

40

1600

14

86

7396

15

66

4356

16

45

2025

17

61

3721

18

87

7569

19

48

2304

20

55

3025

21

75

5625

22

62

3844

23

24

576

24

60

3600

25

33

1089

=1498

=101338

Table 2 of marks earned by students in Mental Mathematics

Calculation of Measures of Spread (mean, variance and standard deviation) of mathematics and mental mathematics marks.

Mean =

=

=77.32

Variance S² =

=

=185.098

Standard Deviation S =

=

=13.61

Mean =

=

= 59.92

Variance S² =

=

=463.11

Standard S =

Deviation =

=21.52

STEM AND LEAF DIAGRAM

Mathematics

Mental Mathematics

9

9

9 8 8 6 5 3 1

6 2 1 0

7 6 5 3 0 0

8 6 5 4 2

0

0

1

2

3

4

5

6

7

8

9

10

4 6

3 9

0 0 5 6 6 8

3 5

0 0 1 2 6

4 5

6 6 7

3 3

0

Key: 9 4 represents 49 marks

Key: 5 3 represents 53 marks

Figure 1: Stem and leaf diagram of marks earned in Mathematics and Mental Mathematics

Calculation of the median Q1, Q3, inter-quartile range, maximum and minimum values of mathematics and mental mathematics

Mathematics

Mental Mathematics

Lower Quartile Q1 =th term

=

=6.5th term

=

=67 marks

Median Q2 =th term

=

=13th term

=76 marks

Upper Quartile Q3 =th term

=

=19.5th term

=

=89.5 marks

Inter-quartile =Q3-Q1

Range =89.5-67

=22.5

Maximum value = 100marks

Minimum value =49marks

Lower Quartile Q1 =th term

=

=6.5th term

=

=42.5 marks

Median Q2 =th term

=

=13th term

=60 marks

Upper Quartile Q3 =th term

=

=19.5th term

=

=80.5 marks

Inter-quartile =Q3-Q1

=80.5-42.5

=38

Maximum value =100

Minimum value =24

BOX AND WHISKER DIAGRAM

Figure 2 of a stem and leaf diagram of mathematics and mental mathematics marks

Figure 3 of a bar graph representing marks earned in mathematics Modal Class: 61-70 marks

Figure 4 of a bar graph representing marks earned in mental mathematics Modal Class: 31-40, 41-50, 51-60 marks

DISCUSSION OF FINDINGS

The data collected of marks earned by a standard 3 class in mathematics and mental mathematics was statistically analysed and conclusion about trends were made.

Measures of central tendency were calculated for both mathematics marks and mental mathematics marks. It was found that students tend to perform better in mathematics than mental mathematics as the mean of marks earned in mathematics (77.32) was higher than that of mental mathematics (59.92).

The modal classes were also determined from the bar graphs. The modal class of marks earned in mathematics (61-70) were also higher than the modal classes of mental mathematics which had three different modal classes (31-40, 41-50, 51-60). This also helps to prove the theory that students perform better in mathematics than mental mathematics is true.

The measures of spread of both subjects were also calculated. Both the variance and standard deviation of mathematics: 185.098 and 13.61 respectively were lower than that of those of mental mathematics: 493.11 and 21.52 respectively. The variance and standard deviation marks calculated for mental mathematics were much higher than mathematics which shows that the marks for mental mathematics were spread over a larger range of values and also shows more consistency in mathematics scores than mental mathematics.

The lower quartile, median, upper quartile, inter-quartile range, maximum and minimum marks were determined from the stem and leaf diagram which helped for easy analysis of data. The median for marks earned in mathematics (76) were higher than the marks earned in mental mathematics (60). This indicates a better performance in mathematics than mental mathematics. From the box and whisker diagram (figure 2), the mathematics marks are more positively skewed that the mental mathematics marks which is almost symmetrical. Also, from the comparative bar charts, the mental mathematics marks are more negatively skewed than the mental mathematics marks. This enforces the theory that students perform better in mathematics than mental mathematics marks.

From these statistics, it is proven that students of San Fernando Boys’ Government perform better in Mathematics than Mental Mathematics. Therefore, statistics can be generated at other primary schools throughout Trinidad to determine whether students of other schools follow the same trend that students score higher marks in Mathematics than Mental Mathematics and results can be compared.