Statistical Data Processing Results of Class 2A and Class 2B



regularly care, encourage, motivate and create many opportunities for students to practice using NNTH in class. In the experimental hours, we often flexibly use the measures proposed in Chapter 2 in teaching. Student Hien has an uncertain NNTH capital, so when providing students with new symbols and terms, the teacher in the class pays more attention to Student Hien, inviting her to answer simple questions about reading and writing. Then, create opportunities for Student Hien to use new symbols and terms in simple situations and link them to known symbols. With mathematical symbols and terms that Student Hien has learned but still often confuses, the teacher trains Student Hien to use terms and symbols in simple situations and then gradually increases the level of complexity. During the experiment, the teacher paid more attention to Student Hien when developing communication skills using NNTH. At first, Hien was still shy and awkward when answering questions, but thanks to the encouragement and motivation of the teacher, Hien gradually became more confident and bold in communicating, using more accurate mathematical notation when answering questions. Hien's ability to read mathematical content through pictures and diagrams is getting better and better, using mathematical symbols to express mathematical content more accurately. However, Hien's ability to express in written language is still limited.

Comments from the teacher after the end of the experiment about student Hien: Student Hien's use of NNTH in learning has improved. Student Hien's learning results have clearly changed, shown in the regular monthly test scores and mid-term test results (scored 7), the end of the second semester scored 8, and the academic performance is classified as Fair. Student Hien's level of NNTH use is level 2.

Full name: Nguyen Duc Hoang Year of birth: 2004.

Student in class: 2A

Ethnicity: Kinh

Gender: Male

Place of birth: Dong Hy, Thai Nguyen



Student Nguyen Duc Hoang is classified as an excellent student, his midterm and final exam scores for the first semester both reached 9 points. Through examining his exercise book, observing before the experiment and comments from the homeroom teacher, we found that student Hoang learned the lesson quickly, participated in constructive comments on the lesson but was not active. Student Hoang's use of NNTH in learning was not accurate, and he was still confused in using NNTH to express himself in spoken or written language. The level of NNTH use of students before the experiment initially reached level 2. During the experiment, in addition to forming a solid foundation for student Hoang and practicing using NNTH, we paid more attention to developing communication skills (speaking and writing) using NNTH. During class, the teacher always created opportunities for student Hoang to present problems in spoken or written language when solving math problems. Create conditions for Hoang students to read and use NNTH to express mathematical content conveyed through images, drawings, diagrams or to re-express the problems heard in their own understanding in front of small groups or the whole class. Through the experimental period, Hoang students' use of NNTH in learning has had certain changes. Hoang students' mid-term and final test results of the second semester both achieved 10 points.

Homeroom teacher Nguyen Thi Nhung commented: Student Hoang used NNTH accurately and tightly in presenting solutions and demonstrating problem solving in front of the group and the class. Student Hoang is more confident in communication, uses NNTH more accurately, and has improved in speaking and writing. Student Hoang's level of NNTH use reached level 3 at the end of the experiment.

3.7.2. Analysis of results of pedagogical experiment round 2

At the end of the second round of pedagogical experiment, we conducted a study sheet for students of the experimental and control classes with the knowledge content learned in the textbook, but with the purpose of assessing the level of students' use of NNTH after the experiment.

3.7.2.1. Qualitative results

Students in the experimental class expressed problems in spoken and written language more clearly and accurately than students in the control class. For example, when asked to look at a drawing and present a problem, students in the control class



The students in the experimental class could read the mathematical content but when expressing it in written language it was not clear, there was a lot of influence from spoken language, the questions were missing question marks, ... meanwhile, the students in the experimental class could observe and state the content of the problem coherently and clearly.

When solving exercises, students in the experimental class expressed their solutions concisely and with full meaning, formed correct calculations, determined units, and wrote correct answers. The phenomenon of forming incorrect calculations or writing incorrect answers did not exist in the experimental class but did exist in the control class.

The problem of reading mathematical content through pictures and drawings of students in the experimental class is better than that of the control class. Students in the experimental class can express mathematical problems in many different ways, while the control class can only express them in one way and not accurately or completely.



In addition to expressing the problem as above, experimental class students can also express the problem as follows:

In addition, with the given data, students were asked to ask questions about the problem, and students in the experimental class were able to ask more questions than those in the control class. For example, with the problem "A rectangle has a length of 60m and a width of 40m", students in the control class were only able to ask the question "Calculate the perimeter of that rectangle" or "Calculate the perimeter of that rectangle", but students in the experimental class asked the same questions as the control class and some other questions.



The conversion from normal written language to mathematical symbols of the experimental class students was quite good. Students formed the calculation and practiced correctly, no students made mistakes in this problem. Meanwhile, in the control class, students showed confusion when converting to sign language. The following is an illustration of the work of Hoang Thi Thanh Tam, class 2A (experimental class).


Qualitative analysis of the results shows that students' use of NNTH is more effective, language errors are overcome, and students use NNTH correctly in learning.

3.7.2.2. Quantitative results

At the end of the second round of the pedagogical experiment, students completed the study sheet. We worked with the teachers participating in the experiment to discuss and agree on the answers and detailed scoring on a 10-point scale. The results of statistical data processing are as follows:

Table 3.7. Results of statistical data processing for class 2A and class 2B


Score

Class 2A (Experimental Class)

Class 2B (Control Class)

Frequency of occurrence

Total score

Frequency of occurrence

Total score

6

2

12

2

12

7

6

42

9

63

8

13

104

15

120

9

10

90

9

81

10

5

50

0

0

Total

36

298

35

276

Sample mean

𝑥 = 8.28

𝑥 = 7.67

Sample variance

S 2 = 1.15

S 2 = 0.76

Standard deviation

S = 1.07

S = 0.87

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To compare the results of the pedagogical experiment, we conducted a hypothesis test H 0 : " The difference between the mean scores in the two samples is not significant with the same variance ".

With significance level = 0.05, look up the t-student distribution table with degrees of freedom N TN + N DC 2 = 36 + 35 2 = 69 we get 𝑡 𝛼 1.67

s

1

N TN N DC

1

( N TN 1) S 2 ( N 1). S 2

TN

DC

DC

N TN N DC 2

Calculate the test value


t x TN x DC

2.64 with s = .



We have 2.64 > 1.67. Therefore, t > 𝑡 𝛼 , so the hypothesis H 0 is rejected. This proves that the difference between the mean scores in the two selected samples is significant. Thus, the experiment is effective.

Table 3.8. Results of statistical data processing for classes 3B and 3D


Score

Class 3B (Experimental Class)

3D Class (Control Class)

Frequency of occurrence

Total score

Frequency of occurrence

Total score

6

3

18

3

18

7

8

56

13

91

8

12

96

14

112

9

9

81

3

27

10

4

40

0

0

Total

36

291

33

248

Sample mean

𝑥 = 8.08

𝑥 = 7.52

Sample variance

S 2 = 1.24

S 2 = 0.61

Standard deviation

S = 1.11

S = 0.78

Conduct hypothesis testing H0 : " The difference between the mean scores in the two samples is not significant with equal variance ."

With significance level = 0.05, look up the student t-distribution table with degrees of freedom N TN

( N TN 1) S 2 ( N 1). S 2

TN

DC

DC

N TN N DC 2

+ N DC 2 = 36 + 33 2 = 67 we get 𝑡 𝛼 1.67 Calculate the test value


t x TN x DC

2.53 with s = .


s

1

N TN N DC

1

We have 2.53 > 1.67. Therefore t > 𝑡 𝛼 so the hypothesis H 0 is rejected. Therefore the experiment is effective.

Through the analysis of the results of the pedagogical experiment round 2, it can be concluded that students use NNTH more accurately, understand the nature of the problem, and communicate better with NNTH. Therefore, the proposed measures are initially effective, contributing to improving the quality of teaching Mathematics in the first grades of primary school.


3.8. General conclusions on pedagogical experiments

Initial results of pedagogical experiments show that students use language in general and NNTH in particular effectively, the level of NNTH use of students is raised. Students' learning results are better and students use NNTH more accurately in learning Mathematics.

Thus, the pedagogical experiment process together with the results obtained after the experiment showed that the experimental purpose was completed, the feasibility and effectiveness of the proposed measures were confirmed, and the scientific hypothesis was accepted. Implementing these measures in the teaching process will help students in the first grades of primary school effectively use NNTH, and at the same time contribute to improving the quality of students' learning of Mathematics.


CONCLUSION OF CHAPTER 3


To initially test the scientific hypothesis and feasibility of the proposed measures, we conducted a pedagogical experiment at Chien Thang Primary School.

- Dong Hy - Thai Nguyen. Experimental lesson plans are built and implemented according to the program distribution, with exchanges and supplements during the pedagogical experiment process.

The results of the pedagogical experiment show that the level of effective use of NNTH by students has changed positively. Students have a solid foundation in NNTH to better absorb mathematical knowledge. Students use NNTH correctly and accurately in expressing (speaking and writing) to solve math problems. Many students have made progress in their studies, using NNTH correctly in solving math problems or in exchanging and presenting mathematical ideas. During class, students are excited and enthusiastic in participating in lesson construction. Students like to exchange and communicate in math lessons.

Thus, it can be affirmed that the measures proposed by the thesis are feasible and can be implemented in teaching Mathematics in Primary School to help students use NNTH effectively.

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