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Content Two: Understanding the Current Situation of Training and Developing Math Self-Study Skills for Elementary Education University Students



University


Total number of students

Level 1

Level 2

Level 3

Level 4

SL

%

SL

%

SL

%

SL

%

Thai Nguyen University of Education

58

30

52%

24

41%

15

26%

6

10%

Northwestern University

49

2

4%

10

20%

31

63%

4

8%

Hai Phong University

151

97

64%

34

23%

15

10%

5

3%

Hue University of Education

200

126

63%

58

29%

13

7%

4

2%

Hung Vuong University

195

134

69%

69

35%

12

6%

1

1%

Vinh University

85

59

69%

8

9%

7

8%

12

14%

Ho Chi Minh City University of Education

163

73

45%

97

60%

29

18%

27

17%

University of Education - University of Danang

284

158

56%

84

30%

32

11%

23

8%

Hanoi National University of Education

124

90

73%

28

23%

6

5%

0

0%

Hanoi National University of Education 2

181

128

71%

44

24%

13

7%

6

3%

Total

1490

897

60%

456

31%

173

12%

88

6%

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Content Two: Understanding the Current Situation of Training and Developing Math Self-Study Skills for Elementary Education University Students


Looking at the table, we can see that the majority of students' level of critical thinking skills is at level 1 (low level), accounting for 60%, while only 6% of students have level 4 (high level) critical thinking skills. Therefore, it can be affirmed that there is a need for measures to improve the level of critical thinking skills of students at the University of Education.

1.8.6.2. Second content: Studying the current situation of training and developing self-study skills in Mathematics for primary school pedagogical university students

Through direct discussions with some teachers teaching Mathematics to students at the University of Education and distributing survey forms to students [Appendix 5], we found that teachers are interested in developing students' self-study skills during the teaching process. However, in the teaching process, teachers do not often focus on developing students' self-study skills. In particular, many students reflect that they do not have a good environment to develop their own self-study skills in class as well as at home. For example, they often have to sit and listen to lectures and take notes, do not have time to focus on solving problems, learning situations in class or do not have enough self-study materials at home... In addition, they do not participate much in seminar activities, do not have regular self-study guidance materials, the results of which are shown in the survey data collected below:

? : Level of participation in self-formation of lesson knowledge through learning situations.



University


Total number of students

Are not

ever

Sometimes

Please

occasionally

Often

through

Do not select

SL

%

SL

%

SL

%

SL

%

SL

%

Thai Nguyen University of Education

58

27

47%

14

24%

4

7%

2

3%

11

19%

Northwestern University

49

42

86%

5

10%

1

2%

1

2%

0

0%

Hai Phong University

151

64

42%

64

42%

13

9%

9

6%

1

1%

Hue University of Education

200

101

51%

75

38%

7

4%

7

4%

10

5%

Hung Vuong University

195

123

63%

47

24%

17

9%

1

1%

7

4%

Vinh University

85

52

61%

24

28%

4

5%

1

1%

4

5%

Ho Chi Minh City University of Education

163

69

42%

51

31%

19

12%

10

6%

14

9%

University of Education - University of Danang

284

139

49%

65

23%

30

11%

26

9%

24

8%

Hanoi National University of Education

124

88

71%

26

21%

7

6%

3

2%

0

0%

Hanoi National University of Education 2

181

95

52%

58

32%

19

10%

5

3%

4

2%

Total

1490

800

54%

429

29%

121

8%

65

4%

75

5%


The table above shows that the level of students regularly participating in activities to self-construct lesson knowledge through learning situations is very limited, only 4%. Of which, 54% of students never participate in activities to self-construct lesson knowledge through learning situations.

? : Extent of use of guided self-study materials during the learning process.



University


Total number of students

Are not

ever

Sometimes

Please

occasionally

Often

through

Do not select

SL

%

SL

%

SL

%

SL

%

SL

%

Thai Nguyen University of Education

58

28

48%

12

21%

4

7%

2

3%

12

21%

Northwestern University

49

0

0%

0

0%

0

0%

0

0%

49

100%

Hai Phong University

151

57

38%

71

47%

10

7%

13

9%

0

0%

Hue University of Education

200

72

36%

87

44%

16

8%

16

8%

9

5%

Hung Vuong University

195

104

53%

71

36%

9

5%

3

2%

8

4%

Vinh University

85

37

44%

33

39%

2

2%

6

7%

7

8%

Ho Chi Minh City University of Education

163

77

47%

62

38%

7

4%

10

6%

7

4%

University of Education - University of Danang

284

127

45%

85

30%

51

18%

9

3%

12

4%

Hanoi National University of Education

124

38

31%

45

36%

8

6%

33

27%

0

0%

Hanoi National University of Education 2

181

76

42%

71

39%

10

6%

16

9%

8

4%

Total

1490

616

41%

537

36%

117

8%

108

7%

112

8%


The table above shows that the percentage of students who regularly use guided self-study materials during their studies is limited, only 7%. In particular, 41% of students never use guided self-study materials during their studies.

? : Level of seminar participation during the course.



University


Total number of students

Are not

ever

Sometimes

Please

occasionally

Often

through

Do not select

SL

%

SL

%

SL

%

SL

%

SL

%

Thai Nguyen University of Education

58

21

36%

13

22%

1

2%

6

10%

17

29%

Northwestern University

49

30

61%

11

22%

1

2%

2

4%

5

10%

Hai Phong University

151

83

55%

38

25%

27

18%

2

1%

1

1%

Hue University of Education

200

106

53%

47

24%

22

11%

14

7%

11

6%

Hung Vuong University

195

118

61%

40

21%

28

14%

6

3%

3

2%

Vinh University

85

30

35%

26

31%

16

19%

4

5%

9

11%

Ho Chi Minh City University of Education

163

101

62%

34

21%

14

9%

6

4%

8

5%

University of Education - University of Danang

284

87

31%

125

44%

12

4%

39

14%

21

7%

Hanoi National University of Education

124

67

54%

38

31%

7

6%

12

10%

0

0%

Hanoi National University of Education 2

181

107

59%

26

14%

26

14%

15

8%

7

4%

Total

1490

750

50%

398

27%

154

10%

106

7%

82

6%

Looking at the table above, it shows that the percentage of students who regularly attend seminars is very limited, only 7%.

In the process of surveying the current status of learning outcomes of some Mathematics contents of students of the University of Education using a set of exercise questions, we found that most students have a firm grasp of basic knowledge and have the skills to apply knowledge to solve exercises. However, many students have not yet mastered some basic knowledge, for example:

? : In the proof of mathematical induction, we pose the question as

Next: Prove that A(n) is true

nn 0 by mathematical induction, with step

Step 1 is to prove that the formula is true for n = n 0 ; step 2 is which of the following two steps?


University


Total number of students

Suppose the formula is true for n = k (k > n 0 )

The statement is true for n = k + 1

Suppose the formula is true for n = k ( kn 0 )

The statement is true for n = k + 1


Do not select

SL

%

SL

%

SL

%

Thai Nguyen University of Education

58

9

16%

15

26%

34

59%

Northwestern University

49

28

57%

17

35%

4

8%

Hai Phong University

151

61

40%

78

52%

12

8%

Hue University of Education

200

92

46%

64

32%

44

22%

Hung Vuong University

195

78

40%

68

35%

49

25%

Vinh University

85

24

28%

41

48%

20

24%

University of Education - University of Danang

284

113

40%

79

28%

92

32%

Hanoi National University of Education

124

66

53%

58

47%

0

0%

Hanoi National University of Education 2

181

49

27%

113

62%

19

10%

Total

1327

520

39%

533

40%

274

21%

The survey results above show that students are not sure about their knowledge of mathematical induction proof problems. 61% of students were confused and chose the wrong answer for the steps of the mathematical induction proof problem. When interviewed, many students said that in step 1, they had shown the specific case k = n 0 which is correct, so step 2 does not need to use the value of n 0 . But in fact, this is a mistake in mathematical logic, n 0 in step 2 is very necessary, it is the fulcrum to show that the propositional function A(n) is correct for the following elements. Or in another question: What is the remainder of the division 429.5:2.8 with the quotient being a natural number? How to find the remainder?


University

Total number of students

11

1.1

0.11

Do not select

SL

%

SL

%

SL

%

SL

%

Thai Nguyen University of Education

58

8

14%

3

5%

3

5%

44

76%

Northwestern University

49

42

86%

4

8%

0

0%

3

6%

Hai Phong University

151

10

7%

61

40%

4

3%

76

50%

Hue University of Education

200

80

40%

64

32%

5

3%

51

26%

Hung Vuong University

195

53

27%

44

23%

26

13%

72

37%

Vinh University

85

5

6%

33

39%

2

2%

45

53%

University of Education - University of Danang

284

111

39%

61

21%

41

14%

71

25%

Hanoi National University of Education

124

24

19%

94

76%

6

5%

0

0%

Hanoi National University of Education 2

181

65

36%

105

58%

7

4%

4

2%

Total

1327

398

30%

469

35%

94

7%

366

28%


Many students do not understand the remainder division, 35% of students chose the correct answer, the remaining 65% chose the wrong answer or did not choose any answer. When interviewed, most students said that the way to find the remainder in the division is to take the dividend minus the product of the quotient and the divisor. This shows that teachers need to have measures to help students deepen and expand their knowledge because it is a part of the knowledge in the Math program in Primary School. In particular, both the Math textbook in Primary School and the Math Methods curriculum in universities do not provide detailed instructions on how to calculate the remainder in the division of fractions by fractions. Therefore, many Primary Education students after graduation often encounter confusion in this part of knowledge. To overcome this situation, teachers need to pay attention to enhancing students' mathematical knowledge.

The survey shows that in the process of training primary school teachers, universities have paid attention to training students in learning skills. However, to develop learning skills for primary school students in the future, schools need to pay attention to the following issues: Forming motivation and attitudes to enhance students' awareness of learning skills, organizing activities to train learning skills, building learning situations, focusing on group discussions through seminars, compiling guided learning materials, fostering and improving students' knowledge of mathematics and teaching methods of mathematics in primary school to meet the requirements of current primary education reform.



CONCLUSION OF CHAPTER 1

The issue of self-study has been studied by many scientists and educators in the world as well as in Vietnam. The self-study skills of primary school students can be divided into two main groups of skills: the cognitive skills group (skills in determining goals, skills in forming self-study motivation) and the activity skills group (skills in planning study; skills in preparing necessary knowledge as a premise for self-study of new mathematical knowledge; skills in reading mathematical documents; skills in taking mathematical notes; skills in discovering - solving - proposing problems in mathematics; skills in working in groups; skills in self-assessment of self-study results; skills in converting problem solutions into primary school mathematics language; skills in organizing situations to stimulate self-study activities in groups for primary school students; skills in applying information technology in teaching mathematics in primary schools; skills in applying mind maps in teaching mathematics in primary schools). During the learning process, students of the University of Education develop their own skills at different levels, so based on the established criteria, we divide the level of students' skills into 4 levels from low to high. In the process of developing students' skills in learning, one of the significant influences is the environmental factor, especially the teaching activities of teachers. With the 15 criteria established above, we can distinguish whether teachers pay attention or not to developing skills in learning during the teaching process. The results of a survey of 1,490 students of the University of Education of 10 universities according to two groups of skills show that students have a relatively good awareness of the role and importance of learning. However, in reality, students still do not have skills in learning and do not regularly carry out learning activities. In particular, in the teaching process, teachers do not pay much attention to students' learning activities. These issues are the theoretical and practical basis for proposing measures to develop teaching skills for students at primary school teacher training universities.



Chapter 2

MEASURES TO DEVELOP SELF-STUDY MATH SKILLS FOR PRIMARY SCHOOL UNIVERSITY OF EDUCATION STUDENTS

2.1. Principles for developing measures

2.1.1. Focus on practicing and developing two main groups of skills in self-study Math skills

The purpose of developing measures is to help students of the University of Education raise their awareness of self-study, help students improve their skills in determining goals and skills in forming self-study motivation. The proposed measures must create a learning environment for students to have the opportunity to practice and develop skills such as: Skills in planning their studies; Skills in preparing necessary knowledge as a premise for self-study of new mathematical knowledge; Skills in reading mathematical documents; Skills in taking mathematical notes; Skills in discovering - solving - proposing problems in mathematics; Skills in working in groups; Skills in self-assessing the results of self-study; Skills in transferring problem solutions into primary school mathematics language; Skills in organizing situations to stimulate self-study activities in groups for primary school students; Skills in applying information technology in teaching mathematics in primary schools; Skills in applying mind maps in teaching mathematics in primary schools.

2.1.2. Closely follow the objectives and content of the primary education university training program

The training objective of Bachelor of Primary Education has clearly stated: " Graduates must have the ability to teach and educate students according to the requirements of innovation in Primary education, be able to teach the Primary program well, conduct educational research, and self-improve their qualifications. Be able to become a core teacher of Primary school " [18, p.67]. To meet this training objective, we must innovate teaching and learning methods appropriately, and the proposed pedagogical measures must closely follow the objectives and content of the program. In addition to helping students grasp basic knowledge and professional knowledge, the measures need to help students develop their potential in Mathematics in teaching and learning, help them understand the Mathematics nature of the lessons; help them be able to adapt to changes and requirements of teaching practice in Primary school.


After graduation, they must have the ability to teach and educate students according to the requirements of innovation in primary education, be able to teach the primary school program well, be able to self-study and research to improve their qualifications, be able to continue studying at higher levels, and at the same time know how to guide and promote the initiative of primary school students in self-study.

2.1.3. Ensuring feasibility and effectiveness

Ensuring feasibility means that it must be suitable to the conditions and abilities of students; meeting the regulations on time and characteristics of the learning environment. Therefore, proposed measures to develop the practical skills of students at the University of Education must come from the practical skills of students, from the characteristics of their cognitive level, from the difficulties, obstacles, and advantages, from the strengths and limitations of students at the University of Education during the practical skills process. From these bases, teachers can build their own teaching methods suitable to the cognitive objects and lesson content. It is important to note that the measures developed must promote the existing potential of students and must bring about a positive change in their cognition, attitude, development of practical skills and knowledge. The measures must ensure that they do not change the structure of the program and the duration of the subject; at the same time, they must be suitable to the current teaching and learning conditions at each university.

2.1.4. Ensuring consistency and flexibility

The measures to develop practical skills have their own requirements, contents and forms, but they are organically related to each other. Depending on the specific conditions, teachers apply and combine measures at appropriate levels. The measures can be implemented simultaneously or chosen to be used independently. Depending on each specific case, teachers can use the level and order of the measures to suit the content, objects and actual circumstances. Synchronization in the use of measures, synchronization in exploitation creates resonance between internal forces and internal forces with external forces in the teaching - self-study process. Internal forces are students' practical skills, external forces are external factors affecting the learning process of learners such as: learning environment, teaching aids, teaching methods, etc. Measures to bring

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