Measure 3: Building and Applying Self-Study Math Situations for Elementary Education University Students

Step 2: Identify and prepare materials related to the lesson content. Prepare necessary learning tools.

Step 3: Write down all the major and minor titles according to the mind map.

Step 4: Read Math documents (follow the Math document reading process above).

Step 5: Use keywords and symbols to record the content you have read on the initial mind map (using the TMT note-taking method).

Step 6: Check on the mind map, the content that you do not understand, have questions about. Refer to other documents to solve that content until you understand them. (If any part is too difficult, you can ask questions for the teacher and friends to discuss in class).

Step 7: Find ways to apply the knowledge you have read to solve problems.

deliver.

Step 8: Find ways to check and evaluate task performance.

Step 9: Review the knowledge system learned. Learn the relationship between Math

Advanced and Elementary Mathematics, set new tasks to solve.

*) Process of self-reviewing lessons and applying learned knowledge

Step 1: Identify the tasks required by the teacher.

Step 2: Identify and review relevant theoretical parts to solve the task. Study carefully the parts that are still unclear. Solve problems in unfinished lessons such as: proving theorems, doing all the examples...

Step 3: Propose questions and find ways to answer them (if any).

Step 4: Remember and represent all the theory you have reviewed on the mind map.

only

Step 5: Check and adjust the review content mind map (if necessary).

Step 6: Apply the reviewed theory to solve teaching tasks.

delivery

Step 7: Find ways to check and evaluate task performance.

Step 8: Learn the relationship between Advanced Mathematics and Elementary Mathematics, and set new tasks to solve.

c) The meaning of teaching and self-learning processes

With the above teaching process, we have helped students develop operational skills such as:

+ Skills to prepare necessary knowledge as a premise for self-study of new Mathematical knowledge: When doing form 1, studying the questions, students must determine the necessary knowledge to be able to answer the questions in form 1. After students have acquired new knowledge by answering form 1, students must equip themselves with the necessary knowledge to answer and complete the questions in form 2 (in class). Or students must determine, research, and supplement the necessary knowledge to meet the basic knowledge to serve the acquisition of new knowledge (at home).

+ Study planning skills: Students can plan to complete the questions within the time limit required by the teacher (in class). Or students can organize and plan for groups and individuals (at home).

+ Math reading skills: Students must read the lesson in advance to understand the objectives and structure of the lesson. At the same time, students must read Math documents when they encounter difficulties in answering questions.

+ Math note-taking skills: Students must take notes of the main content of the lesson according to their own understanding.

+ Skills to propose - discover - solve problems: After researching and answering questions, students must know how to propose ideas or questions related to the lesson content.

+ Group cooperation learning skills: During the entire class, students must work individually and combine work and promote the strength of the group in learning. During the process of preparing lessons or reviewing at home, if necessary, students can work in groups to answer questions and check each other's work.

+ Self-assessment of the results of the lesson: During the group discussion in class to reach a consensus on the common answer, students must self-assess their own answers and those of their friends to be able to reject or agree on the results. In addition, at the end of the discussion, students must self-assess and add to the lesson structure diagram they have built. In addition, after the discussion, students self-assess their own attitudes and learning results and

groups, thereby drawing experience for the next session. In the process of preparing new lessons or reviewing and applying lessons at home, students must self-check their level of understanding, memorization, and reproduction. At the same time, students must find ways to check the results of performing the tasks assigned by the teacher.

+ Necessary skills to meet the teaching requirements in primary school practice: In the lesson, the teacher presents situations and exercises in the Primary School Math program for students to expand and deepen their knowledge and see the practical applications of the Primary School Math courses. In addition, thanks to being approached and directly participating in the active teaching and learning process, students will have a lot of experience and practice to be able to apply active teaching methods suitable for the subject and lesson and organize self-study activities in groups for primary school students.

2.2.3. Measure 3: Building and applying self-study Math situations for primary school pedagogical university students

2.2.3.1. Scientific basis of the measure

Regarding the method of education and training, section 5.2 of the education development strategy 2001 - 2010 affirms: " Innovate and modernize the method of education. Shift from the passive transmission of knowledge, teachers lecture, students take notes to guiding learners to think proactively in the process of accessing knowledge; teach learners self-study methods, systematically acquire information and have analytical and synthetic thinking; develop the capacity of each individual; enhance the initiative and autonomy of students in the learning process, . . . ". Thus, the problem of the method of education is to develop the self-study capacity of each individual, foster self-awareness and positivity in learning, which is one of the important goals in the development of education in Vietnam. Current teaching practice shows that the quality of teaching is greatly influenced by the environment. However, many teachers have not properly assessed the role and influence of the environment in the teaching and learning process. Therefore, studying the interaction and relationship between teachers, learners and the environment is necessary and has very important practical significance. Author Guy Brousseau studies the interaction and mutual relationship between Teachers (Teaching) -

Learner (Learner) - the environment for knowledge in the teaching and learning process. In which, the environment is considered by the author from the perspective of the situation. He defines: " A - didactic situation (a situation containing conditions that allow students to find knowledge, and also conditions that allow students to legitimize personal knowledge into scientific knowledge) is a situation that causes the desired adaptation in students - that situation is understood as a situation in the broad sense - an environment " [91, p.30]. The environment in the view of G.Brousseau is the environment chosen by the teacher for students to operate and develop. According to him, cognitive tasks (as the requirements of the environment) and the necessary conditions and means to solve cognitive tasks have all been planned, carefully considered and prepared by the teacher for students in advance. “ A - didactic situation is a situation that the teacher tries to propose, so that students can build or adjust their own knowledge, as an answer to the requirements of the environment, not to satisfy the teacher's wishes ” [91, p.37]. In an a - didactic situation, students do not transfer knowledge and skills to students but transfer a problematic situation and then the teacher " withdraws " without directly intervening from the time the student accepts the situation until he finds an answer to the situation; and students find new knowledge through the intrinsic nature of the situation.

Teaching by a - didactic situation usually goes through the following 3 phases:

+ Transferring (delegation) a situation: The teacher builds a problematic situation and transfers it in class so that students accept the situation as their own and start solving the situation.

+ Personal research phase: The learner puts himself in the position of a researcher, conducts his own discovery to find " new " knowledge - " personal understanding " through his own actions, the learner has created the initial cognitive product.

+ Institutionalization phase: Is the process of transforming personal understanding into scientific knowledge. Institutionalization is expressed through two levels: local institution and official institutionalization.

We study and also consider the environment from a situational perspective. With the environmental perspective, there are situations that are built for learners to learn.

In order to develop cooperative learning skills for students, teachers can actively create situations and create positive learning environments to create resonance between internal and external forces. Teachers create situations that contain conditions that allow students to find knowledge, and also conditions that allow students to legitimize personal knowledge into scientific knowledge . To develop cooperative learning skills for students at the University of Education, it is necessary to create a cooperative learning environment, so it is necessary to create cooperative learning situations for students to learn, practice and develop.

2.2.3.2. Objectives of the measure

Building and applying problem-solving situations in the process of teaching Mathematics to help students regularly practice problem-solving skills to develop those skills.

2.2.3.3. Content and organization of implementation of measures

1) Concept of self-study math situation

From the concept of a-didactic situation, we build a self-study Math situation as follows: Self-study Math situation is understood as problems, exercises, questions,

. . . . is built to help learners use existing knowledge, experience, and skills and sometimes have to mobilize newly read knowledge and use mathematical activities to solve them to form new knowledge and skills.

2) Requirements of a self-study Math situation

Requirement 1: The THT situation must be suitable for the target audience: Learners feel confident in being able to solve the situation, feel excited when using their own knowledge, skills, and experience to solve the situation. Sometimes learners can read more related documents to solve them.

Requirement 2: The THT situation must ensure development: When learners solve them with old knowledge, skills, and experiences, they must gain new knowledge and skills.

3) Levels of self-study Math situations

Situational level

THT

Activities and results of implementing student THT situations
1	With the THT situation at level 1, students only need to mobilize knowledge, skills, Basic experience is to be able to immediately solve the situation of self-studying Math.
2	With the level 2 problem situation, students need to mobilize existing knowledge, skills, and experiences and perform new mathematical intellectual activities to solve the problem. solve the problem of self-study math
3	With the THT situation at level 3, students mobilize knowledge, skills, experience combined with newly read knowledge to solve the situation. Math self-study situation.
4	In the level 3 THT situation, students mobilize knowledge, skills, and experience, combine document research, and perform intellectual activities. Mathematics solves self-study math situations.

Maybe you are interested!

4) Process of applying self-study math situations in the teaching process

Step 1: Preparation

Step 1: Teachers study the objectives, lesson content, and learning objects. From the lesson content, convert it into real-life situations.

Step 2: Teachers design THT situations to suit the audience, time and lesson requirements; specify the situations with task assignment sheets.

Step 2: Implementation

Step 1: The teacher organizes the transfer of the designed THT situation in class so that the learners accept the situation as their own and start solving the situation.

Step 2: The learner puts himself in the position of a researcher, conducts his own exploration to find " new " knowledge - " personal understanding " through his own actions, the learner has created the initial cognitive product.

Step 3: Local institutionalization: After individual work, students complete the THT situations through interactive group discussions to reach a common consensus. Then, cooperate to reach the main content of the lesson.

Step 4: Formal institutionalization usually takes place in the classroom after learners have practiced cooperation and interaction in teaching to form a certain amount of knowledge in the lesson content. In this phase, scientific knowledge is created, self-study skills continue to be perfected under the formal intervention of teachers.

Step 5: Consolidate knowledge and apply acquired knowledge to specific situations, especially applying lesson knowledge to teaching practice in primary school.

Step 6: Give students new THT situations to prepare at home.

Step 3: Summary and lessons learned

Step 1: The teacher summarizes the results and limitations in the implementation process, and finds out the causes.

Step 2: From those causes, teachers gradually adjust situations and organization methods to achieve higher efficiency in the following lessons.

5) Illustrative example

Applying self-study math situations in the teaching process of the lesson "Sets" [29, pp.3-12].

Step 1: Preparation

Step 1: Teachers study the objectives, content of the lesson, and objects of cognition. From the content of the lesson, they transform it into problematic situations.

Step 2: Teachers design situations that are suitable for the audience, time and requirements of the lesson; specify the THT situations using assignment sheets.

+ Form 1: Includes 21 THT situations for learners to use their existing knowledge and experience to create initial cognitive products for themselves.

+ Form 2: This form presents all scientific knowledge in the correct order and content of the lesson, but that knowledge is not presented in full but in the form of fill-in-the-blank questions. The learner's task is to, through

forming their own cognitive products and through local institutionalization, learners have formed and adjusted their own initial perceptions through the group to form common knowledge.

Step 2: Implementation

Step 1: The teacher organizes the transfer of the designed situation in class so that the learners accept the situation as their own and start solving the situation. By organizing for students to initially learn about the objectives, structure of the lesson and the tasks to complete the lesson.

- Students present a diagram describing the structure of the lesson content.

- Students state lesson objectives.

Step 2: Answer form 1: [Appendix 6].

- Students work individually to answer sheet 1.

- Students work in groups to discuss and agree on the answers on sheet 1.

Step 3: Complete form 2: [Appendix 6].

- Students discuss in groups and answer exercise 2 in each group.

- Each group gives partial answers, the groups come to a common consensus.

Step 4: Unify the content of the lesson

- The teacher is the referee to reach the final consensus.

Step 5: Consolidation - applying new knowledge

- Assign groups to complete the diagram describing the structure of the lesson content.

- Students look at the diagram and review the key content of the lesson.

- Teachers comment and evaluate individuals and groups.

- Teachers organize for students to apply new knowledge to specific situations as follows: (choose some situations to organize in class, the rest can be solved at home). For example, questions 1, 2 are done at home; questions 3, 4 are organized to be done in class.

Question 1: The content of the lesson "Set" can be applied in which parts of the Math program at the Primary level? Give an illustrative example?

Question 2: In primary school, implicitly, the content of knowledge is approached in the concept of sets in several ways, what are the ways? Illustrative examples?

Question 3: Determine the inclusion relationship between the following sets:

Comment