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The Problem of Cultivating Students' Self-Study Math Ability



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is increasingly developing and becoming more effective because ICT has created an environment that allows the integration of individual student self-study with interactive self-study with classmates and teachers remotely via the Internet.

1.2.6. Organizing self-study activities

The Problem of Cultivating Students' Self-Study Math Ability

There are many concepts about organizing self-study activities. Through studying documents [28], [29], [30], [32]... we see that organizing self-study activities is the arrangement of operations, teaching activities with self-study activities. With this point of view, organizing self-study activities for students is the process of designing and arranging teaching organization measures by teachers to guide, control, and direct students' self-design and self-arrangement of self-study and self-research measures, helping students to maximize their self-study and self-research capacity, and to fulfill their learning goals and tasks well. The nature of organizing self-study activities for students is to arrange and carry out teaching measures to maximize students' positivity and self-awareness. Thus, organizing self-study activities is the process of implementing measures to promote students' learning activities in the process of acquiring knowledge in class, at home and in practical and extracurricular activities.

Thus, at high-level self-study, the organization of self-study activities can be led by students or completely independent. In order to achieve the goal of developing students' self-study capacity, teachers will directly organize self-study activities or entrust students to participate in part.

In our opinion, students' self-study activities are highly individual. The effectiveness of self-study depends on internal factors and is also affected by the self-study environment, specifically:

- Learning resources for self-study (printed books, electronic documents);

- Facilities such as library, network, computers;

- Conditions for interaction between students and students and students and teachers...



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1.2.7. Self-study Math ability

Competence is an important attribute of personality. Currently, the concept of competence is proposed by psychologists in many different approaches.

According to the Vietnamese dictionary, capacity is a psychological and physiological product that gives people the ability to complete a certain type of activity with high quality.

According to Pham Minh Hac [7], capacity is a combination of a person's psychological characteristics, this combination operates according to a certain purpose to create the result of a certain activity.

According to Dang Thanh Hung [12], capacity is made up of basic elements: Knowledge about that activity or relationship; Skills to carry out activities or promote behavior with a certain relationship; Psychological conditions to organize and implement certain knowledge and skills in a unified structure and according to a clear direction.

We see that the above concepts all have one thing in common: Capacity is the ability to perform a certain type of human activity and capacity is formed, developed and can be observed in the process of people solving the requirements.

With the above concept, we can consider self-study capacity as psychological attributes that ensure success in self-study of each individual.

According to experts, self-learning ability is demonstrated through the subject's correct determination of his/her own learning motivation, the ability to self-manage his/her own learning, having a positive attitude in activities to be able to work independently, adjust learning activities and evaluate his/her own learning results to be able to work independently and work cooperatively with others [19].

Based on the systematization of documents, Pham Dinh Khuong [13] proposed the structure of self-study capacity in Mathematics including the following components:



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Mathematical Cognitive Ability.

Ability to conduct self-study activities in Mathematics.

Ability to self-manage self-learning activities.

In which, the ability to self-study Math is the psychological condition for the self-study Math activity to take place. If students do not have the ability to self-study Math, they cannot have the self-study Math activity. However, if there is only the ability to self-study Math but lacks other factors such as motivation, purpose, will, and interest in self-study, the self-study Math activity will not take place or if it takes place, it will not achieve the desired results.

Thus, the ability to self-study Math is not only a psychological condition for self-study Math activities but also the purpose of self-study Math activities. It should be noted that the ability to self-study Math is formed and developed through self-study Math activities.

In the self-study capacity of high school students in mathematics, we see that the main components are specific skills in the self-study process such as: Listening skills; skills to ask questions; skills to answer questions; skills to research and work with textbooks and learning materials; skills to exploit information on the internet; skills to interact with teachers and fellow students; skills to apply knowledge and experience accumulated in the process of self-studying mathematics into learning and practice... The self-study capacity of students also includes skills that are not expressed visually such as: Skills to determine needs, purposes, and motivations for self-study; skills to perform intellectual activities; skills to collect and process, store and reuse information; skills to build, implement, test and evaluate self-study [13]...

The reality of organizing self-study activities in Mathematics shows that: the results of self-study depend on the self-study capacity of each student. In order for students' self-study activities to achieve their goals, teachers need to focus on fostering and developing students' self-study capacity, for example, they can use the following synchronous pedagogical measures: Motivating learning activities



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students' practice; develop skills, operations and intellectual activities suitable for students' self-study capacity in Mathematics; practice basic learning skills suitable for students' self-study tasks; organize reasonable self-study activities [13]

In order to exploit some applications on mobile phones to support students in self-studying Math to achieve the purpose and requirements, students' self-studying Math ability is one of the important factors. The research results on self-studying Math ability will be one of the bases for the topic to determine the principles and pedagogical measures for exploiting some applications on mobile phones to support students in self-studying Math.

1.2.8. The issue of fostering students' self-study ability in Mathematics

According to Nguyen Canh Toan [28], Thai Duy Tuyen [32], to foster students' ability to self-study Math, teachers can implement the following measures:

(1). Encourage students to be proactive in developing a self-study plan: Teachers ask students to compare the knowledge and skills they have accumulated with the standards of knowledge and skills in Mathematics so that students can determine their own goals and specific self-study tasks. Next, based on their time and ability, students will develop a suitable self-study plan.

(2). Highly appreciate the results of students' independent work: Students' ability to work independently during self-study is demonstrated through many aspects, for example: Students open the instructions and try to complete the exercises; Students only look at the solutions or "call for help" from teachers and friends after trying their best. Students do not mechanically depend on the problem-solving methods introduced in the HLĐT... In reality, when students study independently, they often tend to want to check their results and whether their problem-solving methods are correct or not? During class, teachers need to encourage students to comment on their results and highly appreciate both their awareness and self-study results in front of the class to increase their motivation for self-study.



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(3). Require students to perform analysis, synthesis, and comparison: Teachers need to install in the Math self-study task requirements that require students to perform thinking activities such as analysis, synthesis, comparison, etc. When working, on the other hand, because students have access to many different sources of information, students must perform comparison, synthesis, etc. to choose the most appropriate ways to solve problems.

(4). Require students to regularly evaluate their own progress: In addition to teacher evaluation, students need to regularly and voluntarily self-evaluate their own learning results in the following ways:

- Do exercises and tests;

- After completing the assisted exercises, students must continue to solve the exercises in the textbook and workbook to self-check their grasp and application of knowledge to solve the exercises.

(5). Encourage students to debate and present their opinions: In addition to organizing students to debate and present their personal opinions based on self-study results in class, teachers need to encourage students to participate in debates and defend their opinions.

1.3. Self-study with the support of information and communication technology

1.3.1. Impact of information and communication technology on students' self-study

Exploiting IT will create new factors that positively impact students' self-study such as:

(i) Besides receiving knowledge from teachers, textbooks, and reference materials, students can also access knowledge and the objective world through "electronic textbooks", CD-ROMs, the Internet, etc.

(ii) Teaching software (PMDH) will provide timely support and encouragement at necessary times not only during school hours but also during self-study time at home, helping students complete the task of acquiring knowledge and have the conditions to develop their own capacity to the maximum. On the other hand, the implementation of each student's learning tasks does not affect other students.



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In other words, students who complete their learning tasks early can continue to access new content and new tasks to develop their full potential.

(iii) Teaching aids create a favorable environment, a miniature vivid world to stimulate curiosity, arouse the need to learn, explore... helping students to be proactive and creative in the process of approaching and acquiring knowledge.

(iv) Students proactively plan and implement their own self-study at any time they need, thanks to online instruction programs or distance learning programs.

(v) Along with exploiting IT to "personalize" each student's learning, organizing groups of students to use the network together in group activities and interact with other groups has contributed to forming and developing students' planning and cooperative activities.

(vi) Students can use PMDH to represent models, charts, drawings, virtual experiments... in a visual and vivid way. With just a few simple operations, they can get images of the research object from different angles, or they can change some elements of the object to study the remaining components, thereby discovering their relationships and properties.

In our opinion: ICT has made the teaching and learning process no longer bound by space and time. Students can learn anywhere, anytime, and learn for life. Learning becomes flexible, adaptable, and based on students' needs. Students are allowed to choose effective learning methods, choose lecture content and related documents that are suitable for their own abilities. Students actively exchange and exploit information on the Internet to meet their knowledge needs related to their learning content. ICT has also created an interactive environment for learners to operate and adapt in that environment. Thus, ICT creates conditions for learners to be highly independent and supports learners to improve in the learning process.



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1.3.2. Exploiting information and communication technology in self-study

Exploiting information and communication technology in the form of self-study with direct guidance from teachers

In the traditional teaching environment, self-study with direct guidance from teachers is understood as the process of self-studying by students, there is always a teacher present to provide support when necessary. Thus, teachers can only directly guide students through class hours. However, the time teachers spend in class is mainly to explain new knowledge, so it is difficult to set aside time to guide students in self-study during regular school hours.

With the support of ICT, the concept of self-directed learning is expanded. Self-directed learning is a form of learning in which students receive direct support from teachers in the classroom or via the Internet (virtual classroom). ICT will help teachers "expand time and space" to guide students in self-study in many forms. Thus, all difficulties of students will receive direct guidance from teachers in a timely manner and students will certainly have more opportunities to complete self-study tasks.

Exploiting information and communication technology in self-study without direct guidance from teachers

In traditional conditions, in order for students to be able to study on their own without direct guidance from teachers, we have to hand them learning materials. The biggest limitation of this form is that the materials can hardly provide all the instructions, so students may encounter difficulties and students are forced to wait for a while to send their difficulties to teachers and also have to continue waiting until they receive support information from teachers. Thus, the process of self-study of students is at risk of not being able to take place continuously according to the planned plan.



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To promptly support students in self-study in this form, we can fully exploit IT&TT to create a "virtual teacher" who is always by the students' side. The "virtual" teacher will immediately provide support for students to overcome obstacles to continue self-study by the following specific measures:

(i) Design interactive learning materials to set up tasks and provide instructions for students to complete self-study tasks as well as multiple-choice questions to test their self-study results. We can imagine the knowledge content that students need to master structured in the form of an unknown number of repetitions. Self-study content is designed into specific tasks. Only when students complete the task they are doing will the document open a new task. For each self-study task, depending on the student's mistakes, the document will provide corresponding instructions.

(ii) Require students to access the website to receive tasks, research documents and answer questions. During the self-study process, students will interact with the Learning Support System to receive tasks, confirm self-study results and receive supporting information to continue completing self-study tasks.

(iii) Exploit web technology and interactivity so that training courses, in addition to presenting knowledge content, also provide guidance on how to detect problems, collect information, process information, draw conclusions, check and evaluate results...

(iv) Through the website, teachers receive feedback on students' learning outcomes after the self-study process and will help adjust students' learning pace to suit their abilities, guiding students to self-study from low to high levels, from self-studying a part to self-studying most of the content.

(v) With the support of ICT, we not only create a "virtual" teacher to support students in part in the self-study process on behalf of the teacher, but this "virtual" teacher can also make a difference from the teacher in the classroom in that it can be "cloned" into many "virtual" teachers and at the same time provide different assistance to support many students at the same time.

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