Abstract
The development of information technology brings new hope for our traditional education mode. However, the combination of information technology and teaching in our country is still in the initial stage. Especially, the research of school district function guidance system based on cognitive guidance algebra I is less. In this paper, the intelligent guidance system was the main research topic, and the development of the project of cognitive guidance algebra I in America was summarized, so as to help the related scholars to better understand the gap between the research of intelligent guidance system and the world level in China. Finally, through the study of the relevant theoretical basis, the development of educational intelligent guidance system was discussed, and finally a relatively complete intelligent guidance system was established.
Introduction
The failure of American students’ mathematics education is a long-term heartache for American basic education. In the ten years since the disclosure of the problem in the 1980s, math applications in the United States have been the worst in the world. Weak math skills make American students suffer a lot in international competitions. In addition, some jobs based on mathematics have also caused a lot of trouble for Americans. Such data made the American government aware of the importance of strengthening children’s access to mathematics. The two presidents of the United States, George W. Bush and Obama, have launched a series of bills to invest heavily in improving the quality of education.
Through many efforts, American students have improved their math scores. And the advanced intelligent tutoring system, such as cognitive guidance, has played a key role. It has become a common measure in improving basic education in the United State. Cognitive guidance algebra I has changed the traditional form of education. It transforms the educational model that needs to be taught in the classroom for students to study in the computer lab, and then in the educational form for classroom group interaction. Based on the education design, it provides students with the opportunity to learn mathematical knowledge in the classroom and in the computer laboratory, thus solving the problem of American students’ mathematics education [1–5].
State of the art
The study of cognitive guidance has been going on for more than 30 years. Earlier studies mainly focused on the panel of experts and scholars from Carnegie Mellon University and the University of Pittsburgh. They mainly focused on the basic subjects such as how to study, think and apply knowledge. Then, in the cognitive science into the classroom edited by Oettinger in 2006, the practical teaching of cognitive guidance into the classroom was described in detail. From the point of view of researchers, the six basic principles of cognitive guidance in the design process were summarized. In the following years, a large number of academic achievements in the field of cognitive navigation emerged. In 2007, Reiter and his team published cognitive guidance: applied research in mathematics education. The current status of cognitive navigation research was analyzed and the use of cognitive navigation in today’s world was proved. The research on cognitive guidance in China started late, and it was relatively basic for the research in this field [6–9]. With the popularization of information technology, the research on intelligent guidance system in our country has developed rapidly. A large number of academic researchers on cognitive guidance have emerged. Through their disdain efforts, some research results have been achieved, which laid a solid foundation for our future development in the field of cognitive guidance teaching [10–12].
Methodology
The development principle of cognitive guidance algebra I
ACT-R theory, that is, cognitive apprenticeship theory and adaptive control thought rational theory, is one of the important factors that affect the successful development of cognitive guidance algebra I. Based on such advanced research ideas, cognitive guidance algebra I can successfully simulate the thinking patterns of students and eventually succeed in the daily course study of students. Declarative knowledge and procedural knowledge are the key concepts of ACT-R theory. Declarative knowledge is the general principles of fact, belief, and so on. In ACT-R theory, declarative knowledge is usually represented by blocks containing basic information plus related types [13–15]. Procedural knowledge is different from the form of declarative knowledge, which is acquired gradually based on practice. In ACT-R theory, procedural knowledge is usually stored in a production system. The representation of procedural knowledge is mainly based on the production rules. The production rule describes how the environment can act in order to achieve a specific goal. Based on this rule, it can be learned that each production type usually contains a particular condition and the corresponding action. The phrase “if” is the beginning of each condition, and the corresponding action is a phrase at the beginning of “so”. The following chart shows the working process of procedural knowledge and declarative knowledge. It shown in Figs. 1 and 2.
Procedural knowledge and working process of declarative knowledge.
Internal information transformation of cognitive guidance.
For declarative knowledge architectures, if a part of it is used more frequently and the last time it is used is nearer, the activation level of the corresponding knowledge unit in the ACT-R is higher. The following formula is the simplest formula for activating the hierarchy.
Usually the relevant knowledge is retrieved every time, and the formula will increase the weight of the knowledge point. With the increase of increasing frequency, different knowledge points are endowed with different weights, thus forming the activation level of knowledge. For the cognitive guidance system, external information is usually obtained in procedural and declarative forms. For the acquired knowledge, the system is transformed into a specific symbolic form to classify and store the system. When the system needs to retrieve the information, only the corresponding symbols need to be activated, and the process is shown in the following figure.
Through the decryption analysis of the task, the system realizes the required knowledge items and activation time, so as to guarantee the time of activating the knowledge and complete the related tasks. It can shown in Table 1.
Understanding of guidance algebra I course composition
In the actual teaching, each course should have its own teaching content. In the course of practical development, the course of cognitive guidance has developed and designed the mathematics curriculum in detail. The basic algebra knowledge which is more difficult to study is selected. The cognitive navigation algebra I adds multiple learning units at the time of design. Each learning unit contains an algebraic knowledge point. Students should study the following points of knowledge unit in the system, including form and diversified representation, percentage ratio, variables and inequality, linear function and equation, quadratic function, exponential function, probability index and reasoning.
In this system design, the actual development process should not only focus on the realization of computer technology, but also combine with supporting teaching materials for the substantive filling of the system content. Only in this way can the practicability of the system be guaranteed. The elements included in the course of cognitive navigation algebra I are summarized as follows.
The course of “cognitive guidance algebra I” is to help students better understand and master the complex mathematical concepts and knowledge points based on stimulating students’ intuitive abilities. Therefore, the curriculum development mainly covers two aspects. The first is mainly for the development of software systems. The second is the learning of textbook knowledge. Based on the learning model of “cognitive guidance algebra I”, students use forty percent of the time to assist computer learning in the process of algebra knowledge learning. The remaining sixty percent times is mainly used for interactive interaction in class to solve practical problems. Therefore, in forty percent of the learning time, the users need to select the content they need to learn when they login the system. For each unit of learning, the guidance system of cognitive guidance algebra I can be divided into three parts: the unit learning specification, the learning of unit knowledge points and the application of problem case analysis. At this point, the system selects the corresponding application cases or examples and other forms, and the related content and knowledge are integrated and applied. In the course of actual use, the development and design of ACT-R theory cannot be seen intuitively. And in fact, students do not need to know, it shown in Fig. 3. The general procedure for actually using the system is as follows.
Process of use of cognitive guidance.
In addition, the system is designed to adhere to several principles. First, the picture is simple and easy to operate. For users, especially the student community, the more concise and direct picture, the people can obtain a brief sense of refining more easily. On the contrary, the more complex the interface, the users will be more impaired browsing, learning interest, and they cannot achieve the purpose of promoting learning. Therefore, the friendly interaction interface is necessary for the design of the system. Second, the function is perfect and humanized. For the system, the primary purpose of the design is to meet the students’ daily learning needs. Therefore, based on ACT-R theory, the design of software must be fully functional, and it is necessary to take into full consideration that the students may encounter problems in the course of learning, establish a complete set of solutions to relevant problems, and guide students to learn how to solve problems. In the initial design, the system needs many modules including definition, explanation, problem solving, answer hint, case analysis and so on. The third is to establish a perfect evaluation system. In the actual learning process, each student’s learning ability and learning situation are different. At this point, the system needs to be established to improve the evaluation system. Based on the evaluation system, each student’s learning in this unit can be evaluated and analyzed, so as to help teachers understand the students’ learning situation. For students who are weak in learning point, teachers can make sure that they know what to do, and make it easier to explain the design, interaction, or problems in the actual classroom learning process, so as to help students improve in the true sense. In addition, the evaluation system can also be open to students, which is helpful for the students to know their learning situation in real time, to train and master the knowledge of short board, and finally to improve their self-ability.
The following example is the addition and subtraction unit of the score, which illustrates the flow of the system and shows the students how the system works. The user account management interface for the system is shown in Fig. 4.
User management interface.
The system supports the user’s self-account management, including secret modification of accounts, cancellation and re registration of accounts. At the same time, the system supports the user to add multiple sub accounts, and each account permissions settings. Using this function, aiming at a small number of students who do not fully grasp the individual knowledge of the training, the teacher can help them quickly master and improve the learning, so as to improve the teaching efficiency of the teacher. The interface style is simple and refined, and the user can find the functional operation button that he needs at a glance.
As mentioned earlier, the system divides each unit into three parts in the design and development phase, which are the unit learning description part, the learning part of the unit knowledge point and the application analysis part of the problem case. The unit learning instructions section is the beginning of the whole unit learning. It mainly describes the knowledge points and the learning methods covered by this unit, which is shown in Fig. 5.
Introduction to learning content.
The same denominator and different denominator addition and subtraction units are explained in the figure, including the objectives of the study. In addition, the system also may be encountered in the learning process of this unit in the days after the terms are listed and explained. Based on this design thinking, it can help students quickly grasp unfamiliar knowledge points in the beginning of the study, so as to improve their learning efficiency and learning initiative. In the learning process of the unit knowledge point, the method of fractional addition and subtraction is illustrated by various styles to help students understand better. The system supports online video learning. Students can choose relevant courses code, and the system can respond to play related knowledge points. For the unclear part of the video, students can drag the video progress bar at will, and make repeated viewing learning without understanding part until they master it.
In addition to what needs to be learned, some key knowledge points and concepts in the learning unit need to be highlighted and remembered, and the system is presented in a different way, as shown in Fig. 6. The two modules of key concepts and techniques mainly introduce the concepts and related skills needed in the learning process of this unit. As shown in the diagram above, the students should master the concepts of “same division, different mother”, “different denominator fraction” and “minimum common multiple” when learning this part. In order to help students better remember and master these knowledge points, the calculation of the scores in the form of correlation model and line segment method in the technical part are also explained in detail. When the students click the “same denominator” key concept option in the picture above, the system will automatically jump to the corresponding definition and explanation interface. In the definition interpretation interface, users can selectively learn other definitions that are not understood, and take learning definition as the starting point and gradually strengthen the understanding of algebra.
Key concepts and techniques.
The learning of definition is not mandatory. Students can choose other forms of learning to study the course, and gradually understand the specific concepts of each definition in the course of learning. If they still can’t understand, they can learn by clicking on the relevant definitions.
The problem case analysis section is the final part of each unit. This module will be targeted to provide some calculation questions for students to practice. The design of the link contains a lot of interactive content. Therefore, a large number of function keys are added during the design to facilitate the user’s operation in the process of solving the problem. In the actual process, there will often be some problems that are not very good to grasp. Click the “prompt” button of the system at this point. The system will automatically pop-up the relevant prompts window, give students a certain problem-solving ideas or concepts to explain, so as to help them sort out ideas, master problem-solving skills.
In the completion of the above content of learning, the system evaluates and evaluates the whole system learning process of the students based on the students’ performance in the course of learning. And the evaluation results are stored in the system to facilitate the later teachers and students access to reading. After many experiments in the field, the system can basically realize the current needs for education. The teaching system based on “cognitive guidance algebra I” can realize the development of education with the core of students’ learning, which is in line with the students’ thinking patterns. In the actual learning layer, it can provide timely help for students, and guide students to complete the content of knowledge learning. For each unit of learning, the system summarizes and scores after the end of the study, feedbacks the final result to the teachers and students, which helps the students to understand their lack of learning. It stimulates students’ interest in learning, and also assists teachers in carrying out educational work and achieves more accurate teaching, which greatly improves the quality and level of modern teaching, it shown in Figs. 7 and 8.
Explanation of the concept.
System prompt window.
With the progress of society, the competition between countries has changed from the competition of the former natural resources and the armament strength to the competition of human resources. The development of high-quality personnel has always been the focus of development in each country. In this paper, the intelligent tutoring system based on cognitive derivative I in America was comprehensively analyzed. The system was developed and designed based on advanced ACT-R theory, so as to simulate the thinking patterns of the students in the course of learning. Taking this as the breakthrough point, the system knowledge explanation and the guidance study were carried out. Therefore, it was favored by many countries, including the United States. In the future, with the continuous progress of society, the traditional mode of education will gradually be replaced by the new intelligent education model which is more in line with the needs of social development. There are still some defects in the study. For example, there is no good experimental investigation into the acceptability of the system. In the later stage, the system can be cooperated with the school and applied to education and teaching for a period of time. After that, the students and teachers who have participated in the experiment have to pay a return visit to understand the auxiliary teaching situation of the system and the shortcomings in the use, so as to better improve the system.