abstract:

Rubik's Cube and Mathematics is a school-based course that follows students' cognitive and psychological development, enriches students' experience in mathematics activities, improves students' interest in mathematics and promotes students' mathematics learning with the help of Rubik's Cube, a physical toy full of mathematical principles. The person in charge of the course first introduces the research background of this study; Then the Rubik's Cube and the school-based curriculum of mathematics are elaborated in detail, including the objectives, planning, implementation and evaluation of the curriculum. Finally, the existing problems and development direction of this course are introduced. Under the background that today's mathematics education reform emphasizes mobilizing students' enthusiasm and strengthening the development of school-based curriculum from interest, as a traditional abstract and logical mathematics subject, the research and development of school-based curriculum is a useful attempt.

Key words:

School-based curriculum of primary mathematics Rubik's cube

First, the background of curriculum development.

(1) The concept of "Rubik's Cube and Mathematics" defines Rubik's Cube as a highly entertaining educational toy. Its invention and development seem to have nothing to do with mathematics education. Most people, even Rubik's Cube players, are unaware of its mathematical principles, and parents and children regard it as a toy to develop their intelligence. But in fact, the Rubik's Cube is closely related to mathematics. Rubik's cube is a changeable three-dimensional figure in space. In the process of playing the Rubik's Cube, primary school students can form the concepts of space and graphics, and have an intuitive understanding of some mathematical concepts such as transformation, group, coordinate and combination, which is convenient for future mathematical study. The structure and operation of the Rubik's Cube contain rich mathematical thinking factors, which is also the reason why playing the Rubik's Cube has a rich sense of hierarchy and skill. The development of Rubik's Cube and Mathematics is not only to teach primary school students to skillfully restore the Rubik's Cube, but more importantly, to let primary school students experience mathematical knowledge, mathematical methods and mathematical ideas while playing the Rubik's Cube, so as to enhance their interest in mathematics, thus promoting primary school students' mathematics learning and improving the effect of mathematics learning. (II) Theoretical and Practical Significance In July, 20001,the Ministry of Education promulgated the Mathematics Curriculum Standard for Full-time Compulsory Education (experimental draft), which put forward a new educational concept, broadened the understanding of the curriculum, and encouraged local and school-based schools to open and develop diversified school-based courses on the basis of improving students' interest in mathematics and meeting their needs. The development of the school-based curriculum of Rubik's Cube and Mathematics is helpful to highlight the particularity of running a school, the specialization and personality growth of teachers, and to carry out vivid quality education for students. At the same time, it plays a positive role in promoting the improvement of traditional mathematics curriculum to modern model. Mr. Zhang Jingzhong said in the preface of the series "Interesting Mathematics" that "in many interesting activities, mathematics is the mastermind behind the scenes and the maker of the rules of the game". Without special introduction, the behind-the-scenes workers will never be known to the audience. In the same way, due to the lack of digging into the connotation of mathematics, many people can't put it down, but they don't realize that they are playing mathematics, and even some math teachers. The development of the school-based course Rubik's Cube and Mathematics is just through excavating the mathematical elements in the Rubik's Cube. In the process of playing the Rubik's Cube, primary school students are taught to look at the Rubik's Cube from a mathematical perspective, explain the Rubik's Cube with mathematical thinking and methods, explore independently, practice hands-on, cooperate and communicate, gain rich experience in mathematical activities in the process of playing the Rubik's Cube, and appreciate the charm of mathematics and the application value of mathematical thinking methods. Therefore, it is of practical significance to develop the school-based curriculum of Rubik's Cube and Mathematics as an aid and supplement to the current mathematics teaching.

Second, the Rubik's Cube and Mathematics course

Firstly, it starts with the objectives of the course, then introduces the applicable objects and basis of the course, and finally explains the course plan, learning methods, teaching methods and course evaluation in detail from the perspective of course implementation. (1) Course objective (1) Understand the history of the invention and development of the Rubik's Cube, and have a clear understanding of the basic principle and structure of the Rubik's Cube; Can successfully restore the second-order Rubik's cube and the third-order Rubik's cube, and can complete some simple Rubik's cube plans; The acknowledged Rubik's Cube is a game full of mathematical truth, which can explain some simple truths. (2) In the process of "playing" the Rubik's Cube, we can consciously look at the Rubik's Cube from a mathematical perspective and use mathematical methods to help solve it, thus improving our awareness and ability to use mathematics in our lives; Improve spatial imagination, hands-on ability, analytical judgment and decision-making ability. (3) In the learning of Rubik's Cube course, you can experience mathematics and improve your interest in mathematics learning; Experience the learning process of trial and error, experience and epiphany, experience the happiness and sense of accomplishment of Rubik's cube reduction and puzzle solving, and exercise good will and psychological quality; Choose active and healthy leisure and entertainment methods, avoid negative entertainment, and face life with optimism and wisdom. (II) Course Object and Foundation "Rubik's Cube and Mathematics" is a school-based course offered by sixth-grade primary school students in the last semester of sixth grade. The selection and starting time of the subjects are as follows: (1) From the cognitive and psychological point of view, the sixth grade students are the highest grade in the primary school stage. In the process of cognitive and psychological development, they have acquired the ability of formal abstraction and have a certain foundation in spatial imagination and logical thinking. Therefore, from the perspective of the development law of primary school students, it is in line with their growth and development law to implement the Rubik's Cube course in the sixth grade. (2) The angle of cooperation with the national curriculum: Cube is a three-dimensional figure of the sixth grade primary school mathematics last semester published by People's Education Press. By offering Rubik's Cube course, students' imagination and analytical ability of abstract thinking in mathematics can be cultivated, which not only contributes to the learning of cuboid and cube content this semester, but also lays a solid foundation and interest for geometry learning in later middle schools, thus contributing to the learning effect of mathematics. (3) Opening time: The Rubik's Cube and Mathematics course is offered in the first semester of the sixth grade of primary school, which not only matches the national curriculum, but also relieves the learning pressure of primary school students, so that primary school students can enhance their interest in learning mathematics in the Rubik's Cube study last semester and avoid the formalism of starting classes next semester, which is practical and operational. (3) According to the objectives of this course, the course plan analyzes the factors that affect teaching (including mathematics, games and Rubik's cube, students' physical and mental development, etc.). ), choose and determine the teaching content, and establish a teaching system suitable for students to learn and cooperate with classroom mathematics teaching according to certain logic and order. The following is the preliminary teaching plan of Rubik's Cube and Mathematics: Rubik's Cube and Mathematics are school-based courses in the sixth grade of primary school, with 45 minutes per class every week, *** 18 class. Unit Name Content Time (18) Unit Target Unit 1 History Introduction 1 Understanding Rubik's Cube Story 1 Family 1 Unit 2 Learning Structure and Principle Introduction 1 Mastering Basic Principles, Structure and Formula of Rubik's Cube and Simple Puzzle 3 Unit 3 Second-order Rubik's Cube Simplification and Simplification Second-order Skills and Methods 2 Proficient in Second-order Simplification Unit 4 Third-order Rubik's Cube Simplification Skills and Methods 3 Learn Third-order Simplification Unit 5 Simplify the Mathematical Thinking of Rubik's Cube 3 Have a certain mathematical understanding of playing Rubik's Cube 3 Don't learn, be interested in mastering advanced Rubik's Cube skills sharing (IV) Curriculum implementation-Learning Rubik's Cube between teachers and students as an educational toy is not exclusive to math lovers. However, the math teacher offered the Rubik's Cube course, which in itself gave students a signal that Rubik's Cube and mathematics are inextricably linked. In this course, teachers teach students not only the skills of restoring Rubik's cube, but also the mathematical ideas and methods contained in it, which are obviously different from ordinary Rubik's cube players in terms of ideas and concerns. On the basis of observation, thinking and hands-on practice, under the guidance of teachers, students try to explore the mathematical connotation of the game and find the rules of the game from a mathematical point of view. Through mechanical imitation and personal experience, the process of the game is analyzed and thought rationally, which improves the understanding and play of the Rubik's Cube game, and at the same time shows the charm of mathematics and the application value of mathematical thinking methods in the game. Learning between teachers and students is a way to ensure the quality of Rubik's cube and mathematics, and it is the key to distinguish it from ordinary Rubik's cube toys. 2. Life-oriented learning In most people's minds, being able to restore the Rubik's Cube is synonymous with "cleverness". Quickly restoring the Rubik's Cube is a challenging game, which is very easy to arouse the interest of primary school students. Moreover, the Rubik's Cube is cheap and easy to carry, and fans can perform wonderful personal performances anytime and anywhere, winning countless envious eyes around them. Therefore, every child who can restore the Rubik's Cube will naturally gather around a group. Students learn from each other, and children who can quickly restore the Rubik's Cube become the playing center of the Rubik's Cube. They will organize discussions and competitions spontaneously, and even parents and other teachers will learn from them. Rubik's cube naturally promotes mutual learning and communication among students and enhances their social development. Students' learning from students is one of the most common and important ways that students spontaneously adopt in this course. It is also a way to popularize Rubik's cube games inside and outside school and at home, and it is also one of the characteristics of this course compared with conventional mathematics courses. 3. Tutorial learning Tutorial learning is the source for students to learn the Rubik's Cube and feel the relationship between Rubik's Cube and mathematics. One of the characteristics of Rubik's Cube and Mathematics, which is different from ordinary Rubik's Cube courses, is to carefully select and write the courses that meet the needs of sixth-grade primary school students and transfer the knowledge that suits their physical and mental characteristics to primary school students. 4. Network and media learning build a platform for online communication and interaction, establish a learning website for Rubik's Cube and Mathematics, and open an online learning area, an experience exchange area and a learning report area. Teachers and students will upload the collected Rubik's cube learning materials and learning videos to realize resource sharing. On the other hand, teachers will organize the establishment of a group cooperation model, set up a group study column, put forward various questions in the column, and discuss and communicate with each other. First, the problem will be solved independently in the group, and when it reaches the class, teachers and students will discuss with each other to find ways to solve the problem. Using the Internet and media to communicate is a learning method that makes more extensive use of time, space and resources. (2) Teaching methods "Rubik's Cube and Mathematics" course is different from the study of general subject knowledge. It is not limited to the simple teaching of Rubik's cube knowledge, but more important is the moral experience of students. In this course, students learn by hands, promote their thinking through practical operation, and feel the great charm of Rubik's cube and mathematics with their own experiences. Facts have proved that students who have never touched the Rubik's Cube show obvious differences in learning Rubik's Cube formula compared with those who have tried to play the Rubik's Cube unsuccessfully. But it is much more effective to explain its principle after students practice than before operation. Therefore, in this course, students should be given enough time and space to experience independently, and teachers should also demonstrate, explain and guide in a timely and appropriate manner. Therefore, as a teacher of Rubik's Cube and Mathematics, we should choose the teaching methods suitable for students according to the characteristics and requirements of this course and pay attention to the demonstration. In the form of teaching organization, we should take the form of class teaching, group teaching and individual guidance. In the teaching process, we should explore, practice and reflect to understand the process of students' mathematics learning and thinking formation, and then teach students in accordance with their aptitude and carry out purposeful, planned and effective teaching. (V) Curriculum Evaluation The evaluation of Rubik's Cube and Mathematics has changed the single tendency of current curriculum evaluation, and adopted a diversified and flexible curriculum evaluation method guided by modern educational evaluation concepts. It does not take students' test scores as the only evaluation object, and adopts a combination of quantitative and non-quantitative methods. The evaluation object includes not only the final written test and operation results, but also the performance evaluation during the class. At the same time, the evaluation subject carries out diversified evaluation. It includes not only teachers, but also students' own self-evaluation and mutual evaluation of group members. It is a process to promote students' active participation, self-reflection and self-development. The specific evaluation methods are shown in the following table: evaluation category evaluation table evaluation subject evaluation content project evaluation table current evaluation classroom evaluation teacher 1. Classroom initiative 2. Classroom discipline III. Classroom creation 4. The fifth group of tasks. Collective contribution 6. Learning report ... 10 Group members evaluate themselves. 30 10 10 test evaluation written test teachers and students judges 1. Symbolic formula of Rubik's Cube 2. Rubik's cube 3 mathematical thinking test questions. Talk about your understanding of Rubik's Cube 70 20 Rubik's Cube Contest 1. Simple puzzle 2. Restore the second order 3. Restore the third order 50.

Three. Existing problems and development direction

Rubik's Cube and Mathematics is a useful attempt to provide fresh materials for primary school mathematics. Its value in improving primary school students' interest in learning mathematics, experiencing mathematical knowledge, mathematical ideas and methods in playing Rubik's Cube, and promoting non-intellectual factors such as mathematical learning and creative analysis ability, willpower and self-confidence is worthy of recognition. However, as a school-based curriculum developed, set up and implemented by primary school teachers, there are still some problems: First, the level of curriculum development is still very limited, and there are many irregularities. In mathematics, curriculum, teaching, Rubik's cube and other aspects, we need to continue to explore, especially the current teaching research on Rubik's cube mathematics teaching for primary school students is very scarce, and we need to think deeply in future study and practice to explore teaching methods suitable for primary school students. Secondly, Rubik's Cube course needs Rubik's Cube as a teaching aid and modern network and media as a platform. Therefore, the school-based courses of Rubik's Cube and mathematics need to be carried out in schools with certain conditions, and it is difficult to implement them in schools with insufficient material security. Thirdly, the Rubik's Cube is an interesting educational toy, and its construction and operation process contain rich mathematical factors. Therefore, for the development of Rubik's Cube and Mathematics, the requirements for teachers are very high. The course teacher will not only play Rubik's Cube, but also organize students to teach them to play Rubik's Cube in a special way. The most important thing is to ask the course teacher to understand the mathematical concepts, mathematical ideas and mathematical thinking in the Rubik's Cube while guiding students to play it. For the sustainable development of this course, there are two attempts: (1) continue to explore the essential relationship between Rubik's cube and mathematics, and carry out research exploration and development, so as to provide further exploration space for students with spare capacity and strong interest in learning. (2) You can try to bring other educational toys such as Tangram and 15 slider games into the classroom, so that students can fully enjoy the fun of mathematics hands-on operation, further improve their interest in mathematics learning and expand mathematics teaching resources.

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