Analogical Reasoning In Mathematics Learning

By analogous inference, it means the thinking process of inferring from two (or two types of) objects with similar or identical attributes to conclude that one of them may have the attributes that the other one already has. Analogous inference is also referred to as analogy, and sometimes as analogous method or analogous reasoning method.In the real world, there are large numbers of similarities, and in mathematics, there are many systems similar to each other. It is this similarity that paves the foundation for analogous thinking. There are various forms of analogies in mathematics. The thinking characteristics of mathematical analogy should often be considered from both qualitative and quantitative aspects. The basic forms of mathematical analogy are logic analogy and intuitive analogy.Analogy and association are intermediary thinking. In the discovery and learning of mathematics, analogy (thinking) should often be used in conjunction with induction and association. Analogy, induction and association are between logic thinking and intuitive thinking. They effectively communicate logic thinking and intuitive thinking, laying the foundation for the qualitative change in cognition from logic reasoning to intuition.Mathematical analogy has played an important role in the mathematical discovery. Similarly, it is also an important method for students to learn and know mathematics. With the analogous method (analogous inference), students can better know and understand new concepts by comparing them with similar concepts, to build up suitable psychological characteristics. The analogous method is also an effective cognition strategy in learning mathematics. The capacity of analogous inference, it should be formed and developed in the mathematical activities.In the teaching of mathematics, we should pay attention to the extensive use of "principle of analogy, association and expansion", i.e. after obtaining models or methods for special cases, efforts should be made to expand the obtained results by analogous association. In the teaching of mathematics, we'll perform teaching design using the "analogous teaching model" guided by the "principle of analogy, association and expansion".