Abstract
Analogies are commonly used by mathematics teachers as one of the major methods for teaching mathematical concepts. However, false analogies may have countereffects, for example, producing mathematical misconceptions. This paper discusses the major mechanism of analogical reasoning, the positive use of analogies, and how false analogies may disrupt mathematical reasoning. In particular, two major factors that possibly cause false analogies in mathematics teaching and learning will be explored. One factor is the allowance of object difference in an analogical mapping. The other factor is homomorphic mapping that allow partial structural mapping in an analogy. Through the investigation of the two factors, it is argued that analogies may not or should not be the means for justifying or proving mathematical statements, although they may be helpful in teachers’ teaching when introducing or explaining new mathematical concepts to students. This paper suggests that mathematics teachers should know the functions and distinctions between analogical and mathematical reasoning, pay attention to the two factors to avoid creating false analogies, and carefully use but not to abuse analogies (e.g., overtaking mathematical reasoning) in mathematics classrooms.
