Set theory is an essential language in learning mathematics, especially in algebra. Set theory, when is a prerequisite to algebra and other mathematical abstract concepts, it enhances their cognition. Dogan (2011) argues that cognitive difficulties in understanding abstract mathematical concepts results from the failure to master set theory language. Dogan (2011) found that set theory language is essential for proper response to linear algebra problems. Moreover, his study revealed that misconception of algebra and other abstract mathematical concepts was highly contributed by lack of mastery of set theory language. There are three elements of set theory that are critical in learning mathematics: The ability to identify the elements of a set, the general description and description of a member, and the recognition of various representations of the same set. Linear algebra variables are represented using sets. The in ability to recognize the elements within a given set cause misinterpretation and misunderstanding of the concepts.
The set theory language can be used to define functions, domain, and other mathematical concepts. For example, a function can be defined as a relationship in which elements of set A are fit into elements of set B, as shown below
Also, the domain of a function F(x) can be defined by the set {a, b, c, d, e, f, g}. Algebra involves the translation of word problems into expressions and equations. Therefore, set theory language provides an effective tool for analyzing relationships between groups. Sets and their subsets are used to describe relationships that can easily be transformed in to expressions and equations.
Properties of set theory can be compared with properties for easy conceptualizing. For example, the distributive properties 8(x +2) = 8x + 8 (2) is analogous to the property of sets BC =
Instructional procedures used by teachers in teaching mathematics should be consistency with the learner’s level of conceptualization of mathematical concepts. However, where learners experience problems in understanding concepts, the teacher should make use of other concepts to simplify current concepts. In this case, the use of set theory is essential in learning of algebra and other mathematical concepts. Set theory representations, such as Venn diagram, form essential tools for solving mathematical problems, and understanding relationships between quantities.
Students having difficulties in understanding mathematical concepts should be taught set theory as a prerequisite to other mathematical concepts, such as algebra. The student should understand the representation of information using sets. This is because sets simplify the information for easy conceptualization. Moreover, sets represent information that involves relationships effectively.
The students should use sets theory as an alternative to solve mathematical problems. For example, union and intersection properties should be used in solving problems involving relationships. Also, set theory is application in solving probability problems and other mathematical problems. Moreover, the properties of sets provide easy steps in finding solutions to complex mathematical problems.
In conclusion, set theory is a prerequisite for understanding abstract mathematical concepts. Therefore, set theory should be taught before other abstract concepts. Students should use set theory concepts to solve problems involving relationships, and enhance their understanding on mathematical ideas.
References
Dogan, H. (2011). Set theory in linear algebra. Mathematica Aetern, 1(5), 317-327.
Libeskind, S., & Lott, J.W. (2010). A problem solving approach to mathematics for elementary
school teachers (10th edition). Pearson Education.
