Question  Discussion – Variables Concept In your own words, explain the concept of a variable. Discuss how you can teach a class about the use of variables and how they can be used to create an algebraic expression.

Discussion – Variables Concept

According to Billstein et al. (2016), a variable is an amount that may change within the context of an experiment or mathematical problem. Existing attempts to improve learners’ understanding of variables have emphasized schematic induction across different solid examples or the oversimplification of relational reasoning from arithmetic. Textbooks reviewing the algebra concept and classes on the concept tend to start by formally defining variables as letters representing numbers and directly proceed to rote procedural practice that includes systematic rules of variable manipulation without encouraging or allowing students first to get an intuitive sense of the purpose and meaning of using the new symbolic representation. The problem escalates due to the fact that the examples used are universal cases of using a variable symbol to represent a single unknown in problems that are so mathematically simplified that they can readily be resolved in an arithmetic form. In addition, no motivation is offered for the algebraic representational advantage forms over the arithmetic hence confusing students about the purpose and meaning of this different formalism.

Therefore, I can teach a class about the use of variables and how they can be used to create an algebraic expression by letting students formulate and attempt solutions for mathematical problems where various unknowns ought to be represented and distinguished from one another. This teaching method would encourage and support students’ intuitive discovery of the concept of variables through purpose-driven disparity comparisons, active learning strategies such as practical struggling with intuitive suggestions and contextual facilitation of learners’ natural problem-solving for concrete and meaningful tasks. I can use this approach to introduce variable representations progressively by first using more interpretable word equations and later converting word phrases into letter symbols, creating algebraic expressions.

References

Billstein, R., Libeskind, S., & Lott, J. W. (2016). A Problem Solving Approach To Mathematics For Elementary School Teachers (12th ed.). Pearson.