Accord to Developing Essential Understanding of Expressions, Equations, and Functions, “understanding algebra requires knowing what variables are and using them as tools to indicate relationships (p. 25).” For this reflection I would like to focus on the definitions of variables, how to introduce variables to students, and why it is valuable for elementary teachers to connect arithmetic to algebra.
Definitions of variables that I want to focus on are unknown and varying. Llyod and Eisenmann (2011) write that variables represent “not just an unknown quantity but also a varying quantity (p. 27).” I had not differentiated the two until reading this section in the book and debriefing in class. Being able to see that these two definitions exist for the word variable has made me understand how a variable can be a placeholder. If there is a place holder, there is one specific, although there may be many, only one will work at a time for an answer for the problem. That type of problem would be an equation. While the varying quantity depends on what the circumstances of the problem and can change this is classified as a function. This is an important detail to make sure student understand so they can find the difference between two types of problems. By teaching students this, they will be able to analyze the type of expression and make more connections. An example is studying the actual relation that variables have in a function instead of just solving to find the answers.
Definitions of variables that I want to focus on are unknown and varying. Llyod and Eisenmann (2011) write that variables represent “not just an unknown quantity but also a varying quantity (p. 27).” I had not differentiated the two until reading this section in the book and debriefing in class. Being able to see that these two definitions exist for the word variable has made me understand how a variable can be a placeholder. If there is a place holder, there is one specific, although there may be many, only one will work at a time for an answer for the problem. That type of problem would be an equation. While the varying quantity depends on what the circumstances of the problem and can change this is classified as a function. This is an important detail to make sure student understand so they can find the difference between two types of problems. By teaching students this, they will be able to analyze the type of expression and make more connections. An example is studying the actual relation that variables have in a function instead of just solving to find the answers.