Assessment Problem:

Is this equation always, sometimes, or never true?

a + b = b Why?

Mathematical Issues:

Questions such as those requiring students to say when A+B=B or L+M+N=L+P+N, are very difficult for the student who sees the letters as concrete objects, since they will probably think that two different objects can never be the same, or that adding an object necessarily increases something. However those who are thinking in a versatile way see the symbols as encapsulated objects representing a range of values.

Domain:

Variables & Expressions

Theme:

Using graphing calculators to build understanding

Common Core Standards:

7.EE: Expressions and Equations

Research References:

Graham, A., & Thomas, M. (2000). Building a versatile understanding of algebraic variables with a graphic calculator. Educational Studies in Mathematics, 41(3), 265-282.