What does: 1 + 7 = ___ + 6
have to do with: 3x + 9 = 5x + 5
…and why are first graders arguing with each other over the meaning of the equal symbol?
Max explains and demonstrates his interpretation of the equal symbol by saying, “This (the equal symbol)…is telling you the answer.”
It is a common elementary grade misperception that the equal symbol is interpreted as “makes” instead of “same as” in an equation. There is considerable research (Falkner K.P., Levi, and Carpenter, T.P., 1999; NCTM, 2014) that links this faulty language being used as early as first grade, when operational equations are often first introduced.
This conceptual difficulty becomes especially problematic in students’ minds when they later approach algebra, as those students perceive the equal symbol with this limited view as a signal to compute, rather than viewing it as representing a relationship model.
Sarah decided to explore her first grade students’ perceptions of the equal symbol by posing the open-ended problem: 1 + 7 = ____ + 6.
She was hoping to facilitate an engaging discussion amongst her students that would enable them to construct a broader understanding of the equal symbol.
Sarah’s thoughts on what she noticed:
This question posed such a rich opportunity for our first graders to think critically about their math understandings and misunderstandings. Through dialogue and discovery, they found themselves in the alternately clear and murky waters of defining and redefining what the equal sign actually symbolizes. This is assuredly the first of many experiences children will need to move through in order to recognize and internalize “=”. It was rewarding to watch their process and meaning-making in real time and has continued to add relevant insight and inquiry to our ongoing investigations. The practice of working in partnership and the expectation that we will bring our ideas together to defend and debate has become a natural thread in the fabric of our math work.
Take a look at her approach and listen in on some students’ reasoning:
Equal Symbol version 2 from Debra on Vimeo.
