Yesterday in our content pedagogy class, we were talking about key ways of thinking in the disciplines, which we called signature pedagogies. A proposal for a signature pedagogy brought up by a chemistry teacher included balancing equations. One of the high school math teachers suggested that balancing equations is a concept in algebra also.
The goal of the discussion was to consider disciplinary ways of thinking. While it is true that there is a procedure called “balancing (or solving) equations” in these two disciplines, they involve very different ways of thinking.
In chemistry, balancing equations is grounded in the big idea that matter cannot be created or destroyed. The key idea is that the same atoms we start with must be the ones we end up with. I used to tell students that balancing chemistry equations is just bookkeeping.
In algebra, we start with a true statement, and “balancing” equations is part of solving them. The solution, finding out what x can be, is about maintaining the integrity of the original true statement. The procedures for solving equations include balanced operations on either side of the equal sign.
Balancing mathematical equations is about logic. Balancing chemical equations is about processes which occur when different atoms react. To some extent, both require bookkeeping. However, understanding them as only bookkeeping does not go to the heart of the disciplines.
While this might seem like a philosophical quibble, I think it has important consequences for learners. When I used to tutor algebra, I would focus on the procedure for solving equations as being about maintaining the truth of the statement. When they went from a procedural understanding to a conceptual one, every young person (but one) that I tutored went from low grades to A’s. One high school student decided she didn’t need to go to class anymore, and started skipping, still getting A’s, at which point her mother ended the tutoring. What kind of commentary that is on math teaching in the US, I will not venture to say since it’s not very comprehensive data.