I was in Indianapolis, Indiana recently at the National Council of Teachers of Mathematics (NCTM) National Conference. First of all, let me say that it was a fabulous meeting of minds! I am full of new ideas to try with my students and to share with teachers in my district.
I was honoured to get to present at the conference. I did my workshop “Packing a Powerful Punch with Patterns” which is about using patterns (especially pictorial ones) to help younger students build algebraic thinking. One of the important points in the workshop is about equality. We, as teachers, need to make sure we offer lots of opportunities for students to build an understanding of this concept. We use the term frequently in our classrooms, saying things like “two plus three equals five” referring to the symbolic notation of that: 2 + 3 = 5. Day after day, week after week, month after month, year after year we use the term “equals”, but seldom do we stop and check to see if the students understand the term as we mean it. It is most likely that they do not. Studies have shown that students then to think that “equals” means “put the answer here”, or “now do the operation”. They tend to have no reference point for the idea that whatever is on one side of the equal sign has the same value as what is on the other side.
Teachers can help students with this by doing a few simple things. First, try writing equations with the “answer” on the left: 5 = 2 + 3. When children see that for the first time, they tend to tell you that you have written it incorrectly! Another great thing to try is to write equations such as 2 + 3 = 4 + 1. You can also leave out any one part of that equation and have students solve it. Again, they are likely to have a misunderstanding and tell you that 2 + 3 does NOT equal 4 since that is where they are used to stopping in their thinking. Using actual balance scales with small blocks or other regularly-sized manipulatives is a great way to help students develop this important concept.
So, the next time you are using equations in a lesson, take some time and find out how well your students understand equality. It’s worth putting some time into this topic!
Mathematically yours,
Carollee
