I was fascinated by the following slide that Dr. Lawson shared. When asked which equation was wrong, most children felt all were wrong except for the third. Why? They rationalized that it was the only equation written in what they perceived to be the correct format. The children were thinking that the equal sign meant 'answer' and had not really internalized the concept that the equal sign represents that each side is the same as the other. They had memorized what they felt was the correct way to write an equation without understanding how the symbols and numbers worked together. This was troubling for me.
I was pleased that many recognized the incorrect equation but wanted to make sure as many children as possible had entry points into thinking about the idea of equivalency and knowing that each side of an equal sign needs to be the same in order for the statement to be correct. I asked the children to sit around the edge of the circle and placed a set of subitizing cards in the middle. The cards show different ways of representing numbers (numerals, dots, ten frames, cubes, fingers, etc.).
This generated a lot of interesting conversation as children debated the numbers. I'm hoping to revisit this idea in another few days and encourage the children to add addition or subtraction signs on either side of the equal sign so they are composing and decomposing numbers yet making each side balanced and equal to the other.
It was so interesting to see how the children interpreted our initial conversations of what 'equal' meant and applied their understandings to new and interesting play situations. We heard many conversations today and noted that some children were beginning to use language that described fractions - this is especially interesting as fractions are one of the topics most children have difficulties with. If kindergarten children are becoming comfortable using rich math language in the appropriate corresponding context, their mathematical mindsets will flourish as they see themselves as capable and invested mathematicians in the classroom and beyond!