Mysteries of the Equals Sign

I discovered a very interesting education phenomenon through a blog post at Cocktail Party Physics. Apparently, sixth grade students in the US have difficulties understanding the equals sign while students from other countries do not.

A basic observation of the phenomenon is described in a journal article

Falkner, Levi,
and Carpenter (1999) reported from their investigation in a single school of the
problem “8 + 4 = a + 5”, all 145 sixth-graders filled the box with 12 or 17.
These types of errors were caused by students’ misunderstanding the equal sign
as a command to carry out calculations just like the “=” button on a calculator.

The reason may be related to how the equals sign is presented in US textbooks and how teachers are trained to discuss it with their students. For example,

Both Reys et al. (2003) and Van de Walle (2004) alerted presevice teachers
to the common misconception that the equal sign meant, “the answer is coming”
(Reys et al., 2003, p. 345). Both of these textbooks’ authors informed readers that
using the calculator reinforced the equal sign misconception, because the answer
came after the equal sign was pressed.

Apparently, if you think of the equals sign as if it were a button on the calculator telling you to compute the answer of everything that precedes it, a math statement like this makes sense

8+4=12+5=17

This result highlights that students can hold quite a few misconceptions and still get to the right answer most of the time. So, probing to discover what their misconceptions are is very important, and that means creating tricky questions like the ones described in this study.

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