References for Equal Symbol Difficulty

Share Cognitive Science Implications for Teaching Mathematics
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I am convinced that misuse and misunderstanding of the equal symbol does not exist in isolation.

I sincerely hope that we all agree that in mathematics the equal symbol expresses a relation.  Outside mathematics that same symbol can, and does, have alternate meanings, but in mathematics the = symbol expresses a relation.

Here are two articles, with many references, about the problems with the equal symbol in our school systems.

“Misuse of the equals sign: An entrenched practice from early primary years to tertiary mathematics”  Click here or copy and paste the following URL

https://www.researchgate.net/publication/286418817_Misuse_of_the_equals_sign_An_entrenched_practice_from_early_primary_years_to_tertiary_mathematics

 

“Equations and the equal sign in elementary mathematics textbooks”

Click here or copy and paste the following URL

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3374577/

It is clear to me and anyone who examines the number line that the three relations “less than”, “equal”, and “greater than” as well as their symbols <, =, and > are so closely related that any instruction or discussion of one must include the other two.

In a less direct fashion “symbolic literacy” as discussed in the previous blog post, cannot be ignored if one strives to understand misunderstanding of the equal sign.

Surely Cognitive Development enters into consideration.  The following articles will shed light on that issue.

“Piaget’s Stages of Cognitive Development” Click here or copy and post the following URL.

https://www.verywellmind.com/piagets-stages-of-cognitive-development-2795457

A Google search yields many more articles which examine Piaget’s theories.

An article which examines the development of reasoning skills is “From inference to reesoning: The construction of rationality” Click here or copy and post the following URL.

https://pdfs.semanticscholar.org/260e/a295deabdacc480327c15a9449096854a611.pdf

The effect of  many topics must be studied in relation to misunderstanding the equal symbol:  Dyslexia, textbooks, teacher preparation, and perhaps others.  One of you readers should take up the study – become the expert!

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