Problems with the equal symbol are very closely related to symbolic literacy in mathematics. The article below briefly mentions symbolic literacy and provides references.
2018 article from Melboure, Australia This is well worth the time.
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It is my impression that research by Abraham Arcavi is the seminal work related to the problem stents experience with symbol literacy.
His paper titled “Developing and Using Symbol Sense in Mathematics”
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Another good source by Arcavi is “Symbol Sense: Informal Sense-making in Formal Mathematics”
These Academic papers and the included lists of references should provide a very good start to any level study you might wish to pursue relative to Symbolic Literacy.