## Thoughts on: Learning from Student Approaches to Algebraic Proofs

Protected PDF for class purposes:  https://mth488.files.wordpress.com/2016/01/learning_student_approaches_to_algebraic_proofs.pdf

Article by  : Beatriz S. D’Ambrosio, Signe E. Kastberg, and João Ricardo Viola dos Santos

The first thing that I noticed was the figures in this article. The proofs given by students were completely wrong and I first wondered how would I go about telling these students that they are wrong. Students feelings all of a sudden became what I was concerned of based off of my own experiences. How to tell these students they are wrong… but that is not the point of the article.

The point is that how can we teach students to conduct proofs? Proofs are one of the hardest things to get a student to conceptually understand. What many people may think is why do I need to prove something that we all know is true, something is just because it is that way. But it is not.  Nothing is the way it is just because. There is always a reason. Why does 2×3=6? Because it does… well why? Because 2×3 = 2 + 2 + 2 = 6; 2 added together 3 times. This isn’t even a standard proof but it gets the mind thinking. Well how can you prove that? This is why proofs are hard. Many students had logical reasoning but that is not a proof.