## 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.

## Common Core – High School Algebra

The Common Core of High School Algebra states the topics of algebra and a basic guideline as to how to go about teaching algebra to high school students. It is important to go over every detail in order for students to understand terminology and then to further understand how to go about equations. It is also helpful in making sure every topic is gone over in order for the student to further advance in mathematics.

After the discussion in class some students said that some of these should be obvious, like what is a variable and stuff like that, we should already know how to teach that to a student. I completely disagree. This gives us a strong approach. What if a student doesn’t understand your explanation of a function? This article gives a guideline as to the steps that a student should understand. Make sure the student knows the simple terms. What is obvious to us may not be obvious to them. As math teachers, these notions come simply to us, but many students are not as math oriented so it takes longer and is more frustrating.