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Students Thinking Algebraically

A few days ago I experienced one of the most inspiring moments as an algebra teacher…  I gave my 9th grade students a quiz on solving equations (one-step, two-step, multi-step, literal, etc.).  One of the questions was a word problem that involved buying a season pass ticket to an amusement park versus buying single passes and making multiple visits to the park.  The first part of the question asked students to determine how many trips to the park they would have to make in order for the season pass to be the better deal.  The second part asked the students to write an equation to model the situation.  The third part asked the students to solve the equation.  Most of the students immediately solved the problem by writing and solving an equation.  When they read the second and third parts of the problem they were confused because they had already completed both parts in the beginning.  I was excited!!!!

This is why I was excited…  The students were initially asked to solve the problem using any method (it was an open-ended question).  Most of the students immediately wrote and solved an equation because that was their first thought.  These students were ahead of the test question!  They were already “thinking algebraically” before the question asked them to think algebraically.

After I collected the quizzes the students told me they were confused by the problem and wondered whether they answered it incorrectly.  I told them they answered the question exactly the way they should have.  I told them they were thinking algebraically and that is how they should be thinking.  They were pleased with my response!

The goal of algebra teachers should be to help students think algebraically.  When this happens, students begin to look at problems differently.  They begin to generalize situations and find solutions quickly (and accurately).  Thinking algebraically is a higher level of thinking that most students (and adults) never achieve.  Most of my 9th grade students are already thinking algebraically!  As much as I would like to take full credit for this, I can’t.  Their teachers before me did a phenomenal job and that makes my job easier.

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