Algebraic Thinking

    Algebraic Thinking

           When I was young, I was (and still am) a lover of Algebra, so I want algebraic thinking to only involve letters, equations and solving for one answer. However this is not the case, as I have moved on in my math career and into teaching my thoughts on algebraic thinking have grown, matured and have changed. Algebraic thinking typically means for me looking for patterns and relationships. It allows for generalizations to be made about something, putting an equation or rule in place. I also think that algebraic thinking means taking some abstract concept and putting a face on it, or applying some type of rule. It is similar to other forms of mathematical reasoning because it challenges the student to think critically and provides a certain level of understand (some more than others). Algebraic thinking differs from other forms of mathematical reasoning like deductive reasoning. Deductive reasoning takes known facts and makes a conclusions.

         My students most use algebraic thinking when they see a concept for the first time. I usually start each unit out with some type of investigation. For example I gave my students many graphs of polynomial functions. I asked them to find some type of relationship or pattern between the number of zeros and the degree of the polynomial. This allowed for many conversations to take place, they had to develop some sort of rule to explain why a 4^th degree polynomial can’t have 5 roots, but a 5^th degree polynomial can have 4 roots. It took a little while for each group to sort through the graphs and come to some type of generalization. I think that this type of thinking paid off in the long run because I did not just give them the rule and memorize it, but figuring it out by themselves. 

        I imagine that algebraic reasoning can mean problem solving, justifying and proving. I am currently struggling with my students and their constant question of “why do I need this in real life?” In real life most of my students are not going to have to solve a quadratic equation by factoring or multiply rational expressions, but they will need to problem solve. The problem solving skills and thought process to answer the questions will help with real life problems. Being able to figure out what the “problem” states, what resources you have and what you need, setting up a way to solve the problem, actually doing it and then checking to see if you are right can translate into most careers.

          Math and the skills used in the math classroom (algebraic thinking and all methods of mathematical reasoning) all us to “sharpen” our critical thinking skills for us to use later on in life when we are given a problem that we do not know how to solve right away. We can use our algebraic thinking skills that were learned in a math classroom to overcome the problem.  Algebraic thinking also does not always have to be for the math classroom or on a homework problem. Anything that calls for problem solving or making generalizations will use algebraic thinking.