The Problem with Algorithms

What is an Algorithm Jess? 
It's basically a set of rules to be followed to perform a calculation. They are great for computers. They are easily performed and consistently give the correct answer.

What's Wrong with Teaching Algorithms?
Basically, students are not computers. Any parent can confirm that children are not designed to take inputs and generate consistent outputs. People make mistakes, they have deeper thoughts, they interpret findings, they think "what if this was different," they forget and they get bored.

By teaching algorithms we are teaching only how to get the answer. We are not teaching how math works and the structure/logic supporting the process. When we treat student like computers, we forget that interpretation is hugely important. We also do not allow for the student to understand how the answer came into being. At best, a student has a surface understanding of what just occurred. They view math as a series of boring rules to be memorized and not as the beautiful logical structure that it is. When you approach math as being a series of interconnected topics student can fill in missing pieces with a little problem solving. They can construct there own understanding and continue to build on that understanding. We can given them those tools that allow for independence in math but not if we keep teaching tricks and have them memorize rules.

Examples of Algorithmic Teaching

• Cross Multiplication: every time students see two fractions, whether there's a equals sign in between or not they want to cross multiply. Instead we should be teaching inverse operations and solving equations.
• The Triangle Trick: This is a new one for me that I was introduced to by a science teacher. Apparently, we are unable to teach how to solve one step equations in science classes. So F=MA, is just too difficult to work with if I asked a student to solve for the mass.  So they teach students how to put this equation into a triangle that somehow makes it easier to understand. Here I thought dividing on both sides was straightforward enough. 
• The Distance Formula: Why memorize yet another formula when the Pythagorean Theorem will suffice? 
• Long Division: There's a few other methods that reinforce what your actually doing when you divide.
• Almost any Volume Formula: If you know what volume is and you can find the area of a triangle and circle your pretty well set.
• The Quadratic Formula: I taught my student how to complete the square and then proved the quadratic formula using that method. Then we timed students doing both methods. Completing the square usually won. I do really enjoy the Quadratics Formula song, so I will continue to teach it. 

I could go on and on. When I look back at when I've enjoyed learning or teaching I was not memorizing or practicing a process. When I've enjoyed math the most I've been figuring something out, asking a question I don't know the answer to, extending a topic and going down the occasional wrong path.