I look at mathematics as a performing art because I believe that just like playing the piano, painting a picture, or playing lacrosse, to learn how to do the activity with some measure of success, and then to become proficient at it, you have to continually do it.

     Because of the different learning styles present in any classroom, and in order to reach every student, I try to teach every math concept in context.  I teach in the context of what students already know, and in the context of real life situations that are believable and easily recognized by students as important to their future as problem-solvers, and that generate the equations that we learn how to solve in their abstract forms.  Being able to switch from real to abstract and back to real in an iterative way is often not intuitive, and not always appreciated.  That is why I point out each time that we are making the switch so students see when and why we are making the switches. 

     Few concepts in Algebra I Pre-AP are introduced that are not directly related to application to certain types of real problems.  Most concepts are presented in the context of their use.  Algebra concepts are presented as ideas that students are led to feel they need to learn.  Students are provided opportunities to work in pairs on projects that help to solidify understanding.  Problem solving is investigated during many classes with the emphasis on reading comprehension, translation of English to math, and being able to draw pictures, define variables, write equations, and eventually solve the equations that will answer the question(s) being asked. 

     Students discover meaningful relationships between the reality of real-life situations that require mathematical thinking, and the abstract computation and equation solving that are inherent in much of mathematics.  Everything we do in Algebra I Pre-AP is based on a mathematical model I helped to develop many years ago.  The model is named STEPS.  This acronym stands for: Students and Teachers Experiencing Problem Solving.  STEPS brings together all the ideas from my other math model, called: The Four Skills Model.  This model shows the relationship between the four characteristics that are necessary to be a good problem solver, they are: Math Skills, Application Skills, Technology Skills, and Human Skills.

     I have taken the time to list most individual skills that must be mastered by students in Algebra I Pre-AP, however, they are meant to be mastered as a set, not as individual techniques that are memorized out of context.  They are woven into the fabric that represents the coherent internalization of all of these skills as a single set of tools that are appropriately selected and used to solve useful real-world problems.

Mike Hansen – The AlgebraGuy