When I last put finger to keyboard, I wrote that we had rearranged the Algebra 1 curriculum so that it fell in with our plan for teaching during the year. So what was our plan? Well, we wanted to have a Function-Based Approach to our lessons. That meant that we wanted our students to understand the concept of functions in mathematics: there are acceptable inputs and outputs based upon criteria defined by the mathematical function that controls the relationship between the inputs and outputs.
(Let's assume you are a mathy person because that last sentence was a mouthful.)
So, our first project concentrated on the concept of what a function is: for each input there is a unique output. The students produced videos to show 3 scenarios. Two had to be a function and one a non-function (or the opposite case). There were scenarios ranging from drive through windows, to opening locked doors, to a boy being slapped for saying inappropriate things to a girl. In addition to teaching the concept of a function these 9th graders learned how to create videos and the basics of video editing.
Our next project explored the concepts of domain and range. To do this we asked our students to create art using the dozen, or so, parent functions that students will be introduced to in their high school career. Here is the video we used to kick off the project. This video was created by my amazing co-teacher, Tara Craig. To create the art we utilized MathGV.com. The students chose the functions, "cut" them by restricting the domain, and then put these together to create artwork.
Since it was late September for this, many students created jack-o-lanterns as their piece of art. In addition to linear functions the Algebra 1 students had explored trigonometric, logarithmic, and cubic functions. Most Algebra 1 students are never exposed to more than quadratic functions and our hope was that they would have less angst when they saw these functions in their Algebra 2 year.
And so, it was the first of October. Our students were conversant in function-eze and creating videos. They were ready for (what most teachers start with) the manipulating of linear equations. When it came to graphing linear equations we could talk about their characteristics and the idea of slope seemed to make more sense to the students.
By front loading the functions in their own projects we could now create projects that were based upon linear relationships and, later, quadratic relationships. Discussions about these relationships could be held at a much deeper, functional, level. That doesn't mean we had 100% success with all students. There were still stumbling blocks created by poor arithmetic skills and skill building needed to be added to our daily plans for scaffolding within the projects.
Whether you are teaching in a PBL environment or a standard classroom environment you must plan on dealing with skill building. A common misconception is that PBL will just take care of all of the holes in a student's abilities. Nothing could be farther from the truth. However, in a PBL classroom, there is more time devoted to listening to your students as they discuss concepts and a recognition of deficiencies is quickly realized.