# Linear Functions With a Bang

Many teachers tell me that it is their creativity that limits their ability to be adaptive in the classroom. Somehow the “reform” movement (or should I say re-movement) has pigeon-holed itself into a connotation where high-energy teachers give vague tasks to groups of interested students. Out of all this, curricular outcomes explode in no particular order. This can’t be further from the truth. In my view, the biggest steps toward changing student learning is changing teacher perception.

When presented with a topic to cover, there are two dominant ends of the Math-Ed spectrum. First, you have the transmission approach which carefully selects examples that represent the questions of that type that will be encountered in homework packages and on unit exams. The teacher can predict exactly what the class will look like, and students have very little control. Second, you have the open-ended approach where students are given a leading question and formulate ideas in order to solve it. In this process, the students may end up wherever their minds (and motivation) take them. The teacher has almost no clue where the class is going, and the students are given ultimate control. If a teacher is presented with these two juxtaposed methods, they will wisely choose control.

In my class, I work to find a happy mix between the two. I focus on designing “tasks” that give students control over certain learnings, but are focused enough that I can also appease the rigid timeline in the front of my curricular documents. The tasks do not require a large amount of creativity, but a willingness to see opportunities to step back and hand control to the students. It involves me being willing to guess where students will go, and ask leading questions to push them further. Every topic becomes an opportunity for me to grow as a teacher, because I don’t know where students will go, what misconceptions they will challenge me with, and what discoveries they will make. (By the way, I hate using the word “discovery” because it has become the whipping boy in every staff room conversation. For some reason, teachers doubt their students’ ability to make connections without explicit instruction.)

The following lesson is an example of viewing the classroom slightly differently. The original idea was not mine, but as one of my Education professors once told me, “Teachers make excellent pirates.” The original lesson plan came from Great Maths Teaching Ideas. They often tweet lessons with interesting connections to nature, sports, and society.

The original lesson was framed under the framework of an “unusual way to teach plotting straight line graphs” by examining the linear function of cricket chirps and temperature. Other that that creative context, there was little difference between this problem and those found in textbooks. They created a worksheet where students were given a function, a table of values, and a grid to plot on. They were then asked a series of questions. A creative, real-world situation doesn’t necessarily constitute a change in teacher thinking.

I took the context and blossomed its potential to include a variety of pathways and afford opportunities for students to practice multiple skills in a cooperative setting. Because of the close ties to science, I chose to place the problem in a lab setting. For background on mathematics labs see “Merit To Mathematics Labs”–an earlier post on this blog.

__Linear Functions Lab__

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__Students are separated into groups of two or three and handed out two handouts. The first is a copy of the “lab report” that looks very similar to the handout from the original lesson, and the second is a copy of a graph that converts degrees Fahrenheit to degrees Celsius. The image I used is below:

*Their task is pointed but autonomous*. Here students work to expand on prior skills and create new understanding. We are working toward the connection between slope and y-intercept of a graph and the values of “m” and “b” in y=mx+b. A class like this creates an anchor lesson where I can always look back on and say, “remember the crickets”. Students dive in and create their own understanding through active learning. You don’t have to be the most creative teacher in the world to allow students to proceed on their own, you just need a little foresight as to where they

*may*go.