In an effort to create an engaging lesson that allows for inquiry, collaboration and self-motivation, I created Version 1 of my pre-algebra lesson for combining like terms. In the context of an eighth grade math class, I felt that it was imperative students get up out of their seats to start the hour, which is why we begin with the shoe activity. I also used the shoe comparison, because each child chose their own shoes, and thus it is works for each person’s unique style.
In our class today, we collaborated by Cooking with TPACK, and ultimately learned how to combine technological knowledge, content knowledge and pedagogical knowledge into any lesson. TPACK is not digitizing traditional teaching methods, just to utilize technology, nor is it creating a lesson around technology. TPACK, created here in East Lansing, embodies the idea that educators will create a lesson that considers all three areas, and how those areas interact with each other (Mishra & Koehler, 2006).
We were also given the chance to use Dr. Matthew Koehler’s blog to play the TPACK game. This game allowed us to look at 2/3 categories, and come up with the third, while keeping in mind how the three areas intermingle. This activity helped me to understand my lesson with TPACK in mind, and to reflect on my lesson. See my Lesson version 1.0 HERE.
Content To effectively prepare middle schoolers for the big bad world of algebra, the concept of “combining like terms” is one that cannot be glossed over. This lesson could be taught to seventh or eighth graders, and would precede any lesson on solving equations. This lesson is the beginning of understanding algebraic problem-solving, and thus starting with a solid foundation will allow students to find success in later algebra chapters/classes.
After the Cooking with TPACK activity, I found that the best way to plan a lesson is to keep the content/context in mind the entire time. To teach simplifying expressions (combining like terms), my students will benefit from a visual representation of variables that can be concretely understood. In our study thus far in MAET, we have discussed that real world examples, and concrete understandings help students to not only learn, but truly understand.
Pedagogy The pedagogy for this lesson, in my opinion, is cross-curricular. By first asking them to stand up and organize themselves, they are being asked to collaborate on a method for grouping that will help them answer the question “how many people are in each shoe category?” Students will then be asked to work with a partner to create an “on-paper” strategy to visually represent the like terms. One example of a visual representation can be seen in the figure below.
It is imperative that the teacher not directly instruct students on any one method or strategy. Inquiry and collaboration are key in the success of this portion of the lesson. Students will ultimately annotate the problems, like they would annotate a text in an English or social studies class, then they will create a key, so that if they passed their paper to another student, the method would be clear.
Technology Through reflecting on this lesson, I realized that if someone asked me two weeks ago to describe the technology, I would have said my powerpoint with the directions on it. After learning about TPACK, I wouldn’t even cite that. In this lesson, students have a choice of tool/technology. The teacher can provide markers, highlighters, pencils, pens, scissors, etc. The tech is low, but the possibilities are endless. Students will be empowered to choose the tools that best suit their strategies. Looking at Mishra and Koehler’s (2006) work on TPACK, and reflecting on my own lesson plan in that context, it appears that I have included all three components thoughtfully. I believe that although the tech is low, it is still a solid tool to help students create their own strategies and methods for learning this concept.
Mishra, P. & Koehler. M. J. (2009). Too cool for school? No way! Using the TPACK framework: You can have your hot tools and teach with them, too. Learning & Leading with Technology, 36(7), 14-18.
TPACK image: (http://tpack.org) Reproduced by permission of the publisher, © 2012 by tpack.org
Graphic is my own.