Our task this afternoon was to create a lesson plan in our content area that involved the maker kits we played with this morning. (See the video below for the fun we had this morning.) My partner and I bounced a lot of ideas around and definitely felt the pressure of frustration as we were coming up with the lesson. Ultimately though, we came up with an inquiry based lesson utilizing circuits, which provides students with immediate feedback, forces them to think before answering questions, uses gaming as a motivator, and forces students to think metacognitively throughout the activity. You can see the lesson plan here and our objective below.
The inquiry piece of the lesson is probably the most important. We are asking students to look at several possible solutions in each station. As is most often the case in mathematics, there is structure behind every correct answer. It is on the student to create hypotheses, test them, and then explain the structure that yielded the correct answer. This phase of the lesson is supported by Bransford, Brown, and Cocking (1999) as they mention that “it can be difficult for them (students) to learn with understanding at the start; they may need to take time to explore underlying concepts and to generate connections” (Bransford et al, 1999, p. 58). This is precisely our aim in the lesson. We want students to experiment with different possibilities and begin to, after numerous opportunities, draw out the underlying structure in the mathematics.
Beyond the inquiry focus of the lesson, a couple other aspects are worth mentioning as I think they are incredibly valuable to learning. First, students get immediate feedback on their reasoning. We would stress early on in the activity that students should justify a choice prior to selecting that choice. They should explain that reasoning. Then they test the reasoning and benefit from immediately knowing if they need to rethink their reasoning or if it was correct. This feedback, coupled with our continuous feedback from monitoring the students Google Doc reflections and conversations, provides an incredibly valuable, diverse feedback loop that supports students learning throughout the activity (Bradsford et al, 1999, p. 59).
This lesson assumes that students are coming to the activity understanding the concept of a variable with coefficients. They should also have a surface level understanding of exponents. I think when we first designed the lesson we didn’t fully consider the prior knowledge students would need to get the full benefit of the activity. As Bransford points out, constructing new knowledge from existing knowledge means teachers need to consider “incomplete understandings” and “false beliefs” about a concept (p. 10). As a revision to the lesson I’m not sure that I would do any direct instruction over the needed concepts, but I would pay close attention to their reflections during each station. I can then help individual students to identify their misconceptions and hopefully eliminate the early misconceptions in the context of combining like terms. This is akin to when Bransford discusses a misconception about the world being flat. The danger is that the student, given new information (the world is actually round) constructs new knowledge that is incorrect (the world is like a pancake on a sphere) (Bransford et al, 1999, p. 10). In the context of the activity I would be monitoring for prior misconceptions and helping to effectively shape them into new, correct knowledge.
In addition to a modification in the way we approach their prior knowledge, I think I would extend this activity to another day. On the second day students would create their own circuit boards and then test each others. Since the creation of the circuit boards is fairly straightforward, I don’t think the math would get lost in the technology. Asking students to create their own problems will force them to do a number of things that are valuable to their learning. First, students would be encouraged to use several of the structures they discovered the previous day. This would force them to go back and evaluate the information they recorded in their reflections. In addition, in trying to make their board “tricky”, they will likely reflect on their misconceptions (that have hopefully been cleared up) and build those into the circuit board as possible choices. This act of metacognition and reflection allows students to “recognize the limits of one’s current content knowledge, and then take steps to remedy the situation” (Bradsford et al, 1999, p. 47). This is how experts approach problems and is often not how novices approach problems. The “day 2” piece of this activity helps students to move in the direction of thinking like experts and helps them construct a deeper understand of combining like terms.
Here are some images of our circuit board that would be utilized in the lesson.
Bransford, J. D., Brown, A. L., & Cocking, R. R. (1999). How people learn: Brain, mind, experience,
and school. Washington, D.C.: National Academy Press.