This spring semester lead to a great opportunity to work with a UNC-Charlotte Math Ed Professor Allison McCulloch (Twitter: @awmcculloch) and her Math Ed Technology students. The coursework focuses on the use of free technology such as Desmos and Geogebra to make lessons. Allison's idea was for her students to develop one lesson within the spectrum of our standards using appropriate technology. Once the students had a solid lesson, I would teach it and they would observe and reflect on the process. She provided a lot of support and feedback in the intial creation of the lessons, then a draft was sent to me. I then had the opportunity to provide feedback and the students made edits. Once they addressed all the edits I reviewed it one more time and a date was set for instruction where I taught the lesson. Now that everything is done I'd like to share my thoughts on how the process and lesson went as well as some of the work that came out of it.
Positive
The first note I want to make is that the reason this process worked so well is because McCulloch made the effort to seek us out with a genuine interest to better the University's program and our own. I often get propositioned by faculty and professors at the University to "do" something with my students. The problem is that these individuals do not let me know what they can do or provide in a partnership. Most of the time I find that they want the benefit of access to our kids for their benefit with no real focus on how the partnership is supporting the teachers and students (future teachers) in our program. The constant question I generally get is "What do you need from us?" or "How can we help?" when I don't often understand the services they could provide or how they intend to get involved at all. I also find that when people have offered these partnerships they do not have a reasonable idea of the work and effort teachers can put in with other things going on. So the reason this partnership worked so well is because McCulloch had a vision of how the process would work, executed it and kept us in the loop when certain stages of the work was being completed. There was a justifiable amount of work for me to get involved and have buy-in to the idea. She had an understandable objective of creating meaningful coursework for her students and providing me with a cohesive lesson within my content standards.
The second note I want to make is about the quality of the work that came to me. Although I left a ton of feedback. (Just my M.O.) The original draft of the lesson was a quality lesson, that if I had written as an undergrad, I would be really proud of. The final lesson was done on a Geogebra workbook with a set of inquiry based questions written in a google doc. The lesson went over four major discoveries: proportional relationships between chords intersecting in a circle, congruent arcs and chords, equidistant chords and congruency, bisected chords and right angles. Of course there are always after thoughts and things you want to polish, but it was a well written and integrated seamlessly into the way I teach my class. It was so well written that it rivaled a PAID product I use all the time: Gizmos. My kids literally operated it the same way and drew the same conclusion they would have in the Chords and Arcs demo. My students could discuss the work and draw conclusions and summaries from this investigation as well as they could a Gizmo. In fact I've stuck to Geogebra workbooks for my circles to write my inquiries. You can access the Geogebra Workbook here.
Professionally (and personally) this was incredibly fulfilling. Since I work at Teaching Early College, my main focus is churning out excited and exposed future teachers. I got to do this in my classroom and hopefully contributed to some of that with the undergraduates by participating in a rich and valid practice. There is also potential to try and inspire other teachers to make these partnerships happen in their own professional learning communities.
Polish
There were a few things that I put into the lesson that I know my kids are used to doing with our inquiries. So one thing I added to lesson was an investigation summary. You can read more about them and see what those normally look like here. So this was a change I made this a day before without discussing the changes, but I knew my kids needed to summarize their findings based on the investigations. I also put together a simple 5 question homework where students looked at some circle problems, solved them and explained how they decided to set up the problem by referencing the investigation that supported their claims. Besides that change I would clarify some of the instructions on the investigation and possibly re-ordered it to help the flow of things.
There are a few things that I would change about the investigation questions and the way I ran it in class. Since I've been pushed to start my final unit so early, I really think I needed another half a class period to finalize thoughts on new vocabulary, and relationships with inscribed and central angles. I would have also like to revisit content from the earlier semester in Math 2 with similarity and congruence in triangles and angles. It could have gone a long way in making the deep connections my students were struggling to make.
The last thing I've considered is my delivery. I like that we did the first two questions and discussed our findings to give students the confidence to keep working. I think next time I would set a timer and do check-ins after each inquiry rather than let students work in their partners through it. I feel as though I rushed through a bit of the findings and might have made it less clear. But when I collected my 5 question homework check the next day almost all of my students got the 5/5 with a few exceptions getting 4/5, meaning they could apply the theorems discussed.
Questions
Finally I want to think about some questions I still have about the partnership and that I'm still thinking about to continue having these genuinely positive experiences.
1. What else can we do next time? McCulloch offered some other involvements in the semester that excited me, but I didn't do a great job following up on them. One thing that was mentioned was recording a modeling lesson or a three-act-task in my classroom to use for undergraduates. Also, there was some mention of students volunteering to participate in after school opportunities to interact with developing technologies in math that I want to be sure I offer my students next year.
2. How can I communicate, to other interested university parties, what a successful partnership looks like to me? How can I encourage rich experiences for all parties? It might be sad that the main question I keep asking myself in reference to this question is : "What is in it for me?" But when teachers put in their extra time into these partnerships there needs to be some payoff. I've got to find a friendlier way to word this in order to convey my message clearer to other interested people.
3. Do I tell my students that the lesson wasn't mine and get feedback on it to pass on? Obviously the feedback from other teachers is totally valuable, but sometimes a fourteen year old has a perspective we haven't visited. I may want to do this tomorrow that way its as fresh as possible. It may just be a follow up blog post.
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