Story of the Question
Big Idea: I have decided to conduct my research on how differentiation can be leveraged to transition students to intellectual autonomy in the learning, application, and creation of math knowledge. I find the potential connection between these two seemingly disparate concepts to be fascinating and exciting, especially since this is an area of research that has yet to be explored in depth.
Roadmap:
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Background
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Research Inquiry
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Significance
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Background
Key Idea: Although my students are very intelligent and quite capable of drawing connections between math content and real-world applications when asked to, I am concerned that they do not yet possess the intellectual autonomy to do so on their own once they move on from my class.
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In my statistics class, I often push my students to think about how the material we learn can be applied to the world around us. When I introduce new topics, I start off with the “standard”, contrived examples–rolling dice or picking cards from a poker deck, for example. Then I move to concrete, real-world examples that, albeit not of utmost societal importance, are localized and relevant to my students’ lives, so that they have an easier time grasping the example. For example, we’ve discussed personal budgeting, food consumption, sleep schedules, video game monetization, cell phone plans, and raffles. Finally, I have my students come up with the real-world examples that we do need to think about as a society–incarceration rates, COVID-19 trends, drug abuse, domestic violence, homelessness, unemployment rates, and the like.
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So far, this sequencing of examples from small to large scale seems to have worked quite well with my students. At this point, when I ask for real-world examples, they no longer ask me to clarify what I mean, or have trouble coming up with ideas. Instead, they focus more on choosing the societal problems that are most applicable to the statistical topic at hand, thinking about how statistics can help us to learn more about the problem, or even pave the way toward a possible solution. I am quite happy with their progress; they have come a long way from the beginning of the semester, when I had to utilize multiple layers of probing questions to help them see the bigger picture.
Despite the success of my structured strategy, however, I am concerned that I am not giving my students enough autonomy to learn and apply new material on their own. They perform spectacularly in class, when they know the expectations, are familiar with the routine, and have someone to push them to make those connections between course material and real life. But what happens after my students leave my class? Will they continue to view what they learn with a broader lens? Will they actively pursue their own learning, in order to gain knowledge that can help them enact change in their lives or to society? I am by all means confident in my students’ ability to learn and apply new material on demand when specifically asked to do so; I am less sure about their instinct to do so autonomously.
Research Inquiry
Key Idea: I have decided to conduct my research on how differentiation can be used to support the transition of math students of all levels and backgrounds to autonomous learning, application, and creation.
I have discussed these concerns, to some extent, with my math instructional coach Taryn Ortlip. Although we both agreed that these concerns are significant, valid, and important to address, we decided that we would need more time to mull over how I might address them. In other words, we have yet to concretely problem-solve together. I have thus decided to incorporate these musings into my research inquiry–not only because I believe this problem to be widespread, but also because it appears to be one that does not yet have obvious solutions or recommendations.
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However, I do not believe that student autonomy should be the sole focus of my inquiry. There is another part of the problem that I think is paramount to address simultaneously: differentiation. Just like any other topic in pedagogy, the backgrounds of the students matter immensely in how they might respond to strategies that promote autonomy, and even how much academic or intellectual autonomy they might already possess. I highly doubt that there exists a single strategy (or sequence of strategies) that acts as a one-size-fits-all for nurturing students’ autonomous learning and application. Rather, teachers likely need to work closely with their students to figure out how to best support their developing autonomy.
And thus I have arrived at my research inquiry: How can differentiation be used to support the transition of math students of all levels and backgrounds to autonomous learning, application, and creation? To provide some clarity, I define differentiation as evaluating students’ mathematical levels, personal and cultural backgrounds, cognitive abilities, and real-time responses before coming up with (and/or adapting) strategies that work best for them specifically. Autonomous learning is the ability for students to independently seek out, discover, learn, and master knowledge that they believe will be useful to their lives. Autonomous application is the ability for students to naturally extend their learnings, without being explicitly asked, to real-world scenarios that matter in some way, for the improvement of either their own lives or society as a whole. Autonomous creation is the ability for students to create recommendations, solutions, or courses of action based on what they have discovered about the problem at hand. Although I did not mention autonomous creation until now, I believe it to be the natural next step after autonomous learning and application (and in some ways, the most important).
Significance
Key Idea: Although differentiation and intellectual autonomy are already both popular topics in education on their own, my research inquiry will attempt to draw connections between the two concepts, which is an area of research that has yet to be explored in depth.
What I find most interesting about my research inquiry is the intersection between differentiation and student autonomy. There exist significant bodies of research on each half. Ongoing research on differentiation, which is a relatively modern pedagogical topic, has already resulted in a myriad of resources and strategies that one might try in the classroom. Past and present research on fostering student autonomy has likewise resulted in the creation and adoption of multiple effective strategies. However, research on differentiation has largely focused on finding the best ways to help students of all levels master and apply material during instruction–with the assistance and scaffolding of the teacher, not on their own. Similarly lacking, research on student autonomy has largely failed to account for differences in student backgrounds, instead focusing on supporting the “typical” white, middle-class (or in many cases, upper-class) student.
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I would therefore like to contribute to the relatively sparse research on the relationship between differentiation and student autonomy–and more specifically, how the former might be leveraged to encourage the latter. I realize that my inquiry, although well-defined, is somewhat broad. However, at this point I am reluctant to exclude any of autonomous learning, application, and creation; I believe they are all quite important in their own way. Nevertheless, I am looking forward to seeing where my research takes me. Depending on my findings, I will likely modify my research question to better represent what exactly I’m able to discover. I’m excited to find out what works best for my students, what they themselves think of their own intellectual autonomy, and how these findings might apply broadly to other (math) classrooms.