Big Idea: Upon surveying my students, I find that numbers have increased across the board regarding my students' thoughts and feelings on differentiation, access, and intellectual autonomy. I draw on the literature to analyze potential pitfalls that I successfully avoided in my research, considering how I might more intentionally counteract them in the future.
Roadmap:
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Background
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Data Analysis
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Connection to Literature
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Reflection and Next Steps
References: Domen, et al. (2020), Ford (2012)
Background
Key Idea: In order to gather my students' feedback on this entire process, I decided to have them fill out a closing survey that expands on the initial autonomy survey that I gave them earlier on.
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Although my analysis of Artifact 8 gave me a lot of insight into my students’ improvement in terms of their ability to autonomously learn, apply, and create math knowledge, I wanted to get their direct feedback on what they thought of the entire process. After all, objective data can only tell us so much. Only by reaching out to our students and seeing what they themselves think can we actually gauge how our teaching is impacting their conception of learning, growth, and knowledge.
There are several different ways that I could have collected this data. I could prepare questions with which to interview my students, I could create another feedback survey for them to fill out, or I could have them write unstructured feedback for me. I ultimately decided to create a closing survey, because I was curious about how their opinions of themselves, math, and my teaching changed from the start of my inquiry. Since I had already given them a survey before, I could reuse some of those questions in my closing survey and directly compare the results.
And so, I set out to make a closing survey that could conclude my applied research. The first five questions are copied directly from the five questions on the initial autonomy survey, so that I can analyze the progression of my students’ thoughts and feelings. The last five questions are new questions that inquire about differentiation and access, as well as a few concerns I had during my research that I will explain shortly.
Data Analysis
Key Idea: Compared to the initial survey, not only did numbers rise across the board regarding student thoughts and feelings on intellectual autonomy, but my students also indicate that they feel heavily aided by both my differentiation and access supports.
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Comparing the responses to the first question across both surveys, 8 students (2, 3, 4, 6, 11, 13, 14, 15) feel more capable now than before at autonomously learning, applying, and creating math knowledge. All the remaining students feel as capable as before, and none of them feel less capable. For the second question, 6 students (1, 3, 9, 13, 15, 16) feel more comfortable being intellectually autonomous, while 3 students (7, 11, 12) feel slightly less comfortable. These results tell me that although it seems like my supports did transition my students towards intellectual autonomy, a couple students may still need further socioemotional support to feel confident in their own abilities. The third question shows that 7 students (3, 4, 12, 13, 14, 15, 17) think that math is more of an open subject than before, and no students think it is less open. Seeing this is so rewarding for me, because it shows that I have been able to convey how interesting, useful, and meaningful math is.
Looking at the average ratings for each question, I can get a sense of how my class as a whole has progressed. How capable they think they are at being intellectually autonomous has risen from 3.06 to 3.53 (question 1), and how comfortable they are doing so has risen from 3.18 to 3.35 (question 2). How open a subject they think math is has risen from 3.12 to 3.59 (question 3), and the amount of autonomous learning support they perceive from me has risen from 4.47 to 4.53 (question 5). In summary, all the numbers have increased across the board! This is fantastic to see. It means that not only have my students objectively improved in their ability to be intellectually autonomous, as seen through my previous artifact analyses, but they subjectively feel their own improvement as well. This is important because I want my students to be confident in their own ability to be intellectually autonomous, so that they are more comfortable leveraging that autonomy in the future, even when they are no longer in my class.
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On the sixth question, my students showed me that they felt like I provided a lot of differentiation that was personally helpful to them, rating me an average of 4.24. Similarly, on the seventh question, my students gave me an average of 4.41 in how much I helped them gain access to a variety of resources that aided their learning. These ratings are great to see, because they once again draw the connection from differentiation and access to intellectual autonomy. Not only do my students feel more capable at being intellectually autonomous, but it can be attributed back to the high amount of differentiation and access support that they felt like they received from me since the start of my inquiry project. This confirms that those supports were both noticed by my students and helpful to them, and that I should continue to leverage both kinds of support in my teaching to aid the growth of all my future students’ learning.
Connection to Literature
Key Idea: Drawing on Domen, et al. (2020) and Ford (2012), I explore two potential pitfalls in my inquiry research that I successfully avoided, but could have done more to specifically counteract.
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The last three survey questions address concerns that had come up for me during my research. Some of the literature had warned against some potential pitfalls to avoid while transitioning students to intellectual autonomy, and I wanted to get some feedback regarding whether or not I had fallen into those traps. The study by Domen, et al. (2020) showed that in some cases, differentiated support could ultimately become controlling rather than autonomy-supporting. By figuring out how to best accommodate every student, it becomes possible to box them into particular ways of learning and exploring, which actually hinders their intellectual autonomy instead of fostering it.
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On my eighth survey question, though, my students gave an average of 2.24 on how much constraint they felt from my differentiation and access supports. Conversely, on the ninth question, they rated me an average of 4.18 on how much autonomy support they felt instead. The significant gap between these two ratings is reassuring, because it shows that my students felt that my various supports were ultimately supportive rather than confining when it came to their intellectual autonomy. However, the constraint rating is still slightly higher than I would like to see, so I will definitely need to keep this potential pitfall in mind as I design differentiation and access supports for my students moving forward.
The other concern I had was that I put so much focus on intellectual autonomy that my students might end up thinking that math, and learning in general, is an individual endeavor. The Ford (2012) article emphasizes how important it is for students to be collaborative. Not only does it contribute to differentiation because students can help each other with their areas of improvement, but it also actually increases intellectual autonomy because working with others can spark fresh ideas, renewed curiosity, and further avenues to pursue.
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My tenth and last survey question, then, asked how important my students think it is to collaborate with others in the field of mathematics. The average rating was a 3.71, and only one student (13) gave a rating below a 3. Although this rating is favorable, it could be higher. I’m glad to see that my focus on intellectual autonomy did not actively turn my students away from collaboration; but at the same time, I could have done more to show them the connection between the two. In the future, I want to design more collaborative supports that highlight the ways in which working together can help us to become more intellectually autonomous in our learning and growth.
Reflection and Next Steps
Key Idea: This artifact has shown me that my inquiry research was overall a success, and the final step is to pull together all my findings in a reflective conclusion to my project.
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This artifact showed me that my inquiry was overall a success. My students all feel more capable and comfortable being intellectually autonomous in the learning, application, and creation of math knowledge, and that autonomy can be attributed back to the differentiation and access supports I provided. Through the process of writing, I was also able to analyze potential areas of future improvement: making sure my supports are not at all constraining, and embedding a secondary focus of collaboration. Although the responses to both those areas were already positive, I can work towards making them even more so.
That concludes the artifact analysis section of my inquiry. The 9 artifacts I collected and analyzed were all extremely helpful in determining the link between differentiation/access supports and intellectual autonomy. The final step, then, is pulling all my findings together in a concluding synthesis and reflection.