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The use of computer programming is ubiquitous for research mathematicians, and two common practices are facilitation of experimentation and testing of conjectures. These practices align with empirical re-conceptualization, which is the process where empirical data is used to identify patterns, form related conjectures, and then re-interpret the conjectures from a structural perspective. However, literature on empirical re-conceptualization has only examined student work done by hand. We present case study data of one student, Allen, using the programming language Python to facilitate empirical re-conceptualization as he found the closed-form solution for binomial coefficient C(n,k). We discuss why the computational environment was productive for empirical re-conceptualization and provide avenues for future research.more » « less
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