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Propositions of Requisite KnowledgeThe first author answered/responded to the chemistry content of each of the 41 items that were obtained from the interviews. This was done to gain an understanding of what was required for a student to (a) understand, and/or (b) solve the item. In many cases, these two sets of requirements were different. As a result, two lists of propositions (statements) were generated for each of the 41 items: One set of propositions described what is required to simply solve the item correctly (“propositions for solving”) and one set described what is required to understand the concepts behind the item (“propositions for understanding”). See Figure 1 for examples of the two types of propositions that were generated for each item.The propositions for understanding described the chemical theories and principles required to gain a full understanding of the phenomenon, while the propositions for solving did not involve any more detail than what was absolutely necessary to respond to the item correctly.These propositions and equations were compiled and sent to the second and third authors for content validation. Propositions were negotiated until all authors agreed that the propositions listed represented the appropriate knowledge requirements for each teacher-generated assessment item. The first author (who was not previously familiar with the interviews) was responsible for the original development of the propositions so that the other authors would not skew the propositions of the items by knowing what the teachers’ goals were, as they were familiar with the previous interviews conducted. Propositions for all items can be found in the Supporting Information.ComparisonsUsing the propositions and summaries, we were able to determine the alignment of teachers’ goals and conclusions (data in the summaries) with what was assessed by the items (propositions). For each of the 41 items, we compared the summaries (capturing teachers’ descriptions viewed through a DDI lens) to the propositions with the aim of generating descriptors that effectively characterized the features of the data corpus. These descriptors were revised and tested as we applied them to more and more items. Through multiple iterations and discussion among the research team, categories became a list of codes that we systematically applied to each item. Originally, the authors set out to determine if the propositions that the first author created aligned or did not align with the teachers’ideas. However, reducing this to a dichotomy severely limited our understanding of data and the conclusions we could make.Alternatively, we present the features that we examined in Table 1, which represent our coding scheme. Some codes originated as themes from the interviews collected, others arose out of the propositions that were created, and some were generated to apply to all items with the aim of capturing broader themes that could emerge. Each item was coded according to the binary outcome in Table 1. An example of this process is given in Figure 2, which shows the outcome based on the summary displayed in Figure 1.
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