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Determining the most appropriate method of scoring an assessment is based on multiple factors, including the intended use of results, the assessment's purpose, and time constraints. Both the dichotomous and partial credit models have their advantages, yet direct comparisons of assessment outcomes from each method are not typical with constructed response items. The present study compared the impact of both scoring methods on the internal structure and consequential validity of a middle-grades problem-solving assessment called the problem solving measure for grade six (PSM6). After being scored both ways, Rasch dichotomous and partial credit analyses indicated similarly strong psychometric findings across models. Student outcome measures on the PSM6, scored both dichotomously and with partial credit, demonstrated strong, positive, significant correlation. Similar demographic patterns were noted regardless of scoring method. Both scoring methods produced similar results, suggesting that either would be appropriate to use with the PSM6. 

The Delphi method has been adapted to inform item refinements in educational and psychological assessment development. An explanatory sequential mixed methods design using Delphi is a common approach to gain experts' insight into why items might have exhibited differential item functioning (DIF) for a sub-group, indicating potential item bias. Use of Delphi before quantitative field testing to screen for potential sources leading to item bias is lacking in the literature. An exploratory sequential design is illustrated as an additional approach using a Delphi technique in Phase I and Rasch DIF analyses in Phase II. We introduce the 2 × 2 Concordance Integration Typology as a systematic way to examine agreement and disagreement across the qualitative and quantitative findings using a concordance joint display table. A worked example from the development of the Problem-Solving Measures Grades 6–8 Computer Adaptive Tests supported using an exploratory sequential design to inform item refinement. The 2 × 2 Concordance Integration Typology (a) crystallized instances where additional refinements were potentially needed and (b) provided for evaluating the distribution of bias across the set of items as a whole. Implications are discussed for advancing data integration techniques and using mixed methods to improve instrument development. 

Using a test for a purpose it was not intended for can promote misleading results and interpretations, potentially leading to negative consequences from testing (AERA et al., 2014). For example, a mathematics test designed for use with grade 7 students is likely inappropriate for use with grade 3 students. There may be cases when a test can be used with a population related to the intended one; however, validity evidence and claims must be examined. We explored the use of student measures with preservice teachers (PSTs) in a teacher-education context. The present study intends to spark a discussion about using some student measures with teachers. The Problem-solving Measures (PSMs) were developed for use with grades 3-8 students. They measure students’ problem-solving performance within the context of the Common Core State Standards for Mathematics (CCSSI, 2010; see Bostic & Sondergeld, 2015; Bostic et al., 2017; Bostic et al., 2021). After their construction, the developers wondered: If students were expected to engage successfully on the PSMs, then might future grades 3-8 teachers also demonstrate proficiency?