Assessing Elemental and Structural Validity: Data from Teachers, Non-teachers, and Mathematicians

By H. Hill, Carol D. Dean, I. Goffney. 2007

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Mathematical content knowledge and knowledge for teaching: exploring their distinguishability and contribution to student learning (2019, background): “5 Although we recognize the possibility of answering an item correctly just by mere guessing or test-taking skills, a validation study (Hill et al. 2007) showed low rates of strategic test-taking and guessing, especially for the content-knowledge items (around 5% of the items taken).”
Relationship Between Chinese Mathematics Teachers’ Knowledge and Their Professional Noticing (2020, methodology): “Besides the content validity mentioned above, “elemental validity” of the instrument was examined referring to approaches by Hill, Dean, and Goffney (2007) and Kane (2001).”
Unpacking Pedagogical Content Knowledge: Conceptualizing and Measuring Teachers' Topic-Specific Knowledge of Students (2008, methodology): “Hill et al. (2007) described the complete coding scheme used to classify teacher answers; we include here only the explanations prevalent in answering KCS items: • KCS—Teacher invokes familiarity with students’ errors as partial or complete explanation for selecting their answer (e.g., “My students…”