Construct and Inference Alignment in Mathematical Problemsolving Research

Source abstract

Research on mathematical problem solving often connects psychological dispositions to mathematical performance, yet the meaning of these connections depends on how constructs are measured and interpreted. This methodological study examines construct and inference alignment through secondary documentary analysis of a historical doctoral study involving 118 preservice mathematics teachers in the Philippines. Analysis of the methods, results, and concluding chapters maps theoretical labels, operational measures, reported relations, and substantive claims. Inventory-based findings are compared with process summaries from six participants and two published solution episodes. Three interpretive transitions require additional evidence: from dispositions to enacted mathematical cognition, from reported metacognitive awareness to task regulation, and from personal problem-solving performance to teaching competence. The reported reduced-model association between need for cognition and test performance was .864, whereas the conditional association between metacognitive awareness and performance was-.164. Neither coefficient directly represents observed reasoning or regulation. Process summaries encompass 42 nested participant-by-task opportunities. Contrasting episodes show how a correct result can emerge through pattern search or through revision of a spatial representation, supplying information absent from inventory scores. An evidence-chain framework makes model-dependent associations a separate evidentiary level, locating changes from measured dispositions to mechanisms and educational uses. A worked mathematical task illustrates how correctness, justification, regulation, and pedagogical response support different judgments. The conclusions are bounded by the published documentary record and do not constitute new model estimation or validation of the framework.