Structural model of metacognition and knowledge of geometry

This structural equation modeling study aimed to investigate both direct and indirect relations between metacognition and geometrical knowledge. The model was tested using data from tenth grade secondary school students (N = 923). It was used to estimate and test the hypothesized effects of two metacognitive constructs (knowledge of cognition and regulation of cognition) on three knowledge constructs (declarative, conditional, and procedural knowledge) together with the interrelationships among these three knowledge constructs. Major findings from the model indicated: (a) a reciprocal relationship existed among declarative, conditional, and procedural knowledge; (b) knowledge of cognition had a positive direct effect on procedural knowledge and a significant but negative direct effect on declarative knowledge; and (c) regulation of cognition had a positive direct effect on declarative knowledge and a significant but negative direct effect on procedural knowledge.     

Project-based geometry learning: Knowledge and attitude of field-dependent/independent cognitive style students

The authors in a convergent parallel mixed method design aimed to investigate whether and how the geometry knowledge and attitude toward geometry of students with field-dependent/independent cognitive style improve differentially within a project-based learning environment. Quantitative data were collected from 97 seventh-grade students before and after the treatment. Repeated measures multivariate analysis of covariance results, controlling for gender and prior mathematics achievement, revealed a statistically significant main effect of time but not cognitive style. Follow-up repeated measures analysis of covariance by controlling the experiment-wise alpha level indicated that field-dependent, field-mixed, and field-independent students achieved a statistically significant mean increase for all measures. The qualitative (classroom observations and interviews with some students) data provided evidence that contextualizing, visualizing, and collaborating opportunities in the project-based learning environment made contributions for mean increase.