Analysing Cognitive Learning Processes through Group Interviews of Successful High School Pupils: Development and Use of a Model

Abstract

The focus is on the metacognitive awareness of ten high-achieving high school pupils in mathematics in Denmark and England and their understanding of their cognitive learning processes and strategies. Mainly unstructured focus group interviews investigate how they explain that they learn a mathematical concept that is new to them. I develop the 'CULTIS model for analysis' (Consciousness, Unconsciousness, Language, Tacit, Individual, Social), which consists of six themes in which various psychological theories of learning are expressed. The model uses the theories of Ernest, von Glasersfeld, Hadamard, Krutetskii, Mason, Piaget, Polya, Sfard, Skemp, and Vygotsky. The model is used to sort the pupils' explanations and it also functions as a tool with which to compare the pupils' explanations with the various theories. I conclude that the pupils can talk about their learning in their own words and each pupil refers to elements that the researcher associates with different theories. Half the pupils furthermore explain that how they are used to learning, or being taught, influences how they later on are able to learn. I also discuss metacognition and whether this can be an aid to enhance learning.

The role of metacognitive skills in developing critical thinking

“…This supports the studies that consider metacognition as composed of specific multiple factors (Allen and Armour-Thomas 1993;Dahl 2004;Israel et al 2005;Whitebread et al 2009;Yildiz et al 2009). The multiple subcomponents of metacognition are evident having the eight-factor model with a better fit as it affects critical thinking.…”

“…For example, the study of Dahl (2004) where they investigated how students learn new knowledge in mathematics were able to arrive with multiple underlying themes that is reflective of the eight specific factors of metacognition. The specific factors of metacognition are most evident when they are practically applied to teaching.…”

“Rising to the challenge”: using generalization in pattern problems to unearth the algebraic skills of talented pre-algebra students

“…2-4 demonstrate several characteristics of mathematically capable students, such as generalization and abstraction abilities, flexibility in applying solution strategies, creativity and reflection, which are in accord with former research (Dahl 2004;Koichu and Berman 2005;Krutetskii 1976;Sriraman 2003). The solutions demonstrate a high level of generalization and abstraction abilities as well as good foundations of algebraic thinking.…”

From Data Through Coding Toward Categorizing: Negotiating Data Analysis in Constructivist Grounded Theory

“…Within mathematics education, research into metacognition has supported improvement in students' mathematical thinking (e.g., Hamilton, Lesh, Lester, & Yoon, 2007;Schoenfeld, 1987) and has identified successful students as those who understand their personal learning processes (Dahl, 2004;Smith, 1999). Emphasizing a shift from knowing to learning, in the reported study I explored students' development toward becoming capable mathematical learners by addressing the question: How can we understand students' learning as they actively engage in developing their processes of learning math?…”