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.