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

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.     

Rechtssprechung Volltext

Rechtssprechung Volltext

Rechtssprechung Volltext     

Waiting for the Second Treat: Developing Culture‐Specific Modes of Self‐Regulation

The development of self‐regulation has been studied primarily in Western middle‐class contexts and has, therefore, neglected what is known about culturally varying self‐concepts and socialization strategies. The research reported here compared the self‐regulatory competencies of German middle‐class (N = 125) and rural Cameroonian Nso preschoolers (N = 76) using the Marshmallow test (Mischel, 2014). Study 1 revealed that 4‐year‐old Nso children showed better delay‐of‐gratification performance than their German peers. Study 2 revealed that culture‐specific maternal socialization goals and interaction behaviors were related to delay‐of‐gratification performance. Nso mothers’ focus on hierarchical relational socialization goals and responsive control seems to support children's delay‐of‐gratification performance more than German middle‐class mothers’ emphasis on psychological autonomous socialization goals and sensitive, child‐centered parenting.     

Sympathiebeziehungen unter Peers im Klassenzimmer: Wie gut wissen Lehrpersonen Bescheid?

Are teachers aware of how well each of their students is embedded in the sympathy-based peer network of the classroom? In this research, we asked students of 39 classes (N = 821) from different types of schools and grades to nominate the three peers they liked most within their class. At the same time, the 39 classroom teachers were asked to reproduce the nominations they thought every single student would undertake. Using the Jaccard coefficient, we compared the similarity of the social networks that emerged from students’ and the respective teacher’s nominations. Results showed that on average, teachers identified 30.1% of the peer nominations correctly. Elementary school teachers were better attuned to their students’ sympathy relations than secondary school teachers. Teachers’ accuracy in identifying peer relations was predicted by the extent to which they intentionally observed peer interactions in the classroom and by their beliefs whether teachers are accountable for the quality of peer relationships in the classroom. Future studies should further investigate whether students profit in their social and academic development from their teacher being highly accurate in the perception of the classroom’s sympathy peer network.     

How can the relationship between argumentation and proof be analysed?

The paper presents a characterisation about argumentation and proof in mathematics. On the basis of contemporary linguistic theories, the hypothesis that proof is a special case of argumentation is put forward and Toulmin’s model is proposed as a methodological tool to compare them. This model can be used to detect and analyse the structure of an argumentation supporting a conjecture (abduction, induction, etc.) and the structure of its proof. The aim of the paper is to highlight the importance of structural analysis between argumentation and proof. This analysis shows that although there are clear cases of continuity between argumentation supporting a conjecture and its proof, there is often a structural distance between the two (from an abductive argumentation to a deductive proof, from an inductive argumentation to a mathematical inductive proof).     

Buchbesprechungen

Ohne Zusammenfassung