Bettina Dahl

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.

Analyzing CS competencies using the SOLO taxonomy

We have used the SOLO Taxonomy to analyze 5,608 competencies stemming from 734 courses from the faculties of science at Aarhus University and University of Southern Denmark. Both faculties have formulated learning outcomes using this taxonomy. This has made it possible to systematically analyze competencies and compare different science subjects. In this talk, we will explain the analysis and outline our main findings.

Retention of differential and integral calculus: a case study of a university student in physical chemistry

This paper reports a study on retention of differential and integral calculus concepts of a second-year student of physical chemistry at a Danish university. The focus was on what knowledge the student retained 14 months after the course and on what effect beliefs about mathematics had on the retention. We argue that if a student can quickly reconstruct the knowledge, given a few hints, this is just as good as retention. The study was conducted using a mixed method approach investigating students’ knowledge in three worlds of mathematics. The results showed that the student had a very low retention of concepts, even after hints. However, after completing the calculus course, the student had successfully used calculus in a physical chemistry study programme. Hence, using calculus in new contexts does not in itself strengthen the original calculus learnt; they appeared as disjoint bodies of knowledge.

Tensions Between the European and the Nordic Dimension in Education, with Particular Reference to Sweden

This paper begins with a description and discussion of the historical development of the five Nordic countries’ relations to the European Union (EU), particularly the arguments for and against membership. I shall attempt to detect some common Nordic attitudes to the EU. Then I shall turn to a discussion of what ‘Nordic’ means in terms of culture and go on to describe Nordic co-operation historically. This includes what is particular for the education systems in the Nordic countries and for Swedish education policy. Finally I shall define what a ‘Nordic dimension in education’ might mean. This leads to a description of the development of the ‘European dimension in education’ in the EU and the possible tensions between this and the Nordic. I shall also discuss how Sweden can deal with these tensions either through the Nordic Council or on its own.

University Students' Retention of Derivative Concepts 14 Months after the Course: Influence of "Met-Befores" and "Met-Afters".

This article reports the concluding part of a larger study on retention of key procedural and conceptual concepts in differential and integral calculus among Croatian and Danish university students in non-mathematics study programmes. The first parts of the study examined the retention of the students’ knowledge through a questionnaire testing core calculus concepts in derivative and integration given two and six months after the students had passed an exam testing those concepts. In the present article we continue to explore the retention of core concepts in derivative through a mixed method approach examining the knowledge of 10 second-year non-mathematics students 14 months after they took the course. The result showed that there were several negative met-befores and met-afters affecting the students’ retention.

Various theoretical frameworks in concept construction and how to move forward as a field: A commentary to Pegg and Tall

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What is the problem in problem-based learning in higher education mathematics

ABSTRACT Problem and Project-Based Learning (PBL) emphasise collaborate work on problems relevant to society and emphases the relation between theory and practice. PBL fits engineering students as preparation for their future professions but what about mathematics? Mathematics is not just applied mathematics, but it is also a body of abstract knowledge where the application in society is not always obvious. Does mathematics, including pure mathematics, fit into a PBL curriculum? This paper argues that it does for two reasons: (1) PBL resembles the working methods of research mathematicians. (2) The concept of society includes the society of researchers to whom theoretical mathematics is relevant. The paper describes two cases of university PBL projects in mathematics; one in pure mathematics and the other in applied mathematics. The paper also discusses that future engineers need to understand the world of mathematics as well as how engineers fit into a process of fundamental-research-turned-into-applied-science.

Commentary on The Fundamental Cycle of Concept Construction Underlying Various Theoretical Frameworks

This paper first summarises and discusses Pegg and Tall’s (this volume) fundamental cycle model of conceptual construction from action to object and its relationship to particularly the SOLO UMR framework. Then the paper compares this with another model of different psychological theories of learning mathematics and discusses how these models can either be merged or learn from each other. This includes a discussion of another use of the SOLO framework. This leads to a general discussion about the problem of having many different theories and fashions, how knowledge grows and accumulates, and if there is a unifying theory to be found. The paper concludes that the development of meta-theories, such as in the work of Pegg and Tall, is necessary rather than uncritical complementarism.

A critique on the role of social justice perspectives in mathematics education

This review of the monograph, International Perspectives on Social Justice in Mathematics Education, is not a chapter-by-chapter summary of each of the 14 chapters per se, but rather, revolves around three overarching themes.