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Papers by Anna-Karin Carstensen

Research paper thumbnail of Laplace Transforms : Too difficult to teach, learn, and apply, or just a matter of how to do it?

Research paper thumbnail of Analytical tools in engineering education research: The "learning a complex concept" model, threshold concepts and key concepts in understanding and designing for student learning

For a long time, most research relating to science and engineering education has examined "m... more For a long time, most research relating to science and engineering education has examined "misconceptions" about "single concepts", despite the fact that one common objective in many subjects is "to learn relationships". In this paper we introduce the notion of "a complex concept", i.e. the idea of describing knowledge as a complex, a holistic unit, consisting of interdependent and interrelated "single concepts". We describe how this conception could be used to identify both problems associated with learning as well potentials for learning. We will also relate the notion of a complex concept to the notion of threshold and key concepts.

Research paper thumbnail of Learning and Teaching Electrical Circuit Theory

Student's conceptions in circuit theory and electricity are not as well investigated as those... more Student's conceptions in circuit theory and electricity are not as well investigated as those in mechanics. Most studies have been on pre-university students understanding of simple circuits and little research has been done on university level students understanding. Some research indicates that the similar inappropriate understandings (For example: Confusion between voltage and current and between energy and current. Problems with sign and an inappropriate ability to reason globally) which can be found among younger students do exist even after that students have followed university level courses in physics or electrical engineering. Students understanding of more advanced topics in DC-theory, AC-theory and in applying transform (phasor, Fourier and Laplace) methods to circuits are, to our knowledge, not investigated at all. We are, by means of videotaping labs and with semistructured interviews, investigating engineering students understanding of electrical circuits including...

Research paper thumbnail of Analysing and modelling engineering students’ learning in the laboratory: a comparison of two methodologies

Research paper thumbnail of Critical aspects for learning in an electric circuit theory course − an example of applying learning theory and design- based educational research in developing engineering education

Transient response is considered to be one of the more difficult parts of learning electric circu... more Transient response is considered to be one of the more difficult parts of learning electric circuit theory, because the mathematics is advanced and the Laplace transform is used to solve differential equations. Usually, the mathematics is taught in math courses and in problem solving sessions, the graphs in lab courses and the conceptual understanding of the transients in lectures, and students are expected to link these components themselves. The idea of conceptual labs has been developed previously for physics courses. In this kind of labs as well physical phenomena as their mathematical and graphical representations are elaborated. In this paper we describe an innovative course in electric circuit theory and how, by introducing systematic changes in lab instruction, it is possible to make students understand the relationship between theory and real circuits.

Research paper thumbnail of Investigating engineering students' learning – learning as the ‚learning of a complex concept

In both engineering and physics education, a common objective is that students should learn to us... more In both engineering and physics education, a common objective is that students should learn to use theories and models in order to understand the relation between theories and models, and objects and events, and to develop holistic, conceptual knowledge. During lab-work, students are expected to use, or learn to use, symbolic and physical tools (such as concepts, theories, models, representations, inscriptions, mathematics, instruments and devices) in order both to understand the phenomena being studied, and to develop the skills and abilities to use the tools themselves. We have earlier argued that this learning should be seen as the learning of a complex concept, i.e. a "concept" that makes up a holistic system of "single" interrelated "concepts" (i.e. a whole made up of interrelated parts). On the contrary, however, in education research it is common to investigate "misconceptions" of "single concepts". In this paper we will show ...

Research paper thumbnail of Understanding phase as a key concept in physics and electrical engineering

Research paper thumbnail of Real Models in Modelled Reality: epistemic confusion when communicating science?

In light of new technology (3D-visualization, VR, haptics) enabling sensory representation of so-... more In light of new technology (3D-visualization, VR, haptics) enabling sensory representation of so-called abstract ideas, we raise some issues related to implementation of models in science teaching. A salient feature of its content is the prolific usage of such representations (Lemke 1998). Science's presumptive high level of abstraction apparently results in the need for apt representations, whose function prima facie

Research paper thumbnail of Modelling and learning a complex concept - an exploration in light of some examples from electric circuit theory

Research paper thumbnail of What questions are raised during lab-work?

During lab-work students are expected to link observed data, often represented by graphs, to eith... more During lab-work students are expected to link observed data, often represented by graphs, to either theoretical models, or to the real world that they are exploring. In recent research some of the problems have been examined, e.g. that students do not generalize in a scientifically epistemic manner and that they do not make links between the object/event world and the theory/model world. That epistemology of science has to be taught explicitly is also a question discussed in research. In this paper we present some questions that students ask during lab-work, and try to compare these questions to the ones teachers expect them to raise and answer during the lab-sessions. We also try to find out which questions the students do not answer, and possibly what changes in the instructions could lead the students to ask relevant questions. We can see that most of the questions, whether asked or answered, are related to different representations in the theory/model world, and that very few qu...

Research paper thumbnail of Student learning in an electric circuit theory course: critical aspects and task design

European Journal of Engineering Education, Jul 10, 2009

Please check the published version for pagination when quoting.

Research paper thumbnail of Keys to learning in specific subject areas of engineering education - an example from electrical engineering

Most previous educational research on university teaching and learning has looked for generic pri... more Most previous educational research on university teaching and learning has looked for generic principles, which could then be used to inform practice" . Research in engineering education has for example dealt with the alignment of assessment to the curriculum or progressive teaching/learning environments. Through research in specific subject areas it has been shown that there are specific "ways of thinking and practicing (WTP) in each subject area" (ibid). In science education the focus has been on students' views of single concepts. One of the common objectives in science and engineering education is "to learn relationships". In our research we have been investigating what we call complex concepts, i. e. concepts that make up a holistic system of "single" interrelated concepts. As in many disciplines we find "threshold concepts"[9], concepts which are transformative, irreversible, integrative and troublesome . These concepts are often recognized by teachers in a field, but we also suggest that it is possible by research to find "key concepts", but not in the sense that the term is often used in some educational contexts, as interchangeable with 'core' concepts, and meaning simply that the concepts are an important part of the prescribed syllabus. Here we use the term as a more precise metaphor to mean that the concept in question acts like a key to unlock the 'portal' of understanding. We use variation-theory [8] in order to find "key concepts", critical aspects that can act like a key to unlock the portal of understanding. In our paper we will describe how we have designed labwork in an electrical circuit course, taking the ideas behind threshold concepts and key concepts into our specific topic Transient Response as one example of how research into specific subject areas is made possible through qualitative research.

Research paper thumbnail of Design-based educational research and development of engineering education - an example from a course in electrical engineering

This study has been developed within a systematic framework to design innovative learning environ... more This study has been developed within a systematic framework to design innovative learning environments in science and engineering education. The aim of our research is to help students acquire a functional understanding of the subject matter. During for example labwork, students are expected to link observed data to either theoretical models, or to the "real world" they are exploring. However, according to a large body of research, establishing relevant connections between the concepts, the representations, the models and the observable objects and events is a very difficult task for students.

Research paper thumbnail of Laplace Transforms : Too difficult to teach, learn, and apply, or just a matter of how to do it?

Research paper thumbnail of Analytical tools in engineering education research: The "learning a complex concept" model, threshold concepts and key concepts in understanding and designing for student learning

For a long time, most research relating to science and engineering education has examined "m... more For a long time, most research relating to science and engineering education has examined "misconceptions" about "single concepts", despite the fact that one common objective in many subjects is "to learn relationships". In this paper we introduce the notion of "a complex concept", i.e. the idea of describing knowledge as a complex, a holistic unit, consisting of interdependent and interrelated "single concepts". We describe how this conception could be used to identify both problems associated with learning as well potentials for learning. We will also relate the notion of a complex concept to the notion of threshold and key concepts.

Research paper thumbnail of Learning and Teaching Electrical Circuit Theory

Student's conceptions in circuit theory and electricity are not as well investigated as those... more Student's conceptions in circuit theory and electricity are not as well investigated as those in mechanics. Most studies have been on pre-university students understanding of simple circuits and little research has been done on university level students understanding. Some research indicates that the similar inappropriate understandings (For example: Confusion between voltage and current and between energy and current. Problems with sign and an inappropriate ability to reason globally) which can be found among younger students do exist even after that students have followed university level courses in physics or electrical engineering. Students understanding of more advanced topics in DC-theory, AC-theory and in applying transform (phasor, Fourier and Laplace) methods to circuits are, to our knowledge, not investigated at all. We are, by means of videotaping labs and with semistructured interviews, investigating engineering students understanding of electrical circuits including...

Research paper thumbnail of Analysing and modelling engineering students’ learning in the laboratory: a comparison of two methodologies

Research paper thumbnail of Critical aspects for learning in an electric circuit theory course − an example of applying learning theory and design- based educational research in developing engineering education

Transient response is considered to be one of the more difficult parts of learning electric circu... more Transient response is considered to be one of the more difficult parts of learning electric circuit theory, because the mathematics is advanced and the Laplace transform is used to solve differential equations. Usually, the mathematics is taught in math courses and in problem solving sessions, the graphs in lab courses and the conceptual understanding of the transients in lectures, and students are expected to link these components themselves. The idea of conceptual labs has been developed previously for physics courses. In this kind of labs as well physical phenomena as their mathematical and graphical representations are elaborated. In this paper we describe an innovative course in electric circuit theory and how, by introducing systematic changes in lab instruction, it is possible to make students understand the relationship between theory and real circuits.

Research paper thumbnail of Investigating engineering students' learning – learning as the ‚learning of a complex concept

In both engineering and physics education, a common objective is that students should learn to us... more In both engineering and physics education, a common objective is that students should learn to use theories and models in order to understand the relation between theories and models, and objects and events, and to develop holistic, conceptual knowledge. During lab-work, students are expected to use, or learn to use, symbolic and physical tools (such as concepts, theories, models, representations, inscriptions, mathematics, instruments and devices) in order both to understand the phenomena being studied, and to develop the skills and abilities to use the tools themselves. We have earlier argued that this learning should be seen as the learning of a complex concept, i.e. a "concept" that makes up a holistic system of "single" interrelated "concepts" (i.e. a whole made up of interrelated parts). On the contrary, however, in education research it is common to investigate "misconceptions" of "single concepts". In this paper we will show ...

Research paper thumbnail of Understanding phase as a key concept in physics and electrical engineering

Research paper thumbnail of Real Models in Modelled Reality: epistemic confusion when communicating science?

In light of new technology (3D-visualization, VR, haptics) enabling sensory representation of so-... more In light of new technology (3D-visualization, VR, haptics) enabling sensory representation of so-called abstract ideas, we raise some issues related to implementation of models in science teaching. A salient feature of its content is the prolific usage of such representations (Lemke 1998). Science's presumptive high level of abstraction apparently results in the need for apt representations, whose function prima facie

Research paper thumbnail of Modelling and learning a complex concept - an exploration in light of some examples from electric circuit theory

Research paper thumbnail of What questions are raised during lab-work?

During lab-work students are expected to link observed data, often represented by graphs, to eith... more During lab-work students are expected to link observed data, often represented by graphs, to either theoretical models, or to the real world that they are exploring. In recent research some of the problems have been examined, e.g. that students do not generalize in a scientifically epistemic manner and that they do not make links between the object/event world and the theory/model world. That epistemology of science has to be taught explicitly is also a question discussed in research. In this paper we present some questions that students ask during lab-work, and try to compare these questions to the ones teachers expect them to raise and answer during the lab-sessions. We also try to find out which questions the students do not answer, and possibly what changes in the instructions could lead the students to ask relevant questions. We can see that most of the questions, whether asked or answered, are related to different representations in the theory/model world, and that very few qu...

Research paper thumbnail of Student learning in an electric circuit theory course: critical aspects and task design

European Journal of Engineering Education, Jul 10, 2009

Please check the published version for pagination when quoting.

Research paper thumbnail of Keys to learning in specific subject areas of engineering education - an example from electrical engineering

Most previous educational research on university teaching and learning has looked for generic pri... more Most previous educational research on university teaching and learning has looked for generic principles, which could then be used to inform practice" . Research in engineering education has for example dealt with the alignment of assessment to the curriculum or progressive teaching/learning environments. Through research in specific subject areas it has been shown that there are specific "ways of thinking and practicing (WTP) in each subject area" (ibid). In science education the focus has been on students' views of single concepts. One of the common objectives in science and engineering education is "to learn relationships". In our research we have been investigating what we call complex concepts, i. e. concepts that make up a holistic system of "single" interrelated concepts. As in many disciplines we find "threshold concepts"[9], concepts which are transformative, irreversible, integrative and troublesome . These concepts are often recognized by teachers in a field, but we also suggest that it is possible by research to find "key concepts", but not in the sense that the term is often used in some educational contexts, as interchangeable with 'core' concepts, and meaning simply that the concepts are an important part of the prescribed syllabus. Here we use the term as a more precise metaphor to mean that the concept in question acts like a key to unlock the 'portal' of understanding. We use variation-theory [8] in order to find "key concepts", critical aspects that can act like a key to unlock the portal of understanding. In our paper we will describe how we have designed labwork in an electrical circuit course, taking the ideas behind threshold concepts and key concepts into our specific topic Transient Response as one example of how research into specific subject areas is made possible through qualitative research.

Research paper thumbnail of Design-based educational research and development of engineering education - an example from a course in electrical engineering

This study has been developed within a systematic framework to design innovative learning environ... more This study has been developed within a systematic framework to design innovative learning environments in science and engineering education. The aim of our research is to help students acquire a functional understanding of the subject matter. During for example labwork, students are expected to link observed data to either theoretical models, or to the "real world" they are exploring. However, according to a large body of research, establishing relevant connections between the concepts, the representations, the models and the observable objects and events is a very difficult task for students.