7 resultados para Philosophy of Mathematics

em Dalarna University College Electronic Archive


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Education is often understood as a process whereby children come to conform to the norms teachers believe should govern our practices. This picture problematically presumes that educators know in advance what it means for children to go on the way that is expected of them. In this essay Viktor Johansson suggests a revision of education, through the philosophy of Stanley Cavell, that can account for both the attunement in our practices and the possible dissonance that follows when the teacher and child do not go on together. There is an anxiety generated by the threat of disharmony in our educational undertakings that may drive teachers toward philosophy in educational contexts. Here Johansson offers a philosophical treatment of this intellectual anxiety that teachers may experience when they, upon meeting dissonant children, search for epistemic justifications of their practices—a treatment whereby dissonant children can support teachers in dissolving their intellectual frustrations.

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Over 20,000 Swedish lower high school students are currently learning mathematics in English but little research has been conducted in this area. This study looks into the question of how much second language learner training teachers teaching mathematics in English to Swedish speaking students have acquired and how many of those teachers are using effective teaching practices for second language learners. The study confirms earlier findings that report few teachers receive training in second language learning but indicates that some of the teaching practices shown to be effective with second language learners are being used in some Swedish schools

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In this paper I investigate how philosophy can speak for children and how children can have a voice in philosophy and speak for philosophy. I argue that we should understand children as responsible rational individuals who are involved in their own philosophical inquiries and who can be involved in our own philosophical investigations-not because of their rational abilities, but because we acknowledge them as conversational partners, acknowledge their reasons as reasons, and speak for them as well as let them speak for us and our rational community. In order to argue this I turn, first, to Gareth Matthews' philosophy of childhood and suggest a reconstruction of some of his concepts in line with the philosophy of Stanley Cavell. Second, in order to examine more closely our conceptions of rationality and our pictures of children, I consider the children's books, The Lorax and Where is My Sister? and Henrik Ibsen's play, The Wild Duck.

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The Swedish government has authorised the teaching of mathematics in English to Swedish speaking students. Much of that teaching is performed by foreign trained native English speaking teachers lacking training in second language learners. This systematic review summarises international studies from the last ten years that deal with the teaching of mathematics to second language learners. The review shows that second language students working in a bilingual environment achieve higher rates of content and language knowledge than learners in a monolingual environment. This study also summarises some of the teacher practices that are effective for teaching mathematics in English to second language learners.

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This thesis explores two aspects of mathematical reasoning: affect and gender. I started by looking at the reasoning of upper secondary students when solving tasks. This work revealed that when not guided by an interviewer, algorithmic reasoning, based on memorising algorithms which may or may not be appropriate for the task, was predominant in the students reasoning. Given this lack of mathematical grounding in students reasoning I looked in a second study at what grounds they had for different strategy choices and conclusions. This qualitative study suggested that beliefs about safety, expectation and motivation were important in the central decisions made during task solving.  But are reasoning and beliefs gendered? The third study explored upper secondary school teachers conceptions about gender and students mathematical reasoning. In this study I found that upper secondary school teachers attributed gender symbols including insecurity, use of standard methods and imitative reasoning to girls and symbols such as multiple strategies especially on the calculator, guessing and chance-taking were assigned to boys. In the fourth and final study I found that students, both male and female, shared their teachers view of rather traditional feminities and masculinities. Remarkably however, this result did not repeat itself when students were asked to reflect on their own behaviour: there were some discrepancies between the traits the students ascribed as gender different and the traits they ascribed to themselves. Taken together the thesis suggests that, contrary to conceptions, girls and boys share many of the same core beliefs about mathematics, but much work is still needed if we should create learning environments that provide better opportunities for students to develop beliefs that guide them towards well-grounded mathematical reasoning. 

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This study explores Swedish Natural Science students' conceptions about gender and mathematics. I conducted and compared the results from two questionnaires. The first questionnaire revealed a view of rather traditional feminities and masulinities, a result that did not repeat itself in the second questionnaire. There was a discrepancy between the traits the students ascribed as gender different and the traits they ascribed to themselves.

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Dissonant Voices has a twofold aspiration. First, it is a philosophical treatment of everyday pedagogical interactions between children and their elders, between teachers and pupils. More specifically it is an exploration of the possibilities to go on with dissonant voices that interrupt established practices – our attunement – in behaviour, practice and thinking. Voices that are incomprehensible or expressions that are unacceptable, morally or otherwise. The text works on a tension between two inclinations: an inclination to wave off, discourage, or change an expression that is unacceptable or unintelligible; and an inclination to be tolerant and accept the dissonant expression as doing something worthwhile, but different. The second aspiration is a philosophical engagement with children’s literature. Reading children’s literature becomes a form of philosophising, a way to explore the complexity of a range of philosophical issues. This turn to literature marks a dissatisfaction with what philosophy can accomplish through argumentation and what philosophy can do with a particular and limited set of concepts for a subject, such as ethics. It is a way to go beyond philosophising as the founding of theories that justify particular responses. The philosophy of dissonance and children’s literature becomes a way to destabilise justifications of our established practices and ways of interacting. The philosophical investigations of dissonance are meant to make manifest the possibilities and risks of engaging in interactions beyond established agreement or attunements. Thinking of the dissonant voice as an expression beyond established practices calls for improvisation. Such improvisations become a perfectionist education where both the child and the elder, the teacher and the student, search for as yet unattained forms of interaction and take responsibility for every word and action of the interaction. The investigation goes through a number of picture books and novels for children such as Harry Potter, Garmann’s Summer, and books by Shaun Tan, Astrid Lindgren and Dr. Seuss as well narratives by J.R.R. Tolkien, Henrik Ibsen, Jane Austen and Henry David Thoreau. These works of fiction are read in conversation with philosophical works of, and inspired by, Ludwig Wittgenstein and Stanley Cavell, their moral perfectionism and ordinary language philosophy.