Generating shared interpretive resources in the mathematics classroom: using philosophy of mathematics to teach mathematics better
- Authors: De Lange, Laura
- Date: 2017
- Subjects: Mathematics -- Study and teaching , Mathematics -- Philosophy
- Language: English
- Type: Thesis , Masters , MA
- Identifier: http://hdl.handle.net/10962/4293 , vital:20645
- Description: Every student has a unique mathematical lived experience: a unique amalgamation of ideas about mathematics, exposure to mathematical concepts and feelings about mathematics. A student's unique set of circumstances means that not every explanatory account of mathematics will cohere with her previous experiences. For an explanation to have explanatory potential, it must provide an account which coheres with the other beliefs a student has about mathematics. If an explanation has no such coherence, it will not be recognisable as an explanation of the phenomenon of mathematics for the student. Our explanatory accounts of mathematics and mathematical knowledge are our philosophies of mathematics. Different philosophies of mathematics will better explain different sets of mathematical lived experiences. In this thesis I will argue that students should be exposed to a multiplicity of philosophies of mathematics so that they can endorse the philosophy of mathematics which has the most explanatory potential for their particular set of mathematical lived experiences. I argue that this will improve student understanding of mathematics. The claims inherent in any given philosophy of mathematics, when combined with other stereotypes or prejudices, can work to unjustly exclude members of subordinated groups, such as poor, black or female students, from mathematical participation. If we want to avoid reinforcing and reinscribing prejudicial claims about people in the mathematics classroom, we need to be aware of how a certain philosophy of mathematics can exclude certain students. In this thesis I will be defending the idea that, as mathematics educators, we should diversify the way we see mathematics so that we decrease this exclusion from mathematics. In order to diversify the way in which we see mathematics so as to decrease unjust exclusion, members of subordinated groups should be encouraged to share their mathematical experiences in a space sensitive to the power dynamics present in the mathematics classroom. These accounts can then be combined with existing philosophies of mathematics to create new ways of making sense of mathematics which do not unjustly exclude members of subordinated groups.
- Full Text:
- Authors: De Lange, Laura
- Date: 2017
- Subjects: Mathematics -- Study and teaching , Mathematics -- Philosophy
- Language: English
- Type: Thesis , Masters , MA
- Identifier: http://hdl.handle.net/10962/4293 , vital:20645
- Description: Every student has a unique mathematical lived experience: a unique amalgamation of ideas about mathematics, exposure to mathematical concepts and feelings about mathematics. A student's unique set of circumstances means that not every explanatory account of mathematics will cohere with her previous experiences. For an explanation to have explanatory potential, it must provide an account which coheres with the other beliefs a student has about mathematics. If an explanation has no such coherence, it will not be recognisable as an explanation of the phenomenon of mathematics for the student. Our explanatory accounts of mathematics and mathematical knowledge are our philosophies of mathematics. Different philosophies of mathematics will better explain different sets of mathematical lived experiences. In this thesis I will argue that students should be exposed to a multiplicity of philosophies of mathematics so that they can endorse the philosophy of mathematics which has the most explanatory potential for their particular set of mathematical lived experiences. I argue that this will improve student understanding of mathematics. The claims inherent in any given philosophy of mathematics, when combined with other stereotypes or prejudices, can work to unjustly exclude members of subordinated groups, such as poor, black or female students, from mathematical participation. If we want to avoid reinforcing and reinscribing prejudicial claims about people in the mathematics classroom, we need to be aware of how a certain philosophy of mathematics can exclude certain students. In this thesis I will be defending the idea that, as mathematics educators, we should diversify the way we see mathematics so that we decrease this exclusion from mathematics. In order to diversify the way in which we see mathematics so as to decrease unjust exclusion, members of subordinated groups should be encouraged to share their mathematical experiences in a space sensitive to the power dynamics present in the mathematics classroom. These accounts can then be combined with existing philosophies of mathematics to create new ways of making sense of mathematics which do not unjustly exclude members of subordinated groups.
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Determinism and reactive attitudes: reflections on our alleged unrenounceable commitments
- Authors: Kelland, Lindsay-Ann
- Date: 2009
- Subjects: Free will and determinism Responsibility
- Language: English
- Type: Thesis , Masters , MA
- Identifier: vital:2713 , http://hdl.handle.net/10962/d1002843
- Description: There seems to exist a tension between our metaphysical and phenomenological commitments in the free will debate. On the one hand, I argue that at the metaphysical level we cannot coherently defend the belief that we are morally responsible in the sense that we deserve to be rewarded and punished for our actions, where desert-entailing moral responsibility is the primary understanding of moral responsibility presupposed in the free will debate. I argue that we are responsible for our actions but only in the weaker sense, termed ‘attributability’ by Gary Watson. On the other hand, we are allegedly unrenounceably committed at the phenomenological level to conceiving of, and treating, ourselves and one another as morally responsible beings in the desert-entailing sense. P. F. Strawson famously defends this claim in his seminal work, ‘Freedom and Resentment’. In my thesis I will set out this tension by exploring both commitments in turn. I then aim to show that the tension can be dissolved by arguing, contra P. F. Strawson, that our phenomenological commitment is not in fact unrenounceable. The dissolution of this tension entails, I argue, that we must examine our conception of self and other. We must explore the implications of adopting a position which denies that we are morally responsible beings for our life-hopes, personal feelings, inter-personal relationships and projects. Most importantly, I argue that we must renounce our current retributive condemnatory practices which are based on the unjustified belief that we are morally responsible beings.
- Full Text:
- Authors: Kelland, Lindsay-Ann
- Date: 2009
- Subjects: Free will and determinism Responsibility
- Language: English
- Type: Thesis , Masters , MA
- Identifier: vital:2713 , http://hdl.handle.net/10962/d1002843
- Description: There seems to exist a tension between our metaphysical and phenomenological commitments in the free will debate. On the one hand, I argue that at the metaphysical level we cannot coherently defend the belief that we are morally responsible in the sense that we deserve to be rewarded and punished for our actions, where desert-entailing moral responsibility is the primary understanding of moral responsibility presupposed in the free will debate. I argue that we are responsible for our actions but only in the weaker sense, termed ‘attributability’ by Gary Watson. On the other hand, we are allegedly unrenounceably committed at the phenomenological level to conceiving of, and treating, ourselves and one another as morally responsible beings in the desert-entailing sense. P. F. Strawson famously defends this claim in his seminal work, ‘Freedom and Resentment’. In my thesis I will set out this tension by exploring both commitments in turn. I then aim to show that the tension can be dissolved by arguing, contra P. F. Strawson, that our phenomenological commitment is not in fact unrenounceable. The dissolution of this tension entails, I argue, that we must examine our conception of self and other. We must explore the implications of adopting a position which denies that we are morally responsible beings for our life-hopes, personal feelings, inter-personal relationships and projects. Most importantly, I argue that we must renounce our current retributive condemnatory practices which are based on the unjustified belief that we are morally responsible beings.
- Full Text:
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