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:
- Date Issued: 2017
- 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:
- Date Issued: 2017
Project 1 - Student teachers' exploration of beadwork : cultural heritage as a resource for mathematical concepts
- Authors: Dabula, Nomonde Patience
- Date: 2001
- Subjects: Ethnomathematics , Beadwork -- South Africa -- Eastern Cape , Beadwork , Mathematics -- Study and teaching , Culture -- Study and teaching
- Language: English
- Type: Thesis , Masters , MA
- Identifier: vital:1415 , http://hdl.handle.net/10962/d1003292
- Description: This portfolio consists of three research projects that predominantly lie within the socio-cultural strand. The first project is a qualitative ethnomathematical study that links students' knowledge of mathematics to their cultural heritage. The study was conducted with a group of final year student teachers at a College of Education in Umtata, Eastern Cape. These students visited a city museum where mathematics concepts were identified from beadwork artifacts. Mathematics concepts that were identified consisted of symmetry, tessellation and number patterns. Students' views about the nature of mathematics shifted radically after their own explorations. Initially students did not perceive mathematics as relating to socio-cultural practices. But now, they have reviewed their position and see mathematics as inextricably interwoven in everyday activities and as such, a product of all cultures. They also pride themselves of their own cultural heritage to have mathematical connections. A more positive attitude towards studying mathematics in this approach was noticed. Data was collected by means of interviews, reflective journal entries and photographs. The second project is a survey with a group of practising teachers who have already implemented Curriculum 2005, and a group which is about to implement it in 2001. The study sought teachers' understanding of connections between mathematics and socio-cultural issues. The new mathematics curriculum in South Africa calls for teachers to grapple well with these issues. About a third of the articulated specific outcomes specifically relate to socio-cultural issues. If teachers' understanding of these issues is poor, implementation of the new curriculum will remain a mere dream. The findings of the survey revealed that the majority of teachers could not identify the culture related specific outcomes in the new mathematics curriculum. Complicated language used in the OBE policy documents was found to inhibit meaning to these teachers. Although, all teachers showed a positive attitude towards the inclusion of socio-cultural issues in the mathematics classroom, the implementation of these outcomes was found to be very problematic. In this survey data was collected by means of questionnaires. The third project is a literature review on the need to popularise mathematics to students in particular, and to the broader public in general. The 21 st century places great technological demands. Mathematics underpins most thinking behind technological development. The role played by mathematics in advancing other fields is largely hidden to the majority of people. There is, therefore, a need to bring forth the vital role that mathematics plays in these fields. The number of students participating in mathematics is decreasing. Mathematics, as a field, is experiencing competition from other science fields. There is a need to bring some incentives to attract more students into this field and retain those mathematicians already involved. Also important, is the need to change the negative image that the public often holds about mathematics. Many people are mathematically illiterate and do not see mathematics as an everyday activity that relates to their needs. There is, therefore, a need to change the face of mathematics.
- Full Text:
- Date Issued: 2001
- Authors: Dabula, Nomonde Patience
- Date: 2001
- Subjects: Ethnomathematics , Beadwork -- South Africa -- Eastern Cape , Beadwork , Mathematics -- Study and teaching , Culture -- Study and teaching
- Language: English
- Type: Thesis , Masters , MA
- Identifier: vital:1415 , http://hdl.handle.net/10962/d1003292
- Description: This portfolio consists of three research projects that predominantly lie within the socio-cultural strand. The first project is a qualitative ethnomathematical study that links students' knowledge of mathematics to their cultural heritage. The study was conducted with a group of final year student teachers at a College of Education in Umtata, Eastern Cape. These students visited a city museum where mathematics concepts were identified from beadwork artifacts. Mathematics concepts that were identified consisted of symmetry, tessellation and number patterns. Students' views about the nature of mathematics shifted radically after their own explorations. Initially students did not perceive mathematics as relating to socio-cultural practices. But now, they have reviewed their position and see mathematics as inextricably interwoven in everyday activities and as such, a product of all cultures. They also pride themselves of their own cultural heritage to have mathematical connections. A more positive attitude towards studying mathematics in this approach was noticed. Data was collected by means of interviews, reflective journal entries and photographs. The second project is a survey with a group of practising teachers who have already implemented Curriculum 2005, and a group which is about to implement it in 2001. The study sought teachers' understanding of connections between mathematics and socio-cultural issues. The new mathematics curriculum in South Africa calls for teachers to grapple well with these issues. About a third of the articulated specific outcomes specifically relate to socio-cultural issues. If teachers' understanding of these issues is poor, implementation of the new curriculum will remain a mere dream. The findings of the survey revealed that the majority of teachers could not identify the culture related specific outcomes in the new mathematics curriculum. Complicated language used in the OBE policy documents was found to inhibit meaning to these teachers. Although, all teachers showed a positive attitude towards the inclusion of socio-cultural issues in the mathematics classroom, the implementation of these outcomes was found to be very problematic. In this survey data was collected by means of questionnaires. The third project is a literature review on the need to popularise mathematics to students in particular, and to the broader public in general. The 21 st century places great technological demands. Mathematics underpins most thinking behind technological development. The role played by mathematics in advancing other fields is largely hidden to the majority of people. There is, therefore, a need to bring forth the vital role that mathematics plays in these fields. The number of students participating in mathematics is decreasing. Mathematics, as a field, is experiencing competition from other science fields. There is a need to bring some incentives to attract more students into this field and retain those mathematicians already involved. Also important, is the need to change the negative image that the public often holds about mathematics. Many people are mathematically illiterate and do not see mathematics as an everyday activity that relates to their needs. There is, therefore, a need to change the face of mathematics.
- Full Text:
- Date Issued: 2001
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