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Mathematics Virtual Learning Village: Occassioning Student Teachers' Learning to Teach Mathematics

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Abstract:

There is agreement in teacher education on the importance of learning from experience. Following this contention, student teaching among other things such as field experiences and school observations, remains a very important part of most teacher education programs. However, while many teacher education programs include student teaching in preservice teacher education, there is increasing evidence from the literature that practicing teachers as well as prospective teachers continue to experience and talk about a gap between theory (University courses) and the lived experiences (practice) of teaching (Grimmet & MacKinnon, 1992).
In mathematics education this problem is compounded by reforms in school mathematics such as those reflected in National Council of Teachers of Mathematics (NCTM) Curriculum and Evaluation standards and Principles and Standards (NCTM, 1989, 2000). In the light of the NCTM standards, the role of teacher education is to enable teachers to choose worthwhile tasks; orchestrate classroom discourse; create a learning environment that emphasizes problem solving, communication and reasoning; and develop the ability to analyze their teaching and student learning. While mathematics teacher educators are making changes in their programs to take account of the reforms there is no evidence of their impact on prospective teachers during their internships. There is an indication that student teachers revert to conventional forms of teaching during their internships. This is not surprising in mathematics education where it is noted that practicing teachers are also struggling with teaching reform mathematics (Boaler, 2003). This begs a question in mathematics teacher education: In what ways can student teaching experiences or teaching practices be supported to make them more educative for both student teachers and practicing teachers?
There is a growing literature in the use of technology as a tool for reforming and improving teacher education programs (Capper, 2001). The common theme running through this literature is that technology provides medium for new forms of pedagogical relations, new collaborative practices and new forms of learning communities.
The literature on the use of technology in teacher education provides some indication on how technology environments might be used to support learning in teacher education programs. However little attention has been paid to the relationship between the supportive technology environments and what preservice students or practicing teachers are learning. What is the nature of this learning? In addition very little is known in terms of the nature of structures of these technology environments and their relationship to worthwhile education tasks that may bridge the gap between theory and the teachers lived experiences of teaching.
This short oral representation will discuss preliminary results of an ongoing research project designed to address these questions. The project involves a number of preservice mathematics teachers as they participate in technology structured mathematics education tasks during their student teaching. As well the research involves some practicing teachers as they engage in these activities as part of their professional development. Specifically the study addresses the following questions:
1. In what ways can technology environments be structured to make student teachers and teachers learning from their practice more educative?
2. What kinds of worthwhile mathematics teaching tasks might these technology environments support?
3. What is the relationship between these mathematics teaching tasks and student teachers’ and practicing teachers’ classroom teaching experiences?
4. What are student teachers or teachers attending to in these technology supported mathematics-teaching tasks?
5. What is the relationship between what student teachers as well as practicing teachers are attending to in mathematics-teaching tasks and their teaching?
The research involves three sites. Each site provides an opportunity to explore particular aspects of the research questions.
1. My own experiences in this study. I keep a journal in which I record my reflections through out the study
2. Online Centre or Virtual Centre:
This is major site in this study. Online prompts or categories are designed where:
a) Teachers and student teachers plan mathematics teaching tasks such as lessons, activities, investigations and assessment tasks both individually and collaboratively.
b) Teachers and student teachers reflect on their teaching using the plans above both individually and collaboratively
c) Teachers and student teachers engage in the discussion around their experiences of teaching around the mathematics tasks
3. School mathematics classes
This site involves teachers and student teachers teaching around mathematics tasks they have planned in the virtual centre. Also the site involves my observations of some of the classes in which these teachers are teaching.
Data is collected from all the records of practice (lesson plans, activities, investigations, reflections and discussions) posted on the online site. In addition data will be obtained from classroom video tapes. I intend to follow up with unstructured interview with some teachers and students.
In the field of mathematics education there is an agreement among educators that there is a great need for research that is focused on mathematics teaching practices. For example, in her plenary presentation at the annual meeting of the Psychology of Mathematics Education (PME), Boaler (2003) argued that, while the field of mathematics education has made great strides in understanding mathematics learning and the creation of rich learning environments for mathematics learning very little is known on what kind of teaching practices might bring about this learning. Boaler contends that what is needed in the field is research that will contribute to understanding of the work involved in the teaching mathematics. This research must start by understanding the act of teaching itself.
Another important point in mathematics education is the observation on the unique nature of mathematics that teachers are engaged with in teaching. Ball and Bass (2002) argue that the mathematics that teachers are engaged with in teaching is different from the kinds of mathematics that research mathematicians or physicists are involved with. Ball and Bass view the work of teaching mathematics as specialized form of mathematical problem solving. That to say as teachers respond to different ways students approach mathematics tasks or as they respond to student errors they are actually engaged in mathematics problem solving. In her plenary presentation at the Canadian Mathematics Education Study Group (CMESG) conference, Sierpinska (2003) puts another swing to this direction, by urging mathematics educators to focus their research on what is common to all mathematics stakeholders, mathematicians, mathematics educators, mathematics teachers, and mathematics students - mathematics. Sierpinska contends that any good mathematics education research should be structured around mathematics activities or tasks.
It is expected that this presentation will open a discussion among mathematics educators on the nature of teaching practices that might bring about learning as articulated by reformers. As well, the presentation will open discussion among mathematics educators not only on the nature of mathematics tasks teacher and students are engaged with but also in what ways teachers attend to these tasks and how does this translate in their teaching.

References
Ball, D., & Bass. H. (2002). Toward a practice-based theory of mathematical knowledge for teaching. Plenary lecture at the 26th Annual Meeting of the Canadian Mathematics Educators Study Group, Kingston, ON, May.
Boaler, J. (2003). Studying and Capturing the Complexity of Practice: The Case of the Dance of Agency. In Neil A. Pateman, Barbara J. Dougherty and Joseph T. Zillox (Eds.). Proceedings of the 2003 joint meeting of Psychology of Mathematics Education International and North American Chapter. CRDG, College of Education, University of Hawai`i
Capper, J (2001) Shoma: A Private sector contribution to South Africa’s teacher development. Teacher Training and Technology Case Study Series. Washington D.C: IIE
Grimmett, P.P., & MacKinnon, A.M. (1992). Craft knowledge and the education of teachers. In G. Grant (Ed.), Review of Research in Education 18 (pp. 385-456). Washington D.C.: The American Educational Research Association.Kennedy, M. (1991). Some surprising findings on how teachers learn to teach. Educational Leadership, 49(3), 14-17.
National Council of Teachers of Mathematics. (1991). Professional standards for teaching mathematics. Reston VA: National Council of Teachers of Mathematics.
National Council of Teachers of Mathematics. (1995). Assessment standards for school mathematics. Reston VA: National Council of Teachers of Mathematics.
National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston VA: National Council of Teachers of Mathematics.
Sfard, A. (2002). On reform movement and limits of mathematical discourse. Mathematical thinking and Learning 2(3), 157 – 189
Sierpinska, A. (forthcoming). Research in Mathematics Education: Through a Keyhole. In Elaine Simmt and Brent Davis (Eds.). Proceedings of the Annual Meeting of Canadian Mathematics Education Study Group, 2003, Acadia University.
Simmt, E., Davis, B., Gordon, L. & Towers, J. (2003). Teachers’ Mathematics: Curious Obligations. In Neil A. Pateman, Barbara J. Dougherty and Joseph T. Zillox (Eds.). Proceedings of the 2003 joint meeting of Psychology of Mathematics Education International and North American Chapter. CRDG, College of Education, University of Hawai`i

Most Common Document Word Stems:

mathemat (62), teacher (58), educ (38), teach (33), student (21), practic (17), research (16), task (15), learn (15), technolog (11), studi (9), experi (9), 2003 (8), environ (7), council (7), involv (7), nation (7), site (6), standard (6), reform (6), engag (6),
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Name: North American Chapter of the International Group for the Psychology of Mathematics Education
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MLA Citation:

Mgombelo, Joyce. "Mathematics Virtual Learning Village: Occassioning Student Teachers' Learning to Teach Mathematics" Paper presented at the annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, Delta Chelsea Hotel, Toronto, Ontario, Canada, Oct 21, 2004 <Not Available>. 2009-05-26 <http://www.allacademic.com/meta/p117712_index.html>

APA Citation:

Mgombelo, J. R. , 2004-10-21 "Mathematics Virtual Learning Village: Occassioning Student Teachers' Learning to Teach Mathematics" Paper presented at the annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, Delta Chelsea Hotel, Toronto, Ontario, Canada Online <.PDF>. 2009-05-26 from http://www.allacademic.com/meta/p117712_index.html

Publication Type: Conference Paper/Unpublished Manuscript
Review Method: Peer Reviewed
Abstract: There is agreement in teacher education on the importance of learning from experience. Following this contention, student teaching among other things such as field experiences and school observations, remains a very important part of most teacher education programs. However, while many teacher education programs include student teaching in preservice teacher education, there is increasing evidence from the literature that practicing teachers as well as prospective teachers continue to experience and talk about a gap between theory (University courses) and the lived experiences (practice) of teaching (Grimmet & MacKinnon, 1992).
In mathematics education this problem is compounded by reforms in school mathematics such as those reflected in National Council of Teachers of Mathematics (NCTM) Curriculum and Evaluation standards and Principles and Standards (NCTM, 1989, 2000). In the light of the NCTM standards, the role of teacher education is to enable teachers to choose worthwhile tasks; orchestrate classroom discourse; create a learning environment that emphasizes problem solving, communication and reasoning; and develop the ability to analyze their teaching and student learning. While mathematics teacher educators are making changes in their programs to take account of the reforms there is no evidence of their impact on prospective teachers during their internships. There is an indication that student teachers revert to conventional forms of teaching during their internships. This is not surprising in mathematics education where it is noted that practicing teachers are also struggling with teaching reform mathematics (Boaler, 2003). This begs a question in mathematics teacher education: In what ways can student teaching experiences or teaching practices be supported to make them more educative for both student teachers and practicing teachers?
There is a growing literature in the use of technology as a tool for reforming and improving teacher education programs (Capper, 2001). The common theme running through this literature is that technology provides medium for new forms of pedagogical relations, new collaborative practices and new forms of learning communities.
The literature on the use of technology in teacher education provides some indication on how technology environments might be used to support learning in teacher education programs. However little attention has been paid to the relationship between the supportive technology environments and what preservice students or practicing teachers are learning. What is the nature of this learning? In addition very little is known in terms of the nature of structures of these technology environments and their relationship to worthwhile education tasks that may bridge the gap between theory and the teachers lived experiences of teaching.
This short oral representation will discuss preliminary results of an ongoing research project designed to address these questions. The project involves a number of preservice mathematics teachers as they participate in technology structured mathematics education tasks during their student teaching. As well the research involves some practicing teachers as they engage in these activities as part of their professional development. Specifically the study addresses the following questions:
1. In what ways can technology environments be structured to make student teachers and teachers learning from their practice more educative?
2. What kinds of worthwhile mathematics teaching tasks might these technology environments support?
3. What is the relationship between these mathematics teaching tasks and student teachers’ and practicing teachers’ classroom teaching experiences?
4. What are student teachers or teachers attending to in these technology supported mathematics-teaching tasks?
5. What is the relationship between what student teachers as well as practicing teachers are attending to in mathematics-teaching tasks and their teaching?
The research involves three sites. Each site provides an opportunity to explore particular aspects of the research questions.
1. My own experiences in this study. I keep a journal in which I record my reflections through out the study
2. Online Centre or Virtual Centre:
This is major site in this study. Online prompts or categories are designed where:
a) Teachers and student teachers plan mathematics teaching tasks such as lessons, activities, investigations and assessment tasks both individually and collaboratively.
b) Teachers and student teachers reflect on their teaching using the plans above both individually and collaboratively
c) Teachers and student teachers engage in the discussion around their experiences of teaching around the mathematics tasks
3. School mathematics classes
This site involves teachers and student teachers teaching around mathematics tasks they have planned in the virtual centre. Also the site involves my observations of some of the classes in which these teachers are teaching.
Data is collected from all the records of practice (lesson plans, activities, investigations, reflections and discussions) posted on the online site. In addition data will be obtained from classroom video tapes. I intend to follow up with unstructured interview with some teachers and students.
In the field of mathematics education there is an agreement among educators that there is a great need for research that is focused on mathematics teaching practices. For example, in her plenary presentation at the annual meeting of the Psychology of Mathematics Education (PME), Boaler (2003) argued that, while the field of mathematics education has made great strides in understanding mathematics learning and the creation of rich learning environments for mathematics learning very little is known on what kind of teaching practices might bring about this learning. Boaler contends that what is needed in the field is research that will contribute to understanding of the work involved in the teaching mathematics. This research must start by understanding the act of teaching itself.
Another important point in mathematics education is the observation on the unique nature of mathematics that teachers are engaged with in teaching. Ball and Bass (2002) argue that the mathematics that teachers are engaged with in teaching is different from the kinds of mathematics that research mathematicians or physicists are involved with. Ball and Bass view the work of teaching mathematics as specialized form of mathematical problem solving. That to say as teachers respond to different ways students approach mathematics tasks or as they respond to student errors they are actually engaged in mathematics problem solving. In her plenary presentation at the Canadian Mathematics Education Study Group (CMESG) conference, Sierpinska (2003) puts another swing to this direction, by urging mathematics educators to focus their research on what is common to all mathematics stakeholders, mathematicians, mathematics educators, mathematics teachers, and mathematics students - mathematics. Sierpinska contends that any good mathematics education research should be structured around mathematics activities or tasks.
It is expected that this presentation will open a discussion among mathematics educators on the nature of teaching practices that might bring about learning as articulated by reformers. As well, the presentation will open discussion among mathematics educators not only on the nature of mathematics tasks teacher and students are engaged with but also in what ways teachers attend to these tasks and how does this translate in their teaching.

References
Ball, D., & Bass. H. (2002). Toward a practice-based theory of mathematical knowledge for teaching. Plenary lecture at the 26th Annual Meeting of the Canadian Mathematics Educators Study Group, Kingston, ON, May.
Boaler, J. (2003). Studying and Capturing the Complexity of Practice: The Case of the Dance of Agency. In Neil A. Pateman, Barbara J. Dougherty and Joseph T. Zillox (Eds.). Proceedings of the 2003 joint meeting of Psychology of Mathematics Education International and North American Chapter. CRDG, College of Education, University of Hawai`i
Capper, J (2001) Shoma: A Private sector contribution to South Africa’s teacher development. Teacher Training and Technology Case Study Series. Washington D.C: IIE
Grimmett, P.P., & MacKinnon, A.M. (1992). Craft knowledge and the education of teachers. In G. Grant (Ed.), Review of Research in Education 18 (pp. 385-456). Washington D.C.: The American Educational Research Association.Kennedy, M. (1991). Some surprising findings on how teachers learn to teach. Educational Leadership, 49(3), 14-17.
National Council of Teachers of Mathematics. (1991). Professional standards for teaching mathematics. Reston VA: National Council of Teachers of Mathematics.
National Council of Teachers of Mathematics. (1995). Assessment standards for school mathematics. Reston VA: National Council of Teachers of Mathematics.
National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston VA: National Council of Teachers of Mathematics.
Sfard, A. (2002). On reform movement and limits of mathematical discourse. Mathematical thinking and Learning 2(3), 157 – 189
Sierpinska, A. (forthcoming). Research in Mathematics Education: Through a Keyhole. In Elaine Simmt and Brent Davis (Eds.). Proceedings of the Annual Meeting of Canadian Mathematics Education Study Group, 2003, Acadia University.
Simmt, E., Davis, B., Gordon, L. & Towers, J. (2003). Teachers’ Mathematics: Curious Obligations. In Neil A. Pateman, Barbara J. Dougherty and Joseph T. Zillox (Eds.). Proceedings of the 2003 joint meeting of Psychology of Mathematics Education International and North American Chapter. CRDG, College of Education, University of Hawai`i

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Joyce Mgombelo Research agenda There is agreement in teacher education on the importance of learning from experience. Following this contention student teaching among other things such as field experiences and school observations remains a very important part of most teacher education programs. However while many teacher education programs include student teaching in preservice teacher education there is increasing evidence from the literature that practicing teachers as well as prospective teachers continue to experience and talk about a gap between
discourse. Mathematical thinking and Learning 2(3) 157 ­ 189 Sierpinska A. (forthcoming). Research in Mathematics Education: Through a Keyhole. In Elaine Simmt and Brent Davis (Eds.). Proceedings of the Annual Meeting of Canadian Mathematics Education Study Group 2003 Acadia University. Simmt E. Davis B. Gordon L. & Towers J. (2003). Teachers' Mathematics: Curious Obligations. In Neil A. Pateman Barbara J. Dougherty and Joseph T. Zillox (Eds.). Proceedings of the 2003 joint meeting of Psychology of Mathematics Education International and


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