PhD & MSc Students: Degrees and Joint Articles

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Below is a list of MSc, PhD and EdD students who have a research component in their degree. Any joint papers listed can be downloaded in PDF format.

Many of the theses listed here can be found on the Warwick Research Archive Portal (WRAP) at http://wrap.warwick.ac.uk Some are available as downloadable PDF files, some need to be consulted in person at the Library as follows:

PDFs to download:

David Tall http://wrap.warwick.ac.uk/2409/

Hatice Akkoc http://wrap.warwick.ac.uk/4053/

Maselan bin Ali http://wrap.warwick.ac.uk/57058/

MdNor Bakar http://wrap.warwick.ac.uk/4006/

Norman Blackett http://wrap.warwick.ac.uk/2307/

Kin Eng Chin http://wrap.warwick.ac.uk/58403/

Phil DeMarois http://wrap.warwick.ac.uk/3968/

Eddie Gray http://wrap.warwick.ac.uk/2309/

Mercedes McGowen http://wrap.warwick.ac.uk/56301/

Yudariah Yusof http://wrap.warwick.ac.uk/55875/

John Monaghan http://wrap.warwick.ac.uk/34626/

Michael Thomas http://wrap.warwick.ac.uk/57212/

Links to information about a thesis:

Amir Asghari http://webcat.warwick.ac.uk/record=b2091254~S9

Erh-Tsung Chin http://webcat.warwick.ac.uk/record=b1652885~S9

Robin Foster http://webcat.warwick.ac.uk/record=b1659637~S9

Anna Poynter http://webcat.warwick.ac.uk/record=b1779745~S9

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**John D. Monaghan, PhD** (1981–1986).

*Adolescent’s Understanding of Limits and Infinity*. (PhD, 1986).

e-mail:J.D.Monaghan@education.leeds.ac.uk,

website:http://edu.leeds.ac.uk/research/staff/jdm.htm

John Monaghan, Shyashiow Sun and David Tall. 1994c, Construction of the Limit Concept with a Computer Algebra System,

Proceedings of PME 18, Lisbon, III, 279–286.

**Michael O. J. Thomas, MSc PhD** (1983–1988)

*The Effects of BASIC Computer Programming on the Understanding of the Use of Letters as Variables in Algebra*, (MSc, 1985), *Conceptual Approach to the Early Learning of Algebra Using a Computer*, (PhD, 1988).

e-mail:m.thomas@scitec.auckland.ac.nz

website:http://www.math.auckland.ac.nz/~thomas/staff/mt/mt.html

David Tall & Michael Thomas. 1986d. Playing algebra with the computer,

Exploring Mathematics with Microcomputers(ed. Nigel Bufton) C.E.T., 59–74.

David Tall & Michael Thomas. 1986i. The value of the computer in learning algebra concepts,Proceedings of P.M.E. 10, London 313–318.

David Tall & Michael Thomas. 1988c. Longer Term Effects of the Use of the Computer in the Teaching of Algebra,Proceedings of P.M.E.12. Hungary, 601–608.

David Tall & Michael Thomas. 1989c. Versatile Learning and the Computer, Focus, 11, 2 117–125.

David Tall & Michael Thomas. 1989d. Verbal Evidence for Versatile Understanding of Variables in a Computer Environment,Proceedings of P.M.E., Paris, volume 3, 213–220.

David Tall & Michael Thomas.1989f. Dynamic algebra [computer program and lesson plans], in Secondary Mathematics with Micros – A Resource Pack, Mathematical Association.

David Tall & Michael Thomas. 1991c. Encouraging Versatile Thinking in Algebra using the Computer,Educational Studies in Mathematics, 22 2, 125–147.

Lillie Crowley, David Tall & Michael Thomas. 1994d. Algebra, Symbols, and Translation of Meaning,Proceedings of PME18, Lisbon, II, 240–247.

Garry Davis, David Tall & Michael Thomas, 1997c. What is the object of the encapsulation of a process?, In F. Biddulph & K. Carr (Eds.)People in Mathematics Education, MERGA 20, Aotearoa. 2,132–139, MERGA Inc.

David Tall, Michael Thomas, Garry Davis, Eddie Gray, Adrian Simpson, 2000a.What is the object of the encapsulation of a process?,Journal of Mathematical Behavior, 18 (2), 1–19.

David Tall, Eddie Gray, Maselan Bin Ali, Lillie Crowley, Phil DeMarois, Mercedes McGowen, Demetra Pitta, Marcia Pinto, Michael Thomas, and Yudariah Yusof, 2001a. Symbols and the Bifurcation between Procedural and Conceptual Thinking,Canadian Journal of Science, Mathematics and Technology Education1, 80–104.

Michael Thomas & David Tall, 2001. Thomas, M. O. J. & Tall, D. O. (2001). The long-term cognitive development of symbolic algebra,International Congress of Mathematical Instruction (ICMI) Working Group Proceedings - The Future of the Teaching and Learning of Algebra, Melbourne, 2, 590-597.

**Norman Blackett, MSc PhD** (1985–1990).* Computer Graphics and Children’s Understanding of Linear and Locally Linear Graphs*, (MSc, 1987). *Developing Understanding of Trigonometry in Boys and Girls using a Computer to Link Numerical and Visual Representations*, (PhD, 1990).

Norman Blackett & David Tall, 1986e. Investigating graphs and the calculus in the sixth form,

Exploring Mathematics with Microcomputers(ed. Nigel Bufton) C.E.T., 156–175.

Norman Blackett & David Tall, 1991g. Gender and the Versatile Learning of Trigonometry Using Computer Software,Proceedings of PME15, Assisi, 1 144–151.

**Lan Li, MSc** (1990–1992). *Studying Functions and Limits Through Programming*, (MSc 1992).

Lan Li & David Tall,1993e. Constructing Different Concept Images of Sequences and Limits by Programming, Proceedings of PME 17, Japan, 2, 41–48.

**MdNor Bakar, PhD** (Jan 1990–Dec 1993).*What Do Students Learn About Function? A Cross-cultural Study in England and Malaysia*. (PhD 1993).

e-mail: mnbbakar@hotmail.com

Md Nor Bakar & David Tall, 1991f. Students’ Mental Prototypes for Functions and Graphs,

Proceedings of PME 15, Assisi, 1 104–111.

Md Nor Bakar & David Tall, 1992c. Students’ Mental Prototypes for Functions and Graphs,Int. J. Math Ed Sci & Techn., 23 1, 39–50. (This paper is different from 1991f above.)

**Eddie M. Gray, PhD** (1990–1993)

*Qualitatively Different Approaches To Simple Arithmetic* (PhD, 1993).

e-mail: E.M.Gray@warwick.ac.uk

website: http://fcis1.wie.warwick.ac.uk/~merc/staffemg.htm

Eddie Gray & David Tall, 1991h. Duality, Ambiguity & Flexibility in Successful Mathematical Thinking,

Proceedings of PME 15, Assisi, 2 72–79.

Eddie Gray & David Tall, 1992k. Success and Failure in Mathematics: Procept and Procedure – A Primary Perspective,Workshop on Mathematics Education and Computers, Taipei National University, April 1992, 209–215.

Eddie Gray & David Tall, 1992l. Success and Failure in Mathematics: Procept and Procedure – Secondary Mathematics,Workshop on Mathematics Education and Computers, Taipei National University, April 1992, 216–221.

Eddie Gray & David Tall, 1993b. Success and Failure in Mathematics: The Flexible Meaning of Symbols as Process and Concept, Mathematics Teaching, 142, 6–10.

Eddie Gray & David Tall, 1994a. Duality, Ambiguity and Flexibility: A Proceptual View of Simple Arithmetic,The Journal for Research in Mathematics Education, 26 (2), 115–141.

Eddie Gray, Demetra Pitta & David Tall, 1997e. The Nature of the Object as an Integral Component of Numerical Processes,Proceedings of PME 21, Finland, 1, 115–130.

Eddie Gray, Demetra Pitta, Marcia Pinto & David Tall, 1999k. Knowledge Construction and diverging thinking in elementary and advanced mathematics,Educational Studies in Mathematics, 38 (1–3), 111–133.

David Tall, Eddie Gray, Maselan Bin Ali, Lillie Crowley, Phil DeMarois, Mercedes McGowen, Demetra Pitta, Marcia Pinto, Michael Thomas, and Yudariah Yusof, 2001a Symbols and the Bifurcation between Procedural and Conceptual Thinking,Canadian Journal of Science, Mathematics and Technology Education1, 80–104.

Eddie Gray & David Tall, 2001i. Relationships between embodied objects and symbolic procepts: an explanatory theory of success and failure in mathematics,PME 25.

**Beryl Fussey, MSc** (1991–1993) *Sixth Form Students Concept Images in Applied Mathematics*. (MSc in Interdisciplinary Mathematics, 1993).

**Yudariah binte Mohammad Yusof, PhD** (1992–1995) *Thinking Mathematically: A Framework for Developing Positive Attitudes Amongst Undergraduates*, (PhD, 1995).

e-mail: yudariah@mel,fs,utm.my

Yudariah Binte Mohd Yusof & David Tall, 1994b. Changing Attitudes to Mathematics through Problem Solving,

Proceedings of PME 18, Lisbon, IV, 401–408.

Yudariah Binte Mohd Yusof & David Tall, 1995c. Professors’ perceptions of students’ mathematical thinking: Do they get what they prefer or what they expect? In L. Meira & D. Carraher, (Eds.),Proceedings of PME 19, Recife, Brazil, II, 170–177.

Yudariah Binte Mohd Yusof & David Tall, 1996g. Conceptual and Procedural Approaches to Problem Solving,Proceedings of PME 20, Valencia, 4, 3–10.

Yudariah Binte Mohd Yusof & David Tall, 1999h. Changing Attitudes to University Mathematics through Problem-solving,Educational Studies in Mathematics, 37, 67–82.

David Tall, Eddie Gray, Maselan Bin Ali, Lillie Crowley, Phil DeMarois, Mercedes McGowen, Demetra Pitta, Marcia Pinto, Michael Thomas, and Yudariah Yusof, 2001a. Symbols and the Bifurcation between Procedural and Conceptual Thinking,Canadian Journal of Science, Mathematics and Technology Education1, 80–104.

**Maselan bin Ali, PhD** (Jan 1993–June 1996).

*Symbolic Manipulations Related to Certain Aspects Such as Interpretations of Graphs*, (PhD 1996).

Maselan bin Ali & David Tall, 1996e. Procedural and Conceptual Aspects of Standard Algorithms,

Proceedings of PME 20, Valencia, 2, 19–26.

David Tall, Eddie Gray, Maselan Bin Ali, Lillie Crowley, Phil DeMarois, Mercedes McGowen, Demetra Pitta, Marcia Pinto, Michael Thomas, and Yudariah Yusof, 2001a. Symbols and the Bifurcation between Procedural and Conceptual Thinking,Canadian Journal of Science, Mathematics and Technology Education1, 80–104.

**Marcia Maria Fusaro Pinto, PhD** (1993–98)

*Students’ Understanding of Real Analysis* (PhD 1998).

e-mail: marcia@mat.ufmg.br

web-site: http://www.marciapinto.com

Marcia Pinto & David Tall,1996h. Student Teachers’ Conceptions of the Rational Numbers,

Proceedings of PME 20, Valencia, 4, 139–146.

Marcia Pinto & David Tall,1999g. Student constructions of formal theory: giving and extracting meaning. In O. Zaslavsky (Ed.),Proceedings of the 23rd Conference of PME, Haifa, Israel, 4, 65–73.

Eddie Gray, Demetra Pitta, Marcia Pinto & David Tall,1999k. Knowledge Construction and diverging thinking in elementary and advanced mathematics,Educational Studies in Mathematics, 38 (1–3), 111–133.

David Tall, Eddie Gray, Maselan Bin Ali, Lillie Crowley, Phil DeMarois, Mercedes McGowen, Demetra Pitta, Marcia Pinto, Michael Thomas, and Yudariah Yusof, 2001a. Symbols and the Bifurcation between Procedural and Conceptual Thinking,Canadian Journal of Science, Mathematics and Technology Education1, 80–104.

Marcia Pinto & David Tall, 2001 . Following student’s development in a traditional university classroom,PME 25

Marcia Pinto & David Tall, 2002 Building formal mathematics on visual imagery: a case study and a theory.For the Learning of Mathematics,22(1) 2–10.

**Robert Donkin, MSc** (1994–5). *Study on the thinking of Mathematicians* (MSc in Interdisciplinary Mathematics, with distinction, 1995).

**Philip DeMarois, PhD** (1994–98)

*Facets and Layers of the Function Concept: The Case of College Algebra* (PhD, 1998).

e-mail: demaroip@mhcc.cc.or.us

Phil Demarois & David Tall,1996f. Facets and Layers of the Function Concept,

Proceedings of PME 20, Valencia, 2, 297–304.

Phil Demarois & David Tall,1999e. Function: Organizing Principle or Cognitive Root? In O. Zaslavsky (Ed.),Proceedings of the 23rd Conference of PME, Haifa, Israel, 2, 257–264.

David Tall, Eddie Gray, Maselan Bin Ali, Lillie Crowley, Phil DeMarois, Mercedes McGowen, Demetra Pitta, Marcia Pinto, Michael Thomas, and Yudariah Yusof, 2001a. Symbols and the Bifurcation between Procedural and Conceptual Thinking,Canadian Journal of Science, Mathematics and Technology Education1, 80–104.

Mercedes McGowen, Phil DeMarois & David Tall, 2000d. The Function Machine as a Cognitive Root for building a rich concept image of the Function Concept, Proceedings of PME-NA, 1, 247–254.

David Tall, Mercedes McGowen and Phil DeMarois, 2000e. The Function Machine as a Cognitive Root, Proceedings of PME-NA, 1, 255–261.

**Mercedes McGowen, PhD** (1994–98)

*Cognitive Units, Concept Images and Cognitive Collages: An Examination of the Process of Knowledge Construction*. (PhD, 1998).

e-mail: mmcgowen@harper.cc.il.us

Mercedes McGowen & David Tall, 1999f. Concept Maps & Schematic Diagrams as Devices for Documenting the Growth of Mathematical Knowledge. In O. Zaslavsky (Ed.),

Proceedings of the 23rd Conference of PME, Haifa, Israel, 3, 281–288.

David Tall, Eddie Gray, Maselan Bin Ali, Lillie Crowley, Phil DeMarois, Mercedes McGowen, Demetra Pitta, Marcia Pinto, Michael Thomas, and Yudariah Yusof , 2001a. Symbols and the Bifurcation between Procedural and Conceptual Thinking,Canadian Journal of Science, Mathematics and Technology Education1, 80–104.

Mercedes McGowen, Phil DeMarois & David Tall, 2000d. The Function Machine as a Cognitive Root for building a rich concept image of the Function Concept, Proceedings of PME-NA, 1, 247–254.

David Tall, Mercedes McGowen and Phil DeMarois, 2000e. The Function Machine as a Cognitive Root, Proceedings of PME-NA, 1, 255–261.

Mercedes McGowen & David Tall. 2001 (draft). Flexible Thinking, Consistency, and Stability of Responses: A Study of Divergence.

**Lillie Crowley, PhD** (1995–2000) *Cognitive Structures in College Algebra*. (PhD 2000).

e-mail: lillie@pop.uky.edu

website: http://www.uky.edu/LCC/MATH/Crowley/

Lillie Crowley, David Tall & Michael Thomas. 1994d. Algebra, Symbols, and Translation of Meaning,

Proceedings of PME18, Lisbon, II, 240–247.

Lillie Crowley & David Tall,1999d. The Roles of Cognitive Units, Connections and Procedures in achieving Goals in College Algebra. In O. Zaslavsky (Ed.),Proceedings of the 23rd Conference of PME, Haifa, Israel, 2, 225–232.

David Tall, Eddie Gray, Maselan Bin Ali, Lillie Crowley, Phil DeMarois, Mercedes McGowen, Demetra Pitta, Marcia Pinto, Michael Thomas, and Yudariah Yusof, 2001a. Symbols and the Bifurcation between Procedural and Conceptual Thinking,Canadian Journal of Science, Mathematics and Technology Education1, 80–104.

Lillie Crowley & David Tall, (2001). Attainment and Potential: Procedures, Cognitive Kit-Bags and Cognitive Units,Proceedings ofPME 25. (Full version)

**Gulden Tasdelen, MSc** (1999–2000). Students’ concept images and central tendencies in the context of linear functions and their graphs. (MSc 2000).

**Robin Foster** (1991–2000). Children’s use of Apparatus in the Development of the Concept of Number. (PhD 2000).

e-mail: r.foster@ucsm.ac.uk

Robin Foster & David Tall, 1996d. Can all children climb the same curriculum ladder?,

Mathematics in School, 25 3,8–12.

**Richard Beare, PhD** (1998–1999). *Researching, developing and applying the potential of spreadsheets for mathematical modelling in educational contexts.* (PhD 1999).

**Soo Duck Chae** (October 1997– Dec 2002), Imagery and construction of conceptual knowledge in computer experiments with period doubling. (PhD 2003)

e-mail:sdchae77@ewha.ac.kr.

Soo Duck Chae & David Tall, 1999i . Aspects of the construction of conceptual knowledge: the case of computer aided exploration of period doubling,

Proceedings of BSRLM Conference, 5th June, St Martin’s Lancaster, 13–18.

Soo Duck Chae & David Tall, 2001c, Aspects of the construction of conceptual knowledge: the case of computer aided exploration of period doubling,Research in Mathematics Education 3.

Soo Duck Chae & David Tall, 2001. Students’ Concept Images for Period Doublings as Embodied Objects in Chaos Theory,PME 25.(Full version).

**Ehr-Tsung Chin**, (October, 1998–2002) Building and using concepts of equivalence class and partition. (PhD 2002).

e-mail: edrdm@csv.warwick.ac.uk

(Abe) Ehr-Tsung Chin & David Tall, 2000c. Making, Having and Compressing Formal Mathematical Concepts. In T. Nakahara and M. Koyama (eds)

Proceedings of the 24th Conference of the International Group for the Psychology of Mathematics Education2, 177–184. Hiroshima, Japan.

(Abe) Ehr-Tsung Chin & David Tall, 2001g. Developing Formal Mathematical Concepts over Time,Proceedings of PME 25.(Abe) Ehr-Tsung Chin & David Tall, 2002, University Students’ Embodiment of Quantifiers.

Proceedings of PME 26.

**Hatice Akkoc** (October 1999 – April 2003) The Function Concept (EdD 2003)

e-mail: haticeakkoc@yahoo.com

Hatice Akkoc & David Tall, 2002. Simplicity, Complexity and Complication of the Function Concept.

2005d Hatice Akkoç & David Tall 2005. A Mismatch between Curriculum Design and Student Learning: The Case of the Function Concept. Presented at BCME-6.

**Nora Zakaria** (October 1999 – 2004) (main supervisor: Adrian Simpson) Procedural and conceptual aspects of Calculus (PhD)

e-mail: edrem@warwick.ac.uk

**Anna Poynter** (January, 2000–2004) Effect as a pivot between actions and symbols: the case of vector. PhD 2004.

Anna was married in 2003, changing her surname from Watson to Poynter.

e-mail: annakol@aol.com

web-site:http://www.annapoynter.net (in progress)

David Tall & Anna Watson, 2001. Schemas and processes for sketching the gradient of a graph

.Anna Watson, 2002. Embodied Action, Effect and Symbol in Mathematical Growth,

PME 26, Norwich.

Anna Watson, Panayotis Spyrou, David Tall, 2002. The Relationship between Physical Embodiment and Mathematical Symbolism: The Concept of Vector.The Mediterranean Journal of Mathematics Education.Anna Poynter & David Tall (2005). Relating theories to practice in the teaching of mathematics. Prepared for the

Fourth Congress of the European Society for Research in Mathematics Education.

Anna Poynter & David Tall (2005). What do mathematics and physics teachers think that students will find difficult? A challenge to accepted practices of teaching. Presented at BCME-6.

**Nino Bregadze** (October 2000 – 2001) *The Function Concept* (MSc).

**Amir Asgari** (October 2001 – 2005) *Equivalence*. (PhD)

e-mail: A.H.Asghari@warwick.ac.uk

Amir Asghari & David Tall, 2005: Students’ experience of equivalence relations: a phenomenographic approach. Proceedings of PME 29, Melbourne, Australia.

**Eirini Geraniou** (October 2001–) (main supervisor: Adrian Simpson).

**Stephanos Iakovidis** (2001 – 2002) *The Concept of Function as a Unifying Topic through Different Representations* (MSc).

**Victor Giraldo** (2002–2004) *Descricoes e Conflitos Computacionais: O Casa da Derivada*. PhD at Universidade Federal de Rio de Janiero.

Victor took his PhD as a sandwich course at UFRJ, working at Warwick for a year.

e-mail:victor@im.ufrj.br

web-site: tba

Giraldo, V., Carvalho, L. M. & Tall, D. O., (

2002k). Theoretical-Computational Conflicts and the Concept Image of Derivative.Proceedings of the BSRLM Conference. Nottingham, England, 22 (3), 37–42.

Giraldo, V., Carvalho, L.M. & Tall, D. O., (2003b). Conflitos Teórico-Computacionais e a Imagem Conceitual de Derivada. In L.M. Carvalho and L.C. Guimarães,História e Tecnologia no Ensino da Matemática, vol. 1, pp. 153-164, Rio de Janeiro, Brasil.

Giraldo, V., Carvalho, L. M. & Tall, D. O., (2003d). Descriptions and Definitions in the Teaching of Elementary Calculus. In N.A. Pateman, B.J. Dougherty and J. Zilliox (eds.)Proceedings of the 27th Conference of the International Group for the Psychology of Mathematics Education, vol. 2, pp.445-452, Honolulu, USA.

Victor Giraldo, David Tall & Luiz Mariano Carvalho, (2003e). Using theoretical-computational conflicts to enrich the concept image of derivative. In Pope, S. and McNamara, O. (eds.)Research in Mathematics Education, Papers of the British Society for Research Into Learning Mathematics, vol. 5, pp. 63–78.

**Juan Pablo Mejia-Ramos** (2003 – 2004, MSc), (2004- , MPhil/PhD).

e-mail: j.p.mejia@warwick.ac.uk

web-site: http://www.warwick.ac.uk/staff/J.P.Mejia

David Tall, Juan Pablo Mejia Ramos, (

2004). Reflecting on Post-Calculus-Reform. Opening Plenary forTopic Group 12: Calculus, International Congress of Mathematics Education, Copenhagen, Denmark.

Juan Pablo Mejia-Ramos & David Tall (2005). Personal and Public Aspects of Formal Proof

David Tall & Juan Pablo Mejia-Ramos (2006). The Long-Term Cognitive Development of Different Types of Reasoning and Proof, presented at the Conference onExplanation and Proof in Mathematics: Philosophical and Educational Perspectives, Essen , Germany.

**Ee Lyne Chong** (pronounced Ee-Lane) (2003 – 2004) (MSc).

**Adam Boddison** (2004-2005) MA.

**Rosana Nogueira de Lima** (2005–2006) PhD at Pontifícia Universidade Católica de São Paulo.

Rosana attended Warwick for a year as part of her preparation for her PhD at PUC/SP.

e-mail:rosananlima@uol.com.br

web-site: tba

Rosana Nogueira de Lima and David Tall (

2006) What does equation mean? A brainstorm of the concept.Third International Conference on the Teaching of Mathematics, Istanbul.Rosana Nogueira de Lima and David Tall (

2006). The concept of equation: what have students met before?Proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education, Prague, Czech Republic, vol. 4, 233–241.Rosana Nogueira de Lima and David Tall (

2006). Procedural embodiment and magic in linear equations. Submitted for publication.

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