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Instructor: Prof. Dr. Benedikt
Löwe
Vakcode: 5314SMLP3Y
ECTS: 6
Goal of the course.
The aim of this course is to learn qualitative and quantitative techniques for the study of research disciplines from the social sciences, and apply them to the discipline of mathematics in concrete research projects. Students should learn how to plan, design and conduct experiments and/or interviews, and how to evaluate claims about the practice of mathematical research.
Content.
Mathematics is the paradigmatic deductive discipline, using the deductive methodology for getting new results, as opposed to many if not most other sciences. This has resulted in claims that mathematics is an "epistemic exception" and that mathematical knowledge is categorically different from knowledge in other sciences. Philosophers of mathematics have thought about the exceptional character of mathematics for a long time, but recently, researchers have become interested in gathering concrete and empirical data about the discipline of mathematics in order to use it in arguing for philosophical claims about mathematics and its exceptional character.
In the last ten years, researchers from philosophy, sociology,
mathematics education, and cognitive psychology have started to
collaborate in order to study mathematical practice about which a great
deal is still unknown. The ILLC in Amsterdam has played an important
role in this development.
This course will teach techniques from the empirical sciences, both
qualitative and quantitative, in order to apply them to the discipline
of mathematics. Students will learn the techniques, their shortcomings
and problems, and apply them in concrete projects dealing with
mathematical or logical research or teaching practice.
The course should enable students to work in the developing research
field of Cultures and Practices of Mathematics (e.g., write a Master's
thesis in this field). An example of a Master's thesis using qualitative
techniques to study a discipline is Maddirala's Philosophy
of logical practice: a case study in formal semantics (MoL-2014-15).
An example of a PhD thesis using a combination of qualitative and
quantitative methods is Müller-Hill's Die epistemische Rolle
formalisierbarer mathematischer Beweise (in German).
Literature. See below. Printed versions of the papers are
available in a folder marked "Course material" in the ILLC Common Room.
Please do not remove this folder from the common room (except to xerox).
Examination. Regular attendance and doing the homework is a
necessary requirement for passing the course. Student will propose
project ideas during 5-minute presentations on 4 and 11 May. Based on
feedback, they will then do a more elaborate project presentation on 18
and 20 May. They then do a project applying some of the techniques and
methods learned in class to an empirical question about mathematical or
logical practice. The term paper is due on 30 June 2016.
Schedule.
| Wednesday 30 March 2016
| 13-15
G2.13
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1st Session. Empirical Philosophy of Mathematics
I. Naturalistic philosophy of mathematics. Experimental Philosophy.
Philosophy of Mathematical Practice.
- Bernd Buldt, Benedikt Löwe, Thomas Müller,
Towards a new epistemology of
mathematics, Erkenntnis 68 (2008), pp. 309-329.
- Benedikt Löwe. Philosophy
or not? The study of cultures and practices of mathematics,
to appear.
- Benedikt Löwe, Mathematics
and the new technologies. Part I: Philosophical relevance of a changing
culture of mathematics, in: Peter Schroeder-Heister, Gerhard Heinzmann,
Wilfrid Hodges, Pierre Edouard Bour (eds.), Logic, Methodology and
Philosophy of Science, Proceedings of the 14th International Congress
(Nancy), Logic and Science Facing the New Technologies, College
Publications, London 2014, pp. 399-407
Homework (due 1 April 2016). Read the papers assigned for the 2nd
session and be prepared to give 5-minute summary presentations.
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| Friday 1 April 2016
| 13-15
G2.13
|
2nd Session. Empirical Philosophy of Mathematics II.
Examples of concrete research.
- Eva Müller-Hill, Formalizability and
knowledge ascriptions in mathematical practice, Philosophia
Scientiae 13:2 (2009), pp. 21-43.
- Christian Geist, Benedikt Löwe, Bart Van Kerkhove, Peer
review and knowledge by testimony in mathematics, in: Benedikt
Löwe, Thomas Müller, PhiMSAMP, Philosophy of Mathematics:
Sociological Aspects and Mathematical Practice, London 2010 [Texts in
Philosophy 11], pp. 155-178.
- Matthew Inglis, Juan Pablo Mejia-Ramos, Keith Weber, Lara Alcock,
On
mathematicians' different standards when evaluating elementary
proofs, Topics in Cognitive Science 5:2 (2013), pp. 270-282.
- Juan Pablo Mejia-Ramos, Keith Weber, Why and how
mathematicians read proofs: further evidence from a survey study,
Educational Studies in Mathematics 85:2 (2014), pp. 161-173.
- Matthew Inglis, Andrew Aberdein, Beauty is not
simplicity: an analysis of mathematicians' proof appraisals,
Philosophia Mathematica 23:1 (2015), pp. 87-109.
Homework (due 6 April 2016). Read the papers assigned for 6 April
2016 and be prepared to give 5-minute summary presentations.
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| Wednesday 6 April 2016
| 13-15
G2.13
| 3rd Session. Modelling and research in the social sciences.
Modelling. Access. Bias. Constructs.
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Benedikt Löwe, Thomas Müller, Data
and phenomena in conceptual modelling, Synthese 182:1 (2011),
pp. 131-148.
- N. L. Gage, The obviousness of social and educational research results, Educational Researcher 20:1 (1991), pp. 10-16.
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Philip M. Podsakoff, Scott B. MacKenzie, Nathan P. Podsakoff,
Sources
of Method Bias in Social Science Research and Recommendations on How to Control It,
Annual Review of Psychology 63 (2012), pp. 539-569.
-
Milton E. Strauss, Gregory T. Smith,
Construct Validity: Advances in Theory and Methodology,
Annual Review of Clinical Psychology 5 (2009), pp. 1-25.
Homework (due 8 April 2016). Read the papers assigned for 8 April
2016 and be prepared to give 5-minute summary presentations.
|
| Friday 8 April 2016
| 13-15
G2.13
|
4th Session. Research Design and Validity.
- Chapter I (What is Research Design?) from
David de Vaus, Research Design in Social Research, Sage:London (2001).
- Clare Rutterford, Research Design,
in:
Clive Seale (ed.),
Researching Society and Culture,
3rd Edition, Sage:London (2012),
pp. 118-133.
- Sam van Gool, Which picture proofs are more convincing? A
possible typology of picture proofs, project paper for a class on
Philosophy of Mathematics 2008/09 at the UvA.
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Clive Seale,
Validity, Reliability and the Quality of Research,
in:
Clive Seale (ed.),
Researching Society and Culture,
3rd Edition, Sage:London (2012),
pp. 528-543.
Homework (due 13 April 2016). Read the papers assigned for 13
April 2016 and be prepared to give 5-minute summary presentations. Do
Exercises 8., 16., and 17. in Chapter 7 of Hanneman et al. (pp. 243 and 245).
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| Wednesday 13 April 2016
| 13-15
G2.13
| 5th Session. Statistics I.
Nominal, ordinal, interval variables. Mode. Median. Mean. Sampling.
- Section Basic elements of research (pp. 14-15) of
Robert A. Hanneman, Augustine J. Kposowa, Mark D. Riddle, Basic Statistics for Social Research, Jossey-Bass:San Francisco (2013).
- Parts of Chapter 3 Central tendency (pp. 83-99) of
Robert A. Hanneman, Augustine J. Kposowa, Mark D. Riddle, Basic Statistics for Social Research, Jossey-Bass:San Francisco (2013).
- Chapter 7 Basic Ideas of Statistical inference (pp. 212-246) of
Robert A. Hanneman, Augustine J. Kposowa, Mark D. Riddle, Basic Statistics for Social Research, Jossey-Bass:San Francisco (2013).
Homework (due 15 April 2016). Read the papers assigned for 15
April 2016 and be prepared to give 5-minute summary presentations. Do
Exercises 1., 2., 3., and 4. in Chapter 8 of Hanneman et al. (pp. 308-309).
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| Friday 15 April 2016
| 13-15
G2.13
| 6th Session. Statistics II.
Hypothesis Testing. Regression to the mean. The "p-value debate".
- Chapter 8 Hypothesis testing for one sample (pp. 247-278) of
Robert A. Hanneman, Augustine J. Kposowa, Mark D. Riddle, Basic Statistics for Social Research, Jossey-Bass:San Francisco (2013).
- Regina Nuzzo,
Scientific method: Statistical errors,
Nature 506:7487 (2014), pp. 150-152.
- Ronald L. Wasserstein, Nicole A. Lazar, The ASA's statement on p-values:
context, process, and purpose, The American Statistician, to appear.
Homework (due 20 April 2016). Read the papers assigned for 20 April
2016 and be prepared to give 5-minute summary presentations.
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| Wednesday 20 April 2016
| 13-15
G2.13
| 7th Session. Questionnaires.
- Constantinos N. Phellas, Alice Bloch, Clive Seale, Structured
Methods: Interviews, Questionnaires and Observation,
in:
Clive Seale (ed.),
Researching Society and Culture,
3rd Edition, Sage:London (2012),
pp. 181-205.
- Claus Moser, Graham Kalton, Questionnaires, from: Survey
Methods in Social Investigation (2nd edition), Gower:Aldershot
(1971).
- Kim Sheehan, Mariea Hoy, On-line Surveys, from: Using
e-mail to survey internet users in the United States: methodology and
assessment, Journal of Computer Mediated Communication 4:3 (1999).
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Winter Mason, Siddharth Suri,
Conducting behavioral research on Amazon's Mechanical Turk,
Behavior Research Methods 44:1 (2012), pp. 1-23.
Homework (due 22 April 2016). Read the papers assigned for 22 April
2016 and be prepared to give 5-minute summary presentations.
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| Friday 22 April 2016
| 13-15
G2.13
| 8th Session. Interviews and Ethics.
-
Bridget Byrne,
Qualitative Interviewing,
in: Clive Seale (ed.), Researching Society and Culture,
3rd Edition, Sage:London (2012), pp. 206-226.
- Herbert H. Hyman, Interviewing in Social Research, from:
Interviewing in Social Research, University of Chicago
Press:Chicago (1954).
-
Suki Ali, Moira Kelly,
Ethics and Social Research,
in: Clive Seale (ed.), Researching Society and Culture,
3rd Edition, Sage:London (2012), pp. 58-76.
Homework (due 29 April 2016). Read the papers assigned for 29 April
2016 and be prepared to give 5-minute summary presentations.
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| Friday 29 April 2016
| 13-15
G2.13
| 9th Session. Corpus studies.
- Sue Atkins, Jeremy Clear, Nicholas Ostler,
Corpus Design Criteria,
Literary & Linguistic Computing 7:1 (1992), pp. 1-16. (pdf of a 1991 version).
- Douglas Biber, Representativeness in corpus design,
Literary & Linguistic Computing 8:4 (1993), pp. 243-257.
Reprinted in: A. Zampolli et al. (eds.), Current issues in computational
linguistics: In honour of Don Walker, Springer-Verlag:Dordrecht (1994), pdf file).
- Ana Montoya Reyes, The presence of
cognitive verbs in mathematical texts (1800-1900) of the Coruña
Corpus, ICAME Journal, Computers in English Linguistics 32
(2008), pp. 139-156.
- Lorenz Demey, It is now easy to see that ... A case study in corpus-based philosophy of mathematics,
project paper for a class on
Philosophy of Mathematics 2008/09 at the UvA.
Homework (due 4 May 2016). Read the papers assigned for 4 May 2016 and be prepared to give 5-minute summary presentations.
Prepare a 5-minute presentation of an idea for a research project.
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| Wednesday 4 May 2016
| 13-15
G2.13
| 10th Session. Observations. Ethnography. Observations.
A case study (Greiffenhagen & Sharrock). First batch of student project
idea presentations.
- David Walsh,
Doing ethnography,
in: Clive Seale (ed.), Researching Society and Culture,
3rd Edition, Sage:London (2012), pp. 245-262.
- Christian Greiffenhagen, Wes Sharrock, Does
mathematics look certain in the front, but fallible in the back?,
Social Studies of Science 41:6 (2011), pp. 839-866.
Homework (due 11 May 2016). Read the papers assigned for 11 May
2016 and be prepared to give 5-minute summary presentations. Prepare a
5-minute presentation of an idea for a research project.
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| Wednesday 11 May 2016
| 13-15
G2.13
| 11th Session. Other methods.
Visual research. Discourse and Conversation. Second batch of student project idea presentations.
- John Collier Jr., Malcolm Collier, Principles of visual
research, from: Visual anthropology: Photography as a research
metho, University of New Mexico Press:Albuquerque (1986).
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Suki Ali,
Visual Analysis,
in: Clive Seale (ed.), Researching Society and Culture,
3rd Edition, Sage:London (2012), pp. 284-301.
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Fran Tonkiss,
Discourse Analysis,
in: Clive Seale (ed.), Researching Society and Culture,
3rd Edition, Sage:London (2012), pp. 405-423.
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Tim Rapley,
Analysing Conversation,
in: Clive Seale (ed.), Researching Society and Culture,
3rd Edition, Sage:London (2012), pp. 424-440.
- Christian Greiffenhagen, The
materiality of mathematics: Presenting mathematics at the
blackboard,
The British Journal of Sociology 65:3 (2014), pp. 502-528.
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| Friday 13 May 2016
| 13-15
G2.13
| 12th Session. Guest lecture.
Anika Dreher (Kiel, Germany): Teachers' professional knowledge and noticing: The
case of multiple representations in the mathematics classroom.
Homework (due 18 or 20 May). Prepare project presentations.
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| Wednesday 18 May 2016
| 13-15
G2.13
| 13th Session. Student project presentations I.
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| Friday 20 May 2016
| 13-15
G2.13
| 14th Session. Student project presentations II.
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Last update: 4 April 2016.
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