International audienceThis discussion group seeks to bring together individuals who are interested in the use of original sources in the mathematics classroom, from the perspective of a classroom teacher or a mathematics education researcher, for a discussion of issues and concerns related to their educational potential and effects. Each of the two sessions will focus on a different theme related to the use of original sources in the mathematics classroom. The two sessions will structured around a common framework but sufficiently independent of each other to allow interested individuals to participate in the second session, even if they did not participate in the first session. Both novice and more experienced users of original sources are strongly encouraged to participate in both sessions

Barnett, Janet H.

Kjeldsen, Tinne Hoff

English

Barnett, Janet

Hoff Kjeldsen, Tinne

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ORIGINAL SOURCES IN THE MATHEMATICS
CLASSROOM
Janet Barnett, Tinne Hoff Kjeldsen
To cite this version:
Janet Barnett, Tinne Hoff Kjeldsen. ORIGINAL SOURCES IN THE MATHEMATICS
CLASSROOM. History and Pedagogy of Mathematics, Jul 2016, Montpellier, France. <hal-
01349274>
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ORIGINAL SOURCES IN THE  
MATHEMATICS CLASSROOM 
 
Janet Heine BARNETT, Tinne Hoff KJELDSEN 
Department of Mathematics and Physics, Colorado State University-Pueblo, Pueblo CO, USA 
janet.barnett@csupueblo.edu 
Department of Mathematical Sciences, University of Copenhagen, Copenhagen, Denmark 
thk@math.ku.dk 
 
ABSTRACT 
This discussion group seeks to bring together individuals who are interested in the use of original sources in the 
mathematics classroom, from the perspective of a classroom teacher or a mathematics education researcher, for a 
discussion of issues and concerns related to their educational potential and effects.  Each of the two sessions will 
focus on a different theme related to the use of original sources in the mathematics classroom.  The two sessions 
will structured around a common framework but sufficiently independent of each other to allow interested 
individuals to participate in the second session, even if they did not participate in the first session.  Both novice 
and more experienced users of original sources are strongly encouraged to participate in both sessions. 
1 Overview: The value of an explicit-reflective framework 
This discussion group will explore issues related to the use of original sources in mathematics 
classrooms as a means to create inquiry based learning experiences that invite students into 
(parts of) some (past) mathematicians’ “work bench,” as a means of allowing them to engage 
in learning processes that to some extent mimic what mathematicians do when they produce 
new mathematical knowledge.  We will consider in particular the importance of (a) making 
the educational ambitions and learning objectives of such experiences explicit and (b) 
designing activities that promote student reflection on their learning experiences.  The notion 
of an explicit-reflective framework1 will thus serve as an organizing theme for a discussion of 
different strategies for using original sources with students as a means to teach them 
mathematics, to enhance their understanding of the nature of mathematics, to develop their 
historical awareness or to achieve more general educational goals.  We will also consider the 
ways in which such a framework opens up the possibility of establishing complex learning 
environments and situations that may address combinations of these learning goals.2   As part 
of this discussion, we will address the questions of “what, how, and why” regarding the 
potential roles, uses and benefits of integrating original sources into mathematics education, 
but with an emphasis on actual classroom teaching practices (versus an investigation of the 
general arguments for using original sources and integrating history into mathematics 
education3).  Additionally, we will consider the value of basing the development of explicit-
reflective frameworks for using original sources in mathematics classrooms on a theoretical 
                                                            
1 We have borrowed this notion from Abd-El-Khalick’s and Lederman’s (2000) work in science education.   See 
Kjeldsen (2014) for an exploration of the framework within an existing practice of mathematics education 
2 See Barnett, Pengelley and Lodder (2014) for concrete illustrations of such learning environments.   
3 For this we refer to Tzanakis et al. (2002), see also the survey paper by Jankvist (2011). 
foundation drawn from the research areas of history and philosophy of mathematics and the 
teaching and learning of mathematics. 
2  Session 1: Educational Potential of Original Sources  
The theme of the first session is the educational potential of original sources and the notion of 
explicit-reflective frameworks. Questions related to this theme that will be discussed include: 
• Why are we as mathematics teachers and/or researchers interested in using original 
sources with students? What are potential gains for students? For instructors? 
• How are original sources being used in math teaching, by whom, for what purpose?  
• Based on different pedagogical goals and learning objectives, what type of original 
source readings and reflective challenges for students are most appropriate?  
3 Session 2: Resources and Research Needed to Support Classroom Use  
The second session will focus on what is needed in terms of classroom resources and 
educational research to support the use of original sources in the classroom in order to 
promote their full potential for students.  Questions related to this theme include: 
• What do we know about the effect of learning mathematics from original sources? 
What would we like to know?  How could we find that out?   
• What resources exist/are needed to assist instructors in using original sources?  
• Can we develop general principles for source selection and guides for creating 
explicit-reflective learning environments? 
4 Overall structure of discussion sessions  
Each session will begin with a brief introduction to that session’s overall theme to set the 
scene for the session.  Participants will then work together in smaller groups for 20-25 
minutes, guided by discussion worksheets to be provided by the organizers, to examine issues 
related to that session’s theme. A plenum discussion that brings all participants back together 
in order to exchange and synthesize ideas generated by the various groups will round out each 
session.  Possible opportunities for and interests in forming future working groups will be 
explored and facilitated in each plenum discussion.   
The two sessions will be sufficiently independent of each other to allow interested 
individuals to participate in the second session, even if they did not participate in the first 
session. Both novice and more experienced users of original sources are strongly encouraged 
to participate in both sessions. 
REFERENCES 
Abd-El-Khalick, F., & Lederman, N. G. (2000). Improving science teachers’ conceptions of nature of science: A 
critical review of the literature. International Journal of Science Education, 22(7), 665-701. 
Barnett, J., Pengelley, D., & Lodder, J. (2014). The pedagogy of primary historical sources in mathematics: 
Classroom practice meets theoretical frameworks. Science and Education, 23(1), 7-27. 
Barbin, E. (1997). Histoire et enseignement des mathématiques: Pourquoi? Comment? Bulletin de l'Association 
Mathématique du Québec, XXXVII(1), 20-25. 
Barbin, E. (2011). Dialogism in mathematical writing: historical, philosophical and pedagogical issues, In V. 
Katz, & K. Tzanakis (Eds.), Recent developments on introducing a historical dimension in Mathematics 
Education (pp. 9-16). Washinngton: Mathematical Association of America. 
Jahnke, H. N., Arcavi, A., Barbin, E., Bekken, O., Furinghetti, F., Idrissi, A., da Silva, C. M. S., & Weeks, C. 
(2002). The use of original sources in the mathematics classroom. In J. Fauvel, & J. van Maanen (Eds.), 
History in mathematics education: the ICMI study (pp. 291-328). Dordrecht: Kluwer Academic 
Publishers. 
Jankvist, U. T. (2009). A categorization of the ‘whys’ and ‘hows’ of using history in mathematics education. 
Educational Studies in Mathematics, 71, 235-261. 
Kjeldsen, T. H., & Blomhøj, M. (2012). Beyond motivation - History as a method for the learning of meta-
discursive rules in mathematics. Educational Studies in Mathematics, 80(3), 327-349. 
Kjeldsen, T. H. (2014). Teaching with and about the nature of mathematics through history of mathematics: 
Enacting inquiry learning in mathematics. Education Sciences, Special issue, 38-55. 
Tzanakis, C., Arcavi, A., Correia de Sa, C., Isoda, M., Lit, C.-K., Niss, N., Pitombeira de Carvalho, J., 
Rodriguez, M., & Siu, M.-K. (2002). Integrating history of mathematics in the classroom: An analytic 
survey. In J. Fauvel, & J. van Maanen (Eds.), History in mathematics education: the ICMI study (pp. 
201-240). Dordrecht: Kluwer Academic Publishers. 


ORIGINAL SOURCES IN THE MATHEMATICS CLASSROOM

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Original Sources in the Mathematical Classroom

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Original Sources in the Mathematical Classroom

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