The mathematics taught at schools today is the cultural and historical product of hundreds, if not always thousands, of years of human endeavor. The history of mathematics is therefore an inspiring resource for the teaching and learning of mathematics. Naturally, the use of history in mathematics education has been a theme of growing international interest for over a century (Fauvel & van Maanen, 2000). Recent studies of the history and pedagogy of mathematics have pointed encouraging directions for the use history in mathematics education. The history of mathematics is seen not only as a window on the human nature of mathematics but also a pedagogical resource for transforming the teaching of mathematics (Furinghetti & Radford, 2008).  The use of history in the schools, however, has been scanty and slow, in part, because of lack of training and interest among teachers (Furinghetti & Radford, 2008; Smestad, 2008).  There has been a growing need to document and understand teachers’ conceptions of the history of mathematics and their responses to history-integrated professional development.

The purpose of this presentation to report inservice elementary school teachers’ thoughts about the history of mathematics delivered in digital videos and its implications for mathematics teaching. In an exploratory case study, we focus on the research question: How do inservice elementary teachers respond to the history of mathematics in professional development?

Theoretical Framework

Mathematics teaching is a complex human endeavor deeply constrained and supported by the cultural and historical conditions of the subject matter.  Over the past two decades, research on mathematics teaching has charted out a complex knowledge base underlying a teacher’s instructional behaviors (Ball, Lubienski, & Mewborn, 2001; Koehler & Grouws, 1992; van der Sandt, 2007), which include, at least,  teacher s’ knowledge (of subject matter, of students, of pedagogical content, of curriculum), teachers’ attitudes (toward mathematics, toward students, toward teaching mathematics), and teachers’ beliefs (about the nature of mathematics, mathematics teaching, students as learners).  Under this overarching framework, we agree with Dossey (1992) that teachers’ perceptions of the nature of mathematics are major factors behind their attitudes toward mathematics and mathematics teaching.  History of mathematics has been used for decades to challenge teachers’ and students’ perceptions about the nature of mathematics and to question the status quo in mathematics teaching. 

Methods

Context

History of mathematics was integrated into an eight-week graduate course on mathematical problem solving for inservice elementary school (K-8) teachers. The course was delivered in a blended form in both online discussions and face-to-face labs. The history component was implemented during the first two weeks.

In search of accessible instructional videos about the history of mathematics, we found du Sautoy’s The Story of Math DVD series in Spring 2010. From ancient Egyptian, Greek, Babylonian, Indian, Chinese mathematics to modern European and American mathematics, the series covers thousands of years of mathematical development, focusing the cultural interactions and the evolving nature of mathematics, using site visits and computer simulations, as well as specific mathematical problems.

Participants

Twenty-seven inservice elementary teachers were enrolled in the course and all participated in the online discussions and written reflections of the study.  The participants were all teaching at the time and had had little exposure to the history of mathematics according to our observations in previous courses.

The teachers were initially directed to watch the episodes online and later provided with DVDs for them to keep.  An online forum was set up for teachers to share thoughts within the class, facilitated by the course instructors. As a written assignment, they wrote an essay address their view of the history of mathematics and the implications for teaching.

Data Analysis

A team of three graduate assistants, independent of the instructional team, conducted a qualitative data analysis of the online discussions and essays.  Initially, three random essays were read through by each coder for preliminary categories, followed by team calibration. Then, they coded all the texts as a team using an open-ended thematic structure. To help organize the codes and raw data, the team used WEFT, an open-source QDA program.

Findings

At the top level, data analysis led to five major categories: (1) nature of mathematics, (2) specific math ideas, (3) math connections, (4) personal connections, (5) mathematics teaching, and other emergent themes.  Each category consists of three to seven repeated ideas. For instance, under “math connections,” there are “across subjects connections,” “within mathematics connections,” and “life and real world connection.”

Specifically, 19 out of 27 teachers connected the history of mathematics to their teaching practice (70%).  One teacher wrote, “Math is truly a building block of patterns and concepts.”  Eighteen teachers talked about specific math ideas such as zero, infinity, or negative numbers (67%).  One teacher wrote, “They also developed a place value, zero. I never really thought about how such things were developed. You just assume that it has always been in existence.” Seventeen teachers addressed math connections (63%). One teacher made an emphatic statement, “Involve the social studies teacher in the process [of teaching math]!”  Fifteen teachers made personal connections (56%).  One teacher reflected on her own learning, “I know that for myself; I was only taught the processes of math and made to memorize a lot of formulas.  I think that the way I learned is probably the norm.” Twenty-four teachers discussed history and its relations to mathematics teaching (89%). One teacher wrote, “Teaching the history of math could provide motivation, perspective, and some overview which I feel is lacking in the current curriculum.”

Conclusion

Our data and feedback show that history of mathematics hosted by a mathematician and delivered in digital media does have significant influence on classroom teachers’ reflections on the nature of mathematics, the purpose of mathematics teaching, and their own mathematical practices. In closing, we note the limitations of the digital videos. They are only the starting point to introduce teachers into the rich world of mathematical history. If time permits, they would benefit more from reading selected original sources or tackle some intriguing problems.

Timeline

The speaker(s) will discuss the context of the research, show certain details of the historical episodes using laptop demos, present the findings, and further engage the audience in exploring related issues and future replications and extensions.

References (left out for space)