Articles by Kathleen (Kathy) Clark
In spring 2015 the authors taught an intensive seminar for undergraduate mathematics students, wh... more In spring 2015 the authors taught an intensive seminar for undergraduate mathematics students, which addressed the transition problem from school to university by bringing to the fore concept changes in mathematical history and the learning biographies of the participants. This article describes how the concepts of empirical and formalistic belief systems can be used to give an explanation for both transitions – from school to university mathematics, and, for secondary mathematics teachers, back to school again. The usefulness of this approach is illustrated by outlining the historical sources and the participants' activities with these sources on which the seminar is based, as well as some results of the qualitative data gathered during and after the seminar.
1 We detail their purchase and rediscovery in Clark and Robson (2008). We are very grateful to Bo... more 1 We detail their purchase and rediscovery in Clark and Robson (2008). We are very grateful to Bob Englund, Steve Garfinkle, Denise Giannino, John Larson, Lucia Patrick, Plato L. Smith II, and Giesele Towels for their help in the research and writing of both articles. We are also indebted to our two anonymous CDLJ referees, whose careful and knowledgeable interventions produced numerous improvements to the reading of the tablets presented here.
British Society for the History of Mathematics Bulletin, Nov 6, 2008
Florida State University owns a collection of twenty-five cuneiform tablets, acquired from Edgar ... more Florida State University owns a collection of twenty-five cuneiform tablets, acquired from Edgar J Banks in the 1920s. We describe their rediscovery, present an edition of one of them (a twenty-first century BC labour account from the Sumerian city of Umma), and discuss their potential for use in undergraduate mathematics education.
British Society for the History of Mathematics Bulletin, Apr 10, 2010
In Clark and Robson (2008), we described the re-discovery, translation, and edition of a collecti... more In Clark and Robson (2008), we described the re-discovery, translation, and edition of a collection of 25 cuneiform tablets that reside in the Robert Manning Strozier Library at Florida State University (FSU). In addition, we discussed the construction of a classroom instructional unit, intended for use with Grade 4 and 5 students (aged 9 to 11) in Eustis, Florida—the retirement home of Edgar J Banks, who sold the tablet collection to FSU in 1922. Here I describe piloting the instructional unit with students, their teachers, and district supervisors in Fall 2008. The unit was created from the historical text found on FSU 22 and FSU 23 and the grade level mathematics standards from Florida's Next Generation Sunshine State Standards (NGSSS) for mathematics (2007).
Educational Studies in Mathematics, Sep 2012
The use of the history of mathematics in teaching has long been considered a tool for enriching s... more The use of the history of mathematics in teaching has long been considered a tool for enriching students’ mathematical learning. However, in the USA few, if any, research efforts have investigated how the study of history of mathematics contributes to a person's mathematical knowledge for teaching. In this article, I present the results of research conducted over four semesters in which I sought to characterize what prospective mathematics teachers (PMTs) understand about the topics that they will be called upon to teach in the future and how that teaching might include an historical component. In particular, I focus on how the study and application of the history of solving quadratic equations illuminates what PMTs know (or do not know) about this essential secondary school algebraic topic. Additionally, I discuss how the results signal important considerations for mathematics teacher preparation programs with regard to connecting PMTs' mathematical and pedagogical knowledge, and their ability to engage in historical perspectives to improve their own and their future students' understanding of solving quadratic equations.
Research in Mathematics Education
The ability to address and solve problems in minimally familiar contexts is the core business of ... more The ability to address and solve problems in minimally familiar contexts is the core business of research mathematicians. Recent studies have identified key traits and techniques that individuals exhibit while problem solving, and revealed strategies and behaviours that are frequently invoked in the process. We studied advanced calculus students working in groups to identify what strategies they employed and how, including what encouraged the opportunities to invoke them. The study revealed behaviours not included in the original taxonomy, including one that we termed ‘group synergy’. We propose extensions to Carlson and Bloom’s original taxonomy to encompass group behaviour and identify the importance of these behaviours in developing problem-solving skills. Finally, we suggest improvements for future problem-solving session iterations, with the goal of promoting opportunity for more expert performance.
This article discusses how the inclusion of history of mathematics in mathematics education draws... more This article discusses how the inclusion of history of mathematics in mathematics education draws heavily on a teacher’s mathematical knowledge for teaching, in particular horizon content knowledge, in the context of curricular changes. We discuss the role of history of mathematics in school curricula, its inclusion in textbooks and its consequences for the mathematical knowledge needed for teaching. We address the matter from three national settings (Denmark, Norway and the United States). These settings exemplify how, in particular, teachers’ horizon content knowledge needs to be broader than what is necessary for only the current curriculum.
BSHM Bulletin, Jan 1, 2008
Books by Kathleen (Kathy) Clark
This monograph presents a groundbreaking scholarly treatment of the German mathematician Jost Bür... more This monograph presents a groundbreaking scholarly treatment of the German mathematician Jost Bürgi’s original work on logarithms, Arithmetische und Geometrische Progreß Tabulen. It provides the first-ever English translation of Bürgi’s text and illuminates his role in the development of the conception of logarithms, for which John Napier is traditionally given priority.
High-resolution scans of each page of the his handwritten text are reproduced for the reader and as a means of preserving an important work for which there are very few surviving copies.
The book begins with a brief biography of Bürgi to familiarize readers with his life and work, as well as to offer an historical context in which to explore his contributions. The second chapter then describes the extant copies of the Arithmetische und Geometrische Progreß Tabulen, with a detailed description of the copy that is the focus of this book, the 1620 “Graz manuscript”. A complete facsimile of the text is included in the next chapter, along with a corresponding transcription and an English translation; a transcription of a second version of the manuscript (the “Gdansk manuscript”) is included alongside that of the Graz edition so that readers can easily and closely examine the differences between the two. The final chapter considers two important questions about Bürgi’s work, such as who was the copyist of the Graz manuscript and what the relationship is between the Graz and Gdansk versions. Appendices are also included that contain a timeline of Bürgi’s life, the underlying concept of Napier’s construction of logarithms, and scans of all 58 sheets of the tables from Bürgi’s text.
Anyone with an appreciation for the history of mathematics will find this book to be an insightful and interesting look at an important and often overlooked work. It will also be a valuable resource for undergraduates taking courses in the history of mathematics, researchers of the history of mathematics, and professors of mathematics education who wish to incorporate historical context into their teaching.
Book/Monograph Chapters by Kathleen (Kathy) Clark
The purpose of this chapter is to provide a broad view of the state of the field of history of ma... more The purpose of this chapter is to provide a broad view of the state of the field of history of mathematics in education, with an emphasis on mathematics teacher education. First, an overview of arguments that advocate for the use of history in mathematics education and descriptions of the role that history of mathematics has played in mathematics teacher education in the United States and elsewhere is given. Next, the chapter details several examples of empirical studies that were conducted with elementary (or, primary) and secondary mathematics prospective teachers. Finally, the chapter outlines examples of research from the “next generation” of infusing history in mathematics education, by providing accounts of practicing teachers who incorporated history of mathematics in teaching at the primary, secondary, and tertiary levels.
In this chapter I summarize research and policy recommendations that call for the inclusion of th... more In this chapter I summarize research and policy recommendations that call for the inclusion of the history of mathematics in the preparation of preservice mathematics teachers (PSTs). Next, I share a model for the course “Using History in the Teaching of Mathematics,” which was designed to encourage PSTs to study and consider including the history of mathematics in teaching. An example of one “topic exploration” from the course is presented.
Proceedings Papers by Kathleen (Kathy) Clark
PARTICIPANTS I considered the dearth of empirical studies on incorporating history of mathematics... more PARTICIPANTS I considered the dearth of empirical studies on incorporating history of mathematics in teaching within the United States as a justification for conducting an exploratory study of teachers who indicated their interest to incorporate history of mathematics in their instructional practice. To identify my purposeful sample, I sent a survey to 26 teachers at the end of an online course, Using History in the Teaching of Mathematics. 1
In the following narrative we share the perspectives from our two different roles in thinking abo... more In the following narrative we share the perspectives from our two different roles in thinking about history of mathematics in mathematics education. The first author's perspective provides insight into how a university professor thinks about her graduate students' learning with regard to incorporating history of mathematics in teaching. The second author's perspective presents the reality of the classroom teacher making a first attempt at both studying history of mathematics and incorporating history in teaching mathematics.
ABSTRACT This research investigated the role of solving historical problems on prospective mathem... more ABSTRACT This research investigated the role of solving historical problems on prospective mathematics teachers' mathematical knowledge for teaching. The primary research question was: In what ways does a prospective secondary mathematics teacher's work on historical problems contribute to their developing mathematical knowledge for teaching?
In the last thirty years quite some initiatives evolved and much material was developed for using... more In the last thirty years quite some initiatives evolved and much material was developed for using the history of mathematics in the teaching of mathematics at all levels.
Online Articles by Kathleen (Kathy) Clark
Revue d'histoire des mathématiques, 2012
There has never been any doubt as to the importance of the logarithm, a mathematical relation who... more There has never been any doubt as to the importance of the logarithm, a mathematical relation whose usefulness has persisted in different aspects to the present day. Within years of their introduction, logarithms became indispensable for mathematicians, astronomers, navigators, and geographers alike. The question of their origins, however, is more contentious. At least two scholars, the Scottish nobleman John Napier and the Swiss craftsman Jost Bürgi, simultaneously and independently produced proposals which embodied the logarithmic relation and, within years of one another, produced tables for its use. In light of this parallel discovery, we read, analyzed, and interpreted the texts of Napier and Bürgi to better understand and contextualize the two distinctly different approaches. As a result, here we compare and contrast the salient features of Napier's and Bürgi's endeavors and the construction of each man's tables of logarithms. Through these details, we will query the focus on the issue of priority and pre-eminence when discussing the historical development of logarithms, and pose critical questions about the phenomenon of parallel insights and what they can reveal about the mathematical environment at the time they arose.
Teaching Documents by Kathleen (Kathy) Clark
Reviews by Kathleen (Kathy) Clark
An etymological transformation perhaps unrivaled in the history of mathematics is that of the evo... more An etymological transformation perhaps unrivaled in the history of mathematics is that of the evolution of the lexical term for sine. Often recounted, 1 the linguistic passage of this term begins in India (jya/jıva), is subject to the methodical magic of the translator's pen as it traverses the Islamic Near East (jaib) and ends up in the Latin west (sinus) as we recognize it today. This passage reveals a mathematical concept that is diachronic and richly multicultural.
Unpublished by Kathleen (Kathy) Clark
This study investigated five secondary mathematics teachers' efforts to study and use the history... more This study investigated five secondary mathematics teachers' efforts to study and use the history of a specific topic. A professional development experience, constructed to reflect the features of effective professional development identified by Garet, Porter, Desimone, Birman, and Yoon (2001) and Smith (2001), was designed to engage teachers in the study of the historical development of logarithms.
Papers by Kathleen (Kathy) Clark
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Articles by Kathleen (Kathy) Clark
Books by Kathleen (Kathy) Clark
High-resolution scans of each page of the his handwritten text are reproduced for the reader and as a means of preserving an important work for which there are very few surviving copies.
The book begins with a brief biography of Bürgi to familiarize readers with his life and work, as well as to offer an historical context in which to explore his contributions. The second chapter then describes the extant copies of the Arithmetische und Geometrische Progreß Tabulen, with a detailed description of the copy that is the focus of this book, the 1620 “Graz manuscript”. A complete facsimile of the text is included in the next chapter, along with a corresponding transcription and an English translation; a transcription of a second version of the manuscript (the “Gdansk manuscript”) is included alongside that of the Graz edition so that readers can easily and closely examine the differences between the two. The final chapter considers two important questions about Bürgi’s work, such as who was the copyist of the Graz manuscript and what the relationship is between the Graz and Gdansk versions. Appendices are also included that contain a timeline of Bürgi’s life, the underlying concept of Napier’s construction of logarithms, and scans of all 58 sheets of the tables from Bürgi’s text.
Anyone with an appreciation for the history of mathematics will find this book to be an insightful and interesting look at an important and often overlooked work. It will also be a valuable resource for undergraduates taking courses in the history of mathematics, researchers of the history of mathematics, and professors of mathematics education who wish to incorporate historical context into their teaching.
Book/Monograph Chapters by Kathleen (Kathy) Clark
Proceedings Papers by Kathleen (Kathy) Clark
Online Articles by Kathleen (Kathy) Clark
Teaching Documents by Kathleen (Kathy) Clark
Reviews by Kathleen (Kathy) Clark
Unpublished by Kathleen (Kathy) Clark
Papers by Kathleen (Kathy) Clark
High-resolution scans of each page of the his handwritten text are reproduced for the reader and as a means of preserving an important work for which there are very few surviving copies.
The book begins with a brief biography of Bürgi to familiarize readers with his life and work, as well as to offer an historical context in which to explore his contributions. The second chapter then describes the extant copies of the Arithmetische und Geometrische Progreß Tabulen, with a detailed description of the copy that is the focus of this book, the 1620 “Graz manuscript”. A complete facsimile of the text is included in the next chapter, along with a corresponding transcription and an English translation; a transcription of a second version of the manuscript (the “Gdansk manuscript”) is included alongside that of the Graz edition so that readers can easily and closely examine the differences between the two. The final chapter considers two important questions about Bürgi’s work, such as who was the copyist of the Graz manuscript and what the relationship is between the Graz and Gdansk versions. Appendices are also included that contain a timeline of Bürgi’s life, the underlying concept of Napier’s construction of logarithms, and scans of all 58 sheets of the tables from Bürgi’s text.
Anyone with an appreciation for the history of mathematics will find this book to be an insightful and interesting look at an important and often overlooked work. It will also be a valuable resource for undergraduates taking courses in the history of mathematics, researchers of the history of mathematics, and professors of mathematics education who wish to incorporate historical context into their teaching.