Archive for the ‘Works in progress’ Category

Doctoral Dissertation (2016)

 

Title:  Formative potential of the history of the Euclidean theory of proportion in the constitution of mathematics teacher knowledge

Author: Edgar Alberto Guacaneme Suárez

 

Abstract:

The general research context in which this thesis is placed is the role of the History of Mathematics [HM] in the constitution of mathematical knowledge for teaching [MKT]. And the specific research question addressed by the thesis is what is the educational potential of the history of Euclidean theory of reason and proportion, contained in Book V of Elements, in the constitution of MKT.

In pursuit of an answer, the need for an approach to the state of the art in the reflection and the research on the relationship between Mathematics Education and History of Mathematics is established. From such a state of the art one seeks to explore the relationship “HM – MKT” guided by questions related to 1) the arguments used in favor of the integration of HM in such processes, 2) the aims pursued with such integration, 3) the characteristics of HM that have been linked to the mathematics teachers educational processes, and 4) the methodological strategies that have been designed and implemented for teachers of mathematics to appropriate and use historical discourses. A framework for the relationship mentioned is thus constructed.

Euclidean theory of reason and proportion of Book V of The Elements is then studied to gain insight into this theory. Documents related to the history of reason and proportion are also studied. Based on these studies, the history of Euclidean theory of proportion is analyzed using the analysis categories for the questions “what HM” and “for what HM”. The overall result shows that the set of documents covers almost all categories of analysis.

Finally, the educational potential that the documents concerning the Euclidean theory of proportion have in favor of the MKT is established.

 

Master’s Theses

 

Title: Categories of Uses of History of Mathematics in Mathematics Education

 

Student: JOHN FREDY ERAZO-CASTRO

Supervisor: LYDA CONSTANZA MORA-MENDIETA

 

 

Title: Contributions of History of Mathematics to Pedagogical Content Knowledge on Trigonometric Equations of a Mathematics Teacher Studying for the Master’s or Doctorate (in Mathematics Education)

 

Students: CINDY YESENIA INDABURO-MORENO, JOJHAN GONZALO JIMÉNEZ-BELLO, CLAUDIA MAYERLY SARMIENTO-MARTÍN

Supervisor: LYDA CONSTANZA MORA-MENDIETA

 

 

Title: The Philosophy of Mathematics in Mathematical Knowledge for Teaching

 

Student: NATALIA MORALES-ROZO

Supervisor: EDGAR ALBERTO GUACANEME-SUÁREZ

 

In the original Spanish:

 

Tesis de Doctorado en Educacion (2016)

 

Potencial formativo de la historia de la teorí a euclidiana de la proporcio n en la constitucio n del conocimiento del profesor de Matema ticas

 

Edgar Alberto Guacaneme Suárez

 

La tesis ubica el papel de la Historia de las Matemáticas [HM] en la constitución del conocimiento del profesor de Matemáticas [CPM] como contexto general de investigación y dentro de este la pregunta ¿cuál es el potencial formativo de la historia de la teoría euclidiana de la razón y la proporción, contenida en el Libro V de Elementos, en la constitución del CPM?

En procura de una respuesta, se establece la necesidad de lograr una aproximación al estado del arte de la reflexión e investigación en torno a la relación “Historia de las Matemáticas – Educación Matemática”. A partir de tal estado del arte se procura explorar la relación “HM – CPM”, guiado por las preguntas relacionadas con los argumentos que se esgrimen a favor de la integración de la HM en tales procesos, las intenciones que se persiguen con dicha integración, las características de la HM que se vincula a los procesos educativos de los profesores de Matemáticas y las estrategias metodológicas que se han diseñado e implementado para que los profesores de Matemáticas se apropien y usen los discursos históricos. Se construye así un marco de referencia para la relación mencionada.

Se estudian entonces la teoría euclidiana de la razón y la proporción del Libro V de Elementos para obtener una perspectiva de esta. Asimismo se estudian los documentos que versan sobre la historia de la razón y proporción. A partir de esto se analiza la historia de la teoría euclidiana de la proporción a través de las categorías de análisis para las pregunta qué HM y para qué la HM. El resultado global muestra que el conjunto de documentos cubre la casi totalidad de las categorías de análisis.

Finalmente, se establece el potencial formativo que los documentos que versan sobre la teoría euclidiana de la proporción tienen a favor del CPM.

 

Master’s Theses

 

Título: CATEGORÍAS DE USOS DE LA HISTORIA DE LAS MATEMÁTICAS EN LA EDUCACIÓN EN MATEMÁTICAS

 

Estudiante: JOHN FREDY ERAZO-CASTRO

Asesora: LYDA CONSTANZA MORA-MENDIETA

 

 

Título: APORTES DE LA HISTORIA DE LAS MATEMÁTICAS AL CONOCIMIENTO DIDÁCTICO DEL CONTENIDO DEL PROFESOR DE MATEMÁTICAS EN FORMACIÓN AVANZADA SOBRE LAS ECUACIONES TRIGONOMÉTRICAS

 

Estudiantes: CINDY YESENIA INDABURO-MORENO, JOJHAN GONZALO JIMÉNEZ-BELLO, CLAUDIA MAYERLY SARMIENTO-MARTÍN

Asesora: LYDA CONSTANZA MORA-MENDIETA

 

 

Título: LA FILOSOFÍA DE LAS MATEMÁTICAS EN EL CONOCIMIENTO DEL PROFESOR DE MATEMÁTICAS

 

Estudiante: NATALIA MORALES-ROZO

Asesor: EDGAR ALBERTO GUACANEME-SUÁREZ

 

Content provided by

Edgar Alberto Guacaneme Suárez;

translation by Luis Puig;

submitted by Kathy Clark

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Founded in 2004 by well-known mathematics historians and educators, Victor Katz and Frank Swetz, Convergence is both an online journal on mathematics history and its use in teaching and an ever-expanding collection of online resources to help its readers teach mathematics using its history.

Convergence is celebrating ten years of publication by continuing to bring you interesting articles and features on the history of grades 8-16 mathematics and exciting ideas and resources for sharing this history with your students.

Articles published this year include:

“Proofs Without Words and Beyond” includes history and philosophy of visual proofs, along with dynamic, interactive “proofs without words 2.0.”

“David Hilbert’s Radio Address” features an audio recording, transcription, and translation into English of Hilbert’s 4-minute radio version of his longer 1930 address with its famous finale, “Wir müssen wissen; wir werden wissen.”

“Cubes, Conic Sections, and Crockett Johnson” shows how author and illustrator Johnson painted his answer to his own question, “What do the straightedge lines and compass arcs do when two parabolas and a hyperbola double a cube, just stand watching?”

“An Investigation of Subtraction Algorithms from the 18th and 19th Centuries” is based on a study of handwritten cyphering books as well as printed arithmetic texts.

We are honoring the best of our ten-year publication history by presenting new, more interactive versions of some of our favorite articles.

“Van Schooten’s Ruler Constructions,” by Ed Sandifer, was among the articles that appeared in the first issue of Convergence in April of 2004.

“Historical Activities for the Calculus Classroom” (2007), by Gabriela Sanchis, consists of three modules that present curve-sketching, tangent lines, and optimization in the context of historical aims and problems, with the aid of 24 interactive applets and 10 animations.

“When Nine Points Are Worth But Eight: Euler’s Resolution of Cramer’s Paradox” (2011), by Rob Bradley and Lee Stemkoski, features a translation of a long lost letter from Euler to Cramer, along with an interactive presentation of Euler’s “elegant example” resolving the paradox.

See all of these articles and more at MAA Convergence:  http://www.maa.org/publications/periodicals/convergence

Convergence is published by the Mathematical Association of America (MAA).

Janet Beery, Editor, MAA Convergence

Greetings HPM Colleagues!

I have been asked to write a “penultimate chapter” (for the forthcoming two-volume International Handbook of Research in History and Philosophy for Science and Mathematics Teaching) on the ways in which
the history and pedagogy of mathematics occurs in mathematics teacher training around the world (and, for mathematics teacher training at any level, say pupils aged 5 to 18).

Although I am using published articles (e.g., through Educational Studies in Mathematics and other international journals, CERME papers) to locate studies that have been conducted with teacher candidates, I only have the ICMI study from 2000 (Fauvel and van Maanen) to refer to what may be formally (and informally) mandated in such programs around the world.

And, so, here is my request:

Could you briefly describe for me the ways in which history or philosophy of mathematics is included (mandated? required?) in the preparation of mathematics teachers in your country? Is it significantly different than what was reported in the 2000 study? Or, have there been developments that I should capture as part of this chapter? Alternatively, if there is a particular person I could write who has
published on this topic, could you please direct me to them?

If you could please me (kclark@fsu.edu) with the information specific to your country and context by 20 March 2012, I would be most appreciative!

Thank you!

Kathy Clark (Florida State University, Tallahassee, Florida USA)