Math Ed Papers by Valeria Aguirre Holguín
This is my presentation of my PhD student's (Valeria Algeria Holguin's) work. It describes her va... more This is my presentation of my PhD student's (Valeria Algeria Holguin's) work. It describes her various findings, especially it has conjecture stages of coming to know and use mathematical definitions that are new to students.
Papers by Valeria Aguirre Holguín
El concepto de representación de la transformación lineal en la comunidad de matemática educativa
RESUMEN Este escrito presenta un paneo enmarcado en la investigacion en matematica educativa; par... more RESUMEN Este escrito presenta un paneo enmarcado en la investigacion en matematica educativa; partiendo del concepto de representacion hasta las unidades significantes del concepto de Transformacion Lineal. No se pretende constituir un estudio exhaustivo de este topico del Algebra Lineal, ni tampoco una revision del estado del arte. Por el contrario, busca colocar en el escenario los diferentes enfoques del concepto de representacion en la comunidad de Matematica Educativa; para asi, abordar los registros de representacion mayormente empleados al atender el concepto de Transformacion Lineal en diversos estudios realizados e identificar las unidades significantes en cada uno de ellos. Palabras Clave: Representacion, registro, semiosis, transformacion lineal. ABSTRACT This article presents an overview related to mathematics education research field. The scenario goes from the representation concept to the significant units of a linear transformation. This is not an exhaust study neith...
Xiv Conferencia Interamericana De Educacion Matematica, Mar 31, 2015
The Better Regulation agenda includes consideration of alternatives to regulation where EU legisl... more The Better Regulation agenda includes consideration of alternatives to regulation where EU legislation is neither specifically required nor uniquely suitable. These take different forms. A basic distinction can be made between two approaches involving measures which are not legally binding. Policy coordination is a non-negotiable alternative to legislation laid down in the treaty. Self-regulation and "co-regulation" in principle provide for a choice in particular cases, and often a dynamic interplay between the threat of legislation and the credibility of private commitments. It has not been clear, however, what "co-regulation" actually means in the EU context. There are in fact two models. In the first, private EU-wide measures are seen as alternatives, notably to Commission acts, for the implementation of EU legislation. In the second, self-regulation is understood as an alternative to the EU legislation itself. In reality the first model, which came to dominate the discourse of Better Lawmaking, has not materialized and is unlikely to do so. Moreover, the second model in practice only consists of a choice between self-regulation and legislation. Attempts at intermediate forms have so far failed to convince. There are successful examples of self-regulation. It would be easier to understand and to exploit such possibilities if political discourse were brought into line with policy practice. possibilities of this "alternative" agenda-and indeed the different usages of the term "alternative"-and, in this perspective, offers a cautious evaluation of the viability of some of those methods which are generally included under the most elusive concept, that of "co-regulation". The first section proposes a simple categorisation for these non-traditional approaches based on two dimensions: the underlying mode of governance and the nature of the interaction between public and private actors. Marketbased instruments offer alternative instruments within the hierarchical mode of governance. Beyond this, a basic distinction is proposed between a) non-binding coordination of national policies as compared to EU legislation and b) self-and co-regulation as "alternatives" to traditional regulation by (EU) public authorities. The second section summarises the different understandings of "co-regulation" which are currently used in the context of EU policy-making. In each case it reviews briefly the state of play in terms of the practical results achieved. The conclusion is that some elements in the first phase of co-regulatory experimentation have been unsuccessful or even misconceived. In the end, what both public and private actors most need are arrangements which guarantee a "level playing field" where competitive conditions are concerned, as well as pursuit of legitimate public interests (such as health and safety, or protection of the environment)
Learning About the Coordinate Plane Through Game-Based Learning: A Case Study on Math Snacks Summer Camp 2012
University students' uses of mathematical definitions that are new to them
This is the Powerpoint for our Conference talk. Our specific research question was: How do univer... more This is the Powerpoint for our Conference talk. Our specific research question was: How do university students use definitions to evaluate and justify examples and non-examples, in proving, and to evaluate and justify true/false statements? Data were collected through individual task-based interviews with volunteers from a transition-to-proof course. Altogether there were five definitions: function, continuity, ideal, isomorphism, and group, but each student was asked to consider only one of the five. One of our conjectures with regard to the definition of function is that such interference occurred due to the students having worked with functions in several previous courses. We found less interference as we analysed the later interviews, when the definitions were not only new to the interviewed students but also more abstract.
Linear Algebra and its Applications, 2014
He would be Good: Abraham Lincoln’s Early Mathematics, 1819–1826
Abraham Lincoln’s Cyphering Book and Ten other Extraordinary Cyphering Books, 2014
ABSTRACT This chapter, jointly written by Nerida Ellerton, Valeria Aguirre Holguín, and Ken Cleme... more ABSTRACT This chapter, jointly written by Nerida Ellerton, Valeria Aguirre Holguín, and Ken Clements, offers a comprehensive analysis of the earliest extant handwritten manuscript of Abraham Lincoln—22 pages (11 leaves), from a cyphering book that Lincoln prepared between 1819 and 1826. The pages are examined from historical, mathematical and educational perspectives, and an order in which they were written is conjectured, with justifications provided. This is the first time all 22 pages have been examined, it having become received tradition that there were only 20 surviving pages. The authors argue that if the corpus of all extant U.S. cyphering books were to be studied, then the future President’s cyphering book would not be particularly outstanding from calligraphic, penmanship, or abstract mathematical points of view. Analysis reveals, nevertheless, that Lincoln succeeded in his quest to prepare an attractive cyphering book in which almost all entries were arithmetically correct—despite his having to cope with rough frontier circumstances.
Learning About the Coordinate Plane Through Game-Based Learning: A Case Study on Math Snacks Summer Camp 2012
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Math Ed Papers by Valeria Aguirre Holguín
Papers by Valeria Aguirre Holguín