Developing Purposeful Mathematical Thinking : a Curious Tale of Apple Trees. 'Desarrollo de un pensamiento matemático intencionado : un relato curioso de manzanos'.

Resumen basado en el de la publicación

Daily Problem-Solving Warm-Ups: Harboring Mathematical Thinking In The Middle School Classroom

In this action research study of my classroom of 8th grade mathematics, I investigated the use of daily warm-ups written in problem-solving format. Data was collected to determine if use of such warm-ups would have an effect on students’ abilities to problem solve, their overall attitudes regarding problem solving and whether such an activity could also enhance their readiness each day to learn new mathematics concepts. It was also my hope that this practice would have some positive impact on maximizing the amount of time I have with my students for math instruction. I discovered that daily exposure to problem-solving practices did impact the students’ overall abilities and achievement (though sometimes not positively) and similarly the students’ attitudes showed slight changes as well. It certainly seemed to improve their readiness for the day’s lesson as class started in a more timely manner and students were more actively involved in learning mathematics (or perhaps working on mathematics) than other classes not involved in the research. As a result of this study, I plan to continue using daily warm-ups and problem-solving (perhaps on a less formal or regimented level) and continue gathering data to further determine if this methodology can be useful in improving students’ overall mathematical skills, abilities and achievement.

Primary school teacher’s noticing of students’ mathematical thinking in problem solving

Professional noticing of students’ mathematical thinking in problem solving involves the identification of noteworthy mathematical ideas of students’ mathematical thinking and its interpretation to make decisions in the teaching of mathematics. The goal of this study is to begin to characterize pre-service primary school teachers’ noticing of students’ mathematical thinking when students solve tasks that involve proportional and non-proportional reasoning. From the analysis of how pre-service primary school teachers notice students’ mathematical thinking, we have identified an initial framework with four levels of development. This framework indicates a possible trajectory in the development of primary teachers’ professional noticing.

Developing Students’ Mathematical Thinking and Algorithmic Culture in IT Classes

Report published in the Proceedings of the National Conference on "Education in the Information Society", Plovdiv, May, 2012

Hydrometallurgical process modeling using advanced mathematical tools

Hydrometallurgical process modeling is the main objective of this Master’s thesis work. Three different leaching processes namely, high pressure pyrite oxidation, direct oxidation zinc concentrate (sphalerite) leaching and gold chloride leaching using rotating disc electrode (RDE) are modeled and simulated using gPROMS process simulation program in order to evaluate its model building capabilities. The leaching mechanism in each case is described in terms of a shrinking core model. The mathematical modeling carried out included process model development based on available literature, estimation of reaction kinetic parameters and assessment of the model reliability by checking the goodness fit and checking the cross correlation between the estimated parameters through the use of correlation matrices. The estimated parameter values in each case were compared with those obtained using the Modest simulation program. Further, based on the estimated reaction kinetic parameters, reactor simulation and modeling for direct oxidation zinc concentrate (sphalerite) leaching is carried out in Aspen Plus V8.6. The zinc leaching autoclave is based on Cominco reactor configuration and is modeled as a series of continuous stirred reactors (CSTRs). The sphalerite conversion is calculated and a sensitivity analysis is carried out so to determine the optimum reactor operation temperature and optimum oxygen mass flow rate. In this way, the implementation of reaction kinetic models into the process flowsheet simulation environment has been demonstrated.

Didáctica de la matemática como disciplina científica.

Se describe el grupo de trabajo 'La didáctica de las matemáticas como disciplina científica'. Se explica su estructura. Esta se compone de varios subgrupos asignados a diversas universidades. Se expone también la actividad del grupo de trabajo. En el marco de la misma se describen dos sesiones de discusión. La primera versa sobre el artículo de Juan Díaz Godino 'Análisis epistémico, semiótico y didáctico de procesos de instrucción matemática'. En el citado trabajo se describe una metodología para la enseñanza de las matemáticas. La discusión se centra en la relaciones entre los distintos conceptos implicados en la metodología citada. La segunda sesión se dedica a la discusión sobre el trabajo ''Didactique fondamentale' versus 'Advanced Mathematical thinking' : ¿Dos programas de investigación inconmensurables?', debatiendo sobre la posibilidad de conciliar los puntos de vista expuestos en ambos trabajos.

Uma análise histórico-epistemológica do conceito de grupo

This work aims to analyze the historical and epistemological development of the Group concept related to the theory on advanced mathematical thinking proposed by Dreyfus (1991). Thus it presents pedagogical resources that enable learning and teaching of algebraic structures as well as propose greater meaning of this concept in mathematical graduation programs. This study also proposes an answer to the following question: in what way a teaching approach that is centered in the Theory of Numbers and Theory of Equations is a model for the teaching of the concept of Group? To answer this question a historical reconstruction of the development of this concept is done on relating Lagrange to Cayley. This is done considering Foucault s (2007) knowledge archeology proposal theoretically reinforced by Dreyfus (1991). An exploratory research was performed in Mathematic graduation courses in Universidade Federal do Pará (UFPA) and Universidade Federal do Rio Grande do Norte (UFRN). The research aimed to evaluate the formation of concept images of the students in two algebra courses based on a traditional teaching model. Another experience was realized in algebra at UFPA and it involved historical components (MENDES, 2001a; 2001b; 2006b), the development of multiple representations (DREYFUS, 1991) as well as the formation of concept images (VINNER, 1991). The efficiency of this approach related to the extent of learning was evaluated, aiming to acknowledge the conceptual image established in student s minds. At the end, a classification based on Dreyfus (1991) was done relating the historical periods of the historical and epistemological development of group concepts in the process of representation, generalization, synthesis, and abstraction, proposed here for the teaching of algebra in Mathematics graduation course

Developing Young Learners’ Logical/Deductive Thinking Skills and Second Language Skills through a CLIL approach

Trabalho de Projecto apresentado para cumprimento dos requisitos necessários à obtenção do grau de Mestre em Teaching English as a Second / Foreign Language.

Using blogs to enhance the capacity of mathematical communication in High School

The aim of this investigation is to analyze the use of the blog as an educational resource for the development of the mathematical communication in secondary education. With this aim, four aspects are analyzed: organization of mathematical thinking through communication; communication of mathematical thinking; analysis and evaluation of the strategies and mathematical thought of others; and expression of mathematical ideas using mathematical language. The research was conducted from a qualitative approach on an exploratory level, with the case study method of 4 classrooms of second grade of secondary education in a private school in Lima. The observational technique of 20 publications in the blog of the math class was applied; a study of a focal group with a sample of 9 students with different levels of academic performance; and an interview with the academic coordinator of the school was conducted. The results show that the organization of mathematical thinking through communication is carried out in the blog in a written, graphical and oral way through explanations, schemes and videos. Regarding communication of mathematical thinking, the blog is used to describe concepts, arguments and mathematical procedures with words and examples of the students. The analysis and evaluation of the strategies and mathematical thinking is performed through comments and debates about the publications. It was also noted that the blog does not facilitate the use of mathematical language to express mathematical ideas, since it does not allow direct writing of symbols nor graphic representation.

Mathematically gifted male adolescents activate a unique brain network during mental rotation

Mental rotation involves the creation and manipulation of internal images, with the later being particularly useful cognitive capacities when applied to high-level mathematical thinking and reasoning. Many neuroimaging studies have demonstrated mental rotation to be mediated primarily by the parietal lobes, particularly on the right side. Here, we use fMRI to show for the first time that when performing 3-dimensional mental rotations, mathematically gifted male adolescents engage a qualitatively different brain network than those of average math ability, one that involves bilateral activation of the parietal lobes and frontal cortex, along with heightened activation of the anterior cingulate. Reliance on the processing characteristics of this uniquely bilateral system and the interplay of these anterior/posterior regions may be contributors to their mathematical precocity.