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Rutas hacia el álgebra Actividades en Excel y Logo
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... "Una de las dificultades que la mayoría de los estudiantes enfrentan al iniciarse en el estudio del álgebra obedece a que ésta ha sido vista como una transición lineal, como una extensión de los cálculos numéricos al cálculo literal" (Butto y Delgado, 2012, p.20). [3] En cuanto a los datos experimentales a través de las lentes teóricas en donde la visión cultural del desarrollo se articula como un proceso del desdoblamiento dialectico entre las formas constituidas culturalmente e históricamente de matemática actividad de complicidad y semióticamente mediada en el aula, revela una vía de desarrollo donde las formas abstractas del pensamiento son superadas o generalizadas en otras más sofisticadas a través de una actividad apropiadamente diseñada mediante un salón de clase. [4] Hay algo inherente de la aritmética en álgebra y algo inherente de lo algebraico en lo aritmético, y que la actividad patrón trae estos dos aspectos juntos. ...
A study on the identification and development of mathematical talent in elementary and secondary school students is presented and based on the Renzulli's School Enrichment Model. The methodology used was mixed type with concurrent embedded design of dominant model. The two stages of the study consisted of: (a) detecting students with mathematical talent in basic and secondary primary education in terms of generalization processes; and (b) designing and implementing an extracurricular enrichment program with students of basic and secondary primary education In terms of generalization processes in expresser and Google Maps environment, as well as in the Excel spreadsheet. The extracurricular enrichment program proved effective as the students managed to move towards multiplicative thinking.
This chapter provides an overview of research about algebraic reasoning among relatively young students (6-12 years), It focuses on mathematics learning and, to a lesser extent, teaching. Issues related to educational policy, epistemology, and curriculum design provide a backdrop for the discussion.
The Culture of the Mathematics Classroom is becoming an increasingly salient topic of discussion in mathematics education. Studying and changing what happens in the classroom allows researchers and educators to recognize the social character of mathematical pedagogy and the relationship between the classroom and culture at large. The volume is divided into three sections, reporting findings gained both in research and in practice. The first presents several attempts to change classroom culture by focusing on the education of mathematics teachers and on teacher-researcher collaboration. The second section shifts to the interactive processes of the mathematics classroom and to the communal nature of learning. The third section discusses the means of constructing, filtering, and establishing mathematical knowledge that are characteristic of the classroom culture. As an examination of the social nature of mathematical teaching and learning, the volume should appeal both to educational psychologists and to cultural and social anthropologists and sociologists. The editors have compiled a volume that explores not only the acquisition of mathematical knowledge but the communal character of such knowledge as well.
This thesis is based on research investigating 12-13 years old pupils' potential to approach through Logo different characterizations of variable prior to formal algebra teaching. The characterizations of variable considered are variable as general number, variables in a functional relationship and variable as specific unknown. Pupils' potential is defined by their capability to solve a range of specific Logo-based tasks involving one characterization of variable. During the solution process peer collaboration was encouraged and support was available from the researcher. The experimental work consisted of case studies of 6 pairs of pupils over a period of one year working in three specially designed Logo microworlds each one focussing on one characterization of variable. The observation of these pupils' work was carried out during their normal computer time with the researcher acting as the teacher of the whole group (34 pupils). Special attention was paid to the strategies pupils used to solve the posed tasks, researcher's interventions, peer collaboration and the influence of the Logo setting. Data included researcher's notes taken during the observation of pupils' work, pupils' written records, individual interviews and the responses to a paper and pencil questionnaire given at the beginning and at the end of the study. Previous studies of pupils' learning of algebra show that they have difficulties with each one of the three characterizations of variable whether they are algebra beginners or more advanced students. Evidence from this study shows that pupils can develop a potential to work with these characterizations of variable prior to formal algebra teaching. Crucial elements provoking this development were: the design of the activities appealing to pupils' prior numeric knowledge; the Logo environment; social interaction between pupils and with the researcher; the use of communicative and egocentric speech. The results of this research show that notions that are crucial to the use of variable can be developed prior to formal algebra teaching. Pupils' arithmetic can provide a basis for the development of these notions.
