El Uso de Las Letras como Fuente de Errores de Estudiantes Universitarios en la Resolución de Tareas Algebraicas

La presente investigación es un estudio realizado con 194 estudiantes del Centro Universitario de la Costa Sur, en Autlán, México, cuyo objetivo es analizar los errores más comunes que los alumnos de primer semestre presentan en las producciones, al operar con los distintos significados que pueden tener las letras en álgebra y con base a esos resultados, establecer su ubicación dentro de alguna de las cuatro categorías de entendimiento en el uso y significado de las letras en álgebra que propone Küchemann (1980). Los resultados muestran que más de la mitad de los estudiantes de este nivel educativo no manifiestan dificultades al evaluar las letras, manejarlas como objetos o considerar su presencia, sin embargo, sí revelan deficiencias en el discernimiento para comprender el uso y significado de las letras como incógnitas de valor especifico, números generalizados y como variables

Sharing teacher training methods: the case of problematic learning situations in geometry

The study reported in this chapter arose from a 3-year Israeli study aiming to increase teachers' awareness of their pupils' thinking processes by exposing them to cognitive theories and to authentic Problematic Learning Situations (PLS). In that study, Gal with Linchevski detected and analysed PLS and used them as video clips in courses for pre- and in-service lower secondary teachers. The universality of these learning situations prompted Cockburn to use the material with pre-service primary teachers in the UK. The research demonstrates a new methodological approach to teacher education which effectively directs student teachers' attention towards the pupils' perspective as opposed to the teachers' which is their natural inclination. This chapter illustrates the value of international collaboration for the enhancement of mathematics teacher education. The paper was refereed by 3 international colleagues. Cockburn contributed 50%

Introducing functional thinking in year 2: a case study of early algebra teaching

Sixty-five Year 2 children with ages ranging from six to seven years participated in a teaching experiment to introduce functional thinking. The results show that young children are capable of generalising, can provide examples of relations and functions, can describe the inverse of such relationships and give valid reasons for how they found the inverse relationships. They also indicate that specific features of instruction assist this process, particularly abstracting underlying mathematical relationships, notably the materials used by the teacher and the children, the types of activities and the questions asked by the teacher. This leads to specific implications for the teaching of arithmetic in the early years

The Effect of Different Representations on Years 3 to 5 students' ability to generalise

Over the past 3 years, in our Early Algebra Thinking project, we have been studying Years 3 to 5 students’ ability to generalise in a variety of situations, namely, compensation principles in computation, the balance principle in equivalence and equations, change and inverse change rules with function machines, and pattern rules with growing patterns. In these studies, we have attempted to involve a variety of representations and to build students’ abilities to switch between them (in line with the theories of Dreyfus in Advanced Mathematical Thinking. Kluwer, Dordtrecht, pp. 25–41, 1991, and Duval in Proceedings of the 21st conference of the North American Chapter of the International Group for the Psychology of Mathematics Education, Vol. 1, pp. 3–26, 1999). The studies have shown the negative effect of closure on generalisation in symbolic representations, the predominance of single variance generalisation over covariant generalisation in tabular representations, and the reduced ability to readily identify commonalities and relationships in enactive and iconic representations. This presentation will use a variety of studies to explore the interrelation between verbal and visual comprehension of context and generalisation. The studies showed in a variety of contexts the importance of understanding and communicating aspects of representational forms which allowed commonalities to be seen across or between representations