Fostering the Development of Logico-Mathematical Thinking in a Card Game at Ages 5-6

A class of 14 kindergartners in Japan was videotaped while playing a card game in groups of three involving the placement of cards in numerical order. The children were followed up in first grade, and it was found that development in one area of logico-mathematical knowledge (for example, the making of temporal relationships) stimulates development in other areas (such as classification and numerical reasoning). This specific, interrelated mode of structuring was not expected and suggested that it is unwise for adults to try to plan a sequence of development. The implication of the findings is that it may be better to provide "natural" play activities that encourage children to think logico-mathematically than to conceptualize specific standards for 3-to-6-year-olds' mathematics education.     

Piaget's theory and specific instruction: A response to Bereiter and Kohlberg

The present paper draws pedagogical implications from Piaget's theory in the light of Bereiter's critical response to Kohlberg's view against specific instruction. It argues that instruction can be more specific in some ways than Kohlberg suggested, e.g., in the teaching of social knowledge and in the structuring of cognitive processes that will eventually result in logical thinking. It shows the relevance of Piaget's theory to early childhood education and argues that specific instruction should take place within a developmental context and within the framework of a broad theory of knowledge.     

La enseñanza del valor posicional y de la adición en dos columnas

En este artículo, la autora sostiene que la enseñanza de los mecanismos operativos de la adición, cuya automatización no por ser necesaria debe imponerse desde fuera, debe hacerse desde una comprensión por parte del niño de las reglas de esa convencionaliaad, pactándola con ellos mediante procedimientos didácticos diferentes a los tradicionalmente utilizados en preescolar.     

El Proyecto Algebra: Un movimiento organizativo inspirado en Ella

En este artículo se plantea uno de los problemas más centrales de la educación: el problema de la verdadera igualdad de oportunidades y del derecho de los individuos a planificar su currículum. Aunque el sistema de selección estadounidense contra el que se rebelan los participantes en el proyecto Algebra pueda parecer muy lejano al sistema pretendidamente igualitario de nuestro país, hay un paralelismo entre ambos mayor de lo que pudiera pensarse. Los mecanismos de la selección son quizá menos explícitos en nuestro sistema curricular, pero igualmente efectivos y sus raíces estriban en la separación entre la cultura escolar y la cultura familiar, entre el niño como alumno y el niño como ciudadano, entre los agentes educativos comunitarios y los agentes educativos escolares.

Lo que los autores de este artículo plantean para el caso concreto del acceso al álgebra en las comunidades negras de Estados Unidos es igualmente válido para cualquier materia y para cualquier colectivo de individuos cuyo entorno social esté disgregado de la cultura oficial impuesta por la escuela: la necesidad de unir sentido con significado en el diseño de la educación. O, lo que es lo mismo, plantear ésta como un desafío para el conjunto de la comunidad, recuperando para los nuevos contenidos que la sociedad exige los modos de enseñanza tradicionales, donde la motivación viene dada por la implicación de todos los agentes educativos de la comunidad en la instrucción del niño.     

Trying to Make a Lever Work at Ages 1 to 4: The Development of "Functions" (Logico-mathematical Thinking)

To find out if children could make functions before age 4, 73 children aged 1 to 4 were encouraged to imitate the use of a lever to make a beanbag fly up. Functions are mental relationships that preoperational children can make between 2 things at a time in a unidirectional way (Piaget, Grize, Szeminska, &; Bang, 1968 Piaget, J., Grize, J.-B., Szeminska, A. and Bang, V. B. 1977. Epistemology and psychology of functions, Boston: Dreidel. (Original work published 1968)[Crossref] , [Google Scholar]/1977). The child's construction of the following 3 functions was hypothesized and confirmed: (a) As a function of being pushed down, the up end of the board (the lever) goes down; (b) as a function of this descent, the down end of the board goes up; and (c) as a function of this ascent of the board, the beanbag flies up. Three developmental levels were found, and educational implications are discussed.     

SUSTAINING FEATURES DEPARTMENT

On November 16, 1972, U. S. District Judge John H. Pratt ruled in Adams v. Richardson. Following is the complete text of the decision.     

Piaget's theory and the teaching of arithmetic

Conclusion For centuries, education has been a folk art based on tradition and opinions called philosophies. With the advent of associationism and behaviourism, however, education began to enter a scientific era. Now that we have Piaget's constructivism—a more adequate scientific theory—it is time to change the way arithmetic is taught in elementary schools.I hope educators and researchers in other countries will also experiment in classrooms to test the hypothesis that I tested. Because logico-mathematical knowledge is universal and the same in all cultures, I expect the same kinds of results in other countries.Constructivist teaching is much harder than the teaching of algorithms and correcting of worksheets. However, in spite of this difficulty, an increasing number of teachers in the United States are becoming convinced of the truth of Piaget's constructivism. When these teachers encounter children's originality and intelligence that they have not observed before, they are truly overjoyed. Once they have seen the possibility that exists in each child, these teachers do not think of going back to their old ways of teaching.Constance Kamii studied under Jean Piaget, Barbel Inhelder and Hermina Sinclair in the late 1960s and during the 1970s and subsequently developed a pre-school curriculum based on Piaget's theory. She later extended this work to mathematics education in the first three grades and is now working at the fourth and fifth grade level. She has taught at the University of Illinois, Chicago, and the University of Geneva, and is now a professor of education at the University of Alabama, Birmingham, in the United States.I am grateful to Janice K. Ewing for critically reading a draft of this paper and making helpful suggestions.     

La autonomía como objetivo de la educación: implicaciones de la teoría de Piaget

RESUMEN

Para Piaget el fin de la educación debe ser el desarrollo de la autonomía, tanto en el terreno moral como en el intelectual. Esto significa desarrollar la capacidad de pensar críticamente por sí mismo. Tanto los valores morales como los conocimientos intelectuales no deben ser interiorizados por los niños, sino construídos desde el interior a través de la interacción con el medio. La educación actual refuerza la heteronomía de los niños y les impide desarrollar su autonomía, que es una tendencia natural en el hombre de base biológica. Algunos principios de enseñanza de una educación que tenga como objetivo el desarrollo de la autonomía son: reducir el poder de adulto del profesor; inducir al niño a intercambiar y coordinar sus puntos de vista con otros niños y con el profesor de igual a igual; incitar a los niños a tener una mentalidad activa y a tener confianza en su propia capacidad de descubrir cosas.