0000000000857669
AUTHOR
Adela Jaime
Visualizing Mathematics
The research presented in this chapter is part of the R+D+I projects EDU2015-69731-R (Spanish Government/MinEco and ERDF) and GVPROMETEO2016-143 (Valencian Government).
Connecting Research to Teaching: Guidelines for Teaching Plane Isometries in Secondary School
Two key concepts strongly supported by the NCTM's Curriculum and Evaluation Standards for School Mathematics (1989) are (1) that geometry should be taught from multiple perspectives and (2) that it is necessary to make mathematical connections. Both concepts can be implemented by appropriately selecting topics that can be presented to students from several points of view in different environments and that can also link different branches of mathematics or mathematics and other sciences.
An Alternative Paradigm to Evaluate the Acquisition of the van Hiele Levels
This article presents an alternative way of analyzing the van Hiele level of students’ geometrical reasoning. We evaluate the students’ answers, taking into account the van Hiele level they reflect and their mathematical accuracy. This gives us a description of how accomplished the students are in applying the procedures associated with each of the van Hiele levels and allows us to determine the students’ degree of acquisition of the van Hiele levels. In this way we obtain a clearer picture of the students’ geometrical reasoning than with the traditional assignment of one van Hiele level to the learners. An example of the application of this method is provided: We describe a test that evalu…
Networked Analysis of a Teaching Unit for Primary School Symmetries in the Form of an E-Book
In mathematics education, technology offers many opportunities to enrich curricular contents. Plane symmetries is a topic often skipped by primary teachers. However, it is important and may be worked in attractive ways in dynamic geometry software environments. In any regular classroom there are students with different levels of mathematical attainment, some needing easy tasks while others, particularly mathematically-gifted students, need challenging problems. We present a teaching unit for plane symmetries, adequate for upper primary school grades, implemented in a fully interactive electronic book, with most activities solved in GeoGebra apps. The book allows student to choose which itin…
Use of Language in Elementary Geometry by Students and Textbooks
This chapter presents some results of a study on the definitions that appear in the Spanish textbooks for Primary School (Jaime, Chapa, and Gutierrez, 1992). Its aim is to point out the errors in the statements of definitions and inconsistent or inappropriate uses of definitions made in individual textbooks, or in series of textbooks. This study concerned geometry and, more specifically, triangles and quadrilaterals. Most of the problems that arose were strongly related to the understanding and use of language.
Análisis de la adecuación de libros de texto de E. Primaria a la enseñanza a estudiantes de altas capacidades matemáticas
Un problema al que se enfrentan los profesores de matemáticas de Enseñanza Primaria es la necesidad de hacer adaptaciones en sus programaciones para ofrecer una educación adecuada a sus alumnos de altas capacidades matemáticas. Las editoriales de libros de texto de matemáticas de estos niveles educativos ofrecen diversas soluciones que, usualmente, consisten en incluir, en el libro del alumno, algunos problemas más difíciles y, en la documentación del profesor, una propuesta de problemas de ampliación. Una cuestión que se plantea al analizar un libro de texto de matemáticas es valorar cómo de útil puede ser el material proporcionado por la editorial (libro de texto y materiales complementar…
The Cognitive Demand of a Gifted Student’s Answers to Geometric Pattern Problems
Mathematically gifted students require specific teaching methodologies to foster their interest in mathematics and their engagement in solving problems. Geometric pattern problems are an interesting context in which to introduce algebra to those students. We present the case of a nine-year-old student engaged in a teaching unit based on geometric pattern problems that was aimed at helping him start learning algebra, equations, and algebra word problems. To analyze and assess the cognitive effort the student made to solve the problems, we used a particularization to this context of the cognitive demand model. We analyzed answers typical of the different kinds of problems posed throughout the…
<p>Análisis del aprendizaje de geometría espacial en un entorno de geometría dinámica 3-dimensional</p>
El creciente uso de software de geometría dinámica 3-dimensional plantea nuevas cuestiones a los investigadores en Educación Matemática. Para aportar información sobre el aprendizaje de geometría espacial en esta disciplina mediante entornos de geometría dinámica 3-dimensional, y sobre posibles fortalezas y debilidades de tales entornos, presentamos resultados de una investigación experimental en la que se analiza cómo un estudiante de altas capacidades matemáticas aprende conceptos relativos a paralelismo entre rectas y/o planos en el espacio mediante la resolución de actividades en un entorno de Cabri 3D.Analysis of space geometry learning in a 3-dimensional dynamic geometry environmentTh…
Reflexiones sobre la enseñanza de la geometría en primaria y secundaria
En este artículo presentamos
 introducciones a algunos modelos didácticos
 centrales de la enseñanza de la geometría en los
 diferentes niveles educativos desde infantil hasta la
 universidad. En primer lugar introducimos el modelo
 de Van Hiele, que es el marco más efectivo para organizar
 la enseñanza de la geometría en los diferentes
 niveles educativos. Nos centramos en uno de sus
 componentes, las fases de aprendizaje, que sugiere
 cómo organizar los contenidos de los temas de enseñanza
 de las matemáticas escolares. Luego, prestamos
 atención al modelo de Vinner de aprendizaje de conceptos
 matemáticos con un fuerte apoyo grá…