Networked Analysis of a Teaching Unit for Primary School Symmetries in the Form of an E-Book

Abstract

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 itinerary to follow and attention is paid to different levels of students’ mathematical attainment. The research objective of the paper is to make a networked analysis of the structure and contents of the teaching unit based on the Van Hiele levels of mathematical reasoning and the levels of cognitive demand in mathematical problem solving. The analysis shows the interest of networking both theories, the suitability of the teaching unit, as the Van Hiele levels and the cognitive demand of the activities increases, and its usefulness to fit the needs of each student, from low attainers to mathematically-gifted students.

Improving the learning of geometric proportionality using van Hiele’s model, mathematical visualization, and GeoGebra

“…As in the studies of Aravena and Gutiérrez (2016), Gualdrón (2011), Gualdrón et al (2020, Gutiérrez et al (2021), andSantos (2014), this research managed to identify the importance of developing teaching units based on van Hiele's (1986) model, since in the different tasks that were proposed in the development of the sections, reasoning in van Hiele's (1986) levels 1 and 2 were emerging, this implies the acquisition of the concepts of proportionality, similarity, and homothecy. The students went from not having a clear notion of similarity to constructing a definition for similarity, proportionality, and homothecy; from not identifying criteria for similarity to identifying and understanding the mathematical properties that remain invariant in similar figures; from not using visualization skills such as mental rotation (MR), and not communicating their arguments using an appropriate mathematical language to using visualization skills and processes to identify, for example, alternate internal angles or configurations in homothetic position, in addition to expressing their reasoning in a symbolic manner.…”

Diseño de libros electrónicos para la enseñanza a distancia a estudiantes con diferentes capacidades matemáticas

“…El libro electrónico que hemos creado (Gutiérrez, Jaime, Gutiérrez, 2021) es un ibook, la versión del formato e-pub desarrollada por Apple. Los ibooks pueden incorporar diversos elementos como videos, enlaces a páginas web, encuestas de auto-evaluación, figuras interactivas y botones de redireccionamiento a otros lugares del libro, entre otros.…”

“…En esta conferencia, presento un ejemplo de uso de las TIC para facilitar la enseñanza de las simetrías del plano de manera individualizada y en un contexto de enseñanza a distancia. Se trata de un libro electrónico (Gutiérrez, Jaime, Gutiérrez, 2021) que ofrece a los estudiantes una secuencia de actividades interactivas, la mayoría de ellas basadas en GeoGebra, es adaptable a distintos objetivos de enseñanza adecuados para estudiantes con diferentes capacidades matemáticas y permite el aprendizaje autónomo de los estudiantes en contextos de enseñanza a distancia o de trabajo independiente en casa o en el aula, lo cual resulta especialmente interesante para los estudiantes con alta capacidad matemática, que pueden seguir un ritmo de aprendizaje más rápido y profundo que sus compañeros.…”

La resolución de problemas matemáticos en estudiantes de educación primaria

“…De la misma manera, (Gutiérrez et al, 2021), propusieron un libro electrónico interactivo de simetrías planas con actividades de una unidad didáctica elaboradas en GeoGebra cuya aplicación se basa en la metodología de enseñanza del descubrimiento guiado por medio de la solución de un problema, las cuales permiten que los estudiantes elijan qué itinerario deben seguir y se presta atención a los diferentes niveles de logros matemáticos de los estudiantes.…”