Infinite limit of a function at infinity and its phenomenology

In this paper we aim to characterise and define the phenomena of the infinite limit of a function at infinity. Based on the intuitive and formal approaches, we obtain as results five phenomena organised by a definition of this limit: intuitive unlimited growth of a function, for plus and minus infinity, and intuitive unlimited decrease of a function, for plus and minus infinity (intuitive approach), and the one way and returned phenomenon of infinite limit functions (formal approach). All this is intended to help overcome the difficulties that pre-university students have with the concept of limit, contributing from phenomenology, Advanced and Elementary Mathematical Thinking, and APOS theory

Mathematical Flexibility of Degree of Primary Education students in solving an area problem: Pick’s Theorem

The development in mathematical flexibility should be included in the mathematics teaching training of students in Primary Education Degree. Teachers in training have to acquire the skill to modify the problem resolution and be able to break with stereotyped methods. This document presents an analysis of spontaneous mathematical flexibility developed by teachers in training against problems in which the calculation of the area is requested. At the same time what type of statement can promote is analysed, in a more effective way, a flexible thought and the comparison of the possible mathematical flexibility between the different problems is established

The use of social networks by pre-service teachers for the design of mathematical activities

Currently, the use of social networks is part of the daily life of young people in Spain and they are at the service of interaction within a group. The main objective of this work is to analyze the activities designed by pre-service teachers for learning in Primary Education in which mathematical notions are involved through the use of social networks. The sample consisted of 148 pre-service teachers in the 3rd year of the Primary Education Degree. They were asked to design an activity focused on students aged 10-11 years in which the material was extracted exclusively from social networks. From a frequency and reticular analysis, we obtain the results that there is a greater frequency of use of the social network Twitter and the absence of specific educational social networks. Likewise, the mathematical contents that predominate in the proposals are statistics and probability. It can be affirmed that the use of the proposals with social networks is not appropriate for the educational level for which it is intended. In addition, the high frequency of content on statistics and probability is attributed to their own shortcomings in previous educational levels. These results will make it possible to adapt the training of pre-service teachers, both in relation to mathematical content and to the possible social networks to be used

Pre-service teachers develop their mathematical knowledge for teaching using manipulative materials in mathematics

This manuscript aims to describe aspects of mathematical knowledge for teaching, MKT, identified in pre-service teachers (PSTs) when explaining an arithmetic property using manipulative materials. In particular, we are interested in the specialized mathematical knowledge, SCK, the pedagogical knowledge related to teaching, KCT, and the knowledge of content and curriculum, KCC. We proposed to record a video to a sample of 27 primary education students enrolled in their first mathematics education course. They had to explain an arithmetic property of natural numbers using manipulative materials. PSTs do not create contexts by the mere presence of manipulative material, but only rely on it for visual purposes; the meaning of these values are modified during the explanation. Evidence has been found of difficulties relating to the SCK such as the inadequate varying of the meanings given to the manipulative material, and to the KCC such as the selecting of an unsuitable material

Límite infinito de una sucesión: fenómenos que organiza

El límite es una noción estudiada por el Análisis Matemático, y las dificultades de su proceso enseñanza-aprendizaje una de las líneas de investigación en el área de la Didáctica de las Matemáticas en las últimas décadas. Partimos de la premisa de que cada uno de los límites debe ser estudiado minuciosamente, por ese motivo, en esta tesis doctoral nos ocuparemos de uno de ellos: el límite infinito de una sucesión.Este estudio se sostiene sobre cuatro pilares fundamentales: la fenomenología dada por Freudenthal, el Pensamiento Matemático Avanzado, los Sistemas de Representación y la Teoría APOS. A partir de ellos, mediante un estudio teórico, caracterizamos tres fenómenos organizados por una definición del límite infinito de una sucesión: crecimiento intuitivo ilimitado, c-i.i. y decrecimiento intuitivo ilimitado, d-i.i., considerando un enfoque intuitivo, e ida-vuelta en sucesiones de límite infinito, a partir de un enfoque formal..

Analysis of Interdisciplinary STEM Lessons Generated by Pre-Service and Inservice Teachers in the United States

This study views STEM as a space with the potential to dismantle the narrow disciplinary silos that have led to inequitable gaps in achievement. Responding to the latest recommendations for teachers from NCTM and NSTA, this study aims to examine the instructional design of secondary mathematics and science pre-service teachers in an interdisciplinary STEM lesson about a pandemic. Starting with two images, teachers are asked to design the associated activities that they would implement in the classroom. Researchers utilized a qualitative methodology based on the categories of the 5E Model: Engage, Explore, Explain, Elaborate and Evaluate. The findings highlight responses to each of the 5E factors are very mixed. Teaching strategies consisting of posing questions predominate, promoting the Engage factor; while the Explore factor is barely considered, which could hinder the incorporation of group skills and critical thinking. This study offers a pathway on how to assess the professional learning of novice teachers following the 5E model through a contextualized activity with bacterial growth

Math Anxiety in Primary Education during Covid-19 Confinement: Influence on Age and Gender

Background: The closure of schools in Spain due to the Covid-19 pandemic confronted teachers, students, and families with a new reality. Previous studies have shown that anxiety levels increase during pandemic times. Therefore, it highlights the interest of the affective domain in primary education. Objectives: To analyse some general aspects of math anxiety, such as primary school students’ fear, nervousness, and blockage before mathematics both at the educational centre and at home during the Covid-19 confinement. Design: Quantitative study using a closed questionnaire of seven questions with a Likert-type scale. Settings and participants: 496 Spanish primary school students. Data collection: Through the questionnaire hosted in Google Forms and provided by the teachers responsible for the students one month after the closure of all the educational centres and the confinement of all the participating children. Results: Fear of math increases during primary education, with the highest levels of fear and restlessness in the third and sixth grades; the girls presented the highest levels in all aspects, except for nervousness during classes. Conclusions: The general aspects of math anxiety are intimately linked and evolve increasingly throughout primary education. These facts are justified based on the proximity of the change in the educational stage and its influence on teaching, as well as the students’ social conditions

Specialized Content Knowledge of pre-service teachers on the infinite limit of a sequence

This paper analyses how pre-service teachers approach the notion of the infinite limit of a sequence from two perspectives: Specialized Content Knowledge and Advanced Mathematical Thinking. The aim of this study is to identify the difficulties associated with this notion and to classify them. In order to achieve this, an exploratory qualitative approach was applied using a sample of 12 future teachers. Among the results, we can affirm that preservice teachers mainly use algorithmic procedures to solve tasks in which this type of limit is implicit, although they would consider a resolution that specifically involves the notion with an intuitive approach if they had to explain it to their students

La discalculia en la Educación Infantil: un estudio de caso

En este artículo se pretende conseguir un mayor conocimiento de la Discalculia, dificultad que afecta principalmente al ámbito matemático, pudiendo explicar de qué manera afecta al proceso de aprendizaje de determinados alumnos, concretamente en la etapa de Educación Infantil. Con la utilización de diferentes cuestionarios el profesorado puede identificar un posible caso, y a través de la propuesta descrita en este documento se ofrecen los primeros pasos de intervención con este tipo de alumnado. El método de investigación seguido ha sido el estudio de un caso, además de ser llevado a cabo en un aula con alumnado sin dificultades. Con todo ello, ha sido posible desarrollar una serie de actividades con las que un alumno discalcúlico pueda adquirir los mismos conocimientos matemáticos que un alumno sin esta dificultad

The impact of sending letters in improving teaching-learning process of natural number of pre-service teachers

The first contact that a pre-service teacher has with didactics of mathematics is the notion of natural number, being still in the university classroom and not having started working a real classroom. Therefore, the main objective of this work is to relate the knowledge of a trainee teacher to the different difficulties developed by the children and to evaluate the learning processes in a real environment. The participants were 20 future teachers and 40 (9-year-old) children. During the experience, six letters closely related to the contents of the university subject were exchanged; as well as two socialisation letters; and four videos, including two presentation and two farewell videos. Among the results obtained, we highlight that the participating university students have been able to reinforce the knowledge learned in class through the analysis of the children's resolutions, specifically the following: a) counting, b) resolution of additive-concrete situations, c) resolution of multiplicative-concrete situations, d) resolution of a monetary problem, and e) being aware of the manipulation of Cuisenaire's rods