Strategies of pre-service early childhood teachers for solving multi-digit division problems

Unlike previous research, this study analyzes the strategies of pre-service early childhood teachers when solving multi-digit division problems and the errors they make. The sample included 104 subjects from a university in Spain. The data analysis was framed under a mixed-method approach, integrating both quantitative and qualitative analyses. The results revealed that the traditional division algorithm was widely used in problems involving integers, but not so frequently applied to problems with decimal numbers. Often, number-based and algebraic strategies were employed as an alternative to the traditional algorithm, as the pre-service teachers did not remember how to compute it. In general, number-based strategies reached more correct solutions than the traditional algorithm, while the algebraic strategies did not usually reach any solution. Incorrect identifications of the mathematical model were normally related to an exchange of the dividend and divisor roles. Most pre-service teachers not only failed to compute the division, but also to interpret the obtained solution in the problem context. The study concludes that, during their schooling, students accessing the Degree in Early Childhood education have not acquired the necessary knowledge and skills to solve multi-digit division problems, and thus the entrance requirements at the university must be rethought.This research was funded by Erasmus+ programme, grant numbers 2019-1-CZ01-KA201-061377 and 2020-1-ES01-KA201-082102; and FEDER/Ministerio de Ciencia, Innovación y Universidades—Agencia Estatal de Investigación/, grant number EDU2017-84979-R

Proyecto STEMforYouth

STEMforYouth es un proyecto H2020 de la Unión Europea, que se enmarca dentro del bloque Science with and for Society (ciencia por y para la sociedad), de dos años de duración (http://www.stem4youth.eu/). Está conformado por 10 organizaciones participantes de seis países diferentes (España, Italia, Grecia, Polonia, Eslovenia y República Checa). El objetivo principal del proyecto consiste en despertar el interés de los jóvenes de entre 12 y 19 años por el aprendizaje de las materias STEM (Science, Technology, Engineering and Mathematics). Se pretende informar a los jóvenes sobre las potencialidades de las carreras STEM y su proyección profesional en diferentes sectores laborales; mostrando además que estas carreras están abiertas a toda la sociedad independientemente de su género. Para lograrlo, el proyecto desarrollará una guía para profesores sobre las materias STEM, con una parte de desarrollo curricular y otra extracurricular. En particular los miembros del STEMforYouth diseñarán diferentes actividades STEM para su implementación en el aula, y también para su experimentación en eventos extraescolares. En este momento estamos desarrollando las actividades e invitando a institutos españoles a participar en el proyecto

Using dynamic software for developing thai students' analytical thinking skills in mathematics

The purposes of this study were (1) to develop student mathematics analytical thinking skills, targeting a benchmark of 70 percent in scores, and (2) to enhance students' mathematics achievement through the 5 E's instructional model and dynamic mathematics software, with the goal of surpassing 70 percent in both scores and classroom performance. A total of 29 students who participated in this study were from a school in Nakhonphanom Province, Thailand during the 2021-2022 academic year. The data collection included the collection of lesson plans, mathematics assessment, and behavioural assessment of analytical thinking skills. The statistics used in the data analysis are mean, standard deviation, percentage, and comparison with quality criteria. The results indicated that the proposed model could improve students' analytical thinking skills across three components: component analysis, relational analysis, and principle analysis, with average scores of 80.25%, 75.75%, and 54.25% respectively. The total mean score for analytical thinking was 70.25%. Additionally, students' mathematics achievement was 75.86%, meeting the established criteria

An attempt to identify the issues underlying the lack of consistent conceptualisations in the field of student mathematics-related beliefs

This paper aims to clarify the inconsistencies present in the field of student mathematics-related beliefs. Despite the general agreement about the important role that beliefs play in the learning of mathematics, the study of student mathematics-related beliefs has resulted in a body of uncoordinated research. The lack of consensus on defining and classifying beliefs has generated much confusing terminology, preventing a consistent conceptualization of the phenomenon. To identify the problem underlying existing inconsistencies, we have undertaken a systematic review of the literature to analyse the belief conceptualisations proposed by the most cited authors in this field of research. Our analysis suggests that authors often fail to conceptualise beliefs in four important ways: existing theories related to the phenomenon under research are normally not considered; definitions are often too broad and do not clearly confine the construct under evaluation; and existing beliefs sub-constructs are rarely defined and thus not explicitly distinguished. Our study has also revealed that some of the scales developed to measure the belief constructs lack of content and internal validity. We believe that these findings open new lines of research that may help to clarify the field of student mathematics-related beliefs.This work was supported by Horizon 2020 (710577), Ministerio de Ciencia e Innovación (EDU2017-84979-R), Erasmus+ (2017-1-ES01-KA203-038491) and (2019-1-CZ01-KA201-061377), Ministerio de Ciencia e Innovación (PGC2018-100758-B-I00), RED8-Educación matemática y formación de profesores (EDU2016-81994-REDT) and Junta de Castilla y León (Q3718001E)S

Creencias acerca de las matemáticas de estudiantes colombianos : adaptación y validación de un cuestionario

RESUMEN: El presente trabajo es un estudio preliminar sobre las creencias acerca de las matemáticas que tienen los estudiantes de último grado de educación secundaria en Medellín, Colombia. Se presentan resultados parciales obtenidos, con una muestra de 276 estudiantes, tras aplicar la versión española del Mathematics-Related Beliefs Questionnaire (MRBQ)? un instrumento diseñado y validado inicialmente por expertos de la Universidad de Lovaina. Tras la adaptación del cuestionario al contexto colombiano, este se validó mediante un análisis factorial como en investigaciones anteriores. Los análisis mostraron la existencia de cuatro factores consistentes, que se corresponden con los obtenidos en los estudios originales. Los análisis respecto a la variable sexo permitieron identificar diferencias significativas en dos de los factores extraídos.ABSTRACT: The present work is a preliminary study on mathematics-related beliefs undertaken with students from the last academic year of the secondary education in Medellín, Colombia. Partial results are presented, with a sample of 276 students, after applying the Spanish version of the Mathematics-Related Beliefs Questionnaire (MRBQ) ? an instrument that was initially designed and validated by experts from the University of Leuven. After the questionnaire adaptation to the Colombian context, it was validated by applying factor analysis as in previous researches. The analysis revealed the existence of four consistent factors, which shown to be aligned with those obtained in the original studies. The analyses concerning the variable sex allowed identifying significant differences in two of the factors

Teacher growth in exploiting mathematics competencies through STEAM projects

This article is aimed at educators concerned with curricular initiatives that foster STE(A)M projects in secondary education to promote mathematics competencies. Research has recently reported that these projects superficially address mathematics content, hampering the development of competencies the consensus deems necessary to prepare citizens for daily life. This study shows that learning goals may be achieved when teachers receive personalised training and sustained assistance in their project experiences. We examine how two Spanish teachers, with advisors? support, progress in exploiting mathematics competencies within the implementation of a single project each over a period of 3 years. Their evolution was not the result of minor recommendations but of continuous interactions with the advisors. These interactions intended to maintain a balance between teacher confidence and project enhancements, which required commitment and constancy. Four of the five competencies considered in the Spanish curriculum emerged powerfully after sustained refinement. The frequently mobilised competencies were intra-mathematics, representations, as well as collaborative work and positive identity, followed by modelling. The last of which was difficult to address, but when it was, the other three emerged more naturally. Computational thinking was poorly represented mainly because of the advisors? background and its recent incorporation into the reference curriculum. The teachers? progress was influenced by the advisor?s academic background, pedagogical expertise, ability to transfer research outcomes into teaching, and experience supporting others.This work is supported by the Spanish State Plan (PID2021-122326OB-I00) and the Erasmus+ Program of the European Union (2020-1-ES01-KA201-082102). The European Commission support to this publication does not constitute endorsement of the contents, reflecting only authors’ views. The Commission is not responsible for any use of the present information

Adaptation and validation of the Mathematics-Related Beliefs Questionnaire (MRBQ) to the Colombian context with high school students

RESUMEN: Este artículo presenta la adaptación y validación del MRBQ (Mathematics-Related Beliefs Questionnaire) al contexto colombiano. El MRBQ es un instrumento, desarrollado en la Universidad de Lovaina (Bélgica), que evalúa las creencias de los estudiantes sobre las matemáticas y que ha sido validado en varios países. El instrumento fue administrado a 670 estudiantes de secundaria en centros públicos de la ciudad de Medellín (Colombia). Los análisis revelaron que las creencias sobre las matemáticas de estos estudiantes se representan mejor con un modelo de 10 factores, y no con uno de cuatro como sugieren estudios anteriores. Los 10 factores identificados explican más fielmente el modelo teórico original y muestran una varianza de 56.34%, mayor que la obtenida en investigaciones previas. Estos resultados no solo sugieren mejoras significativas del MRBQ, sino que proporcionan la base para el desarrollo de una herramienta fiable que evalúe las creencias en el contexto colombiano. Hasta lo que estos autores conocen no se dispone de otro instrumento en este contexto que permita identificar las creencias, y como consecuencia estudiar su influencia en el aprendizaje de las matemáticas.ABSTRACT: This article presents the adaptation and validation of the MRBQ (Mathematics-Related Beliefs Questionnaire) to the Colombian context. The MRBQ is an instrument for assessing student mathematics-related beliefs, originally developed at the University of Leuven (Belgium) and validated in several countries. The instrument was administered to 670 students, from public high schools in Medellín (Colombia). The analyses revealed that these student mathematics-related beliefs are better represented with a ten-factor model, rather than with a four-factor model as suggested in previous studies of the MRBQ. The 10 factors explain more faithfully the original theoretical model and account for a variance of 56.34%, higher than that obtained in previous research. These results not only suggest significant improvements of the MRBQ, but also provide the basis for developing a reliable tool to assess beliefs in the Colombian context. To what these authors know, a consistent instrument has not been designed yet in this context for identifying beliefs, and consequently studying their influence on the learning of mathematics.Este trabajo se ha elaborado bajo el marco del proyecto de investigación EDU2017-84979-R del gobierno de España. También ha recibido apoyo del programa de Investigación e Innovación Horizon 2020 de la Unión Europea, bajo el acuerdo Horizon 2020- Seac-2015- 1-710577

Creating Realistic Mathematics Tasks Involving Authenticity, Cognitive Domains, and Openness Characteristics: A Study with Pre-Service Teachers

Creating mathematics tasks provide opportunities for students to develop their thinking, reasoning, communication, and creativity. This paper presents a study on teaching pre-service teachers to create realistic mathematics tasks in real contexts and amending them through an iterative process of analysis and refinement. The study was undertaken with pre-service teachers from two university training courses in Spain, undergraduate students from a primary teacher training course, and graduate students from an educational Master’s course. The students worked in groups to collaborate in the creation of the requested tasks and improvement of them based on critical thinking and creativity. The tasks were not only evaluated concerning their level of realism, but also regarding their level of authenticity, the cognitive domains involved, and their openness characteristic. These are the key characteristics related to environmental and sustainability aspects. The outcomes confirmed that the creation of realistic mathematics tasks was a challenge for future primary teachers; however, they were able to create tasks with high levels of cognitive domain, authenticity, and openness. This evidences, on the one hand, the difficulty that future teachers have in understanding the realism of a mathematics task, and, on the other, the possibilities offered by the task’s creation and the revision activity, which has educational implications and opens paths for future researchThis work was partially supported by the Project Science, Innovation and University Ministry, Spain [PGC2018-100758-B-100]; Project Junta de Castilla-León, Spain [SA050G19]; Project University of Salamanca, Spain [MODELGEO-CEI 18.K133]; FEDER/Ministerio de Ciencia, Innovación y Universidades–Agencia Estatal de Investigación/Proyect EDU2017-84979-R; Mathematics EduLarp (EDUMATH) [2019-1-CZ01-KA201-061377]S

Skill Levels on Visualization and Spatial Reasoning in Pre-service Primary Teachers

We apply theoretical tools from the onto-semiotic approach to present skill levels on tasks requiring visualization and spatial reasoning. These scales are derived from the analysis of visualization and spatial reasoning skills involved in solving a questionnaire supplied to 400 pre-service primary teachers. In order to set skill levels, we describe different types of cognitive configurations considering the network of mathematical objects involved in solving the items. The results show that there may be several configurations at each level and the levels depend on both certain conditions of the task and the visualization skills required. In most cases, the ratio of students expressing high level is significantly below than those of exhibiting low level. The analysis manifests that students put into play variety and quantity of visual objects and processes; however, most did not reach the solution successfully. This leads to the need for specific training actions.This work was funded by the Spanish FEDER/ Ministry of Science, Innovation and Universities – Research Agency / project EDU2017_84979-R, and the European Erasmus + program (2019-1-CZ01-KA201-061377)

How do future teachers describe, analyze and value their reading training?

Resumen: Estudios recientes han planteado que los futuros maestros no son lectores expertos y tienen serias limitaciones al enfrentarse a textos literarios. Sin embargo, desconocemos cómo describen, analizan y valoran su formación lectora. En este artículo analizamos, mediante entrevistas semiestructuradas, la trayectoria lectora de 15 futuros profesores de educación primaria, desde su infancia hasta finalizar sus estudios universitarios. Los resultados muestran que la mayoría de los sujetos evaluados: (1) carecen de hábito lector y mantienen una visión instrumental de la lectura y la literatura; (2) sugieren que su paso por la Educación Primaria y Secundaria no ha supuesto para ellos un estímulo en el conocimiento de prácticas de animación a la lectura; y (3) valoran la formación pedagógica recibida en la carrera como insuficiente. Todos coinciden, sin embargo, en (4) su compromiso como dinamizadores de la lectura en su futuro como profesores. Este estudio evidencia, a diferencia de estudios anteriores, que el futuro profesor de primaria reconoce sus carencias en cuanto a su formación lectora, y señala la necesidad de abordar con prontitud este problema que incide directamente en la competencia lectora de nuestros escolares.Abstract: Recent studies have suggested that pre-service teachers are not expert readers and have serious limitations when confronting literary texts. We however ignore how they describe, analyze and value their reading training. In this article, we analyze, by means of semi-structured interviews, the reading career of 15 primary pre-service teachers, since their childhood until the end of their university degree. The results revealed that most of the participants: (1) lack a reading habit and reflect an instrumental view of reading and of literature; (2) suggest that passing through Primary and Secondary Education has not meant for them a stimulus for gaining knowledge about dynamic practices in reading; and (3) consider the pedagogical training received at the university as insufficient. All they agree, however, (4) in their commitment as facilitators of reading in their near future as teachers. This study suggests, unlike previous research, that primary pre-service teachers recognize the limitations of their reading training, and points out the need to address this problem that directly affects the reading competence of our school students