This study aimed to determine the quality elements of flexible learning to be used as basis for the development of a quality assured module and instructional videos in Data Management of Mathematics ...in the Modern World subject. It also investigated experiences in flexible learning, the quality elements, strengths, and weaknesses of the developed learning module and video recorded lectures, and the challenges encountered by mathematics teachers and students in flexible learning. This study utilized a mixed method of research design. Results showed that there are challenges and difficulties that need to be addressed because these might be the factors that hamper the attainment of quality of flexible learning beyond face-to-face learning. Further, the developed learning module and video-recorded lectures were much valid and much acceptable. However, there were identified strengths and weaknesses of the materials which were the bases in improving the materials to produce a quality assured module and instructional videos in Data Management. It is recommended that researchers study the implementation of flexible learning to the mathematics program and other programs in the curriculum and discover solutions to the challenges that might be encountered by the teachers and students in its implementation. The improvement of the quality of education through program enhancement could be achieved through this.
Abstract Acquiring mathematical literacy requires students to apply mathematics in various real-world contexts. However, mathematics classes often provide brief, content-focused descriptions of ...reality-based tasks and tasks that describe the situation as more complex, closer to reality, are still lacking. Students with different sociodemographic characteristics and cognitive factors have difficulties in solving reality-based tasks in mathematics lessons. The relationship between sociodemographic characteristics and cognitive factors (language and mathematical competence) concerning complex situation descriptions has not yet been investigated. To identify disadvantaged students in integrating such complex-situation tasks in mathematics lessons, this study aims to investigate which sociodemographic characteristics predict the solving of complex-situation tasks and whether cognitive factors mediate the relationship. Experts created 30 complex situations with different mathematical questions. A total of 519 9th- and 10th-grade students participated in a paper–pencil test. Path analysis revealed that the competence to solve complex-situation tasks is directly linked to gender and social background, with mathematical content-related skills and language competence mediating this relationship.
This study aimed to develop a specific Mathematical Content Knowledge (MCK) test focused on multiplication for pre-service mathematics teachers in Indonesia and Türkiye. No assessment tool exists to ...measure MCK related to multiplication among pre-service mathematics teachers. We used convenience sampling to obtain data from third- and fourth-year pre-service teachers in Indonesian and Turkish mathematics teacher education programs. The test items were administered to 423 Indonesian pre-service mathematics teachers and 413 Turkish pre-service mathematics teachers, and their responses were analyzed using factor analysis. The MCK test was found to be reliable, with 18 items that were grouped into four components: procedural knowledge of multiplication (C1), understanding of multiple representations (C2), conceptual knowledge of multiplication (C3), and anticipating students' thinking (C4). The study results suggest that a valid MCK test helps evaluate multiplication in these four components. Additionally, the study findings indicate that Indonesian pre-service teachers score higher in the C1 and C4 categories, while Turkish pre-service teachers score higher in the C2 and C3 categories.
This study aimed to develop a specific Mathematical Content Knowledge (MCK) test focused on multiplication for pre-service mathematics teachers in Indonesia and Türkiye. No assessment tool exists to ...measure MCK related to multiplication among pre-service mathematics teachers. We used convenience sampling to obtain data from third- and fourth-year pre-service teachers in Indonesian and Turkish mathematics teacher education programs. The test items were administered to 423 Indonesian pre-service mathematics teachers and 413 Turkish pre-service mathematics teachers, and their responses were analyzed using factor analysis. The MCK test was found to be reliable, with 18 items that were grouped into four components: procedural knowledge of multiplication (C1), understanding of multiple representations (C2), conceptual knowledge of multiplication (C3), and anticipating students' thinking (C4). The study results suggest that a valid MCK test helps evaluate multiplication in these four components. Additionally, the study findings indicate that Indonesian pre-service teachers score higher in the C1 and C4 categories, while Turkish pre-service teachers score higher in the C2 and C3 categories.
•There are six levels of knowledge within each of the reasoning processes.•The three upper levels have an inclusive relation due to their comprehensive nature.•Prospective teachers need to develop ...specialised knowledge of reasoning processes.
The development of mathematical reasoning is part of the school curricula from the first years, as reflected in teacher education. This study focuses on the prospective primary teachers education, aiming to construct a framework which describes the knowledge about mathematical reasoning processes of teachers and prospective teachers, in the context of a prospective teacher education experiment. Audio and video records of lessons, participant observation and the collection of written records of the prospective teachers are used. The results enable the construction of a framework organised into six levels of knowledge within each of the reasoning processes looked at – generalising, justifying, comparing, classifying and exemplifying – in order to analyse the evolution of this type of knowledge.
Resumo Neste artigo apresenta-se um estudo sobre construção de escalas, com base na Teoria da Resposta ao Item (TRI), para medir proficiência em conteúdos matemáticos básicos, necessários ao ...acompanhamento das disciplinas de Cálculo e similares, de ingressantes em cursos da área de Ciências Exatas. Adotou-se o modelo logístico unidimensional de três parâmetros, que estabelece média zero e desvio padrão 1, para as proficiências dos indivíduos. As proficiências estimadas foram transformadas em outra escala, optando-se por valores adotados por sistemas de avaliação brasileiros, a saber, 250 e 50. O instrumento de medida consistiu em uma prova com 36 itens, de cinco alternativas, somente uma correta, elaborados com base em uma matriz de referência, dividida em três temas, “Espaço e Forma”, “Grandezas e Medidas” e “Números e Operações, Álgebra e Funções”. Cada tema é composto por competências, que descrevem as habilidades que se deseja medir. Para a construção da escala foram especificados níveis de proficiência, representando pontos selecionados pelos pesquisadores para serem interpretados pedagogicamente. Estabelecidos os níveis âncora, foram definidos os itens âncora, a partir de critérios, como, por exemplo, o número de acertos, os percentuais de acertos e a diferença entre seus valores, para níveis consecutivos. Com base nestes critérios, comparou-se três métodos de posicionamento dos itens, mostrando as dificuldades de interpretação em pontos da escala. Tais dificuldades oportunizaram a propositura de outro método, segmentando a escala em faixas de proficiência, com base em agrupamentos hierárquicos dos níveis, o que permitiu a interpretação da escala em toda a sua amplitude.
Abstract This article presents a study on scale construction, based on the Item Response Theory (IRT), to measure the proficiency in basic mathematical contents, which are key to the follow-up of Calculus and similar subjects, for those entering courses in the Exact Sciences area. The one-dimensional logistic model with three parameters was adopted, which establishes zero as the mean and a standard deviation of 1, for individuals’ proficiencies. The estimated proficiencies were transformed in another scale, opting for values adopted by Brazilian evaluation systems: 250 and 50. The measurement instrument consisted of a test with 36 items, with five alternatives each, only one of them correct, that were elaborated based on a reference matrix, divided into three themes, “Space and Form”, “Quantities and Measures”, and “Numbers and Operations, Algebra and Functions”. Each subject is composed of competencies, which describe the skills to be measured. To build the scale, proficiency levels were specified, representing points selected by the researchers to be pedagogically interpreted. Once the anchor levels are established, anchor items were defined based on some criteria, such as the number of correct answers, the percentage of correct answers and the difference between their values, for consecutive levels. Based on these criteria, three methods of items’ positioning were compared, showing the difficulties of interpretation in points of the scale. Such difficulties made it possible to propose another method, segmenting the scale into ranges of proficiency, based on hierarchical groupings of levels, which allowed the scale to be interpreted in all its breadth.
•Mathematical reasoning is an important feature in the learning of mathematics.•Many primary teachers unclear about the term ‘mathematical reasoning’.•Teaching mathematics to develop mathematical ...reasoning is challenging.•Phenomenographic analysis and development of outcome space (OS) is explained.•OS demonstrates range of teachers’ perceptions of mathematical reasoning.•OS provides framework for track development of mathematical reasoning.
Mathematical reasoning has been emphasised as one of the key proficiencies for mathematics in the Australian curriculum since 2011 and in the Canadian curriculum since 2007. This study explores primary teachers’ perceptions of mathematical reasoning at a time of further curriculum change. Twenty-four primary teachers from Canada and Australia were interviewed after engagement in the first stage of the Mathematical Reasoning Professional Learning Program incorporating demonstration lessons focused on reasoning conducted in their schools. Phenomenographic analysis of interview transcripts exploring variation in the perceptions of mathematical reasoning held by these teachers revealed seven categories of description based on four dimensions of variation. The categories delineate the different perceptions of mathematical reasoning expressed by the participants of this study. The resulting outcome space establishes a framework that facilitates tracking of growth in primary teachers’ awareness of aspects of mathematical reasoning.
Soñar… ¿te da alas? González Martín, Alba
Pensamiento matemático,
2021, Letnik:
11, Številka:
1
Journal Article
Odprti dostop
This paper shows one of the tales presented to the contest about tales with mathematical content organized by the Innovation Educative Group “Mathematical Thinking”. In this case it is a tale writen ...by a high school student.
En este artículo se muestra uno de los cuentos presentados al concurso de relatos con contenido matemático organizado por el GIE (Grupo de Innovación Educativa) Pensamiento Matemático de la UPM (Universidad Politécnica de Madrid), para alumnos de la ESO, Bachillerato y universitarios. En este caso se trata de un cueto realizado por una alumna de bachillerato.
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