Digital Games for Teaching and Learning of Mathematics in Nigeria Schools

Fractions are among some concepts in mathematics that pupils in Nigeria primary find difficult to learn, and teachers find difficult to teach. These problems require solutions because mathematics knowledge is germane for technological advancement and national development. Pupils need to be actively involved in constructing their knowledge and digital mathematics learning games could be helpful. Thus, this study investigated the effects of digital mathematics games on primary pupils' achievement in fractions concepts. An appropriately validated pupil fractions achievement test (PFAT) was used to collect data for the study. Data collected were analyzed using t-test. It was revealed that pupils exposed to digital mathematics games performed significantly better than those exposed to conventional method. There is significant difference between achievements of male and female pupils exposed to game-based strategy.

Saberes matemáticos na orientação de professores paranaenses: expertises e contribuições (1970-1980)

A pesquisa aqui apresentada, de caráter investigativo, aponta evidências presentes em documentos produzidos por professores paranaenses para responder a uma demanda de pesquisa manifesta das décadas de 1970 e 1980: como se apresentaram os saberes para ensinar matemática nas orientações para os professores do ensino de 1º Grau no estado do Paraná? Procurou-se responder à essa questão tomando por base a teoria e metodologia da história cultural, a leitura e análise de documentos como a Lei de Diretrizes e Bases da Educação (1971), o Projeto HAPRONT (modelo curricular de formação de professores), “Revista Currículo” (PARANÁ, 1977; 1978; 1979) da SEC do PR, e a “Revista A voz da Escola” (PARANÁ, 1981) do IEP. A organização e abordagem das propostas educativas que fizeram parte do contexto de produção de manuais didáticos para a orientação de formação, tanto inicial quanto continuada de professores, tiveram a participação de educadores cuja expertise associou os saberes para ensinar às teorias educacionais e métodos de ensino em voga na educação brasileira, traduzindo as expectativas para o período em questão. A fundamentação teórico-metodológica da história cultural nas teorias de Julia, Chervel e Chartier deram sustento às argumentações aqui expostas.Mathematical knowledge in the teacher’s orientation of Paraná: expertises and contributions (1970-1980)The research presented here, of an investigative nature, points to evidence present in documents produced by teachers from Paraná to respond to a clear demand for research from the 1970s and 1980s: how was presented the knowledge for teaching mathematics in the guidelines for teachers of elementary school in the state of Paraná? We sought to answer this question based on the theory and methodology of cultural history, the reading and analysis of documents such as Lei de Diretrizes e Bases da Educação (1971), the HAPRONT Project (curricular model for teacher education), “Curriculum magazine” (1977, 1978, 1979), from Education Secretary of Paraná, and “The voice of the school magazine” (1981) from Educational Institute of Paraná. The organization and approach of educational proposals that were part of the context of the production of textbooks to guide both initial and continuing teacher education had the participation of educators whose expertise associated the knowledge to teach with the educational theories end teaching methods in vogue in Brazilian education translating expectations for the period in question. The theoretical methodological foundation of cultural history in the theories of Julia, Chervel and Chartier supported the arguments presented here.Keywords: Education; Teachers’ training; Mathematics knowledge.

Simulation as a Resource in the Calculus Solving Problem

This article is derived from the research project and developed at School of Computer Sciences of the National Polytechnic Institute of Mexico. The article reports on the problems found among engineering students with respect to their resistance to using different representation registers when solving optimization problems in the Calculus Learning Unit. Use of such registers could help the students to build mathematics knowledge and to solve calculus problems. As a didactic strategy, simulations are used in an electronic environment in order to support the students by fostering their use of tabular, graphical and algebraic representation registers. Interviews are undertaken of six of the professors who gave the calculus courses, and a diagnostic questionnaire was applied to 68 students prior to and after working with the proposal. As for the theoretical framework, the work reported by Duval and Hitt is salient in this report, particularly their emphasis of the fact that working on activities by way of one single representation system is not sufficient. From the first responses provided by the students, one can conclude that the algebraic register is preferred by the majority of students. It is however used in a mechanical fashion without affording any meaning to the content of the problem and to the process of solving it. Another conclusion reported is that implementing tasks in the classroom in which the mathematics activity requires coherent use of different representations is necessary

Professional Teachers using Technological Pedagogical Mathematics Knowledge, are Mathematics Pre-Service Teachers Ready?

In today’s information age, the informatization of education requires teachers to become a new type of teacher with information capabilities. The subject teaching knowledge of integrated technology is the knowledge basis for the professionalization of teachers in the information age. This research aims to analyze Pre-service teachers’ perception of Technological, Pedagogical, and Mathematical knowledge. This research adopts the case study method, using Questionnaires for data collection tools. The sample of this research is 84 pre-service teachers from Guangxi Normal University, China. The respondents are undergraduate and master students that are chosen randomly. The instrument used is 20 questionnaire items on pre-service teachers’ perception of their TPMK ability. The data was processed by using SPSS and Microsoft Excel. The research result shows that pre-service teachers have a good Technological Pedagogical Mathematical Knowledge ability but their Technological knowledge is still lacking. Teacher education programs should provide pre-service teachers with opportunities to develop TPMK to integrate technology into teaching effectively.

Enhanced Language Model with Hybrid Knowledge Graph for Mathematical Topic Prediction

Understanding mathematical topics is important for both educators and students to capture latent concepts of questions, evaluate study performance, and recommend content in online learning systems. Compared to traditional text classification, mathematical topic classification has several main challenges: (1) the length of mathematical questions is relatively short; (2) there are various representations of the same mathematical concept(i.e., calculations and application); (3) the content of question is complex including algebra, geometry, and calculus. In order to overcome these problems, we propose a framework that combines content tokens and mathematical knowledge concepts in whole procedures. We embed entities from mathematics knowledge graphs, integrate entities into tokens in a masked language model, set up semantic similarity-based tasks for next-sentence prediction, and fuse knowledge vectors and token vectors during the fine-tuning procedure. We also build a Chinese mathematical topic prediction dataset consisting of more than 70,000 mathematical questions with topics. Our experiments using real data demonstrate that our knowledge graph-based mathematical topic prediction model outperforms other state-of-the-art methods.

Teachers’ Mathematics Knowledge for Teaching Early Algebra: A Systematic Review from the MKT Perspective

The mathematical knowledge for teaching (MKT) model emerged from the advances proposed by Shulman in 1986 and 1987 as part of the teacher’s professional knowledge model, and refers to the mathematical knowledge that the teacher employs to carry out the instruction process in the classroom. MKT has become an international benchmark for research into mathematics education and boasts a great scope and impact to date. The objective of this study is to conduct a systematic review of the way in which the MKT of early algebra teachers has been conceptualized and empirically studied in the scientific literature from 2010 to 2021. A systematic search in the Web of Science and Scopus databases led to a review of 17 papers. The results show great advances in the conceptualization of mathematical knowledge for teaching early algebra, focusing mainly on primary education teachers and on specialized knowledge of the content. In turn, there is a predominance of studies that address functional thinking as a content area. We conclude that more empirical studies are needed that address the mathematical knowledge that childhood and primary education teachers have of early algebra.

Inferential Reasoning of Secondary School Mathematics Teachers on the Chi-Square Statistic

Statistics education has investigated how to promote formal inferential reasoning from informal inferential reasoning. Nevertheless, there is still a need for proposals that explore and progressively develop inferential reasoning of students and teachers. Concerning this, the objective of this article is to characterize the inferential reasoning that secondary school mathematics teachers show in the practices that they develop to solve problems regarding the Chi-square statistic. To achieve this, we use theoretical and methodological notions introduced by the onto-semiotic approach of mathematics knowledge and instruction. In particular, we have taken a theoretical proposal of levels of inferential reasoning for the Chi-square statistic. Based on the results, the main conclusion was that the proposal above effectively predicted the teachers’ practices, allowing us to distinguish characteristic elements of the levels of inferential reasoning.

An Exploration into Teachers’ Technological Mathematics Knowledge: Changling Xiwang Elementary School as A Case Study

The role of teachers in educational institutions in this era must at least know the duties of teachers as professional educators, namely educating, teaching, guiding, directing, training, assessing, and evaluating students in early childhood education. The main purpose of this study is to find out how the teacher's ability to explore technological mathematical knowledge is in teaching mathematics in the classroom. The research paradigm adopted in this study is qualitative research. The main sample in this study were 24 teachers who teach at Changling Xiwang Elementary School. This research was carried out from March to May of the 2020/2021 academic year. The results showed that the teacher's perception of technological abilities in teaching technology-based mathematics, the ability of mathematics teachers to teach mathematics, and the ability of technology-assisted mathematics teachers to teach mathematics in class were categorized as good. These results indicate that most of the teacher's abilities are classified as good about using technology in teaching mathematics. The research suggests furthering researchers to be able to develop technology-based learning media, especially in the field of mathematics in teaching mathematics material in the classroom. Teachers in this century are advised to keep up with the times that are filled with facilities based on information and communication technology (ICT).