Pythagoras is a scholarly research journal that provides a forum for the presentation and critical discussion of current research and developments in mathematics education at both national and international level.

Editorial Office

Pythagoras

Acknowledgement to reviewers

致谢审稿人

Rajendran Govender

A reflection on the use of artificial intelligence tools for the meaningful learning of mathematics

人工智能工具在数学有意义学习中的应用反思

The narrative permeating higher education institutions globally is the intention to advance the quality of preservice mathematics teachers to gain better performance than mathematics school learners. In this article we report on a qualitative case study which explored the pedagogical content knowledge (PCK) of preservice teachers (PST) (n = 20) at a South African university of technology. These preservice teachers were provided with activity sheets with past examination questions in analytical geometry. Their written responses were analysed, and verification interviews were conducted. This was followed by an analysis of the preservice teachers’ lesson plans for teaching the topic to Grade 11 learners. The domains and subdomains of the Shulman’s PCK derived Mathematics Teacher’s Specialised Knowledge (MTSK) model were used as the theoretical framework. The study established that the PSTs had limited content knowledge, and knowledge for teaching analytical geometry at Grade 11 as their responses to the activities confirmed that they mostly had procedural understanding. The study was conducted in a context with multilingual PSTs who are training in multilingual classrooms.Contribution: The study will highlight the misconceptions and existing gaps in the PSTs’ knowledge for teaching analytical geometry in multilingual classrooms.

Sibongile Zulu

Deonarain Brijlall

Exploring preservice teachers’ pedagogical content knowledge for teaching analytical geometry in multilingual classrooms

探究多语课堂中职前教师教授解析几何的学科教学知识

This study explores how pre-service mathematics teachers build alternative model simulations of real-world scenarios. Inclusion in the formal structures for wealth generation and accumulation is a fervently debated issue in South Africa. Share owning in companies listed on the Johannesburg Stock Exchange (JSE) in South Africa is one of many wealth-building tools. Related discussions evolved on the spread of share ownership among black and white citizens. Two mathematically motivated positions were reported in a newspaper. In one of their mathematics courses, prospective mathematics teachers were presented with the article and asked to reflect on it with the prompt 'Which of these two methods for determining the "number of Black South Africans holding shares on the JSE" would your group support?' Audio- and video-recorded data were collected and subjected to thematic analysis. The themes that emerged from the analysis were economic empowerment, authority of research and trustworthiness of information. The discussions reflected on the complexities and rationalities involved in decision-making of mathematically driven opposing positions on issues of social importance. The mathematically derived results of such issues will eventually be resolved in the political field. The findings revealed that building of alternative mathematical models by pre-service mathematics teachers begins with an explicit problem setting, followed by the development of mathematical models that included real-world problems.Contribution: This article contributes to pre-service mathematics teacher education by exploring how such teachers deal with the issue of critical engagement of mathematically based arguments, highlighted in the Curriculum Assessment and Policy Standards (CAPS) document for school mathematics.

Belinda Cornelissen

Cyril M. Julie

Pre-service mathematics teachers’ perceptions based on two differing mathematically underpinned debates

职前数学教师基于两种不同数学支撑辩论的认知

Mathematics achievement is core to South Africa’s readiness for digital innovation, yet current pass rates in this subject are below the global average. Simply attributing mathematics performance to intelligence does not fully account for the multifaceted reality of achievement in the subject. The current study investigated the value of both cognitive and behavioural factors in predicting mathematics performance, as well as explored the interactions between these factors. A quantitative, cross-sectional design was employed. Grade 9 learners (N = 187) completed the Ravens’ Standard Progressive Matrices and the Study Orientation towards Mathematics assessments to establish their fluid intelligence, study attitude, mathematics anxiety, study habits, problem-solving behaviours and study milieu. Pearson correlation coefficients established the relationships between fluid intelligence, study orientations towards mathematics, and mathematics marks. These factors were also included in a linear regression and dominance analysis to compare their relative weights in influencing mathematics performance. Study attitude and fluid intelligence were found to be the most dominant, significant factors in the model, which explained 39% of the total variance (R2 = 0.390, F(6, 180), = 19.2, p 0.001). Moderator regressions between fluid intelligence and each of the study orientations further found that fluid intelligence and study orientations, with the exception of study milieu, independently influence mathematics performance.Contribution: This study proposes that educators and parents should support curriculum change that encourages positive attitudes towards mathematics and create supportive environments conducive to effective learning, rather than blaming a lack of cognitive potential for the disappointing mathematics pass rate.

Pakeezah Rajab

Benny Motileng

The predictive value of study orientations on mathematics performance in South African Grade 9 learners

南非九年级学生数学成绩的研究取向预测价值

The teaching and learning of mathematics in sub-Saharan African countries is dominated by teacher-centred pedagogies rather than student-centred ones. Observations of mathematics teachers at two private schools in South Sudan confirmed such practices. This inspired the researchers to design an intervention to help six primary mathematics teachers shift their practices through problem-solving and mathematical discourse. Design-based research methods were implemented, and data were gathered using observations supported by video and audio recordings and field notes. The participants were selected using convenience sampling, and the data were analysed using Stephan’s checklist of student-centred teaching as a framework. The findings revealed that initially, teachers were using tasks from textbooks, and the teachers themselves were engaged in solving the tasks while their students reproduced their actions. Additionally, all the teachers dominated classroom discussions. After the intervention, the teachers began to select tasks that could enhance learning through problem-solving and mathematical discourse among the students, shifting the teacher’s role to facilitation as the students engaged in solving the tasks on their own. However, the shift in practice was highly dependent on the intervention, as the teachers’ tasks were adopted from the workshop.Contribution: This study contributes to the literature on student-centred mathematics teaching in sub-Saharan Africa by providing insights into the factors that enable or hinder teachers’ adoption of student-centred approaches, and by suggesting ways to support teachers’ professional development and learning within their own contexts.

Oduho G.B Soforon

Svein A. Sikko

Solomon A. Tesfamicael

Engaging primary mathematics teachers in two private schools in South Sudan: A case study on student-centred teaching in problem-solving and mathematical discourse

南苏丹两所私立小学数学教师参与情况：以学生为中心的教学在问题解决和数学交流中的个案研究

In this article, we explored Grade 11 learners’ algebraic and geometric connections when solving Euclidean geometry riders. A qualitative interpretive case study design was followed. Thirty Grade 11 learners from a non-fee-paying secondary school in the Capricorn North district of South Africa were conveniently sampled to participate in this study. Data were collected through learners’ responses to classwork, homework exercises, and task-based interviews. Data were analysed thematically. The findings revealed that to solve Euclidean geometry riders successfully, learners need to establish the feature connections embedded in the given figure or diagram. The ability to make feature connections provides a point of departure in the solution process of a geometric problem.Contribution: Once the feature connection is established, other connections will subsequently emerge. In addition, the reversibility connections become a form of feature connection when solving Euclidean geometry riders. Therefore, we recommend that mathematics teachers emphasise and use mathematical connections in their daily teaching of mathematics.

Hans Bila

Kgaladi Maphutha

Paul Mutodi

Learners’ algebraic and geometric connections when solving Euclidean geometry riders

学习者在解决欧几里得几何问题时的代数与几何联系

During the pandemic and lockdown situations of the last few years, we transitioned to online, physical, and hybrid education approaches at various times. We had difficulty teaching multiple calculus and analytical geometry units online. In light of the current situation, a graphical user interface (GUI) teaching tool has been developed to teach university students many plane curve modules through a flipped classroom. With a few inputs and a single click as output, these executable spreadsheets can assist physics and mathematics students in practising several principles of analytical geometry. Spreadsheets can readily draw planes in three-dimensional geometry due to their widespread use. Some online vector GUIs present the results; however, this GUI conveniently illustrates the plot. The well-designed user interface also helps create new questions with answer keys and gives access to the teachers of physics and mathematics, which can make online teaching very easy. The effectiveness of this GUI was checked through Kolmogorov-Smirnov and Shapiro-Wilk tests, and a good agreement has been found in the results. Contribution: This article contributes to Mathematics teaching through GUIs.

Atteeq Razzak

A graphical user interface tool to teach plane curves in pandemic situations through a flipped classroom

通过翻转课堂在疫情期间教授平面曲线的图形用户界面工具

Mathomo M. Moila

Ephraim Mhlanga

Teachers’ competence in the use of technology in teaching and learning mathematics in two rural schools

两所农村学校教师在数学教学中运用技术的能力

Table of Contents Vol 44, No 1 (2023)

目录 第44卷, 第1期 (2023年)

Pythagoras is a scholarly research journal that provides a forum for the presentation and critical discussion of current research and developments in mathematics education at both national and international level. Pythagoras publishes articles that significantly contribute to our understanding of mathematics teaching, learning and curriculum studies, including reports of research (experiments, case studies, surveys, philosophical and historical studies, etc.), critical analyses of school mathematics curricular and teacher development initiatives, literature reviews, theoretical analyses, exposition of mathematical thinking (mathematical practices) and commentaries on issues relating to the teaching and learning of mathematics at all levels of education.

Pythagoras is a scholarly research journal that serves as a platform for presenting and critically discussing current research and developments in mathematics education at both national and international levels. Pythagoras publishes articles that significantly enhance our understanding of mathematics teaching, learning, and curriculum studies. This includes research reports (experiments, case studies, surveys, philosophical and historical studies, etc.), critical analyses of school mathematics curricula and teacher development initiatives, literature reviews, theoretical analyses, expositions of mathematical thinking (mathematical practices), and commentaries on issues related to the teaching and learning of mathematics at all levels of education.

《Pythagoras》是一本学术研究期刊，旨在提供一个平台，以展示和深入讨论当前在数学教育领域的研究和发展，涵盖国内外的相关内容。《Pythagoras》发表的文章显著推动了我们对数学教学、学习和课程研究的理解，包括研究报告（实验、案例研究、调查、哲学和历史研究等）、对学校数学课程和教师发展计划的批判性分析、文献综述、理论分析、数学思维的阐述（数学实践）以及关于各级教育中数学教学与学习相关问题的评论。

Journals	Pythagoras
ISSN	1012-2346, 2223-7895
h-index	12
Journal Impact	0.44
Quartiles(Global)	EDUCATION, SCIENTIFIC DISCIPLINES(Q4)