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。

Pythagoras

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

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

Acknowledgement to reviewers

致谢审稿人

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

Concerns have been expressed that although learners may solve linear equations correctly they cannot draw on mathematically valid resources to explain their solutions or use their strategies in unfamiliar situations. This article provides a detailed qualitative analysis of the thinking of 15 Grade 8 and Grade 9 learners as they talk about their solutions to linear equations in interviews. The article stems from a study that describes whether learners use mathematically endorsable narratives to explain and justify their solutions. Sfard's theory of commognition is used to develop a framework for analysis of their discourse. The findings show that all learners use ritualised rather than explorative discourse, characterised by applying strict rules to operations with disobjectified entities. The only mathematical objects they produce endorsed narratives about are positive integers. Thus they do not meet the relevant curriculum requirements. Nevertheless, the analytic tools – adapted from Sfard specifically for the study of linear equations – give a particularly nuanced account of differences in the learners' ritualised discourse. For example, some learners used endorsed narratives about negative integers, algebraic terms and the structure of an equation when prompted by the interviewer. There is not sufficient evidence to suggest that any learners are in transition to explorative discourse. However, the article shows that learner discourse is a rich resource for teachers to understand the extent to which learners are thinking exploratively, and offers suggestions for how their thinking can be shifted. This is an opportunity for teacher professional development and further research.

Anthea Roberts

Kate le Roux

A commognitive perspective on Grade 8 and Grade 9 learner thinking about linear equations

八年级和九年级学生关于线性方程思维的共同认知视角

Various efforts are underway to improve achievement in high-stakes examinations in school mathematics. This article reports on one such initiative which focuses on the development of quality teaching of school mathematics by embedding it within an examination-driven emphasis. A quantitative approach was used to analyse the performance of Grade 10 learners in three consecutive end-of-year school-based examinations set by the initiative. Results indicate a trend in a positive direction over the three-year period. Nevertheless, there was a discernible decrease between the first and second administration of the examinations. It is concluded that examination-driven teaching holds a promise for enhancing achievement in high-stakes school mathematics examinations if sensibly and sensitively implemented.

Onyumbe Okitowamba

Cyril Julie

Monde Mbekwa

The effects of examination-driven teaching on mathematics achievement in Grade 10 school-based high-stakes examinations

考试驱动教学对高中10年级校内高风险数学考试成绩的影响

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.

Abbreviation	Pythagoras
Journal Impact	0.44
Quartiles(Global)	EDUCATION, SCIENTIFIC DISCIPLINES(Q4)

ISSN	1012-2346, 2223-7895
h-index	12

Publication Information	Publisher: AOSIS (Pty) Ltd，Publishing cycle: ，Journal Type: journal，Open Access Journals: Yes
Basic data	Year of publication: 2012，Proportion of original research papers: 75.00%，Self Citation Rate:0.00%， Gold OA Rate: 96.77%
Journal Fees	$Details
Average review cycle	网友分享经验：20 Weeks

Pythagoras

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

Acknowledgement to reviewers

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

A commognitive perspective on Grade 8 and Grade 9 learner thinking about linear equations

The effects of examination-driven teaching on mathematics achievement in Grade 10 school-based high-stakes examinations

Acknowledgement to reviewers

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

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

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

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