Mathematics Teaching Research Articles

Experience With Breakout for Collaborative Learning and Assessment in Higher Education

Aim: The aim of this study is to verify empirically that the combination of ICT and game-based teaching for teaching and assessment of mathematics at university level allows students to obtain meaningful learning that favours performance in the subjects of mathematics and statistics. Theoretical framework: The main concepts and theories underpinning the research are presented, thus providing a solid basis for contextualising and gaining a better understanding of the research. Method: The methodology adopted for this research comprises on the one hand a systematic review of the literature. Quantitative data were collected from experience with students in the fields of Economics and Engineering in quantitative and technical subjects. Results and Discussion: The results obtained revealed that the students who carried out this experience performed better than those who did not. Therefore, focusing the activity as a game using different ICT tools (specifically, GeoGebra), allows us to change the classroom routine and, in a secondary way, to check the skills and competence level of each student in the use of technology and the subject itself. Likewise, in order to be able to base the decisions taken to formulate the evaluation activity, we have indicated the precedents in the literature that have been taken into consideration. Implications of the research: These implications could cover all areas related to education and especially higher education, as it is not usual to use gamification at university levels, although on the other hand, it is more usual to use ICT. Originality/Value: The implementation of an evaluative activity based on gamification and specifically on escape games (specifically a breakout) is not common in the field of university teaching in mathematics. This type of disruptive activities with the usual routine in the classroom not only favours meaningful learning, but also the motivation and interest of students before new situations. Therefore, there is a clear need to generate new projects that break the educational monotony in which students currently find themselves so that they can also learn social competences with their peers that facilitate their incorporation as citizens into society, promoting a better and sustainable world.

Exploring innovative interconnection between Project Based Teaching in Mathematics and CLIL

Exploring innovative interconnection between Project Based Teaching in Mathematics and CLIL

Delving into the Critical Thinking Skills of Pre-Service Mathematics Teachers with Their Metacognitive Awareness

Metacognitive awareness (MA) and critical thinking (CT) are crucial higher-order thinking skills in mathematics education. MA and CT skills of pre-service teachers are considered important predictors of their future teaching practices in the teaching and learning of mathematics. In this context, the study examines the potential effects of socio-demographic (e.g., gender) and academic variables (e.g., academic year and academic achievement) on MA and CT skills of pre-service mathematics teachers (PSTs). Additionally, the aim of this study is to explore the relationship between the MA and CT skills of PSTs. Employing a quantitative research methodology, the study was structured around a correlational model. It involved 218 PSTs, using the “MA Inventory” and “CT Standards Scale” for data collection. The data were analyzed through independent sample t-test, one-way analysis of variance, correlation analysis, and simple linear regression analysis. The findings indicate that PSTs possess a high level of MA and CT skills. Significant differences in MAs of PSTs were observed with respect to academic year and academic achievement, while the CT skills of PSTs showed significant differences concerning gender and academic achievement. A strong, positive, and significant correlation was found between MA and CT skills of PSTs. Furthermore, the MAs of PSTs were identified as a significant predictor of their CT skills, explaining 38% of the variance in CT skills.

Analysis of Gender Issues in Computational Thinking Approach in Science and Mathematics Learning in Higher Education

In the contemporary era, Computational Thinking has emerged as a crucial skill for individuals to possess in order to thrive in the 21st century. In this context, there is a need to develop a methodology for cultivating these skills within a science and mathematics content education framework, particularly among pre-service teachers. This study aimed to investigate the impact of Educational Robotics on the development of Computational Thinking skills, with a particular focus on the role of gender, through a scientific and mathematical content teaching approach. A pre-experimental design with a quantitative approach was employed, and it was implemented with a total of 116 pre-service teachers, 38 males and 78 females. The results demonstrated a notable enhancement between the pre-test (8.11) and post-test (9.63) scores, emphasising specific concepts such as simple functions, while, and compound conditional. With respect to gender, statistically significant differences were identified prior to the intervention, but not following its implementation. The high level of Computational Thinking exhibited by both genders was comparable (53.85% in females and 55.26% in males) following the intervention. This indicates that the intervention is a promising approach for enhancing Computational Thinking proficiency, independent of gender and initial proficiency levels. The implementation of Educational Robotics in the teaching of science and mathematics enables the enhancement of Computational Thinking abilities among pre-service teachers, while reducing the observed gender disparity in this area of skill development.

A Systematic Literature Review on ICT Integration: Opportunities and Challenges in Teaching Mathematics

Integrating information and communication technology in modern education is very instrumental in changing the way mathematics is taught and learned. Research in the Philippines explores how ICT is integrated into the country's teaching of math, outlining opportunities and challenges for Filipino teachers and students. This study used a systematic literature review with the aid of the PRISMA framework. A total of 22,800 scholarly articles in Google Scholar was reduced to 994 after title and keyword screening. After the final analysis, 12 articles met all criteria. Literature review shows that integrating ICT into math education offers an incredible number of benefits such as increased student engagement, new pedagogies, improved classroom management, flexibility in learning and teaching, and enhanced assessment. ICT improves contact between teachers and students as it creates possibilities for computer-supported collaborative learning using tools such as virtual manipulatives and simulations to deepen understanding of skills referred to as higher-order thinking. Several challenges still exist despite the benefits. Most schools lack proper ICT infrastructure: reliable internet and enough devices. The budget makes it hard to acquire equipment or relevant software needed for such instruction. Some teachers are not confident and need training in using ICT, and technical support is not adequate. These will only lead to uneven use of ICT in classrooms, hence limiting the possible impact on mathematics teaching. Infrastructural improvements, funds, and training of teachers, when coupled with technical support, might propel more efficient integration of ICT in math instructions within Philippine education. These will build vibrant learning environments that pave the way for learners toward success in a world increasingly dominated by digital technology.

On mathematics education for women in Russia prior to 1917

This paper attempts to describe women’s mathematics education in certain types of educational institutions in Russia before 1917. The history of women’s education (inclusive of the humanities) begins effectively in the eighteenth century. This education was inevitably limited, since the role assigned to women did not imply any special study of mathematics – mathematics was needed primarily for maintaining the household. To be sure, to this was also added the problem of intellectual development, which sometimes led to girls being taught geometry, and even algebra, although this did not happen often. At the same time, women’s mathematical talents could be valued quite highly. Gradually, the situation changed, and already in the twentieth century the opinion that women’s mathematics education should not differ from men’s was very widely expressed. This paper analyzes various views expressed in surviving documents, as well as textbooks written for girls, and memoirs that make it possible to imagine to a certain degree how exactly the teaching of mathematics at women’s educational institutions was implemented and perceived.

Arguing for Access: Teachers’ Perspectives on the Use of Argumentation in Elementary Mathematics

This study investigates teachers’ perspectives on the use of a mathematical argumentation teaching strategy in elementary mathematics in which students disprove mathematical statements they already know to be false. Mathematical argumentation is a process through which students develop an argument about a mathematical concept and rationalize its truth or untruth through mathematical reasoning but is if often underused in mathematics. In this study we focused on a argumentation tasks which involved providing students with number statements which they already knew to be false, and inviting them to argue, using visuals, numeric notation, and/or written explanations, why it was false. Through practical action research, seven teachers from two different schools implemented this approach in their mathematics programs to one hundred and thirty-one students over the course of five months. Findings indicate this approach was easy to implement, improved student engagement, supported learners who struggled and deepened students’ mathematical knowledge. We believe that this approach can be used as a precursor to more formal proofs and provide more access for teachers and students in exploring mathematical proofs in elementary classrooms.

The Impact of Introducing Scientific Calculators to Junior High School Graduates on Their Academic Performance in Mathematics

Scientific calculators are commonly and widely used tools in senior high schools, offering students the ability to perform mathematical calculations faster and more efficiently. This study aimed to investigate the Impact of Scientific Calculators usage on Junior High School graduates Performance in Mathematics. The study was purely quantitative hence data was collected through survey questionnaires and a mathematics achievement test. The study's accessible population size and sample size consisted of 280 and 162 respectively. The sample of 162 students was selected using a systematic random sampling method. Data collected were analysed using descriptive statistics, a simple linear regression model, and a paired sample t-test. The study found a significant difference in students' test scores before and after the use of scientific calculators, t (162) = 17.199, p < .001, leading to a rejection of the null hypothesis. Additionally, a significant correlation was found between calculator usage and students' achievement test scores, F (162) = 24.614; p < .001. Based on these findings, the study recommended that the Ghana Education Service consider allowing and granting permission to schools to incorporate the use of scientific calculators into the teaching and learning of mathematics at the junior high level. This would enhance students' mathematics learning and academic performance. Furthermore, teachers at the senior high school level should introduce enrolled junior high school graduates in Form One to the proper and efficient use of scientific calculators. Students should be taught how to use calculators to solve simple mathematical questions, which would facilitate effective teaching and learning of mathematics

Model of Bilingual Mathematics Teaching at a Technical University

The article highlights issues related to the implementation of bilingual education in Ukrainian technical universities. The study of this problem contributes to the training of engineering specialists who are able to carry out professional activities in the conditions of a foreign-language multicultural environment. The model and levels of implementation of bilingual higher mathematics teaching/learning for students of engineering and technical specialties is considered. It is noted that the system of bilingual education should be integrated into the general model of the organization of training engineering personnel in a specific specialty. The formation of a certain level of students' foreign language communicative competence is considered as a criterion for the allocation of training stages. The following stages of bilingual mathematics teaching/learning in technical university are distinguished: preparatory, transitional, actual bilingual. Each stage of bilingual teaching/learning is analyzed in detail from the following points: 1) direction of content (socio-cultural, mathematical, scientific), main unit of content (bilingual didactic element, bilingual subject-thematic module, discipline in a foreign language); 2) organizational forms and methods of training (integrated lectures and practical classes; conversation; project activity; information technologies; traditional, developing learning methods; elective course, special course or optional classes; text information activity; solving language tasks; methods of active learning; soft immersion; problem-based learning, independent work with educational and scientific literature); 3) the ratio of native and foreign languages (duplicative model, additive model, parity model and displacing model). The designed model of bilingual mathematics teaching/learning ensures the formation of bilingual subject competence in mathematics and provides an interdisciplinary synthesis of subject, linguistic, general technical (engineering) and cultural components.

Pedagogical responsiveness of mathematics instruction at inclusive secondary schools: A particularistic case study

This qualitative particularistic case study explores the perspectives and experiences of learners with visual and hearing impairments regarding the teaching of mathematics. Extreme-case sampling was employed to select four learners (three hearing impaired and one visually impaired) from the only two inclusive secondary schools in the northern part of Namibia. The study qualitative study utilised open-ended questionnaires and interviews. Verbatim quotes from the research participants were used as inferences to identify descriptors within the first-generation Cultural Historical Activity Theory, which served as a theoretical and analytical tool. The findings revealed that the activity system of learners with visual and hearing impairments exhibited tensions that negatively affected their performance in mathematics. Learners experienced marginal responsive pedagogy in mathematics classrooms due to teachers' lack of knowledge and pedagogical skills for delivering meaningful mathematical instruction. While learners without disabilities struggled with comprehension and effective communication skills, learners with visual and hearing impairments faced a lack of equipment to support the conceptualisation and visualisation of mathematical subject content. The authors emphasise the critical importance of addressing communication barriers and adapting teaching practices to support the learning and inclusion of visually and hearing-impaired learners in mathematics, with an emphasis on mathematical language that promotes a better understanding of mathematical concepts. Teacher training should also incorporate responsive pedagogy to enhance outcomes and foster a more inclusive learning environment that promotes academic success and positive social experiences for all learners. Recommendations at a policy level, including advocating for a decolonised curriculum were made.

Pedagogical responsiveness: Focus on the Ukuqonda institute’s mode of engagement in mathematics

This paper was prompted by mathematics teachers’ challenges in implementing the proposed framework that centres on teaching for understanding, as opposed to teaching aimed at producing marks as evidence of achievement. Teaching for understanding in mathematics, among other factors, requires the creation of engaging and inclusive learning environments underpinned by teachers’ pedagogical responsiveness to the diverse needs of learners. We investigated pedagogical responsiveness, focusing on the Ukuqonda Institute’s mode of engagement in mathematics. We specifically pursued two research questions: 1) What are the key elements of the Ukuqonda Institute’s mode of engagement in mathematics? and 2) What characterised the pedagogical responsiveness of mathematics educators at the Ukuqonda Institute? We adopted collaborative autoethnography and used two data sets generated from audio recordings captured by the authors. We employed narrative analysis and organised the findings using the characteristics of pedagogical responsiveness as heuristic devices. The findings show that the participants’ pedagogical responsiveness was stimulated by the iterative process of team planning, deliberate implementation, and reflection. The prevalent characteristics were learner interactions, learner focus, inclusivity, dialogue and relationality, knowledge work, social justice, and equity. We recommend that similar studies be conducted targeting pedagogical responsiveness with a focus on other mathematical themes. Furthermore, this study suggests that, to remain pedagogically responsive, there should be constructive alignment among the types of tasks, questions, classroom interactions, and targeted content that underpin mathematics teaching and learning across different educational levels.

Pedagogical and Social Transformations in Post-Apartheid Mathematics Education

This special issue addresses the complexities of mathematics teaching and learning in post-apartheid South Africa by exploring themes such as pedagogical reasoning, decoloniality, rural education challenges, and teacher preparation. It contributes to the ongoing dialogue on mathematics education's role in social transformation, enhancing the body of knowledge and deepening practitioners' understanding of its impact.

Enhanced GDM Algorithms for College Mathematics Teaching Quality Evaluation Under Interval-Valued Intuitionistic Fuzzy Sets

The college mathematics teaching quality evaluation is the multiple-attribute group decision-making (MAGDM). Currently, the Exponential TODIM (ExpTODIM) and MABAC was executed to put forward MAGDM. The interval-valued intuitionistic fuzzy sets (IVIFSs) are executed for portraying fuzzy data during the college mathematics teaching quality evaluation. In this study, the interval-valued intuitionistic fuzzy number ExpTODIM-MABAC (IVIFN-ExpTODIM-MABAC) approach is put forward the MAGDM with IVIFSs. At last, numerical example for college mathematics teaching quality evaluation is executed to verify the IVIFN-ExpTODIM-MABAC. The major contributions are executed: (1) the ExpTODIM-MABAC based was extended to IVIFSs along with Entropy model; (2) the entropy is employed to execute the weight under IVIFSs. (3) the IVIFN-ExpTODIM-MABAC approach is put forward MAGDM with IVIFSs; (4) numerical example for college mathematics teaching quality evaluation and comparative analysis is executed to proof the IVIFN-ExpTODIM-MABAC approach.

Educational robotics for science and mathematics teaching: Analysis of pre-service teachers' perceptions and self-confidence

Educational Robotics has had an important impact in recent years as it offers a number of advantages for students. The inclusion of robotics in any educational stage requires teachers with adequate predisposition and training, making it necessary to know the opinions of pre-service teachers. The aim of our study is to analyze the perceptions and self-confidence of 109 pre-service primary education teachers before and after an intervention based on educational robotics and challenge-based learning to teach scientific and mathematical content, in their third academic year. A quasi-experimental design was used involving pretest and posttest, using the nonparametric Mann-Whitney and Wilcoxon U tests. The results showed a significant improvement in the overall mean self-confidence. In addition, the intervention led to a more positive perception of the benefits and possibilities of robotics for teaching of scientific and mathematical content, although it also increased the difficulties of implementation due to the lack of training in this digital resource. It is concluded that interventions are required based on educational robotics that allow pre-service teachers to gain the necessary self-confidence and perception to facilitate its introduction for the teaching of scientific and mathematical content.

Investigation on the Present Situation of Mathematics Large Unit Teaching in Middle Schools in Anyang and Its Improvement Countermeasures

Under the background of educational reform, large-unit teaching strategy is of great significance to improve the quality of middle school mathematics teaching and promote students' deep learning. Based on the integration of pedagogy theory and practice, this paper deeply analyzes the challenges and opportunities faced by middle school mathematics teachers in Anyang when implementing large-unit teaching strategies, and puts forward targeted professional development strategies for teachers at different stages, such as rookie, backbone and senior. At the same time, this paper also discusses how to combine teachers' internal motivation and external support to build an effective strategy system. These research results not only provide concrete guidance for middle school mathematics teachers to implement large-unit teaching strategies, but also provide in-depth insights and references for educators to promote the sustainable development and innovation of middle school mathematics education.

Validation of the SISRE-P Software for Teaching Reflection in Mathematical Didactics using the DELPHI Method

This research addresses the use of software in the mathematics education process, which has been growing in popularity and has proven to be a valuable tool to improve teaching and learning. The study aimed to validate the SISRE-P software in the teaching of mathematics, with the purpose of reducing the gap between theory and educational practice, and improving pedagogical practice. From the methodological point of view, a qualitative, cross-sectional and descriptive study was carried out, using the Delphi method for the validation of the instrument, which was applied to 36 teachers. For its development, a questionnaire was applied in the form of interviews, which were sent through Google Forms, through the process, they were analyzed to evaluate the effectiveness of SISRE-P. Within the results obtained, it is observed that the implementation of the SISRE-P software demonstrates its effectiveness to improve teaching practice in mathematics teaching. Recurrent participation in weekly reflective sessions, both in pedagogical pairs and with colleagues or individually, has strengthened the reflective process through methods such as class recording, collaborative conversations and records in field diaries. It is concluded that SISRE-P is an effective tool to enhance teaching practice in the teaching of mathematics. Its constant use in reflective sessions strengthens the process of teacher self-reflection and is fundamental within the constructivist pedagogical framework, focused on student autonomy and the active construction of knowledge.

Teachers’ Perceptions towards Practical Instruction Approach in Teaching Mathematics: A case of Selected Teachers in Ugandan Secondary Schools

Globally, there is a need to address learners' academic achievement, which has historically been poor, particularly in underdeveloped countries. Practical instruction (PI) approach has been perceived by many teachers as a better teaching strategy. Students in Ugandan secondary schools have consistently performed poorly in their O'Level national mathematics examinations. This has been attributed to teachers' failure to teach these students with practical approach in some examinable topics, making the subject very abstract to candidates. This qualitative case study analyzed teachers' perceptions of the practical instruction approach to teaching mathematics and its impact on students' academic achievement in mathematics. Sixteen teachers from chosen secondary schools in Kigezi and Ankole regions were interviewed for the study in order to understand more about their opinions on the value and use of practical instruction in the teaching and learning of mathematics. The data gathered were analyzed using thematic analysis. The study showed that teachers regard PI as one of the best teaching methodologies since it incorporates components that help improve students' creativity and critical thinking. The study also indicated that teachers' perceptions of practical instruction approaches for teaching mathematics are diverse and influenced by a variety of circumstances. Creating supportive settings, offering professional development opportunities, and providing access to resources can assist teachers in effectively incorporating practical instruction methodologies into their teaching practice, resulting in improved student learning outcomes in mathematics. It is recommended that teachers should be well prepared before commencing the teaching and learning process, including all PI components.

Harnessing Asynchronous Digital Simulations of Problem-based Lessons to Support Mathematics Teachers’ Professional Development: A Design-based Approach

AbstractThe complexity of mathematics teaching is especially evident in lessons where teachers build on students’ genuine ideas, such as problem-based lessons. To enhance teachers’ capacity for rich discussions in problem-based instruction, we have developed a unique approximation of practice: digital asynchronous simulations where teachers make subject-specific decisions for a virtual teacher avatar. The simulations are based on materials and principles from a practice-based professional development (PD) program, implemented with small groups of teachers. The self-paced simulation model offers flexibility and scalability, allowing more teachers to participate on their own schedules, but it lacks key affordances of collaborative PD. To examine how to leverage the affordances of collaborative, practice-based PD, this paper uses a design-based research approach to explicate the mechanisms in which digital simulations can support mathematics teachers’ learning about problem-based lessons. We focus on two cycles of design, implementation, analysis, and revisions of the simulation model, drawing on data from focus groups with mathematics teacher educators, prospective teachers’ performance, and teachers’ reflective assignments. The analysis illustrates how two design principles – Authenticity to the teacher’s work, and Nuanced feedback – were transformed to better reflect aspects of practice-based teacher learning. We argue that self-paced, asynchronous simulations with indirect feedback can effectively emulate aspects of collaborative, practice-based PD in supporting teachers’ growth. The paper also contributes to the literature on mathematics teachers’ noticing and decision-making, examining how the two interact in simulated environments. We suggest implications for designing practice-based asynchronous digital simulations, drawing on emerging technologies.

Vilnius University professor Michał Pełka-Poliński: research of scientific work and book marks

The article examines the books of Vilnius University professor Michał Pełki-Poliński from the collection of the library of St. Volodymyr University, the collection "Library of the Volyn Lyceum", from the collection of literature in Polish of the department of library collections and historical collections of the Institute of Bibliography of the Vernadskyi National Library of Ukraine. The results of the research of Ukrainian, Polish, and Lithuanian researchers, which contain materials about the scientific activity of Michał Pełka-Poliński, are analyzed and his important role in the development of mathematical science in Lithuania and Poland is emphasized, the influence of his works on the teaching of mathematics in educational institutions of Galicia and Volyn. Information about the scientist's scientific work is provided, his scientific connections with Ukraine are noted. Bibliographical information about books authored by Polinsky from the funds of the Vasyl Stefanyk National Scientific Library of Ukraine in Lviv. His printed and handwritten works are indicated, his library work, his bibliophile preferences, and collecting achievements are highlighted. Bibliographical and historical information about books from his private library is provided and infor­mation about its history is presented. Bibliographical materials on the study and attribution of book marks on the books of Michał Pełka-Poliński are represented.

Scaffolding-informed design of open educational resources in Chinese secondary school mathematics: insights from multi-cycle formative evaluation

In the post-pandemic world, open educational resources (OER) have the potential to ensure educational equity by providing all students with access to learning materials and by supporting teachers’ instructional practices through readily available, adaptable resources. However, the quality of OER continues to be a concern. Therefore, this study explored the use of (1) GeoGebra and scaffolding strategies to develop OER for secondary school mathematics teaching and (2) formative evaluation techniques to enhance the quality of the OER. A GeoGebra expert and a total of 40 frontline teachers participated in three review cycles of the OER development in the project. The feedback from each cycle informed the application of scaffolding strategies in the development of OER for the subsequent cycles. In Cycles 2 and 3, teachers rated the OER and provided feedback through surveys for further improvement. The results indicated that teacher ratings were significantly higher in Cycle 3 (n = 40, Mdn = 5) than in the previous cycle (n = 21, Mdn = 4) regarding the appropriateness of the OER for students with different learning preferences, z = − 2.87, p < 0.05. The results of the project-end satisfaction survey further revealed that all of the teacher participants were satisfied with the OER, which also enhanced their teaching practices. The results of the study offer a theoretical foundation that OER developers can ground upon to enhance their OER design. They also provide practical insights into the application of formative evaluation in the OER development that OER developers can adopt to create resources that are finely attuned to the needs of frontline teachers.