Teaching Mathematics and Developing Citizenship: How to Use Contexts to Enhance Problem-Based Learning

In his song “Still Crazy after All These Years,” Paul Simon (1974) writes, “I seem to lean on old familiar ways.” Shipley's article “Algebra in the Elementary Schools,” written in 1912, offers the opportunity for us to reflect on what we have accomplished, what we have learned, and what remains hazy even 100 years later with respect to teaching and learning mathematics. Do we still lean on old familiar ways of teaching algebra? This article has many messages that are relevant to us today in thinking about algebra and about teaching and learning mathematics in general. In addition, it raises the following questions: How does Shipley's conception of algebra compare with our conception of it today? What broader issues does he address that are still prevalent today? How far have we come in our implementation of his ideas? What aspects of teaching and learning mathematics in elementary school remain hazy after all these years?

This paper aimed to discuss the meanings, dimensions, and categories of teacher beliefs about teaching and learning mathematics. I reviewed the relevant literature about teacher beliefs in general, beliefs about mathematics, and beliefs about mathematics teaching and learning in particular. Based on the review of the literature, I outlined the meanings of teacher beliefs and conceptualized three dimensions of teacher beliefs – affective dimension, cognitive dimension, and pedagogical dimension. Then, I discussed three viewpoints to observe teacher beliefs – relational, institutional, and praxis lenses. I utilized these lenses to categorize belief constructs into three classes of beliefs about mathematics, teaching mathematics, and learning mathematics. These classes’ included-instrumentalist, constructivist, and integral beliefs. I addressed the pedagogical implications of these categorical beliefs in the end.

Teaching Secondary and Middle School Mathematics combines the latest developments in research, standards, and technology with a vibrant writing style to help teachers prepare for the excitement and challenges of teaching secondary and middle school mathematics today. In the fully revised fifth edition, scholar and mathematics educator Daniel Brahier invites teachers to investigate the nature of the mathematics curriculum and reflect on research-based "best practices" as they define and sharpen their own personal teaching styles. The fifth edition has been updated and expanded with a particular emphasis on the continued impact of the Common Core State Standards for Mathematics and NCTM’s just-released Principles to Actions, as well as increased attention to teaching with technology, classroom management, and differentiated instruction. Features include: A full new Chapter 7 on selection and use of specific tools and technology combined with "Spotlight on Technology" features throughout clearly illustrate the practical aspects of how technology can be used for teaching or professional development. Foundational Chapters 1 and 2 on the practices and principles of mathematics education have been revised to build directly on Common Core State Standards for Mathematics and Principles to Actions, with additional references to both documents throughout all chapters. A new Chapter 4 focuses on the use of standards in writing objectives and organizing lesson plan resources while an updated Chapter 5 details each step of the lesson planning process. A fully revised Chapter 12 provides new information on teaching diverse populations and outlines specific details and suggestions for classroom management for mathematics teachers. Classroom Dialogues" features draws on the author’s 35-year experience as an educator to present real-world teacher-student conversations about specific mathematical problems or ideas "How Would You React?" features prepares future teachers for real-life scenarios by engaging them in common classroom situations and offering tried-and-true solutions. With more than 60 practical, classroom-tested teaching ideas, sample lesson and activities, Teaching Secondary and Middle School Mathematics combines the best of theory and practice to provide clear descriptions of what it takes to be an effective teacher of mathematics.

Recent research has shown the need to present knowledge to students in a manner consistent with the characteristics of the human brain, especially during learning mathematics, which contributes to the development of achievement and inductive reasoning. The current study aimed to develop achievement and inductive reasoning by employing brain-compatible learning theory in teaching and learning mathematics for sixth-grade students in Oman. The sample included (74) students, who were divided into two equal groups: experimental and control. Study data were collected using mathematical achievement tests and inductive reasoning. There were significant differences between the two groups in the post-application of the achievement and inductive reasoning tests in favor of the experimental group, which indicates that teaching mathematics according to the theory of learning compatible with the brain had a significant impact on the development of achievement and inductive reasoning among the participants. The study recommended the need to develop and teach mathematics curricula in a way that allows for the practice of many activities and exercises that contribute to the development of students’ achievement and inductive reasoning skills.

Este artículo hace referencia a la teoría de campos conceptuales de Vergnaud y sus implicaciones en la enseñanza de las matemáticas. Se examinan conceptos fundamentales de dicha teoría a la luz de la enseñanza y aprendizaje de las matemáticas; dando ejemplos concretos en la disciplina y estableciendo relación con otros referentes relacionados, por ejemplo, resolución de problemas de Polya, situaciones didácticas de Brousseau, entre otros.

This chapter explores the integration of technology in teaching mathematics; for example, Dynamic Geometry Software (DGS), for example a Geometrics sketch pad, helps in teaching and learning geometry at different levels of education. During the past quarter of a century, university-level mathematics teaching has encountered new challenges and this is contributing to changes in teaching practices in higher education. On one hand, we have an increase in the university enrolment of those students interested in STEM (Science, Technology, Engineering and Mathematics) and on the other hand college entry-level students who are inherently weak in mathematics. The National Council of Teachers of Mathematics (NCTM) stated: Technology is essential in teaching and learning mathematics; it influences what is taught and enhances students' learning. Integrating technology into the mathematics classroom can increase students' achievement, increase students' motivation and foster students' positive attitude. The positive effects of mathematics and technology instruction such as Computer-Mediated Learning are becoming more prevalent in mathematics courses.

The aim of the study was to find the role of technology in teaching and learning mathematics in public secondary schools of Rwanda. It has three specific objectives: To assess the level of using technology in teaching and learning mathematics in public secondary school in Rwanda, to examine the levels of students learning achievement due to use of Technology in mathematics subject in public secondary school of Rwanda and to analyze the influence of technology on students ‘mathematical academic achievement in mathematics in public secondary schools in Rwanda. This research would benefit the Rwandan government, educational planners, policymakers, teachers, students and future researchers. The study took Quantitative method to collect the data, descriptive research design was used, target population were 854, sample size was 272 which include 4 teachers and 268 students from three secondary schools, Questionnaire was used as the data collection tools. Statistical Package for Social Sciences or SPSS version 21 used to analyze the data, which was then displayed in the form of tables, the findings of my studies Teachers on the level of using technology in teaching and learning mathematics for teachers 25% were strong disagree that the they have not been using technology tools for teaching mathematics at all, 25% were disagree that the I have not been using technology tools for teaching mathematics at all, the students on the levels of students learning achievement due to the use of Technology in mathematics subject, 41% were agree that Technology enhanced student engagement in the learning process in classroom and 53% were strong agree that Technology enhanced student engagement in the learning process in classroom, teachers on the levels of students learning achievement due to the use of Technology in mathematics subject in public secondary school,75% were strong agree that Teachers can effectively integrate technology tools, 50% were agree that Technology into their mathematics instruction to support diverse learners, teachers on the influence of technology on students ‘mathematical academic achievement in mathematics, 75% were strong agree that the integration of technology impact students’ engagement and motivation in learning mathematics, 50% were agree that the accessibility of technology resources both inside and outside the classroom influence students’ proficiency in mathematical concepts and skills and students on the influence of technology on students ‘mathematical academic achievement in mathematics, 23% were agree that the integration of technology impact students’ engagement and motivation in learning mathematics and 55% were strong agree that the integration of technology impact students’ engagement and motivation in learning mathematics, as conclusion teachers and students was used to form a conclusion about how to address the second research questions on What is the levels of students learning achievement due to the use of Technology in mathematics subject ’’it were conclude that the Technology enhanced student engagement in the learning process in classroom and teachers and students was used , Teachers should recognize the transformation potential of technology in enhancing mathematics education and The Ministry recommends providing ongoing professional development for teachers to ensure they are proficient in using technology to enhance mathematics instruction.

This research mapped the scientific productions published in the Proceedings of the National Meeting on Mathematics Education (ENEM) on electronic games for teaching Mathematics in Inclusive Education. The objective was based on the State of Knowledge of Brazilian research in the process of teaching and learning Mathematics for the inclusion of students in need of Specialized Educational Assistance (AEE). The research question was based on the inquiry of which digital games have been used as teaching resources in the process of teaching Mathematics, and their contributions. For data collection, the source of the ENEM annals was used, from 2007 to 2022. The use of Electronic Games as an investigative object was revealed in some researches, however, with only three studies on the subject in this time period. Due to the lack of scientific, academic productions focusing on Electronic Games in the scope of Inclusive Mathematics Education, it becomes necessary.

The use of the history of mathematics in teaching has long been considered a tool for enriching students’ mathematical learning. However, in the USA few, if any, research efforts have investigated how the study of history of mathematics contributes to a person's mathematical knowledge for teaching. In this article, I present the results of research conducted over four semesters in which I sought to characterize what prospective mathematics teachers (PMTs) understand about the topics that they will be called upon to teach in the future and how that teaching might include an historical component. In particular, I focus on how the study and application of the history of solving quadratic equations illuminates what PMTs know (or do not know) about this essential secondary school algebraic topic. Additionally, I discuss how the results signal important considerations for mathematics teacher preparation programs with regard to connecting PMTs' mathematical and pedagogical knowledge, and their ability to engage in historical perspectives to improve their own and their future students' understanding of solving quadratic equations.

There is a growing emphasis on the role of language in teaching and learning mathematics, most significantly in classrooms with increased language diversity. Consequently, teachers face considerable challenges in accommodating diverse needs and must employ strategies to support all students. It is, therefore, crucial to provide prospective teachers with opportunities to enhance their pedagogical approaches while raising their awareness of the relationship between language and mathematics. In this respect, Live Brief assessments in Higher Education, which involve students working on authentic projects/tasks from a school, may be a promising avenue. This research draws on the 19 Live Brief group presentations prepared by a total of 118 Year 1 prospective primary school teachers, specifically focusing on the language-related challenges faced by a local school in early years mathematics. The data encompassed prospective teachers’ proposed practices, including one-to-one, small group and whole class activities, that aimed to address language diversity. Data analysis was informed by Moschkovich’s three perspectives on the relation between language and teaching and learning mathematics, namely lexicon, register and situated-sociocultural perspectives. While a lexicon perspective was commonly evident in the activities, the manifestation of a situated socio-cultural perspective mainly in the one–to-one activities is noteworthy, given its social and discursive nature. Three themes encapsulated a range of practices suggested in the findings: explicit vocabulary teaching, different strategies of scaffolding and utilising multi-sensory approaches. While the lexicon and register perspectives were commonly evident, the situated socio-cultural perspective was much less commonly manifested in the practices. We offer implications to initial teacher education curriculum, future research and policies about teaching and learning mathematics.

In this paper we first present a theoretical approach to study mathematics teacher knowledge and conditions for developing it. Then some interesting activities and games are presented. As a result, this paper supplies teachers with information that may be useful in better understanding the nature of games, activities and their role in teaching and learning mathematics. At the age of 10 pupils can concentrate less than 20 minutes during a lesson. However, a lesson in primary and secondary schools lasts for 45 minutes and 50 at universities. What a contradiction! To solve this problem we try to attract their attention with different techniques. As children and adults enjoy playing games we can teach and learn mathematics through games and activities. Experience reveals that games can be very productive learning activities. Are some games better than others? What educational benefits are there to be gained from games? How to integrate games in mathematics lessons? How to distinguish between ‘activity’ and ‘game’? How to teach students specialising in electrical engineering and informatics using such an approach?

The article is devoted to the problems of teaching mathematics in a school with practiceoriented content. The aim of the study is to develop a methodology for teaching students to solve problems with practical content in the process of implementation of practice-oriented teaching mathematics. The development of students ‘ abilities to solve practice-oriented problems in the process of teaching mathematics should be considered as one of the ways of forming their mathematical competence. Practice-oriented tasks are understood as mathematical tasks, the content of which describes the situation of reality associated with the formation of practical skills of using mathematical knowledge and skills needed in everyday life. The solution of this type of problem is largely based on the construction of a model of the real situation described in a particular problem. This model of compilation requires a high level of mathematical training and is the result of training that is appropriately called culture-universal. The constant use of practice-oriented tasks in teaching mathematics at school will allow the learner to generalize and deepen knowledge, acquire skills and knowledge on the subject, be able to link the learning process with the real conditions of life, to show initiative and independence. The researchers describe didactic goal-setting and examples of practice-oriented tasks in mathematics developed by the authors. Monitoring of learners ‘ activities indicates that the frequent use of practice-oriented tasks increases the interest of learners in educational activities, forms a positive motivation in the classroom Key words: secondary school mathematics, practice-oriented tasks, motivation.

Currently, various interactive teaching methods are being used to increase students' interest in the subject of mathematics. Computer programs integrated into education worldwide are proving to be successful. This article provides brief information about the benefits of using GeoGebra in teaching and learning mathematics. Utilizing GeoGebra's software support in teaching and learning mathematics helps to enhance students' interest in the subject, fosters critical thinking and problem-solving skills, facilitates analysis, and develops cognitive and creative abilities.

Digital game-based learning (DGBL) had been regarded as a sound learning strategy in raising pupils’ willingness and interest in many disciplines. Normally, video and digital games are used in the teaching and learning mathematics. based on literature, digital games have proven its capability in making pupils motivated and are more likely to contribute to effective learning mathematics. Hence this research aims to construct a DGBL in the teaching of Mathematics for Year 1 pupils. Then, a quasi-experimental study was carried out in a school located in Gua Musang, Kelantan, involving 39 pupils. Specifically, this article tests the effectiveness of the use of DGBL in the teaching of the topic Addition of Less than 100 on pupil’s achievement. This research employed a quasi-experiment, Pre and Post Test of Non-equivalent Control Group design. The data were analysed using the Nonparametric test namely the Mann-Whitney U. The research finding shows the use of the DGBL could increase the pupils’ achievement in the topic of Addition of Less than 100. In practice, this research indicates that the DBGL can utilized as an alternative reference strategy for Mathematics teacher.

This paper studies the pre-service teachers’ mathematics teaching self-efficacy throughout the bachelor’s degree in Primary Education. Our hypothesis is that the mathematical courses included in the bachelor’s degree can influence their mathematics teaching self-efficacy. To carry out the study, pre-service teachers of each year of the Primary Education Degree answer the Mathematics Teaching Efficacy Belief Instrument (MTEBI) at the end of the 2016-17 academic year. The MTEBI is comprised of two sub-scales, namely, Personal Mathematics Teaching Efficacy (PMTE) and Mathematics Teaching Outcome Expectancy (MTOE). Obtained results evidence a statistically significant difference (in positive) between the pre-teachers of the first and the last year of the bachelor’s degree in the PMTE subscale. Therefore, these results show that the three teaching and learning mathematics courses (TLM) included in the bachelor’s degree do change the students’ PMTE. Concretely, the second TLM course, which is connected to a student teaching practice period, really makes the difference. Scores obtained in the MTOE subscale, on the contrary, do not increase throughout the Degree. To sum up, this study shows that the Mathematical Curriculum of the bachelor’s degree can influence on the PMTE of the pre-teachers. Therefore, teacher educators should be aware of the importance of the Mathematical Curriculum and design the teaching and learning mathematics courses in order to promote the PMTE of the pre-teachers.