Quality Of Mathematics Education Research Articles

О НЕКОТОРЫХ БАЗОВЫХ АКЦЕНТАХ ИЗУЧЕНИЯ КУРСА «МАТЕМАТИЧЕСКИЙ АНАЛИЗ» В ВУЗАХ

The article explores the problem of improving the quality of mathematical education at universities. Recent frequent transitions to various Federal State Educational Standards, the shift of the learning vector towards obtaining new scientific knowledge, and recently possible long-term distance learning, suggest that a modern bachelor has such qualities as the ability to work effectively and cope with a large flow of information. Unfortunately, not all students due to various reasons are ready to meet new requirements (especially freshmen, since at the present stage the thinking operations that underlie the organization of educational actions cease to develop effectively already at school: school education has other priorities). Almost all mathematical disciplines are connected by basic concepts (vector, matrix, determinant, limit, derivative, integral, continuity, etc.), therefore, the main task at the first stage of teaching mathematics at a university, in our opinion, is to “cement” basic concepts with their transformation in subsequent courses into the foundation of studying other disciplines. The motivational component of this process, as shown by many years of experience, is the initial keen interest in the subject of study, which arises when solving simple, unusual and interesting problems (examples of such problems are given in the article). While studying “Mathematical Analysis”, it is proposed to place in-depth emphasis on its basic concepts, such as the limit of sequence, integral, etc. The set of notions is justified both from the point of view of the content of sections of mathematical analysis, and from the point of view of interdisciplinary connections of mathematical disciplines studied later. These are the cornerstones of all mathematics. Without exaggeration, it can be stated that the degree of understanding by students of such mathematical phenomena depends on the result of the subsequent work of teachers, and, therefore, the totality of knowledge and scientific knowledge of future graduates, the high potential of which will allow them to successfully realize themselves in professional occupation.

Using Records of Practice to Bridge from Teachers’ Mathematical Problem Solving to Classroom Practice

It is often the case that high quality mathematics education professional development involves enhancing both teachers’ content knowledge and their pedagogical skills, specifically for teaching mathematics. However, when teachers are immersed in their own learning of mathematics, they are often unaware of the facilitators’ instructional decisions and moves that influence their own learning outcomes, as well as how these might apply to their future teaching. Thus, while the teachers can appreciate their new understanding of content, they may not have added significantly to their understanding of the instructor’s pedagogical moves that facilitated their growth. As a result, teachers may leave even high quality professional development without assurance that they will be able to adjust their teaching in ways that support their own students’ meaningful learning of mathematics. In this work we describe one way in which professional development can both enhance teachers’ subject matter knowledge and help to transform these new understandings into pedagogical content knowledge; the mathematics content sessions provide the platform for reflection on pedagogy. To facilitate this reflection, a “record of practice” is created by facilitators, and thereafter utilized for participants and facilitators to identify and analyze critical moments in the mathematics content session. This paper offers two specific examples of records of practice and how they were used, as well as teachers’ reactions and insights. It also discusses various formats of records of practice, the logistics of developing them, and ends with the potential benefits of using records of practice in professional development for teachers.

Active teaching through mathematical problems in primary school

Active teaching is a key component in the education system at all stages of education. In practice, introduction of active teaching in mathematics teaching in primary school poses significant challenges for teachers. To solve this problem, we have developed a methodological approach described in this article. In particular, we suggest an active teaching model whose realization is linked to the inclusion of problems with developmental and interdisciplinary content in the teaching process in mathematics classes. The solutions of these problems are associated with particular themes in mathematics classes. We discuss the methodology for constructing the systems of problems with developmental and interdisciplinary content in accordance with particular themes in mathematics classes in primary school, which is based on the scheme that we developed. We have also analyzed the indicators of including such problems in mathematics classes in primary school and the results of the educational experiment demonstrating that the author’s methodological approaches provide a high quality of mathematical education for primary school pupils, make the teaching process interesting and attractive, and ensure their involvement in the process of active teaching and learning through the systems of specially selected problems.

Escola, Educação Inclusiva e Etnomatemática em Tempos de Isolamento Social

O objetivo neste artigo é apresentar reflexões a partir da análise dos resultados de uma pesquisa realizada com oito docentes da Educação Básica que atuam em contextos socioculturais distintos, como na Educação Escolar Indígena, Educação Escolar do Campo, Educação Especial e Inclusiva, Educação de Jovens e Adultos, entre outras, em diferentes cidades e regiões brasileiras. A intenção é apresentar indícios de como a Educação Escolar está tentando acontecer nestes tempos de isolamento social; quais os desafios e as implicações educacionais enfrentadas pelos educadores e seus educandos; como a Educação Matemática está sendo praticada e; como a Etnomatemática pode ser mobilizada. As informações que respaldam as discussões perpassam as respostas a um questionário encaminhado remotamente e a sua apreciação acontece qualitativamente por meio de aproximações com a análise textual discursiva. Trata-se de uma pesquisa exploratória e os dados indicam que as escolas e os docentes estão atuantes, implementando práticas e aulas remotas usando diferentes tecnologias, apesar das suas limitações e dificuldades, intentando a inclusão de todos com uma Educação Matemática dinâmica e de qualidade, e na medida do possível, mobilizando a Etnomatemática, mesmo diante das adversidades e consequências incertas.

Utilization of information technology in the implementation of active learning in Muhammadiyah Private Schools 21 Dolok Batu Nanggar online

In general, junior high school students view mathematics as a difficult and boring subject. In addition to students, teachers also experience difficulties in delivering material, including time constraints in delivering quite a lot of material, and a lack of student interest in learning mathematics when using conventional learning methods such as from textbooks and explanations from the teacher. With these considerations, the proposer wants to apply knowledge and technology by making mathematics learning media tutorials so that they can increase understanding and attract students' interest in learning and help improve the quality of mathematics education and teaching. The result achieved is that community service for active learning and ICT should be reproduced because there are still many schools that have not implemented it. Meanwhile, from the progress of the times, namely Industry 4.0, ICT-based learning is very much needed.

The impact of the quality of early mathematics instruction on mathematics achievement outcomes

The examination of teaching quality in mathematics in relation to student learning outcomes has become increasingly important following the research reports indicating that early mathematics teaching and learning experiences are critical contributors to students’ learning and later achievement in mathematics and other content areas. The purpose of this study is to investigate the relationship between the quality of early mathematics instruction and students’ mathematics learning outcomes in 73 Pre-K to 3rd grade classrooms in an urban public schools system. The results suggested that the quality mathematics instruction varies across observed classrooms but mostly mediocre. Limited but significant associations between instructional quality and mathematics achievement were also documented at the classroom level. More specifically, there was a positive significant interaction between quality of mathematics teaching and students’ mathematics achievement at the end of the school year in classrooms where ratings of the instructional quality was identified as “high,” after controlling for students’ pre-test scores and gender.

In China, What We Need is More Than Mathematics: A Literature Review of Numeracy

In China, the importance of quality mathematics education has never been called into a question, whereas numeracy as a general capability that is more than the mastery of mathematical knowledge and skills is seldom discussed in the literature about Chinese schools and education systems or considered in teaching practices, presenting an overall picture that numeracy development seems to be missing from Chinese education or considered as a tacit outcome automatically produced by the acquisition of mathematical knowledge. This issue may stem from the linguistic differences between English language and non-English language that render the interpretation of numeracy distorted and further evolve into a whole situation in China as a result of the longstanding debate on the essence of numeracy and the heavy emphasis laid on mathematics education rather than numeracy development as a whole. In this paper, the nature of numeracy is discussed by referring to a number of classic literature works, with special attention to clarifying the relationships between numeracy and mathematics that can be confused at a conceptual level.

The Mediating Effect of Study Approaches between Perceptions of Mathematics and Experiences Using Digital Technologies

The learning process of constructing concepts in mathematics can be supported by visualization in graphical, numerical, and symbolic representations. However, previous research suggests that students have not fully taken advantage of the opportunities provided by these technologies. Two key factors, including mathematics conception and mathematics study approaches differentially used such technologies and consequently promote the quality of mathematics education. We hypothesized that these key factors play a key role in this shortcoming. A survey of 442 high school students from Iran was conducted to examine the hypotheses through structural equation modeling. Results confirmed that mathematics conception and mathematics study approaches were associated with students’ experiences and evaluations of using supportive digital technologies in mathematics learning. Moreover, mathematics study approaches mediated the relationship between mathematics conception and students’ experiences and evaluation of using these digital technologies. These findings explain how mathematics conception contributes to learning experiences when students use such digital technologies.

Mining the Gap: Analysis of Early Mathematics Instructional Quality in Pre-Kindergarten Classrooms

ABSTRACT Research Findings A total of 54 videotaped mathematics activity observations drawn from 27 different pre-kindergarten classrooms in an urban public schools system in the U.S. were coded using 2 observational measures: (a) a general measure, the Classroom Assessment Scoring System (CLASS); and (b) a math-specific measure, the High Impact Strategies in Early Mathematics (HIS-EM). Criterion validity analysis revealed varying levels of convergent and discriminant patterns between the two tools. Indications of these results are twofold: (1) to some extend both tools document the similar aspects of quality of instruction (e.g., instructional support), and (2) a math-specific measure can be more sensitive to document the various levels of mathematics specific instructional support provided during teaching episodes (e.g., math representations, establishment of math learning communities). Results also indicated that the quality of mathematics instruction observed was revealed to be low to medium levels. Practice or Policy: Even though the CLASS may be a useful tool in terms of understanding overall instructional quality, as a subject-specific tool, the HIS-EM might offer a benefit of the multidimensional measure of mathematics teaching quality, which enables the researcher to pinpoint the kinds of strengths that teachers exhibited in math instruction and areas in need of improvement and may assist the field to better identify potential instructional areas to target with professional development.

Supporting novice mathematics teacher educators teaching elementary mathematics content courses for the first time

In order to be effectively prepared by a teacher education program, prospective elementary teachers (PTs) need to experience high quality mathematics instruction in their mathematics content courses. The instructors of these courses typically consist of individuals (mathematicians and mathematics educators) with ranging experiences, from tenured faculty members to first-year assistant professors or graduate students. This paper explores how to support novice mathematics teacher educators (MTEs) who are teaching elementary content coursework for PTs for the first time. We detail and describe how to implement three systems for supporting novice MTEs: working with a mentor, being provided with educative curriculum materials, and working in a collaborative teaching environment. We close by discussing specific challenges associated with these supports, and call for more institutions to share how they have successfully implemented systems to support novice MTEs.

SOME PROBLEMS OF QUALITY ASSURANCE OF MATHEMATICAL EDUCATION OF FUTURE PRIMARY SCHOOL TEACHERS

The article discusses the most significant problems of ensuring the quality of mathematical education of students studying in the direction of Pedagogical Education, profile "Primary Education". The presented results were obtained as a result of the analysis of theoretical studies published in Russian scientific sources, and on the basis of a survey of mathematics teachers and methods of teaching mathematics working in leading pedagogical universities of Russia. As a result of processing the obtained data, the identified problems are ranked by degree of relevance. In the article, the authors proposed possible solutions to the identified problems within the existing regulatory requirements on the basis of their personal experience in teaching mathematical disciplines at a teacher training university, as well as possible risks that arise when they are implemented. The authors present individual examples of the implementation of these ideas in the practice of teaching students at the Herzen State Pedagogical University of Russia.

TECHNOLOGY OF DESIGNING OF MATHEMATICAL EDUCATION ON AN INNOVATIVE BASIS IN A GENERAL EDUCATIONAL ORGANIZATION

The actual need of the design of mathematical education in a general education organization that takes into account socio-economic and pedagogical realities, is substantiates in this article. The concepts “design of mathematical education in a general education organization”, “innovative educational system for teaching mathematics”, “design technology” are defined. The design of mathematical education as an innovative educational system for teaching mathematics in a general education organization has a landmark nature. It is reflected in specific design procedures, which determines the manufacturability of pedagogical design. The technology includes instructions for step-by-step actions and methods for their implementation, forms and methods of activity. The technology of designing mathematical education on an innovative basis is presented in the form of an algorithm (consisting of three interrelated steps and 9 procedures) describing a sequence of actions and methods for their implementation. The design algorithm developed in the framework of the research is an organizational form of development and further effective implementation of the design model of mathematical education on an innovative basis. Designing of mathematics education in a general education organization allows you to balance the individual desires and capabilities of all subjects of education, taking into account the socio-economic context, which improves the quality of mathematical education.

A longitudinal study of novice primary school teachers’ knowledge and quality of mathematics instruction

Little is known about the relationship between knowledge and instructional quality of novice primary school teachers during their first 3 years of teaching mathematics. This study utilizes the Classroom video analysis and the Mathematical quality of instruction to examine changes in beginning teachers’ usable knowledge and instructional quality, respectively, and their relationship in each year. The analyses reveal positive associations between knowledge and instructional quality in the second and third year of teaching. Two case study teachers illustrate the tight link between knowledge and practice and how different school contexts provide contrasting opportunities to learn from practice, thus contributing to the different patterns of knowledge and instructional quality over time. The findings suggest that usable knowledge of student mathematical thinking at the beginning of the profession supports teacher improvement in both knowledge and practice over time if the vision of the school context is aligned with student-centered instruction.

Measuring the Quality of Early Mathematics Instruction: A Review of Six Measures

Recent evidence demonstrates that mathematics knowledge in the early years is an important contributor to students’ learning and later achievement in mathematics. As early mathematics education has assumed heightened importance, the quality of early mathematics teaching and learning experiences has attracted global attention. Several researchers have designed and used a number of instruments to measure and portray the quality of mathematics teaching in early childhood classrooms. As this body of work is growing fast, it is imperative to explore similarities and differences among the existing research tools that aim to measure the quality of early mathematics instruction. This paper takes a step towards exploring such similarities and differences by reviewing six observation instruments designed to measure early mathematics teaching quality. Therefore, the aim of this paper is twofold: (1) to provide an up-to-date overview by examining these measures’ theoretical bases, foci, and psychometrics; and (2) to examine the similarities and differences between the reviewed tools.

Does disability matter in mathematics educational research? A critical comparison of research on students with and without disabilities

Using a Disability Studies in Education framework, this systematic review analyzed international research published in English (2013–2017) on the teaching and learning of mathematics from the prekindergarten to 12th-grade level, comparing research on students identified as having disabilities to research on students without disabilities. Coding articles (N = 2477) for methodology, participants, mathematical domain, and theoretical orientation, we found that research on students with disabilities was overwhelmingly quantitative (81%) and tended to use behavioral and medical theoretical orientations. Research on students without disabilities was both qualitative (42%) and quantitative (42%) and tended to use constructivist and sociocultural theoretical orientations. In addition, research on mathematical learning that included students with disabilities lacked sustained qualitative inquiry documenting learning processes of students with disabilities and rarely included the teacher as an explicit focus. Following Gervasoni and Lindenskov (2011), we contend that these pronounced differences in research contribute to the segregation of students with disabilities and low-achieving students in lower quality mathematics instruction and may lead to low expectations of the mathematical competence of students with disabilities. We call for increased attention to research that considers how disability is produced and enacted in the complex context of mathematics classrooms.

Effectiveness of Integrating Innovative Quality Cultivation into Higher Vocational Mathematics Teaching

Mathematics teaching is the foundation and focus of higher vocational education. However, there are still a series of problems in the mathematics education of higher vocational colleges in China, such as students’ enthusiasm for mathematics learning remain to be improved, and teachers still practice traditional teaching methods. In order to effectively improve this situation, it is necessary to reform the teaching of mathematics courses in higher vocational colleges, integrate the content of innovation quality cultivation, and implement scientifc and reasonable teaching methods to achieve the effectiveness of mathematics teaching in higher vocational colleges. This paper mainly studies the effectiveness of cultivating innovative quality in the higher vocational mathematics teaching, with the hope to improve the overall quality of mathematics teaching.

Multilingual Approach to Mathematics Education

Multilingual approach to pedagogical practices in mathematics has the potential to target high level mathematical competence and abstraction. Content and Language Integrated Learning (CLIL) is an innovative educational approach to learning, a dynamic and motivating force with holistic features. Not only does it image a shift towards curricular and cultural integration but also helps greatly to focus on deeper conceptual understanding in Mathematics. CLIL’s basic principle of integration of the content and languages if accepted in a broader sense as ‘Content connected to regional language and a new language, culture, nature, real-life’ might solve various problems associated with the teaching-learning of mathematics, and thus ensures to support ‘learning for real life’. This paper establishes the need for ‘Multilingualism’ through a comprehensive literature research. It highlights multilingualism as a trigger for active approach to the quality of Mathematics education, mainly in Indian scenario. The importance of teaching mathematics as a language and specific strategies for teaching mathematics vocabulary are discussed. The illustrations provided for such approaches are entirely based on author’s teaching experiences.

Early Mathematics Teaching Profiles

Responding to the scarcity of research on early mathematics teaching profiles, this article reports on
 a novel assessment approach to identifying characteristics of early mathematics teaching occurring
 in early childhood settings. The new approach uses the interplay between teachers’ content
 knowledge in mathematics, knowledge of students and learning, and knowledge of how to teach
 mathematics effectively during the course of early mathematics as a proxy to identify quality of
 mathematics instruction provided. In this study, 210 pre -kindergarten to 3rd grade teachers in a
 large public school system in the Midwest were observed as they taught mathematics. The
 descriptive results revealed that the quality of mathematics instruction varies considerably among
 early childhood teachers. Some teachers are identified as delivering high quality mathematics
 instruction because they provide students with opportunities to fully and purposefully engage in
 deepening their understanding of important mathematics concepts, whereas others are rated as far
 lower in quality, because their mathematics teaching is procedural in terms of content emphasized
 and instructional strategies used. As a whole, observed quality of mathematics teaching was
 revealed to be mediocre. Implications of results for early math professional development are
 discussed. 

The Quality of Mathematics Instruction in Kindergarten: Associations with Students’ Achievement and Motivation

AbstractWe examined associations between the quality of kindergarten teachers’ mathematics instruction and their students’ achievement and motivation in mathematics. Using a sample of 20 kindergart...

Exploring Grade Nine Geometry Spatial Mathematical Reasoning in the South African Annual National Assessment

The purpose of this study was to explore geometry spatial mathematical reasoning in Grade nine Annual National Assessments, South Africa. Conceptual Blending was the guiding theory. Document analysis within the exploratory case study was used to explore available data, the 2014 Annual National Assessment learners’ scripts (n=1250). Results revealed that on average 70.5 percent of the total number of learners remembered and blended irrelevant prior knowledge not reflective to the contexts of the geometry problems. For learners who recalled the correct prior knowledge, its manipulation was either fragmented or irrelevant. The use of recalled information in wrong contexts could be due to the incorrect manipulation of the meaning of the problems. Also, responses reveal challenges on the quality of mathematics education on geometry. Therefore, the teaching and learning of geometry should focus on empowering learners with skills of recalling, blending and on manipulating problems in their contexts.