High-quality Mathematics Instruction Research Articles

Principals’ conceptions of mathematics instruction: Co-constructing sophisticated instructional vision through professional development

ABSTRACT Objectives Although a principal’s instructional vision is recognized as important for schoolwide improvement efforts, little is known about how principals conceive of mathematics instruction or how professional learning opportunities shape their instructional vision. This article explores principals’ conceptions of mathematics instruction after participating in learning experiences designed to support the development of a vision of high-quality instruction. Methods Through a design-based research approach, we created classroom-based learning experiences for six elementary school principals to develop their vision of high-quality mathematics instruction in the context of a research-practice partnership. Transcripts from the learning experiences and follow-up interviews were analysed qualitatively. Results Findings illustrate nuances in participating principals’ conceptions of mathematics instruction and how their role shaped their vision. Principals attended to the importance of the teacher in actively shaping learning experiences, but were less consistent in describing other dimensions of high-quality instruction such as mathematics tasks. Findings suggest that principals’ conceptions aligned with features of high-quality instruction to the extent they were discussed or elevated during the professional learning experience. Conclusions Our analysis highlights the importance of considering principals’ unique perspectives in professional development around high-quality mathematics instruction and has implications for future practice-embedded principal learning opportunities.

Examining the elements of culturally relevant pedagogy captured and missed in a measure of high-quality mathematics instruction

Mathematics instruction is not race or culture neutral. For students who have been historically marginalized in mathematics classrooms, high-quality mathematics instruction, instruction that helps students build conceptual understanding, on its own might not be enough to disrupt inequities. These students might also need instruction that is culturally relevant, with teachers who demonstrate cultural competence, build critical consciousness, and support student learning. Our goal in this study was to understand which components of culturally relevant pedagogy (CRP) are captured and which are missed in a typical U.S. framework of high-quality mathematics instruction. To find the overlaps and gaps, we analyzed the mathematics lessons of three elementary teachers through both the lens of CRP and the Mathematics-Scan, a mathematics observation tool. We found the strongest overlap between the two frameworks in the patterns of strengths and weaknesses in the teachers’ lessons. When the teachers were delivering high-quality instruction, they were also often supporting students’ learning or showing cultural competence. When the teachers were delivering lower quality instruction, they were also often missing opportunities to enact CRP. At the same time, key elements of CRP including linguistic support for students, high expectations, critical consciousness, and nuances within cultural competence, were missed by the high-quality instruction framework. High-quality instruction was the foundation for CRP in the teachers’ classrooms, but CRP was more than just high-quality instruction. We conclude with recommendations for increasing the alignment between the frameworks and implications for international educators also grappling with equity in their own frameworks of mathematics instruction.

The Critical Roles of a Mathematics Specialist in Establishing Effective, Coordinated Professional Development Systems

ABSTRACT For nearly three decades, mathematics research has indicated the need for high-quality mathematics instruction including both ambitious and equitable practices, as well as continuous, innovative learning opportunities for educators. Teaching practices and standards for mathematical practice have been identified to provide guidance. While research connects effective professional development (PD) to improved instructional practices, there is a need for additional research on the role mathematics specialists play in developing and sustaining PDs. This qualitative case study examined the multiple roles of a specialist while laying the foundational components for a coordinated PD system to improve and strengthen mathematics teaching and learning in elementary classrooms. The PD efforts included the implementation of a teacher subsystem where a specialist led all components consisting of pull-out PD, mathematics coaching, collaborative time, and teacher networks. This study took place at a rural, pre-K through fourth-grade school in a southeastern state. Analysis of the data identified the specialist’s key roles in each component of the teacher subsystem. The results indicated that the development and implementation of a teacher subsystem impacts the overall effectiveness of PD. Findings serve as a foundation for specialists to design and implement coordinated efforts that can have positive impacts on the teaching and learning of mathematics.

Just Dollars and Cents: Making Change via a Virtual Money Manipulative

Providing high-quality services to students with disabilities in rural settings can be challenging, as rural schools often lack resources both in and out of the classroom. One potential option to provide high-quality mathematics instruction to students with disabilities in rural areas is using virtual manipulatives and online instruction. In this study, a single-case research design was used to examine the progress of three high school students with intellectual and developmental disabilities (IDDs) as they used a virtual money manipulative within an online learning environment to solve making change problems. The researchers found a functional relation between the intervention package (i.e., a virtual money manipulative, modeling, system of least prompts) and the dependent variable of accuracy in solving making change problems across three students. In addition, all three students demonstrated an increase in independence during each session and maintained their accuracy and independence after the intervention concluded.

Math phobia and maths anxiety: multidisciplinary aproaches for a more inclusive and equitable education in Brazil

Maths anxiety, commonly referred to as "math phobia", is a challenge in the context of mathematics education in Brazil. While research on the impact of math phobia in the classroom and its direct relationship to learning disabilities is not yet well established, it is widely accepted that math phobia has the potential to increase students' aversion to the subject. This study explores math phobia by analysing text fragments from the mathematics education literature, using lexicometric analyses with the IRaMuTeQ software and Textual Discursive Analysis (TDA). The results emphasise that math phobia is influenced by various cognitive and emotional factors that have a negative impact on learning. Addressing this issue requires a multidisciplinary approach, with a focus on teacher training to create inclusive and welcoming learning environments. Therefore, investment in teacher training is essential to reduce math phobia and promote equitable, high quality mathematics education in the country.

Aspects of mathematics instruction and education policy in Lithuania

High-quality mathematics instruction for all means high expectations and strong support for all students. An insightful math teaching policy when apdating both school math curriculum and assessment system as well as mathematics teacher training and in-service training program are required to implement this provision. This policy should be based on international mathematics education reserach. How realistic is it to implement in Lithuania? From that point on, we will take mathematics teaching seriously depends on society's readiness for existing and future challenges.

Content-focused coaches' opportunities for professional learning: The influence of positionality in coach discourse

As content-specific instructional coaching gains theoretical and empirical support, the field needs to better understand how such coaches develop content-specific knowledge and effective coaching practices. Collaborative engagement in mathematics has been found to be a useful support for teachers' professional learning about high-quality mathematics instruction. This discourse analysis explores how collaborative engagement in mathematics might support coaches' development. Since coaches are positioned differently than teachers, we analyze how coaches' discursive positioning while collaboratively engaged in mathematics influences their opportunities for professional learning. Drawing on video and interview data, our analysis highlights that positioning coaches as practitioners of mathematics and as teachers of record opened up opportunities for coaches to empathize with students' thinking and to consider instructional adaptations with respect to this empathetic view. However, coaches were rarely positioned as coaches while collaboratively engaged in mathematics, which constrained coaches' learning opportunities about coaching. Implications for future research and practice are discussed.

Marginalized within the margins: Supporting mathematics meaning making among students with learning disabilities

Students with learning disabilities are often excluded from conversations about high-quality mathematics instruction as well as conversations about equitable mathematics instruction. As such, they may not be provided many opportunities to engage in mathematics with teachers who implement practices that the field of mathematics education would consider “high-quality” or “equitable”. In this paper, we examine how three students with learning differences participate in instruction that demonstrates aspects of high quality and equitable mathematics instruction. Our findings outline practices that appeared to support increased opportunities for students to demonstrate their own reasoning and sense making in mathematics. Contributions of this work include illuminations of specific pedagogical moves that may support students identified as having learning disabilities to engage in more student-centered, conceptually-oriented mathematics.

Profiles of Mathematics Teachers’ Job Satisfaction and Stress and Their Association with Dialogic Instruction

High-quality mathematics instruction is a primary element for quality education and the sustainable development of society. Some studies have highlighted the critical role of teacher job satisfaction and stress on their instruction. However, limited research has focused on the combinational influence of job satisfaction and stress on mathematics teachers’ dialogic instruction. This study aims to examine their combinational influence on mathematic teachers’ dialogic instruction using latent profile analysis and draws three conclusions. First, this study found three profiles: high job satisfaction and very low stress, very low job satisfaction and high stress, and moderately high job satisfaction and slightly high stress. Second, latent profile membership was differentially related to self-efficacy and leadership support. Third, mathematics teachers with very low job satisfaction and high stress were less likely to implement dialogic instruction compared to teachers in other profiles. This study also provides implications based on these results.

Cognitively demanding tasks and the associated learning opportunities within the MathTwitterBlogosphere

The purpose of this study was to determine if the MathTwitterBlogosphere (MTBoS), an online community of practice, provides opportunities for mathematics educators to learn about the knowledge and conceptions that support the effective use of cognitively demanding tasks, including mathematical knowledge for teaching, visions of high-quality mathematics instruction, and views about how to support struggling students. A qualitative case study was used to explore how content within the MTBoS, and perceptions of the effects of participation in the MTBoS, related to learning specified knowledge and conceptions. Results suggest the MTBoS is a promising avenue for providing learning opportunities related to mathematical knowledge for teaching and visions of high-quality mathematics instruction, although it may provide fewer learning opportunities related to engaging struggling students.

Mathematics education in the spotlight: Its purpose and some implications

This article proposes a reframing of the purposes of mathematics education for the twenty-first century that combines apparently divergent philosophical approaches, arguing that the consequent empowerment should as a matter of individual equity be available to all young people (as well as of benefit to wider society). It suggests that the global mathematics attainment 'spotlight', and the English policy context in particular, offer both opportunities and constraints for the development of such a high-quality mathematics education. The article also discusses the challenging implications for the curriculum, and for the nature of teacher expertise, particularly subject-specific expertise, that is needed.

English Learners in K–12 Mathematics Education: A Review of the Literature

Alongside the increased presence of students classified as English learners (ELs) in mathematics classrooms exists a persistent pattern of the marginalization of ELs. Educators have sought research to identify how to provide ELs with high-quality mathematics education. Over the past two decades, education researchers have responded with increased attention to issues related to the teaching and learning of mathematics with ELs. In this review we analyzed literature published between 2000 and 2015 on mathematics teaching and learning with K–12 ELs. We identified 75 peer-reviewed, empirical studies related to the teaching and learning of mathematics with ELs in Grades K–12 and categorized the studies by focus (Learning, Teaching, and Teacher Education). We synthesize the results of these studies through the lens of a sociocultural perspective on language in mathematics. We then discuss avenues for future research and calls to action based on the extant body of literature.

Teachers’ Views of Students’ Mathematical Capabilities: Challenges and Possibilities for Ambitious Reform

BackgroundResearch suggests that teachers’ views of their students’ capabilities matter when attempting to accomplish instructional reform, particularly in settings serving historically marginalized groups of students. However, to date, this issue has received minimal attention in the scholarship and practice of mathematics instructional reform.PurposeThis study offers a large-scale snapshot of middle-grades teachers’ views of their students’ mathematical capabilities in the context of instructional reform. It contributes to the field's understanding of the learning demands for teachers inherent in achieving a vision of high-quality mathematics instruction and suggests potentially critical foci for professional learning opportunities.SettingThe study took place in two large urban districts pursuing ambitious reform in middle-grades mathematics.ParticipantsParticipants included 122 middle-grades mathematics teachers.Research DesignThe study consisted of a qualitative analysis of semistructured interviews conducted with each of 122 teachers regarding their perspectives on the district's reform efforts, including their views of their students’ mathematical capabilities in relation to the reform. Conceptually, we approached our analysis of teachers’ views of their students’ mathematical capabilities by attending to how they framed a common problem of practice—students facing difficulty in mathematics—diagnostically (i.e., how they explained the source of students’ difficulty) and prognostically (i.e., what they described doing to support students facing difficulty). Analysis also focused on patterns in the relations between teachers’ diagnostic and prognostic framings.FindingsOn the whole, most teachers did not view all of their students as capable of participating in rigorous mathematical activity. Most teachers attributed at least some of their students’ difficulty to inherent traits of the students or deficits in their families or communities, and most described lowering the cognitive demand of an activity if they perceived that students were facing difficulty. Moreover, our analysis of the relations between teachers’ diagnostic and prognostic framing revealed that even when teachers explained students’ difficulty in terms of instructional opportunities, thereby taking responsibility for their students’ learning, they did not necessarily respond in ways that would enable students to participate substantially in rigorous mathematical activity.ConclusionsFindings suggest that a significant challenge in accomplishing ambitious reform entails supporting shifts in how teachers view their students’ capabilities along two dimensions: how teachers explain the source of students’ difficulties in mathematics and how they address such difficulties. Implications for designing professional learning opportunities to support productive shifts in teachers’ views of their students’ capabilities are discussed.

Negotiating Perceptions of Tracked Students: Novice Teachers Facilitating High-Quality Mathematics Instruction

In this article, the author reports on a participant-observation case study that explored how alternatively certified, middle school teachers' expectations of tracked students affect their ability to learn to teach in ways that promote students' mathematical struggle and participation in productive mathematical discussions. Two teachers--one teaching a "high-tracked" course and the other a "low-tracked" course--were participants. Both teachers initially held perceptions of their students that limited their efficacy and self-efficacy with respect to providing high-quality mathematics instruction. However, through program- and school-based mentoring, including participation in a modified reflective-teaching cycle, the teachers learned to learn from their teaching and modify their practice. Both teachers began to allow their students opportunities to struggle with rigorous mathematics and partici-pate in student-centered discussion.

Curriculum enactment patterns and associated factors from teachers’ perspectives

As part of a larger effort to improve teacher capacity for high-quality mathematics instruction, we investigated the factors that are associated with different enactment patterns at three levels: contextual (e.g., type and quality of textbook), individual (e.g., teacher knowledge), and teachers’ opportunity-to-learn (e.g., professional development experiences). Analysis of 183 teachers’ self-reports on their practices revealed three notable findings. First, the factors at the three levels were all found to be significantly related to the different patterns of enacted curriculum. However, the use of quality textbooks and the alignment of teachers’ views and instructional goals with curriculum goals were found to be the two factors that are most strongly associated with the enactment pattern of high-level problems and high-level teacher questions in instruction. Furthermore, teachers with the enactment pattern of increasing lower cognitive demand of problems into higher ones tended to rate their curriculum knowledge higher than teachers with the enactment pattern of using low-level problems and teacher questions in their teaching. In particular, deviation from and dissatisfaction with their assigned low-quality textbooks were found to be critical factors that are associated with the enactment pattern of increasing lower cognitive demands of problems in instruction.

A Comparative Analysis of the Relationship among Quality Instruction, Teacher Self-efficacy, Student Background, and Mathematics Achievement in South Korea and the United States

The purpose of this study is to compare and contrast student, teacher, and school factors that are associated with student mathematics achievement in South Korea and the United States. Using the data from the Trends in International Mathematics and Science Study (TIMSS) 2011, this study examines factors that are linked to teachers who deliver quality instruction with high self-efficacy in both countries. We also investigate the association between teachers with high-quality instruction and high self-efficacy and 8th graders’ mathematics achievement. It was found that teachers’ perceived academic emphasis was commonly associated with teachers who claimed to provide high-quality mathematics instruction with high self-efficacy. However, the two countries’ results differed in the association between teachers’ opportunities to learn in professional development programs and high-quality instruction with high self-efficacy. While ‘teachers’ opportunities to learn in professional development programs’ was a significant factor that leads to quality instruction and high self-efficacy in the United States, it was not significant in South Korea. In addition, while students in the United States tended to have higher math achievement scores when their teachers delivered high-quality instruction with high self-efficacy, there was no such association in South Korea.

An investigation of elementary preservice teachers’ self-efficacy for teaching mathematics

AbstractResearch has consistently shown that teacher efficacy is related to a variety of desirable student outcomes, thus, making teacher efficacy an important factor in high quality mathematics instruction. The purpose of this study was to determine elementary preservice teachers’ self-efficacy beliefs related to teaching mathematics. Forty-one participants from a single university responded to the Mathematics Teaching Efficacy Beliefs Instrument (MTEBI) after completing a constructivist-based elementary mathematics methods course prior to student teaching. The MTEBI is 21-item survey using a 5-point, forced choice Likert-like scale to provide an individual's perceptions of mathematics teaching efficacy beliefs on two subscales—Personal Mathematics Teaching Efficacy Belief (PMTE) and Mathematics Teaching Outcome Expectancy (MTOE). Responses on the PMTE subscale (Mean = 51.08, SD=5.171) indicate that the respondents’ personal mathematics teach efficacy is positive. Participants’ responses (Mean = 29.32, S...

Application of Technology in Teaching Mathematics: A Concept Paper for Measuring Determinants of Acceptance among School Teachers

In the context of Bangladesh, there is no substantial research going beyond level of belief of mathematics teachers of technology use in teaching learning process. While belief influences to motivation, perception, intention, awareness and acceptance therefore, is has been assumed in this study that there must be some determinants of acceptance among school teachers in Bangladesh. Calculators and other technological tools, such as computer algebra systems, interactive geometry software, applets, spreadsheets, and interactive presentation devices, are vital components of a high-quality mathematics education. With guidance from effective mathematics teachers, students at different levels can use these tools to support and extend mathematical reasoning and sense making, gain access to mathematical content and problem-solving contexts, and enhance computational fluency. In a well-articulated mathematics program, students can use these tools for computation, construction, and representation as they explore problems. The use of technology also contributes to mathematical reflection, problem identification, and decision making. Unfortunately, in Bangladesh bringing technology in mathematics teaching is less studied and overlooked. This has led this particular research to conduct this study.

Developing Visions of High-Quality Mathematics Instruction

This article introduces an interview-based instrument that was created for the purposes of characterizing the visions of high-quality mathematics instruction of teachers, principals, mathematics coaches, and district leaders and tracking changes in those visions over time. The instrument models trajectories of perceptions of high-quality instruction along what have been identified in the literature as critical dimensions of mathematics classroom practice. Included are a description of the methods by which an analysis of interview data was integrated with previous findings from the research literature in order to develop leveled rubrics for assessing visions of high-quality mathematics instruction, a report of the results of using the instrument to code more than 900 interviews, and a discussion of the possible applications and benefits of such a methodological approach.

English

The quality of mathematics education depends largely on the quality of education in general. The main idea may be summarized as follows: in order to educate the younger generation of people to be able to meet adequately the demands of the time, it is necessary to create conditions for the high-quality mathematics education. Improving the quality of mathematics education of pupils in secondary school is one of the most pressing problems. Contents of the school course of mathematics and its teaching method has always been the subject of undammed and sometimes stormy scientific debates. There are especially true methods of teaching algebra and the analisis in the high secondary school. Still in the study process the algebraic concepts and principles of analysis are given in such an abstract and generalized form that the student may has considerable difficulties to map these general abstract concepts to the certain concrete images, they are generalizations of. Improving education quality indicators can be achieved by using the appropriate computer technology. The article deals with the use of the cloud-oriented systems of computer mathematics (SCM). The prospects of development of the Web-SCM in terms of cloud-based learning environment are considered. The pedagogical features of the SageMath Cloud use as a tool for mathematics learning are revealed. The methodological aspects of algebra and elementary analysis teaching in a high profile school using the cloud-oriented the SCM SageMath Cloud are revealed.