Mathematics Reform Research Articles

Designing an Assessment to Measure Students' Inferential Reasoning in Statistics: The First Study, Development of a Test Blueprint

Accompanied with ongoing calls for reform in statistics curriculum, mathematics and statistics teachers purposefully have been reconsidering the curriculum and the content taught in statistics classes. Changes made are centered around statistical inference since teachers recognize that students struggle with understanding the ideas and concepts used in statistical reasoning. Despite the efforts to change the curriculum, studies are sparse on the topic of characterizing student learning and understanding of statistical inference. Moreover, there are no tools to evaluate students' statistical reasoning in a coherent way. In response to the need for a research instrument, in a series of research study, the researcher developed a reliable and valid measure to assess students' inferential reasoning in statistics (IRS). This paper describes processes of test blueprint development that has been conducted from review of the literature and expert reviews.

Effective Engagement Strategies for Non-Tenure-Track Faculty in Precollege Mathematics Reform in Community Colleges

The success of efforts to improve student outcomes in precollege mathematics at community colleges hinges on engaging and supporting non-tenure-track faculty [NTTF], who comprise a significant proportion of precollege instructional staff. Although research suggests weak departmental support and barriers and constraints to NTTF engagement, no studies have focused specifically on NTTF in the context of precollege mathematics reform in community colleges. This qualitative case study fills a gap in our understanding through interviews with seven tenure-track faculty [TTF] and 11 NTTF from three departments participating in the Washington State Rethinking Pre-College Mathematics grant. The case study examines the nature and effectiveness of strategies and incentives developed by TTF to engage their NTTF peers in department-led reform of precollege mathematics. Each department was successful in securing NTTF engagement across a broad spectrum, using strategies that included offering perquisites, professional development, and targeted instructional support. The NTTF detailed some changes in their practice, such as diversifying classroom instruction and approaches to assessment. Strategies that successfully initiated engagement (e.g., compensation) differed from those that sustained engagement, with the latter leveraging NTTF interest in growing professionally in order to improve student outcomes and build professional relationships with peers. Findings inform the delivery of NTTF professional development by suggesting that education and training expand beyond the delivery of new content to include relationship building with other faculty. The study's findings also consider NTTF professional development to be a shared responsibility among departments, colleges, systems, and NTTF.

Infrastructure Redesign and Instructional Reform in Mathematics

Designing infrastructures to support instruction remains a challenge in educational reform. This article reports on a study of one school system's efforts to redesign its infrastructure for mathematics instruction by promoting teacher leadership. Using social network and interview data from 12 elementary schools, we explore how the district's infrastructure redesign efforts were internally coherent with and built upon existing infrastructure components. We then explore relations between infrastructure and school practice as captured in the instructional advice- and information-seeking interactions among school staff, finding that teacher leaders emerged as central actors and brokers of advice and information about mathematics within and between schools. Further, changes in school advice and information networks were associated with shifts in teachers' beliefs about and practices in mathematics toward inquiry-oriented approaches consistent with district curriculum. We argue that the district's redesign efforts to support teacher leadership coupled district curriculum and school and classroom practice in mathematics.

Structural and conceptual interweaving of mathematics methods coursework and field practica

This paper describes a study of observed relationships between the design of a preservice elementary mathematics methods course with accompanying field practicum and changes in the extent to which participating prospective teachers identified themselves with the mathematics reform movement after becoming practicing teachers. The curriculum of the course with its embedded field practicum experiences was designed to support prospective teachers in interweaving methods coursework and pedagogical instruction with classroom practice. University and elementary school structures were interwoven by conducting weekly mathematics methods course sessions at a school site followed immediately by related practicum experiences in classrooms in the school. The interweaving of conceptualizations about mathematics teaching and learning was facilitated as the methods instructor provided professional development for classroom teachers simultaneously with the methods course, encouraging the teachers to create “reform-friendly” classroom environments. Survey data from 68 prospective teachers involved in the project were analyzed to identify and describe relationships between course/practicum experiences and the degree to which they as practicing teachers, 1–3 years following the course/practicum, identified with a reform mathematics perspective, as well as to examine factors influencing those relationships.

Utilising a construct of teacher capacity to examine national curriculum reform in mathematics

This study involving 120 Australian and Chinese teachers introduces a construct of teacher capacity to analyse how teachers help students connect arithmetic learning and emerging algebraic thinking. Four criteria formed the basis of our construct of teacher capacity: knowledge of mathematics, interpretation of the intentions of official curriculum documents, understanding of students’ thinking, and design of teaching. While these key elements connect to what other researchers refer to as mathematical knowledge for teaching, several differences are made clear. Qualitative and quantitative analyses show that our construct was robust and effective in distinguishing between different levels of teacher capacity.

Transposing reform pedagogy into new contexts: complex instruction in remote Australia

This article draws on the outcomes of a 4-year project where complex instruction was used as the basis for a reform in mathematics teaching in remote Aboriginal communities in Australia. The article describes the overall project in terms of the goals and aspirations for learning mathematics among remote Indigenous Australians. Knowing that the approach had been successful in a diverse setting in California, the project team sought to implement and evaluate the possibilities of such reform in a context in which the need for a culturally responsive pedagogy was critical. Elements of complex instruction offered considerable possibilities in aligning with the cultures of the remote communities, but with recognition of the possibility that some elements may not be workable in these contexts. Complex instruction also valued deep knowledge of mathematics rather than a tokenistic, impoverished mathematics. The strategies within complex instruction allowed for mathematical and cultural scaffolding to promote deep learning in mathematics. Such an approach was in line with current reforms in Indigenous education in Australia where there are high expectations of learners in order to break away from the deficit thinking that has permeated much education in remote Australia. The overall intent is to demonstrate what pedagogies are possible within the constraints of the remote context.

Supporting Sustainability: Teachers’ Advice Networks and Ambitious Instructional Reform

Scaling up instructional improvement remains a central challenge for school systems. While existing research suggests that teachers’ social networks play a crucial role, we know little about what dimensions of teachers’ social networks matter for sustainability. Drawing from a longitudinal study of the scale-up of mathematics reform, we use qualitative social network analysis and qualitative comparative analysis (QCA) to investigate the relationship between teachers’ social networks and sustainability. Teachers’ social networks in the first 2 years of the initiative influenced their ability to sustain reform-related instructional approaches after supports for reform were withdrawn. Social networks with combinations of strong ties, high-depth interaction, and high expertise enabled teachers to adjust instruction to new conditions while maintaining the core pedagogical approach. This research contributes to our understanding of the dynamics of sustainability and to social network theory and research.

Classroom Culture, Mathematics Culture, and the Failures of Reform: The Need for a Collective View of Culture

Background/Context Despite the tremendous amount of effort devoted by many mathematics educators to promote, defend, and implement reform-based mathematics education, procedural mathematics, which locates mathematical correctness in the procedures learned from textbooks and teachers, persists. Many researchers have identified school and classroom culture as the source of the problem; however, the exact meaning of school culture and its influence on teachers’ practices remains unclear. What is needed is a clearer understanding of classroom culture and how it influences practice. Purpose The purpose of our study was to examine how the aspects of a culture reinforce each other (and how they resist aspects alien to the cultural system) to understand the sui generis nature of culture. We use five aspects or indicators of culture—language usage, standard practices, tools and equipment usage, ongoing concerns and values, and recurring problems—to describe how they work together to create a culture. Population/Participants/Subjects The primary participant in this study was an eighth-grade mathematics teacher renowned for being a good teacher whose teaching conformed to the intentions of the reform-oriented National Council of Teachers of Mathematics (NCTM) standards, with a particular emphasis on problem solving. Research Design An ethnographic case study was conducted. Conclusions/Recommendations Although Ms. Bryans appropriated some of the rhetoric and practices of reform mathematics, her goals and assessment methods and most of her instructional methods were inconsistent. The analysis of the case shows that three conceptions of culture—individual, interactive, and collective—lead to quite different understandings of the problem. This case suggests the importance of differentiating each of these three conceptions of culture and discusses their implications for educational reform policies and professional development efforts.

Towards empowering learners in a democratic mathematics classroom: To what extent are teachers’ listening orientations conducive to and respectful of learners’ thinking?

In an effort to make education accessible, to ‘heal the divisions of the past and establish a society based on democratic values’, the South African Department of Education claims that a series of mathematics reforms that has so far been introduced is underpinned by the principles of ‘social justice, fundamental human rights and inclusivity’. Critics however argue that the system has remained ‘undemocratic’ in that those groups of learners who were supposed to be ‘healed’ continue to underperform and hence be disempowered. In this study, we conceptualised a democratic and mathematically empowering classroom as one that is consistent with the principle of inclusivity and in which a hermeneutic listening orientation towards teaching promotes such a democratic and mathematically empowering learning environment. We then worked with three different orientations teachers might have towards listening in the mathematics classroom: evaluative, interpretive and hermeneutic. We then used these orientations to analyse 20 video-recorded lessons with a specific focus on learners’ unexpected contributions and how teachers listened and responded to such contributions. The results were consistent with the literature, which shows that teachers tend to dismiss learners’ ways of thinking by imposing their own formalised constructions.

Innovative approaches to teaching mathematics in higher education: a review and critique

This paper provides a snapshot of emerging trends in mathematics teaching in higher education for STEM subjects (Science, Technology, Engineering and Mathematics). Overwhelmingly, papers identify a focus on conceptual understandings of mathematics in comparison to understanding that is instrumental or procedural. Calls for reform of mathematics teaching have been the basis for a range of studies; responses to these calls have embraced innovative methods for implementing changes in learning and teaching of mathematics, sometimes rooted in constructivist ideology. Observed trends have been categorised in six groups. In many studies, technology is being used as an enabler of reforms. Constraints to implementing new approaches in mathematics teaching are indicated. Discussion of contemporary research questions that could be asked as a result of the shift towards teaching mathematics in innovative ways is provided and is followed by a critique of the underlying theoretical positions, essentially that of constructivism.

Mathematical Modeling and Cultivation of Student Mathematics

The article analyzes undergraduate Mathematical Modeling Competition’s characteristics and the theory foundation thoroughly,and points out the significance of this competition both in improving colledge students’innovation ability and in higher mathematical education reform. It concentrately summarizes and expatiates the prominent problems in present undergraduate Mathematical Modeling education from four aspects:students’ ability,teachers’quality,teaching facilities and the management and organization of the school,on basis of this,the article puts forward teaching strategies for undergraduate Mathematical Modeling,and also dwells on how to improve the thinking principles and capabilities about undergraduate Mathematical Modeling by examples. Establishes the teaching mode of colledge mathematical modeling and thoroughly analyses the hierarchy of mathematical modeling’s teaching and basic principles for selecting titles.At last,the article proposes several questions which we should pay attention to about colledge mathematical modeling teaching.

Learning to Teach in the Figured World of Reform Mathematics: Negotiating New Models of Identity

Starting from the assertion that traditional and reform mathematics pedagogy constitute two distinct figured worlds of teaching and learning, the authors explore the initiation of prospective teachers into the figured world of reform mathematics pedagogy. To become successful teachers in reform-oriented classrooms, prospective teachers must learn more than pedagogical tools and moves: They must understand what it is to participate in the figured world of reform pedagogy, develop models of identities for participants in this world, and negotiate new constructions of mathematics. In this article the authors present three episodes from an elementary mathematics teacher education class where positions of “teacher” and “child” were offered by instructors in activities designed to approximate practice in the reform figured world. Students negotiated new models of identity and conceptions of mathematics as they took up these positions in varying ways.

Longitudinal investigation of the curricular effect: An analysis of student learning outcomes from the LieCal Project in the United States

In this article, we present the results from a longitudinal examination of the impact of a Standards-based or reform mathematics curriculum (called CMP) and traditional mathematics curricula (called non-CMP) on students’ learning of algebra using various outcome measures. Findings include the following: (1) students did not sacrifice basic mathematical skills if they are taught using a Standards-based or reform mathematics curriculum like CMP; (2) African American students experienced greater gain in symbol manipulation when they used a traditional curriculum; (3) the use of either the CMP or a non-CMP curriculum improved the mathematics achievement of all students, including students of color; (4) the use of CMP contributed to significantly higher problem-solving growth for all ethnic groups; and (5) a high level of conceptual emphasis in a classroom improved the students’ ability to represent problem situations. (However, the level of conceptual emphasis bears no relation to students’ problem solving or symbol manipulation skills.)

Teaching of differential and integral calculation basics in Lithuanian schools after the teaching reform in mathematics (in 1929–1940)

The article discusses teaching of differential and integral calculation fundamentals after the reform in the teaching of mathematics (1929–1940) with reference to the textbook of Juozas Stoukus “Basics of Infinite Smallness Analysis” (1925), textbook of Antanas Juška “Basics of Mathematical Analysis” (1934), contemporary curricula of higher schools and articles of mathematicians.

How Do We Learn? African American Elementary Students Learning Reform Mathematics in Urban Classrooms

In this article, the author uses qualitative methodology to investigate how African American elementary students in an urban school engaged with a National Council of Teachers of Mathematics standards-oriented mathematics curriculum and how their engagement converged with or diverged from the offered patterns of teaching practices in classrooms. The findings suggest that student practices converged with teaching practices that reflected the African American cultural dimension of social/affective interactions such as focused collaboration and active participation and diverged when students enacted practices that reflected expressive creativity and nonverbal interactions as with dramatic expression and improvisation. Rather than looking at the divergent behaviors as social problems or behaviors needing remediation or punishment, considering what can be learned from these behaviors could enhance the mathematical identity and academic achievement of African American students.

Teachers’ assessment practices in mathematics: classrooms in the context of reform

This article responds to calls that have been made for research into how teachers incorporate new assessment ideas into their practice. We draw on a large‐scale study that examined the implementation of reform in mathematics in grades 7–10 in Ontario, Canada. We present teacher questionnaire data, and focus on data gathered from case studies for details of what new assessment practices look like in classrooms. We show teachers using a variety of forms of assessment and using assessment to improve student learning. Observed assessment practices went beyond tests to include the use of journals, observation, questioning, self‐assessment and unique forms of ‘quizzes’. These practices allowed teachers to examine students’ mathematical thinking and provided feedback to students and teachers to improve student learning. We also observed the important role of collaboration, coherence, and the teachers’ beliefs in supporting new assessment practices.

Mathematics Reform Curricula and Special Education: Identifying Intersections and Implications for Practice

In many general education classrooms today, teachers are using “reform” mathematics curricula. These curricula emphasize the application of mathematics in real-life contexts and include such practices as collaborative, group problem solving and student-generated algorithms. Students with learning disabilities in the area of mathematics can experience challenges with these curricula due to lack of content knowledge and requisite skills along with processing and strategy deficits. The purpose of this article is to present information on strategies that can be used to complement math reform curricula to meet the needs of students with math learning disabilities.

Mathematics Reform and Teacher Quality in Elementary Grades: Assessments, Teacher Licensure, and Certification

We analyzed the gap in mathematics standards, assessments and accountability, and teacher licensure and certification requirements in mathematics for elementary grades. We found states delineated mathematics academic standards in specific content areas. Licensure and certification requirements were weak indicators since they lacked the specificity of conceptual and procedural knowledge that could strengthen mathematics content knowledge and inform instructional practices. The most recent changes in licensure and certification requirements intended to affect teacher quality are not reaching a large proportion of elementary teachers; thus, their overall impact on teacher quality is likely to be limited. We discuss policy strategies for licensure and certification requirements likely to have a broader reach in addressing teacher quality at the elementary grades.

Teaching of differential and integral calculation basics in Lithuanian schools before the teaching reform in mathematics (in 1918– 1928)

The article discusses teaching of differential and integral calculation fundamentals before the reform in the teaching of mathematics (1918-1928) with reference to the textbook of Juozas Stoukus “Basics of Infinite Smallness Analysis”, contemporary curricula of higher schools and articles of mathematicians.

Approaches and practices in developing school mathematics textbooks in China

In this study, we aim to examine and discuss approaches and practices in developing mathematics textbooks in China, with a special focus on the development of secondary school mathematics textbook in the context of recent school mathematics reform. Textbook development in China has its own history. This study reveals some common practices and approaches developed and used in selecting, presenting and organizing content in mathematics textbooks over the years. With the recent curriculum reform taking place in China, we also discuss some new developments in compiling and publishing high school mathematics textbooks. Implications obtained from Chinese practices in textbook development are then discussed in a broad context.