Mathematics Education Reform Movement Research Articles

Learning and Engagement in the Flipped Classroom of Analytical Mathematics

Learning techniques have changed over time in order to try and improve student engagement across different subjects in higher education. Mathematics has dominantly adhered to certain learning methods that use a more conventional approach. Interactive and active learning in Mathematics tend to be more common in further education yet, university level Mathematics is more complex, heavy in content and poses more difficulty in applying active learning approaches as a passive approach of traditional lectures has always been applied. The issues of learning problems in mathematics is ignored and the lack of metacognitive awareness of mathematical thinking and problem-solving skills seem to persist despite differences amongst educators on an effective learning methodology.
 Following the reform movement in mathematics education in the mid 1980’s, resulting from the dissatisfaction of conventional approaches, recommending the restructuring of mathematical delivery marked the need for modifications in teaching methodology. Employing multiple models to deliver lessons may implement the changes needed to drive student engagement and satisfaction to improve the experience in learning mathematics. In order for these methods to become applicable and effective in students’ experiences in mathematical education, educators need to be encouraged to present active learning techniques so that students can begin to facilitate their own learning which can be done through introducing approaches specific to the individual such as student-centred approaches.
 This paper evaluates the techniques used by mathematicians to deliver lessons and how it reflects on learning and engagement of students in comparison to the flipped classroom approach which inverts the common traditional lecture style used in classrooms. The flipped classroom model in this study is adopted to a topic from the university foundation level module, Analytical Mathematics, whereby results from the quantitative analysis undertaken show a decrease in the success of students’ performance suggesting a lesser impact on improved learning. With regards to engagement, observations from the qualitative analysis of the study highlight positive aspects of the flipped classroom model, specifically an optimistic engagement amongst peers.

What’s in a Name? Framing Struggles of a Mathematics Education Reform Community

Concerns over the quality and diversity of the future workforce in science, technology, engineering and mathematics (STEM) in the United States have led to repeated calls to reform undergraduate education. This paper focuses on the efforts of one mathematics education reform movement in higher education to frame itself and its inquiry-based learning (IBL) teaching methods. Since its inception, members of this IBL movement struggled to negotiate their historical connection to the legacy of the late mathematician R. L. Moore and their need to modernize to recruit new mathematics instructors. A strong initial connection to Moore and his now-troubling racial and sexist views led to intense disputes over the framing, or branding, of the movement that at first inhibited its growth, but over time led to an understanding of IBL that embraces a broader range of methods and people.

WHAT HAPPENS WHEN TEACHERS AND STUDENTS ARE INTRODUCED TO MATHEMATICAL INVESTIGATIONS: AN EXPLORATORY STUDY

A mathematical investigation (MI) encapsulates the reform movement in mathematics education by addressing content and process simultaneously and providing a novel opportunity for students to develop thinking skills and good mental habits. However, introducing MI to teachers and students who are used to routinized teaching approaches and pen-and-paper testing presents many challenges. This study introduced MI to two junior classes and the mathematics teachers of a regular public high school. After the MI orientation workshops, the students engaged in the processes of pattern-finding, problem posing, conjecturing, verifying, and proving. Data were gathered through focus group discussions, interviews, observations, teachers' reflection notes, audiotapes, and analysis of students' outputs. The challenges of doing MI included the teachers' and students' lack of exposure to and/or competence in the investigative processes, the teacher's traditional views and teaching practices, and some sociosystemic factors in schools. Issues raised here could give insights into the areas where teachers and students needed reinforcement and how teachers could redesign mathematics instruction to focus on the development of processes and thinking skills needed for investigations.

Social and analytic scaffolding in middle school mathematics: managing the dilemma of telling

The current reform movement in mathematics education urges teachers to support students as they make sense of mathematics, while also ensuring that they gain specific mathematical skills and knowledge. The tension between these two expectations gives rise to what we call the dilemma of telling: how to ensure that students come to certain mathematical understandings, without directly telling them what they need to know or do. Our study focused on how two middle school mathematics teachers who were incorporating many aspects of reform mathematics into their instruction responded to this dilemma. Data sources include classroom observations and videotapes of lessons over a three-year period. We found that both teachers devoted the majority of class time to student conversations, both small group and whole class; however, the teachers strategically entered the student-dominated conversations by “telling” to meet specific curricular goals.

How Confident are Students in their Misconceptions about Hypothesis Tests?

Both researchers and teachers of statistics have made considerable efforts during the last decades to re-conceptualize statistics courses in accordance with the general reform movement in mathematics education. However, students still hold misconceptions about statistical inference even after following a reformed course. The study presented in this paper addresses the need to further investigate misconceptions about hypothesis tests by (1) documenting which misconceptions are the most common among university students of introductory courses of statistics, and (2) concentrating on an aspect of research about misconceptions that has not yet received much attention thus far, namely the confidence that students have in their misconceptions. Data from 144 college students were collected by means of a questionnaire addressing the most common misconceptions found in the literature about the definitions of hypothesis test, p-value, and significance level. In this questionnaire, students were asked to select a level of confidence in their responses (from 0 to 10) for each item. A considerable number of participants seemed to hold misconceptions and lower levels of concept-specific self-perceived efficacy were found to be related to misconceptions more than to the correct answers. On average, students selected significantly lower levels of confidence for the question addressing the definition of the significance level than for the other two items. Suggestions for further research and practice that emerge from this study are proposed.

Lenses on Learning: Administrators' Views on Reform and the Professional Development of Teachers

If the intellectual norms and values embedded in the mathematics education reform movement are to move beyond individual classrooms and significantly influence entire schools and districts, school and district administrators will need to become centrally, rather than peripherally, involved. This paper discusses the ways administrators' ideas about the nature of mathematics, learning, teaching, and school culture affect their interpretations of the nature and intent of the elementary mathematics reform movement and their thoughts about of how they might support it. In particular, administrators' views of parents' concerns, professional development for teachers, and of how new ideas move around in a school are discussed. I argue that administrators have well-formed ideas about mathematics, learning, and teaching, which influence their views of reform and their ideas of how to provide support. These ideas need to be taken into account if administrators are to be central actors in reform.

The Technological Revolution and the Reform of School Mathematics

Technology and technology-intensive mathematics curricula are catalysts for the mathematics education reform movement. Students can understand mathematics more deeply when they assume responsibility for their own learning as they engage in and reflect on authentic mathematical activity. Analyzing technology in mathematics classrooms as cognitive technologies with differing degrees of transparency and different abilities to externalize representations, viewing technology used to enhance computational skills as amplifiers, and viewing technology used to encourage students to investigate mathematical phenomena and real-world situations as reorganizers, I evaluate the ways in which empirical research supports this vision or calls it into question.

Practitioner's Research: A Study in Changing Preservice Teachers’ Conceptions About Mathematics and Mathematics Teaching and Learning

Educators involved in the current reform movement in mathematics education recommend that students be actively involved in constructing their own knowledge and developing powerful mathematical concepts. This study suggests how ideas based on constructivist learning theory can be put into practice in a preservice mathematics education class.

Young Children's Perceptions of Mathematics in Problem-Solving Environments

Thirty-six first graders from 2 different school systems participated in individual interviews to determine the children's stated perceptions regarding what it means to engage in mathematics and the rationale and conditions under which they held such perceptions. These children were in classrooms that reflected the spirit of the current reform movement in mathematics education. Generally, the children perceived of mathematics as a problem-solving endeavor in which many different strategies are considered viable and communicating mathematical thinking is an integral part of the task. The children recognized and accepted a variety of solution strategies, with many of the children valuing all solutions equally and assuming a shared responsibility with the teacher for their mathematics learning. Children had varying perceptions of what it meant to succeed in mathematics, but success was not determined by speed and accuracy. As we begin to understand children's perceptions of mathematics as they participate in reform-minded mathematics classrooms, we become aware of issues concerning the impact of the children's perceptions on both the development of their future perceptions and their mathematics learning.

The Clock Is Ticking: Time Constraint Issues in Mathematics Teaching Reform

Abstract Time issues raised by sixth and seventh-grade teachers involved in field testing an NSF-sponsored investigation-centered mathematics curriculum (the Connected Mathematics Project—CMP) for middle-grades students were examined in this study. Questions investigated included the following: How much scheduled time is actually available for mathematics instruction in elementary and middle schools and how is it configured? How do project teachers and students spend their time in class? What factors influence CMP teachers' pacing through this new curriculum? Findings indicate that teaching in the spirit of the current mathematics education reform movement may be highly dependent upon flexibility in class scheduling. Innovations in teaching mathematics (e.g., increased group work, writing, extended projects, and alternative forms of assessment) seem to require additional time, and new ways of thinking about using class time.

Soundoff: Coaching versus Competence

Recently educators have been beset by complaints from parents and businesses—and the news media has run related stories—that educational standards are falling. In partial response to these complaints and stories, some states now demand, as a condition for a high school diploma, a passing score on a standardized elementary mathematical competency test. The introduction of these tests could represent a positive step in the present reform movement in mathematics education—but only if the tests are integrated into the overall framework of that movement. A recent incident in my local school system suggests that a competency test can actually undercut the reform movement if the test is allowed to impose its own reference frame. The discussion that follows derives from that specific incident, but I believe it applies, in principle, to the handling of any standardized test imposed solely to establish a minimum competency requirement. Broader spectrum, multilevel instruments, such as the New York State Regents Examination, raise more complex issues that cannot be addressed here.

Discipline, control, and the school mathematics tradition

Classroom management and discipline are primary concerns of many teachers, especially beginners. The current reform movement in mathematics education advocates a classroom atmosphere and teaching strategies that are substantially different than those that characterize the traditional approach to school mathematics. This paper considers the problems involving discipline and control that arose in the course of a beginning high school teacher's acculturation into the school mathematics tradition. The analysis relates these discipline and control problems to certain tensions and contradictions in the school mathematics tradition and suggests how efforts to cope with these problems serve to reflexively validate the tradition. In addition, the paper suggests some possible reasons for why discipline and control, and not pedagogical content knowledge, are primary concerns for many teachers. Finally, the paper considers how the conditions that foster the emphasis on discipline and control in the school mathematics tradition stand as obstacles in the face of the current reform movement.

Teaching with Problem-Oriented Curricula: A Case Study of Middle-School Mathematics Instruction

Abstract A major goal of the current reform movement in mathematics education is to develop students' problem-solving ability by helping them to make connections among mathematical concepts. The author of the present case study explored this recommended reform by profiling an experienced teacher and examining her use of two problems from a problem-oriented unit developed by an in-progress middle school mathematics curriculum project. In studying the teacher's instruction before and during the problem-oriented unit and unpacking some of her students' solutions, the author found that problem-oriented mathematics curriculum can help teachers offer opportunities for students to make substantive mathematical connections. However, the teacher also had problem-solving goals that focused on the application of known rules and procedures. These teacher goals may have prevented students from making some connections among mathematical concepts that were possible in this problem-oriented unit. These case study finding...

Review: School Mathematics and Multiple Realities: New Paradigms for Assimilation

The mathematics education community owes thanks to Bob Davis and Carolyn Maher for their attempt to promote a discussion, through the conference that preceded this book and the volume itself, about how wide-ranging societal issues interact with mathematics education reform. Rutgers's Dean of the Graduate School of Education Loujse Cherry Wilkinson introduces the volume as a critical analysis of the mathematics education reform movement in the United States. The title, and the DavisMaher introduction, suggest a different agenda for this volume, one which auends seriously to the “world of reality.” They argue that schools are not designed to serve the needs of today's children. who will live and work in the 21st century, and claim that the volume chapters suggest a theoretical foundation for the creation of new approaches that incorporate broader concerns about chools and society. Mixed missions notwithstanding, the collected papers form a readable, interesting set that give some new perspectives on mathematics reform and provide a sampler of the issues that are important to individual projects and research groups.

Making broadcast television participative: Eliciting mathematical behavior throughSquare One TV

The current reform movement in mathematics education has called for new ways of teaching that encourage children to become active participants in mathematical problem solving. In this article, the potential of educational television to elicit such behavior is investigated by reviewing research on theSquare One TV television series. A sizable body of evidence indicates that, through viewer participation,Square One TV can promote mathematical behavior directly among its target audience of 8- to 12-year-olds. Described in the article are the types of viewer participation that have been observed, threeSquare One TV formats that have consistently been found to elicit participative behavior, and several characteristics of these formats that may have been responsible for increased viewer participation. If these characteristics are incorporated into future television-based materials, they may increase the potential of the materials to elicit active participation among viewers.

Needed: An agenda for equity in mathematics education

The purpose of this special issue of the Peabody Journal of Education is to help bring issues of equity to the fore of the current mathematics education reform movement. Over the past decade, we have been inundated with studies, reports, and policy initiatives based on the belief that the American educational system is in crisis. A main focus of that concern has revolved around the teaching of school mathematics. We agree with many of the concerns that underlie calls for reform and note that public education has undergone similar periods of crisis and reform at least since the formation of the common school in the late 1800s. Yet mathematics educators should be concerned that issues of

Elementary school mathematics in the 1970s

Following the successful launching of Sputnik, Congress created the National Science Foundation with instructions and funds to upgrade the scholarship of teachers of mathematics and science. Prestigious professors of mathematics, in cooperation with committees of the Mathematics Association of America and the National Council of Teachers of Mathematics, set out to produce a modern program of instruction in school mathematics. The then-existing programs were analyzed and found to be seriously inadequate in structure, in definitions and assumptions, in development of properties of operation with their appropriate symbolism, and in precision of vocabulary. During the early 1960s institutes and writing teams were engaged in producing and promoting the so-called new mathematics. The resulting reform movement in mathematics education eclipsed any previous one, both in scope and in speed of implementation.