Barbara J. Reys

University of Missouri | Mizzou · Department of Learning, Teaching and Curriculum

This article focuses on the career paths in higher education taken by 351 doctoral graduates in mathematics education and provides insight into their career path and their resulting workload. Because some of the sample is drawn from graduates of programs with NSF funding related to doctoral preparation, it represents a best-case scenario of doctora...

This landmark study of doctoral graduates in mathematics education provides benchmark data that we hope will be useful to the mathematics education community. Five hundred three doctoral graduates from twenty-three institutions participated in the study with a response rate of over 90 percent. This article focuses on doctoral graduate satisfaction...

We offer some ideas for improving doctoral preparation based on a survey of faculty members from twenty-three different institutions.

Institutions in the United States have been producing PhDs in mathematics education for more than a century. Teachers College at Columbia University and the University of Chicago produced the first graduates in mathematics education in 1906 and 1912, respectively [1]. In those institutions, doctoral students in mathematics education typically took...

This commentary highlights the contribution that careful and systematic analyses of curriculum or content standards can make to questions and issues important in the mathematics education field. We note the increased role that curriculum standards have played as part of a standards-based education reform strategy. We also review different methods u...

The Common Core State Standards for Mathematics (CCSSM) is a primary focus of attention for many stakeholders' (e.g., teachers, district mathematics leaders, and curriculum developers) intent on improving mathematics education. This article reports on specific content shifts related to the geometry domain in the middle grades (6–8) mathematics curr...

This chapter examines the impact of the Common Core State Standards for Mathematics (CCSSM in relation to expectations related to computational fluency in elementary grade levels. Comparison with previous state standards are provided to illustrate the shifts apparent in CCSSM.

Using Clairaut's historic-dynamic approach and dynamic geometry tools in middle school can develop students' conceptual understanding before they encounter formal proof in geometry.

In the U.S. three curriculum strategies are being used to improve school mathematics programs and student learning outcomes: (a) the movement to common standards; (b) advances in technology-based instructional resources; and (c) the pressure of accountability measured by end-of-year assessments. Together, these strategies are creating a “perfect st...

Readers can view and mathematically compare the sizes of various playing surfaces.

This op-ed piece gives a historical perspective on curriculum change.

The Missouri Middle Mathematics (M3) Project is an NSF-funded 3-year professional development project involving teacher/administrator teams from districts statewide. Project activities focus on collaborative investigation of emerging reform-based middle school mathematics curricula to support individual and systemic reform. Collaborative review and...

This paper reports selected findings from a study of number sense proficiency of students aged 8 to 14 years in Australia, Sweden, United States, and Taiwan. It comments on the meaning and importance of number sense, the development of the assessment instruments, and student responses to the items. Some implications for classrooms of the findings a...

In this paper is reported the extent of textbook use by 39 middle school mathematics teachers in six states, 17 utilizing a textbook series developed with funding from the National Science Foundation (NSF-funded) and 22 using textbooks developed by commercial publishers (publisher-generated). Results indicate that both sets of teachers placed signi...

A group of 25 undergraduate students was given seven estimation tasks that involved computation of whole or decimal numbers. The subjects (10 elementary education majors, 7 mathematics majors, and 8 undecided or premajors) were selected because of high achievement in their current college mathematics class. They were asked to estimate an answer to...

Different forms of curriculum determine what is taught and learned in US classrooms and have been used to stimulate school improvement and to hold school systems accountable for progress. For example, the intended curriculum reflected in standards or learning expectations increasingly influences how instructional time is spent in classrooms. Curric...

The No Child Left Behind Act of 2001 (NCLB, 2002) elevates the importance of educational research and thereby provides opportunities for mathematics education researchers in its support for and funding of rigorous research studies and its requirement of effective, research-based practices. At the same time, by demanding more of overburdened teacher...

Why curriculum matters in teacher education: Helping future teachers expand their views of mathematics curriculum.

This study analyzes measurement learning expectations involving area and volume in grades 1–8 across several U.S. states and high-performing TIMSS Asian countries, including Singapore, Taiwan, and Japan. Based on a review of official curriculum documents, results of this study indicate that the mathematics content, grade placement, and cognitive le...

We examine student achievement of 2533 students in 10 middle schools in relation to the implementation of textbooks developed with funding from the National Science Foundation (NSF) or publisher-developed textbooks. Using hierarchical linear modeling (HLM), curriculum type was not a significant predictor of student achievement on the Balanced Asses...

This study examined number sense strategies and misconceptions of 280 Taiwanese pre-service elementary teachers who responded to a series of real-life problems. About one-fifth of the pre-service teachers applied number sense-based strategies (such as using benchmarks appropriately or recognizing the number magnitude) while a majority of pre-servic...

The similarities and differences in grade-level learning expectations for fourth graders in ten different states that publish mathematics standards.

Clearly, much work and effort at the state level have gone into articulating learning expectations for mathematics in grades K-8. The state GLE documents present specific learning goals and describe learning sequences for attaining these goals across the elementary years. For many states, these grade-level learning expectations represent a new leve...

In this era of high-stakes testing and public accountability, school personnel are scrambling for ways to improve mathematics learning opportunities for all students. Although there is no single silver-bullet solution, Principles and Standards for School Mathematics (NCTM 2000) provides guidelines for designing high-quality school mathematics progr...

The No Child Left Behind Act of 2001 (NCLB, 2002) elevates the importance of educational research and thereby provides opportunities for mathematics education researchers in its support for and funding of rigorous research studies and its requirement of effective, research-based practices. At the same time, by demanding more of overburdened teacher...

PREFACE Since 2001, many states have developed new, more specific mathematics curriculum frameworks outlining the intended curriculum, K-8. While some of these documents are intended to be "models" for districts to utilize in shaping local curriculum specifications, others are mandatory, specifying the mathematics all students within the state are...

Fiercely competing textbook publishers claim that their materials are research-based and will produce student success. The authors offer sound advice to educators trying to sort out these claims as they select mathematics textbooks that will truly fit their schools' objectives.

Textbook selection strongly influences on what students will learn and what the teachers will teach. Certain statements regarding the process of development and selecting mathematics textbooks are given and assessed.

The federal No Child Left Behind Act (Public Law 107-110, HR 1, 2001) calls for all teachers in schools receiving federal funds to be “highly qualified.” That is, they must hold a bachelor's degree, demonstrate competence in the subject matter that they teach, and have full state teacher certification—their certification requirements cannot be waiv...

Welcome to the new “Spotlight on the Principles.” September's “Spotlight on the Standards” brought to a close the set of articles examining the ten Standards envisioned in NCTM's Principles and Standards for School Mathematics (2000). With this article, the MTMS Editorial Panel is directing the focus of the department on the six Principles, beginni...

Introduces standards-based middle grades mathematics instructional materials designed to engage and challenge students in mathematical investigation. Details the challenges of change for teachers, administrators, parents, and students. Highlights a study of the Missouri Middle School Mathematics Project, which implemented one of the NSF curricula,...

We frequently ask students in our preservice elementary mathematics methods courses if they realize that they are preparing to become mathematics teachers. Many, if not most, of the students are uncomfortable with thinking of themselves as “mathematics teachers,” preferring to call themselves “elementary classroom teachers.” They consider themselve...

This study compared the mathematics achievement of eighth graders in the first three school districts in Missouri to adopt NSF-funded Standards-based middle grades mathematics curriculum materials (MATH Thematics or Connected Mathematics Project) with students who had similar prior mathematics achievement and family income levels from other distric...

The authors describe six central characteristics of standards-based mathematics curriculum materials and discuss how these characteristics are related and how each one sets the stage for and supports the others.

Since the publication of NCTM's Principles and Standards for School Mathematics in April 2000, considerable discussion has taken place about “key messages” of the document. The breadth of the content of Principles and Standards may hamper attempts to identify messages about particular topics. In addition, many of the fundamental messages are not ea...

Have you seen it? Have you read it? Have you begun talking with colleagues about the ideas that it presents? Have you reflected on how it will influence your instruction? Have you examined your curriculum materials in light of the expectations that it outlines?

The goal of the project was to improve the teaching and learning of middle school mathematics through collaborative Standards-based mathematics curriculum investigations. The project not only contributed to the improvement of teaching mathematics in the participants’ classrooms, but it also significantly affected the program for prospective middle...

The use of benchmarks, such as 0, 1/2, and 1, for comparing the size of fractions is not emphasized very often in instruction. Comparing fractions with 0, 1/2, or 1 by comparing the numerator with the denominator or by mentally modeling the fraction is a powerful tool for gauging the size of fractions, making quick estimates, and judging the reason...

Several common factors contribute to the effectiveness of teachers in implementing a standards-based mathematics curriculum in their classrooms, the authors maintain. Awareness of these factors and the development of ways to address them will increase the likelihood of success.

Teachers, administrators, and parents need to become informed about the unique characteristics of the mathematics curricula based on the NCTM Standards and about the support structures that are being established to make it easier for schools to adopt them. For sources of such information, read on.

The amount and placement of instructional time devoted to various types of computation are crucial. Reviews messages regarding what and how computation should be developed in elementary school mathematics and offers a proposal for a K-8 computation curriculum. (ASK)

Discusses the implementation of a standards based mathematics curriculum at the middle school level that engages students' active learning. Considers obstacles to this reform, including traditional beliefs, student initial reactions to new teaching practices, parental perceptions, transition from middle grades to high school, assessment of student...

Describes a mathematics fair prepared by the University of Missouri Mathematics Teachers Organization (UM2TO) which includes games involving numbers and computation, logic puzzles, geometry and spatial-visualization exploration, and probability and statistics activities. Presents tips for developing a mathematics fair. (ASK)

At the primary-grades level, the benefits of developing and using mental strategies for computing have been well articulated (see, e.g., Beberman (1959); Brownell [1972); Cobb and Merkel [1989]: Kamii [1989]; Reys and Barger [1994): Shuard [1987); Trafton [1978)), and many primary-grades teachers are now encouraging students to invent and use think...

In this article we report an analysis of how computation is developed in Japanese textbooks in grades 1-3. The results are based primarily on an analysis of 3 popular Japanese textbook series. We also observed mathematics instruction in several teachers' classes. We found that basic facts and multidigit whole-number computation are developed in ric...

The study was conducted to explore performance on a variety of mental computation tasks using two presentation formats (visual and oral). Students at four grade levels between grades 2 and 9 in three countries (Australia, Japan, United States) were given a group administered mental computation test consisting of two parts (oral presentation format,...

This study assessed attitude, computational preferences, and mental computational performance of 176, 187, 186, and 206 Japanese students in grades 2, 4, 6, and 8, respectively. A sample of students in grades 4 and 8 scoring in the upper and middle quintiles on the mental computation test was interviewed to identify strategies used to mentally comp...

This study assessed attitude, computational preferences, and mental computational performance of 176, 187, 186, and 206 Japanese students in grades 2, 4, 6, and 8, respectively. A sample of students in grades 4 and 8 scoring in the upper and middle quintiles on the mental computation test was interviewed to identify strategies used to mentally comp...

Japan's stature as an economic and political power worldwide has caused growing interest in the country's culture and. more specifically, its system of educating its youth. International comparisons of mathematics achievement highlight Japanese students' unquestioned superiority in mathematical performance. Factors that contribute to the relatively...

Discusses good mathematical tasks and where they may be found. Good tasks are authentic, are challenging, pique the curiosity of students, encourage students to make sense of mathematical ideas, encourage multiple perspectives, and nest skill development in the context of problem solving. (MKR)

The mathematics education community has been recommending the integration of calculators into mathematics curriculum and instruction for nearly twenty years.

Phrases such as “number sense,” “Operation sense,” and “intuitive understanding of number” are used throughout the Curriculum and Evaluation Standards for School Mathematics (NCTM 1989) to describe an intangible quality possessed by successful mathematics learners. Number sense refers to an intuitive feeling for numbers and their various uses and i...

The objective of this study was to determine how students' strategies for solving percent problems change over grades 5, 7, 9, and 11. The questions addressed included the following: What intuitive knowledge do students bring to the study of percent? Do students use this intuitive knowledge in solving percent problems? What processes do students us...

The objective of this study was to determine how students' strategies for solving percent problems change over grades 5, 7, 9, and 11. The questions addressed included the following: What intuitive knowledge do students bring to the study of percent? Do students use this intuitive knowledge in solving percent problems? What processes do students us...

What computational estimation skills and strategies do Mexican students possess? Does the theoretical model based on interviews with a select United States sample accurately describe the Mexican sample? These were questions studied based on interviews with 8 eighth graders (those scoring in the top 5%) out of a sample of 177 eighth graders from twe...

Four hundred and sixty-six fifth- and eighth-grade Japanese students were administered a computational estimation test. The fifth-grade mean was 7.39 and the eighth-grade mean was 11.15 on the 39-item open-ended test. Interviews with 21 students who had scored in the top 5% revealed that the Japanese students employed the three general cognitive pr...

Four hundred and sixty-six fifth- and eighth-grade Japanese students were administered a computational estimation test. The fifth-grade mean was 7.39 and the eighth-grade mean was 11.15 on the 39-item open-ended test. Interviews with 21 students who had scored in the top 5% revealed that the Japanese students employed the three general cognitive pr...

Do you estimate? Of course you do. Everyone estimates. Research shows that estimation is used in real-world problem solving far more than exact computation. Furthermore, estimation relates to every important mathematics concept and skill developed in elementary school. It is a process that allows the user to form an estimate or to judge the reasona...

The content and emphasis of mathematics programs has been the subject of much discussion in recent years. Such technological advances as the increased availability and use of computers and calculators have caused a tremendous and sudden shift in the mathematical needs of today's citizens. Whereas twenty years ago mathematical operations using paper...

Although curriculum and teaching method change slowly, we have witnessed some major changes in mathematics instruction over the last ten years, most notably the emphasis placed on the problem-solving process. We've also observed vast amount of resources funneled into microcomputer equipment for young students. In part because of this interest in mi...

Changing curricula in mathematics is more difficult than moving an old graveyard in January. Nevertheless, cries for changing our mathematics programs are coming from many directions as ideas for a forward-looking, futuristic mathematics curriculum are offered. Although calls for specific curricular changes are varied, all seem to agree on one thin...

The ability to compute mentally. that is. to calculate exact numerical answers without the aid of any calculating or recording device, varies tremendously among indi vidual s. A quick survey of any elementary or secondary school classroom will document that some students perform mental computation quickly and accurately, whereas others are greatly...

Thesis (Ph. D.)--University of Missouri--Columbia, 1985. Vita. Includes bibliographical references (p. [164]-167). Photocopy.

Parents have many opportunities every day to develop, nurture, and refine their children's mathematics skills. This pamphlet was designed to help parents become aware of these opportunities and to encourage them to participate in their children's learning process. Estimation is the skill of making a reasonably accurate guess and is prominently invo...

Vad är överslagsräkning? Överslag är något som vi alla använder många gånger varje dag. Exempel 1 visar några vardagssituationer. Överslagen har många gemensamma drag – de görs i hu-vudet utan skriftliga räknemetoder och ger resultat som inte är exakta men som ger underlag för beslut som behöver tas. Överslagräkning kan beskrivas på olika sätt. Här...