National Council Of Teachers Of Mathematics Standards Research Articles

ANALYSIS OF 8 GRADER STUDENTS’ PERFORMANCE AT SMP AM IN UNDERSTANDING THE TRIANGLE CONCEPT BASED ON NCTM GEOMETRY STANDARD

Geometry plays a pivotal role in mathematics education, contributing significantly to the development of students' spatial awareness, intuition, and visualization skills. Despite its importance, there are reported challenges in students' understanding of geometry, with the Merdeka curriculum geometry standard noted for not adequately emphasizing the fundamental understanding of triangle properties before introducing congruence. Conversely, studies have highlighted the effectiveness of incorporating NCTM (National Council of Teachers of Mathematics) standards in fostering mathematical comprehension in this domain. This research study delves into the performance of eighth-grade students in comprehending triangle concepts, guided by the NCTM geometry standard. Employing a content analysis technique on student work, created based on NCTM indicators and assessed accordingly, the study reveals deficiencies in students' understanding. These challenges include difficulties in describing and categorizing triangles, identifying angle relationships, constructing logical arguments using both inductive and deductive reasoning, and recognizing relationships between side lengths. These findings underscore the urgent need to address these knowledge gaps and bridge the disparity between NCTM standards and students' current comprehension levels regarding triangle concepts.

Work-family Conflict and Psychological Stress among Nurses in Irbid Hospitals

Objectives: This study aimed to investigate the extent to which the content of the basic first-grade mathematics textbook in Jordan complies with the standards of the National Council of teachers of mathematics (NCTM). The study's authors expect that it will help those responsible for creating mathematics curricula at all levels, and in the fundamental first grade in particular, by highlighting areas of strength and need.
 Method: The study sample consisted of a mathematics book for the first grade in Jordan, with its first and second parts, and two exercise books. An analysis instrument was designed; the validity and reliability of the instrument were ensured. The analysis process was carried out by monitoring the set of paragraphs, each of which includes one idea, and then calculating the number of ideas that represent one of the elements of the analysis, and calculating their repetitions and percentages in light of the sum of repetitions of the elements of the criterion.
 Results: The results of the study showed that the content of the first-grade mathematics textbook was the highest in data analysis and probability (0.00−79.31)% while it was the lowest in numbers and operations (0.00−18.69)%. The results also showed that the extent of the operations standards was the highest in problem-solving (0.00−76.92)% and the lowest was in communication (3.57−35.71)%.
 Conclusions: The study recommended the necessity of developing the book according to NCTM standards, and conducting studies to evaluate mathematics books for other classes in light of the current curricular development movement in Jordan.

The Examination of Representations used by Classroom Teacher Candidates in Solving Mathematical Problems

AbstractThis study was designed according to the mixed research method in which quantitative and qualitative research methods were used in order to identify the challenges confronted by classroom teacher candidates in solving mathematical problems and the factors affecting how they choose these representations. The population of this study consisted of 100 3rd year students attending the primary teaching department of Cukurova University during the 2012-2013 academic year. In identifying the samples, the criterion sampling method, a purposeful sampling method, was used. The data collection tools consisted of The Use of Multi pie-Representations in Problem Solving Test and a semi-structured interview form prepared by the researcher. At the end of the research it was discovered that classroom teacher candidates could use different types of multiple representations in solving mathematical problems. However, they used spoken language and algebraic representations the most. During the interviews, teacher candidates emphasized that experience arid the content of the problem are the most important factors in identifying which multiple representations to use. Another important result obtained from the research is that teacher candidates can have problems forming a suitable theme for problems and shifting between representations. For this situation, it can be suggested that giving importance to the concept of multiple representations in the teaching of mathematics as well as doing in-class application studies intended to solve and associate problems using the concept of multiple representations would be beneficial. In that way, teacher candidates can guide their students towards different points of view while solving problems.KeywordsMultiple Representations, Classroom Teacher Candidates, Problem Solving, Mathematics, Polya.The concept of using multiple representations has an important place in the teaching of mathematics (Cai, 2005; Cobb, Yackel, & Wood, 1992; Goldin, 1998; Janvier, 1987), especially in the understanding of mathematical concepts and interpreting them from different points of view through the use of multiple representations (Cathcart, Pothier, Vance, & Bezuk, 2006; Hjalmarson, 2007; Pape & Tchoshanov, 2001). According to Tripathi (2008), the use of multiple representations in teaching mathematics is a strong instrument that eases the understanding of mathematical subjects for students. Also, the use of multiple representations strengthens the understanding of students for learning how to form and solve problems in a mathematics course.The new standards of the American National Council of Teachers of Mathematics (NCTM) published in 2000 especially emphasize the importance of the concept of representation. Within this context, according to the NCTM, the use of diagrams, graphics, tables and symbols, as well as transitioning between them, is of capital importance in expressing mathematical thoughts and relations. Stemming from the NCTM (2000) standards, representations are also a part of the required abilities in the mathematics curriculum of Turkey for use in problem solving, communication (verbal lectures, written statements, images, graphics, concrete concepts), and associations (Milli Egitim Bakanligi [MEB], 2005, 2009). Stylianou (2010) also states that students should be effective in using representations and their transitions for solving mathematics and understanding mathematical concepts.As a general term, a representation is a way to show an actual situation from a different point of view (Even, 1998; Goldin & Kaput, 1996). In mathematics, however, teaching representation is a part of forming or shaping a mathematical concept. The different representations that teachers use during in-class activities affect the knowledge, and accordingly, the success of students (Cai, 2005; Neria & Amit, 2004; Stylianou & Silver, 2004). That is why the understanding of representations and how to use different types of representations should be an active part of the teaching process (Hjalmarson, 2007; Pape & Tchoshanov, 2001). …

The Trials of a Poor Middle School Trying to Catch Up in Mathematics: Teachers' Multiple Communities of Practice and the Boundary Encounters

This article details a 5-year evolution of a middle school mathematics faculty serving predominantly economically at-risk students. Faculty members worked to improve students' mathematics test scores, used a scripted curriculum, and integrated National Council of Teachers of Mathematics (NCTM) standards-based activities. Schools nationwide are transforming with the No Child Left Behind legislation, accountability mandates, and the NCTM standards. The demands on these teachers are typical of high-stakes systems. Drawing on Lave and Wenger's “community of practice” and Cobb, McClain, Lamberg, and Chrystal's extension, this article describes how teachers accommodate to the process of change and the group dynamics encountered within a school structure.

Mathematics Subject Headings for the PreK-12 Community: A Comparison of Key Terms from the National Council of Teachers of Mathematics (NCTM) Mathematics Standards to ERIC Thesaurus Descriptors and the Library of Congress Subject Headings

ABSTRACT The National Council of Teachers of Mathematics (NCTM) is an international organization which supports the teaching and learning of mathematics for children from Pre-Kindergarten through Grade 12. In the year 2000, the NCTM produced Principles and Standards for School Mathematics, a document that has become the basis for state and local mathematics curriculum standards across the United States. This article examines the key terms identified in the NCTM standards, identifies their equivalents in the ERIC Thesaurus and the Library of Congress Subject Headings, and makes recommendations to bring library subject headings closer to reflecting the language common to mathematics educators.

The ‘Last Mile’ in Standards-Based Reform: Conducting a Match Study Linking Teacher-Certification Tests to Student Standards

BY charging that U.S. schools were fostering a rising tide of mediocrity, A Nation at Risk, the 1983 report of the National Commission on Excellence in Education, unleashed its own tidal wave within U.S. public education. The report elicited responses from numerous bodies. The states' answer was to immediately begin development of student academic standards in key subject areas. While this might have seemed like a feeble response to the flaming rhetoric of the report, the development of systematic, state-based standards has in fact generated potent aftershocks that continue to affect American education. The logic of focusing on student standards proved to be disarmingly powerful. The knowledge, skills, and abilities that a state expected its students to acquire became the true north with which the state's entire education system would be aligned. At one stroke the terrain of public education in the states became clear: student standards would guide classroom instruction, and the demands of instruction would shape teacher preparation and qualifications. This fundamentally student-centered effort at improving education became known as standards-based reform. Since the mid-1980s, nearly all states have endorsed this idea by creating learning standards for their students in at least the central academic areas. The states were encouraged to expend the considerable resources necessary for developing sound standards by such federal initiatives as 1994's Goals 2000, which politely urged states to define standards, and the more forceful No Child Left Behind (NCLB) Act of 2002, which replaced politeness with compulsion. At the same time, the states' individual efforts were at times reinforced and at times overwhelmed by a landslide of standards documents produced by academic and professional associations. The most seismic of these was undoubtedly Curriculum and Evaluation Standards for School Mathematics, produced in 1989 by the National Council of Teachers of Mathematics (NCTM). The 1989 NCTM standards (and their revised, 11-years-younger sibling, Principles and Standards for School Mathematics) became probably the most influential educational standards ever published by an academic association and inspired the development of many similar documents in other disciplines. At present, every state save Iowa has its own student academic standards. What is remarkable about these standards is that they are truly state specific. Although a state's standards may be inspired by the standards documents of the professional associations or based on the standards published by other states, they remain distinctive state products, reflecting the state's understanding of what is most salient in the fields that they address. THE INDIVIDUALITY OF STATE STANDARDS Standards vary in their content, organization, wording, and emphases, and they differ in the scope and sequence of the content that they cover at the different grade levels. Consider, for example, the grade-8 mathematics standards of Georgia and Pennsylvania. (1) The topic of Statistics and Probability in grade 8 may at first glance seem to be relatively impermeable to interstate variance, but this is not entirely the case. The two states' sets of standards are different. Georgia expects its eighth-graders to use set theory as an approach to data analysis, to be familiar with concepts and procedures of data analysis, to understand the basic laws of probability, and to analyze data closely. Pennsylvania expects its eighth-graders to use their knowledge of statistics critically in real-world contexts, to analyze and explain the applications of statistical concepts, and to compare predictions with observations. These are different approaches and different expectations, and achieving them would require classroom instruction and teacher preparation with different emphases. The point is not that one set of standards is better than the other or more detailed or more anything else. …

Increasing Math and Science Achievement: The Best and Worst of the East and West

IN MARCH 2005, during the annual session of the Chinese National People's Congress, a group of members of the Chinese legislative body introduced a proposal calling for an immediate overhaul of the New Mathematics Curriculum Standards for elementary and secondary schools. A similar proposal was introduced by members of the Chinese People's Political Consultative Conference, the highest political organization representing non-Communist parties and social elites without party affiliations. Both proposals were initiated and supported by prominent mathematicians and scientists who believe that the New Math Curriculum Standards, released by the Chinese Ministry of Education in 2001 and largely modeled after the 1989 version of the standards issued in the U.S. by the National Council of Teachers of Mathematics (NCTM), are ruining education in China. The New Math Curriculum has been sharply criticized for betraying an excellent educational tradition, sacrificing mathematical thinking and reasoning for experiential learning, giving up disciplinary coherence in the name of inquiry learning, lowering expectations in the name of reducing students' burden, and causing confusion among teachers and students. 10 years, when we find our next generation cannot think logically and reason mathematically, says Jiang Boju, a professor at Peking University and a member of the Chinese Academy of Sciences who sponsored the proposal, it will be too late. Similar concerns have been voiced by ministry officials, parents, mathematicians, and textbook publishers. BACK TO THE FUTURE: THE IRONY OF EDUCATION REFORM IN THE EAST AND WEST The math wars in China are also taking place in other East Asian education systems. Over the past decade, Chinese Taipei, Hong Kong, Japan, Korea, and Singapore have all engaged in dramatic curricular reforms and are now beginning to debate the results. (1 When they first embraced reform, these high performers in international and science tests appeared to be extremely unhappy with their own and science education. They seemed eager to abandon what the rest of the world, particularly the United States, would love to have: a rigorous, coherent, systematic and science curriculum instead of inquiry-based, constructivism-driven, child-centered, progressive and science education, which many American educators now seem similarly eager to throw away. The East Asian reformers were not crazy, nor were they agents of the U.S. government on a secret mission to wipe out America's competition by lowering and science achievement elsewhere, as some Chinese teachers jokingly accused. They were well-intentioned and diligently looking for a way to address their own problems: students' lack of creativity, an overemphasis on testing, a focus on memorization over application, a disconnection between school learning and real-life situations, and overworked students. In essence, what the East Asian reformers wanted for their future was America's past and present. In their eyes, students in the United States were happy, creative, and socially responsible--products of an education system that focused on children over knowledge, pedagogy over content, and the individual over the group--all traits seen as the secret to America's economic success and dominance. Comparing their own curriculum with that of the United States, the reformers found that they tried to teach too much and were knowledge--and teacher-centered. Thus they began to ease students' burdens by removing basic concepts, formulae, and computation skills; turning a staircase curriculum into a spiral one; and requiring students to construct and discover knowledge through inquiry. Meanwhile, on this side of the Pacific and in the land that exported NCTM and AAAS (American Association for the Advancement of Science) standards and constructivism, Singaporean textbooks have become increasingly hot commodities for parents, (2) Japanese lesson study is viewed as an exemplary teacher professional development model, (3) Chinese teachers have become models of excellence, (4) and coherent and logical East Asian curricula are synonymous with the path to and science excellence in U. …

Balancing mathematics education research and the NCTM standards

The release of the Principles and Standards for School Mathematics in the United States by the National Council of Teachers of Mathematics (NCTM) brought to the forefront the debate of whether research should determine the validity of the espoused Standards? Or conversely whether the Standards should influence the research agenda of the mathematics education community? How should university teacher educators address this issue? Should pre-service and practicing teachers blindly, accept the Standards as well as the research, or do we cultivate the critical thinking skills that will allow preparing teachers to resolve this dilemma? In this article a university mathematics educator and an idealistic pre-service elementary teacher try to resolve the dilemma of balancing the Standards with research and personal beliefs about the teaching and learning of mathematics.

A Comparative Analysis of Third-Grade Mathematics Textbooks Before and After the 2000 NCTM Standards

We previously conducted a curriculum analysis of third-grade mathematics textbooks aimed at investigating the extent to which teaching the recommended methods for problem solving adhered to the 2000 National Council of Teachers of Mathematics (NCTM) Standards and instructional design criteria. In this article, we extend the previous findings by comparing the teaching of problem solving presented in the same textbooks published after the 2000 NCTM Standards to that in older editions published before the Standards were in effect. Results indicated that the changes in textbooks varied with regard to meeting the different Standards. However, results for instructional design criteria indicated more consistent changes, favoring the textbook series published after 2000. Additional findings and implications for practice are discussed.

Perceptions and Application of NCTM Standards by Special and General Education Teachers

This study determined teachers' perceptions related to application of, and barriers to implementation of the National Council of Teachers of Mathematics (NCTM) Standards with students labeled learning disabled (LD) and emotionally disturbed (ED). A stratified random sample of 129 secondary general education math and special education teachers responded to a mail survey. A majority of special education teachers indicated they had not heard of the NCTM Standards. Respondents reported teaching mostly basic skills/general math to secondary students with LD and ED, versus higher-level math, such as algebra and geometry. Teachers identified lack of adequate materials as a considerable barrier to successful implementation of activities based on the Standards. Implications for practice and future research are also provided.

The Cyclical Relationship Between Research and Standards: The Case of Principles and Standards for School Mathematics

The link between standards and research may not be clearcut. However, in this article the authors argue that there is a notable relationship between standards and research, one that is cyclical in nature. Using the standards for school mathematics developed by the National Council of Teachers of Mathematics (NCTM) as a case in point, the authors examine how NCTM's standards have influenced the agenda for mathematics education research and stimulated research on the impact of those standards. In turn, this and other research played a significant role in the development of NCTM's new Principles and Standards for School Mathematics. The authors conclude with a discussion of ways in which the Principles and Standards may continue this cyclical relationship in coming years, potentially promoting investigation of new research areas and systematic research on the impact of standards.

Curriculum Materials Supporting Problem‐Based Teaching

The vision for school mathematics described by the National Council of Teachers of Mathematics (NCTM) suggests a need for new approaches to the teaching and learning of mathematics, as well as new curriculum materials to support such change. This article discusses implications of the NCTM standards for mathematics curriculum and instruction and provides three examples of lessons from problem‐based curricula for various grade levels. These examples illustrate how the teaching of important mathematics through student exploration of interesting problems might unfold, and they highlight the differences between a problem‐based approach and more traditional approaches. Considerations for teaching through a problem‐based approach are raised, as well as reflections on the potential impact on student learning.

Evaluating Instructional Materials

IN 1996, WE WERE ASKED TO EVALUATE A new set of mathematics instructional materials for the middle school classroom. The instructional unit included a wide assortment of materials, so we decided to begin with some explicit criteria on which to base our evaluation. We turned to several sources, including the National Council of Teachers of Mathematics (NCTM) and local school districts, seeking evaluation guidelines that were in the spirit of the NCTM's Standards documents (1989, 1991, 1995).

Comments: NCTM's Curriculum and Evaluation Standards

The comments in this article provide a background to the key notions underlying the National Council of Teachers of Mathematics (NCTM) Curriculum and Evaluation Standards for School Mathematics: first, the organization's intent when it decided to prepare this document; second, the anticipated use of the standards by teachers, schools, and states to change how mathematics has been organized and taught in American schools; third, the current process of preparing revisions to the standards by NCTM. The author ends by offering comments about unanticipated reactions to the document.

The Relationship Between Teacher and Student Beliefs About Mathematics

In this study the relationship between teacher (n = 7) beliefs about mathematics, the learning and teaching of mathematics and their respective students' beliefs about mathematics (n = 158) are examined. The data were collected by means of two instruments specifically designed to measure belief systems about mathematics. Teacher scores were adjusted so that a higher score reflected beliefs in aligntnent with the National Council of Teachers of Mathematics (NCTM) Standards. Results indicated that the students of teachers whose beliefs were in alignment with the NCTM Standards had significantly different beliefs about factors that lead to success in mathematics than did other students. Specifically these students felt that working hard to solve problems and striving for understanding would lead to success. No student differences were found for subscales of ego orientation, competitiveness, interest and extrinsic factors such as neatness and cooperation. These findings suggest that this group of teachers practiced what they believed and that these practices affected what their students believed about mathematics. We suggest that using these two assessments in tandem give a clearer picture of the mathematical environment within a classroom and can be used in professional development workshops to initiate teacher reflection about classroom practices.

The NCTM standards in light of the new math movement: A warning!

Although many have assailed the failure of the New Math Movement of the 1950s and 60s and extolled the virtues of the National Council of Teachers of Mathematics (NCTM) Standards, little has been written from the perspectives of those most instrumental within each movement. It is the perspective of those who took part in each reform effort into which this paper investigated. Interviewees ably delineated the philosophical perspectives of their respective movements, reasons for its success or failure or both, and their prognosis for the future of mathematics education. The telephone interviews of some of the seminal people involved within the two movements were transcribed, coded, analyzed, and are here reported. Many of the results could not have been imagined by anyone outside of the inner circles within these reform efforts. This article offers many surprising opinions that have not been available anywhere else and which offer a stern warning to the NCTM.