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Journal articles on the topic 'Curriculum evaluation Mathematics'

Author: Grafiati

Published: 4 June 2021

Last updated: 7 February 2022

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1

Thompson, Charles S., and Edward C. Rathmell. "NCTM's Standards for School Mathematics, K – 12." Mathematics Teacher 81, no. 5 (May 1988): 348–51. http://dx.doi.org/10.5951/mt.81.5.0348.

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The National Council of Teachers of Mathematics is in the process of generating a set of Curriculum and Evaluation Standards for School Mathematics (Standards) (Commission on Standards of the NCTM 1987). NCTM has committed considerable resources to this project, anticipating that the Standards will have a pervasive effect on mathematics education during the next five to ten years. The expectation is that the Standards will influence curriculum writing at the state and local levels and that the resulting curricular changes will influence the content of textbooks adopted by states and school districts. Furthermore, the newly written curricula, together with the new Standards for the evaluation of mathematics learning, should influence the content and emphasis of local, state, and national tests.

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Shealy, Barry E. "Becoming Flexible with Functions: Investigating United States Population Growth." Mathematics Teacher 89, no. 5 (May 1996): 414–18. http://dx.doi.org/10.5951/mt.89.5.0414.

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Real-world contexts are appearing more often in international curricula, and the arguments for using modeling and applications are broadening (Blum and Niss 1991). The National Council of Teachers of Mathematics, in its Curriculum and Evaluation Standards for School Mathematics (1989), suggests that modeling is a great context for developing problem-solving and reasoning skills. These types of experiences promote communication and allow students to make connections among mathematical ideas and between mathematics and other disciplines. Modeling activities are also consistent with the concept of a core curriculum, offering contexts for a variety of types and depths of problems. It is not surprising that the Curriculum and Evaluation Standards points out that students should be able to “apply the process of mathematical modeling to real-world problem situations” (NCTM 1989, 137)

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Gailey, Stavroula K. "The Mathematics-Children's-Literature Connection." Arithmetic Teacher 40, no. 5 (January 1993): 258–61. http://dx.doi.org/10.5951/at.40.5.0258.

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The Curriculum and Evaluation Standards for School Mathematics (NCTM 1989) promotes mathematical power for all students so that they can function a informed citizens in a rapidly changing and technologically complex society. A way of working toward this goal is by investigating connections within mathematics and between mathematics and other instructional areas. The mathematic— children's-literature connection is examined in this article.

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Hatfield, Mary M., and Gary G. Bitter. "Communicating Mathematics." Mathematics Teacher 84, no. 8 (November 1991): 615–22. http://dx.doi.org/10.5951/mt.84.8.0615.

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Affording more opportunities to engage students in thinking and communicating mathematically and integrating technology into mathematics education are clear trends in curricular reform. Recent recommendations emphasize adopting a more active, process-oriented approach to mathematics learning and teaching. The Mathematical Sciences Education Board's document Reshaping School Mathematics (1990) emphasizes that a person engaged in mathematics gathers, discovers, creates, and expresses facts and ideas about patterns. The National Council of Teachers of Mathematics in its Curriculum and Evaluation Standards for School Mathematics (1989) advocates mathematics teaching through activities that encourage students to explore mathematics, to gather evidence and make conjectures, and to reason and communicate mathematically as they discuss and write about ideas that use the language of mathematics. This vision of the classroom specifies a mathematics curriculum in which students are “doing and investigating” mathematics rather than just “knowing” mathematics.

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Elliott, Portia. "One Point of View: Reclaiming School Mathematics." Arithmetic Teacher 37, no. 8 (April 1990): 4–5. http://dx.doi.org/10.5951/at.37.8.0004.

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The framers of the Curriculum and Evaluation Standards for School Mathematics (NCTM 1989) call for a radical “design change” in all aspects of mathematics education. They believe that “evaluation is a tool for implementing the Standards and effecting change systematically” (p. 189). They warn, however, that “without changes in how mathematics is assessed, the vision of the mathematics curriculum described in the standards will not be implemented in classrooms, regardless of how texts or local curricula change” (p. 252).

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Collison, Judith. "Using Performance Assessment to Determine Mathematical Dispositions." Arithmetic Teacher 39, no. 6 (February 1992): 40–47. http://dx.doi.org/10.5951/at.39.6.0040.

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The proliferation of information and information technology demands educational change, especially in mathematics. The emphasis must shift from mere acquisition to the use of information to deepen mathematical understanding and appreciation. The NCTM 's Curriculum and Evaluation Standards (1989) envisions a new curriculum. Among its goals are the development of “mathematical power,” or “numeracy” (National Research Council 1989) and an appreciation of the beauty and power of mathematic (NCTM 1989). Mathematics instruction must not merely expand students' knowledge of mathematics but must also foster intellectual courage and a set of positive personal attitudes, or dispositions, that enable and empower students.

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Litwiller, Bonnie H., and David R. Duncan. "Combinatorics Connections: Playoff Series and Pascal's Triangle." Mathematics Teacher 85, no. 7 (October 1992): 532–35. http://dx.doi.org/10.5951/mt.85.7.0532.

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One major theme of the National Council of Teachers of Mathematic's Curriculum and Evaluation Standards far School Mathematics (1989) is the connection between mathematical ideas and their applications to real-world situations. We shall use concepts from discrete mathematics in describing the relationship between sports series and Pascal's triangle.

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Miller, L. Diane. "Preparing Elementary Mathematics-Science Teaching Specialists." Arithmetic Teacher 40, no. 4 (December 1992): 228–31. http://dx.doi.org/10.5951/at.40.4.0228.

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The Curriculum and Evaluation Standards for School Mathematics “expresses the consensus of professionals in the mathematical sciences for the direction of school mathematics in the next decade” (NCTM 1989, vi). It represents a response to the call for reform in the teaching and learning of mathematics. As one familiar with the preparation of elementary school teachers examines the Curriculum and Evaluation Standards, a sense of doom pervades the otherwise enthusiastic attitude toward the reform represented by the document. Many practicing and prospective teachers are not adequately prepared to meet the challenge of implementing the curriculum standards.

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Thomas, Christine, and Carmelita Santiago. "Spotlight on the Principles/Standards: Building Mathematically Powerful Students through Connections." Mathematics Teaching in the Middle School 7, no. 9 (May 2002): 484–88. http://dx.doi.org/10.5951/mtms.7.9.0484.

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Connections in mathematics can be implemented in ways that create excitement in the classroom, develop in students a love for doing mathematics, and foster students' natural inclination for pursuing mathematical tasks. According to the Curriculum and Evaluation Standards for School Mathematics, “If students are to become mathematically powerful, they must be flexible enough to approach situations in a variety of ways and recognize the relationships among different points of view” (NCTM 1989, p. 84). Principles and Standards for School Mathematics (NCTM 2000) further asserts that students develop a deeper and more lasting understanding of mathematics when they are able to connect mathematical ideas. The 1989 and 2000 Standards clearly delineate the power and importance of connections in the mathematics curriculum. This article examines and compares curricular recommendations for connections in the two documents.

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van den Eeden, Pieter, and Jan Terwel. "Evaluation of a mathematics curriculum: Differential effects." Studies in Educational Evaluation 20, no. 4 (January 1994): 457–75. http://dx.doi.org/10.1016/0191-491x(94)00037-h.

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Pacyga, Robert. "Implementing the Curriculum and Evaluation Standards: Making Connections by Using Molecular Models in Geometry." Mathematics Teacher 87, no. 1 (January 1994): 43–47. http://dx.doi.org/10.5951/mt.87.1.0043.

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As instructors of mathematics, we need to demonstrate to our students the use and value of connections between mathematics and other disciplines. The authors of the Curriculum and Evaluation Standards for School Mathematics (NCTM 1989) state that the mathematics curriculum should include investigations of the connections and interplay among various mathematical topics and their applications so that all students can apply mathematical thinking and modeling to solve problems that arise in other disciplines.

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Szydlik, Jennifer Earles. "Photographs and Committees: Activities That Help Students Discover Permutations and Combinations." Mathematics Teacher 93, no. 2 (February 2000): 93–96. http://dx.doi.org/10.5951/mt.93.2.0093.

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The vision of Mathematics Curriculum promoted by the NCTM's Curriculum and Evaluation Standards for School Mathematics (1989) is based on two guiding principles: “First, activities should grow out of problem situations; and second, learning occurs through active as well as passive involvement with mathematics” (1989, 9). In particular, curriculum should be designed to support students in constructing their own mathematical ideas and connections. Students should solve problems, communicate ideas both orally and in writing, engage in mathematical reasoning, and search for mathematical connections.

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Loewenberg Ball, Deborah, and Susan N. Friel. "Implementing the Professional Standards for Teaching Mathematics: Improving, Not Standardizing, Teaching." Arithmetic Teacher 39, no. 1 (September 1991): 18–22. http://dx.doi.org/10.5951/at.39.1.0018.

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In March of this year, NCTM published the Professional Standards for Teaching Mathematics (Professional Teaching Standards) (1991), a companion to the earlier Curriculum and Evaluation Standards for School Mathematics (Curriculum and Evaluation Standards) (1989). Whereas the earlier document focuses on curriculum, the new document addresses teaching. It elaborates the Curriculum and Evaluation Standards's vision of teaching, in which mathematical reasoning, problem solving, communication, and connections are central. It addresses such questions as, What are classrooms like in which students are able to encounter, develop, and use mathematical ideas and skills in the context of genuine problem and situations? What role might a teacher play in helping students learn to use a variety of resources and tools, such as calculators and computers, and concrete and pictorial models? What is meant by engaging students in mathematical reasoning—in making conjectures, presenting arguments, constructing proofs—at various grade levels? How can adequate mathematical skill be developed in concert with mathematical reasoning? The list of questions can be extended indefinitely, for what we are trying to create is quite different from what we experienced when we were in school and even quite different from much of what we are doing now as teachers.

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Lester, Frank K., and Diana Lambdin Kroll. "Implementing The Standards: Evaluation: A New Vision." Mathematics Teacher 84, no. 4 (April 1991): 276–84. http://dx.doi.org/10.5951/mt.84.4.0276.

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Teaching according to the vision of the NCTM's Curriculum and Evaluation Standards will involve numerous changes in the content and instruction of the school mathematics program. Moreover, this vision will also require a change in testing procedures and methods for evaluating the effectiveness of instructional practices (Clarke, Clarke, and Lovitt 1990; EQUALS and California Mathematics Council 1989; NAEP 1987; NCTM 1989). As is pointed out in NCTM's curriculum standards, an evaluation program that is properly aligned with the proposed curriculum standards can no longer use only written tests. Calculators, computers, and manipulatives must be included in the evaluation process.

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Piazza, Jenny A., Margaret M. Scott, and Elizabeth C. Carver. "Thematic Webbing and the Curriculum Standards in the Primary Grades." Arithmetic Teacher 41, no. 6 (February 1994): 294–98. http://dx.doi.org/10.5951/at.41.6.0294.

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The National Council of Teachers of Mathematics's Curriculum and Evaluation Standards for School Mathematics (1989) reflects the importance of understanding the development of knowledge at the K-4 level. The standards document recognizes that current instructional and curricular content must focus on students' active construction of mathematical knowledge. Instructional practices need to be conceptually oriented, involve children actively, emphasize the development of mathematical thinking and application, and include a broad range of content.

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Edgerton, Richard T. "Sharing Teaching Ideas: A Mathematical Investigation of Quality Control." Mathematics Teacher 88, no. 3 (March 1995): 200–202. http://dx.doi.org/10.5951/mt.88.3.0200.

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One way to apply the principles of the Curriculum and Evaluation Standards for School Mathematics (NCTM 1989) is to use real-world problems. The curriculum standards are enacted as students develop “mathematical power” while they communicate, reason, and make connections within and outside mathematics.

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Embse, Charles Vonder, and Arne Engebretsen. "Technology Tips: Using a Graphing Utility as a Catalyst for Connections." Mathematics Teacher 90, no. 1 (January 1997): 50–56. http://dx.doi.org/10.5951/mt.90.1.0050.

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One of the most important ideas expressed in the Curriculum and Evaluation Standards for School Mathematics (NCTM 1989) is that of connections. The Standards document recommends that “the mathematics curriculum should include investigation of the connections and interplay among various mathematical topics and their applications … ”

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Clements, Douglas H., and Julie Sarama. "Experimental Evaluation of the Effects of a Research-Based Preschool Mathematics Curriculum." American Educational Research Journal 45, no. 2 (June 2008): 443–94. http://dx.doi.org/10.3102/0002831207312908.

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A randomized-trials design was used to evaluate the effectiveness of a preschool mathematics program based on a comprehensive model of research-based curricula development. Thirty-six preschool classrooms were assigned to experimental ( Building Blocks), comparison (a different preschool mathematics curriculum), or control conditions. Children were individually pre- and posttested, participating in 26 weeks of instruction in between. Observational measures indicated that the curricula were implemented with fidelity, and the experimental condition had significant positive effects on classrooms’ mathematics environment and teaching. The experimental group score increased significantly more than the comparison group score (effect size = 0.47) and the control group score (effect size = 1.07). Early interventions can increase the quality of the mathematics environment and help preschoolers develop a foundation of mathematics knowledge.

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Scavo, Thomas R., and Nora K. Conroy. "On My Mind: Conceptual Understanding and Computational Skill in School Mathematics." Mathematics Teaching in the Middle School 1, no. 9 (March 1996): 684–86. http://dx.doi.org/10.5951/mtms.1.9.0684.

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Evaluation standard 9 of the NCTM's curriculum and Evaluation Standards for School Mathematics (1989) addresses the issue of mathematical procedures including, but not limited to, computational methods and algorithms. The standards document relates that.

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Trezise, Kathleen A. "Mathematics Fitness." Mathematics Teaching in the Middle School 3, no. 7 (May 1998): 458–62. http://dx.doi.org/10.5951/mtms.3.7.0458.

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Students who are involved in mathematics instruction that is relevant to life will understand that mathematics is a part of the real world and not just another school subject. Teachers who connect mathematics with other content areas and the real world afford students the opportunity to see the daily importance of mathematics. The activity that follows is consistent with the following NCTM curriculum and evaluation standards. In grades 5-8, the mathematics curriculum should include—

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Hoffmann, Miklós, and Attila Egri-Nagy. "A New Model of Mathematics Education: Flat Curriculum with Self-Contained Micro Topics." Philosophies 6, no. 3 (September 13, 2021): 76. http://dx.doi.org/10.3390/philosophies6030076.

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The traditional way of presenting mathematical knowledge is logical deduction, which implies a monolithic structure with topics in a strict hierarchical relationship. Despite many recent developments and methodical inventions in mathematics education, many curricula are still close in spirit to this hierarchical structure. However, this organisation of mathematical ideas may not be the most conducive way for learning mathematics. In this paper, we suggest that flattening curricula by developing self-contained micro topics and by providing multiple entry points to knowledge by making the dependency graph of notions and subfields as sparse as possible could improve the effectiveness of teaching mathematics. We argue that a less strictly hierarchical schedule in mathematics education can decrease mathematics anxiety and can prevent students from ‘losing the thread’ somewhere in the process. This proposal implies a radical re-evaluation of standard teaching methods. As such, it parallels philosophical deconstruction. We provide two examples of how the micro topics can be implemented and consider some possible criticisms of the method. A full-scale and instantaneous change in curricula is neither feasible nor desirable. Here, we aim to change the prevalent attitude of educators by starting a conversation about the flat curriculum alternative.

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Cuevas, Gilbert J. "Implementing the Standards: Developing Communication Skills in Mathematics for Students with Limited English Proficiency." Mathematics Teacher 84, no. 3 (March 1991): 186–89. http://dx.doi.org/10.5951/mt.84.3.0186.

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The Curriculum and Evaluation Standards for School Mathematics (NCTM 1989) emphasizes the need to address communication skills. These skills, including reading, writing, listening, and speaking, enhance mathematical understanding and problem-solving ability. Moreover, to communicate effectively, one must be able to interpret and analyze mathematical ideas. The curriculum and evaluation standards recommend that opportunities be afforded students to “use language to communicate their mathematical ideas” (NCTM 1989, 78). Although these recommendations are valuable, teachers may find them difficult to implement with students who are not proficient in English.

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Cramer, Kothleen, and Lee Karnowski. "The Importance of Informal Language in Representing Mathematical Ideas." Teaching Children Mathematics 1, no. 6 (February 1995): 332–35. http://dx.doi.org/10.5951/tcm.1.6.0332.

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Mathematics as Problem Solving, Mathematics as Communication. Mathematics as Reasoning, and Mathematical Connections—these four Standards, which open the NCTM's Curriculum and Evaluation Standards for School Mathematics (1989), can be considered the pedagogical standards.

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Embse, Charles Vonder, and Arne Engebretsen. "Technology Tips: A Mathematical Look at a Free Throw Using Technology." Mathematics Teacher 89, no. 9 (December 1996): 774–79. http://dx.doi.org/10.5951/mt.89.9.0774.

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Technology can be used to promote students' understanding of mathematical concepts and problem-solving techniques. Its use also permits students' mathematical explorations prior to their formal development in the mathematics curriculum and in ways that can capture students' curiosity, imagination, and interest. The NCTM's Curriculum and Evaluation Standards for School Mathematics (1989) recommends that “[i]n grades 9–12, the mathematics curriculum should include the refinement and extension of methods of mathematical problem solving so that all students can … apply the process of mathematical modeling to real-world problem situations” (p. 137). Students empowered with technology have the opportunity to model real-world phenomena and visualize relationships found in the model while gaining ownership in the learning process.

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Hirsch, Christian R., Harold L. Schoen, and Harold L. Schoen. "Implementing The Standards: A Core Curriculum for Grades 9–12." Mathematics Teacher 82, no. 9 (December 1989): 696–701. http://dx.doi.org/10.5951/mt.82.9.0696.

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A three-year core curriculum is the most fundamental change proposed for grades 9–12 in the Curriculum and Evaluation Standards for School Mathematics (National Council of Teachers of Mathematics, Commission on Standards for School Mathematics 1989). The Standards document identifies a common body of mainstream mathematical topics that all high school students should have the opportunity to learn. Present curricula attempt to accommodate differences in students' backgrounds, interests, and educational goals through the selection of topics. Unfortunately, the narrow, trackable programs that evolve from this perspective restrict many students to arithmetic computation only and thus serve as an early critical filter to opportunity and careers. Within the proposed core curriculum, differentiation would occur primarily in the manner in which topics are treated. It would be based on the depth to which common topics are pursued, the degree of difficulty of exercises and applications, the level of abstraction at which ideas are discussed, and, of course, the pace of instruction.

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Glidden, Peter L., and Erin K. Fry. "Illustrating Mathematical Connections: Two Proofs That Only Five Regular Polyhedra Exist." Mathematics Teacher 86, no. 8 (November 1993): 657–61. http://dx.doi.org/10.5951/mt.86.8.0657.

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The reforms proposed in the NCTM's Curriculum and Evaluation Standards (1989) call for specific changes in the grades 9-12 mathematics curriculum, as well as for general themes that should be emphasized throughout the curriculum. In particular, the standards document calls for including topics from discrete mathematics and three-dimensional geometry, and it calls for increased emphasis on paragraph-style proofs. Overall, these and other topics should be taught with the ultimate goals of illustrating mathematical connections and constructing mathematical models to solve real-world problems.

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Hirsch, Christian R., Glenda Lappan, and Harold L. Schoen. "Implementing the Standards: Transition to High School Mathematics." Mathematics Teacher 82, no. 8 (November 1989): 614–18. http://dx.doi.org/10.5951/mt.82.8.0614.

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The Curriculum and Evaluation Standards for School Mathematics (NCTM 1989) proposes a common core of mainstream mathematical topics that all high school students should have the opportunity to learn. The need for such a reconceptualization of the curriculum is dramatically documented in the NRC report Everybody Counts (MSEB and National Research Council 1989). But the success of the proposal hinges to a large degree on the nature of mathematical experiences in the transition years, grades 7-8.

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Asturias, Harold. "Implementing the “Assessment Standards for School Mathematics”: Using Students' Portfolios to Assess Mathematical Understanding." Mathematics Teacher 87, no. 9 (December 1994): 698–701. http://dx.doi.org/10.5951/mt.87.9.0698.

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In 1989, NCTM published the Curriculum and Evaluation Standards for School Mathematics, which presented the mathematics profession with a broad view of the important mathematics that should be taught in schools. Two years later, the Professional Standards for Teaching Mathematics gave teachers the opportunity to address the pedagogical issues inherent in teaching a broad-based, thinking curriculum as described in the curriculum standards. The next link, assessment, though part of the first document, required specific attention. Assessment Standards for School Mathematics, currently in progress, will present the criteria for judging the appropriateness and quality of assessment tools and systems.

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Leitze, Annette Ricks. "Connecting Process Problem Solving to Children's Litcrature." Teaching Children Mathematics 3, no. 7 (March 1997): 398–406. http://dx.doi.org/10.5951/tcm.3.7.0398.

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Since the publication of the Curriculum and evaluation Standards for School Mathematics (NCTM 1989), many mathematics teachers and educators have become especially interested in making mathematical connections, such as that found between mathematics and children's literature.

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Riyanto, Bambang, Zulkardi Zulkardi, Ratu Ilma Indra Putri, and Darmawijoyo Darmawijoyo. "SENIOR HIGH SCHOOL MATHEMATICS LEARNING THROUGH MATHEMATICS MODELING APPROACH." Journal on Mathematics Education 10, no. 3 (September 27, 2019): 425–44. http://dx.doi.org/10.22342/jme.10.3.8746.425-444.

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By modeling learning students enjoy learning and doing mathematics in new ways. This study aimed firsly to produce senior high school mathematics modeling tasks, lesson plan, and student worksheet for valid mathematical learning; secondly, to produce senior high school mathematics modeling, lesson plan, and student worksheet for practical mathematics learning; lastly, to produce senior high school mathematics modeling tasks, lesson plan, and student worksheet for potentially effective mathematics learning. This study used method of development research that consisting of 3 steps, i.e., analysis, design, and evaluation. In the analysis stage, researcher did student analysis, curriculum, and mathematical modeling. Second stage are to design and product. Finally, researchers applied a design of formative evaluation consists of self-evaluation, one-to-one, experts review, small group, and field test. Based on experts review, one-to-one, small groups, and field test were obtained valid, practical, and potentially effective, i.e. mathematical modeling tasks, lesson plan, student worksheet to teach mathematical modeling in senior high school and Mathematical modeling tasks and student worksheets to learn mathematical modeling in senior high school.

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Edgerton, Richard T. "Apply the Curriculum Standards with Project Questions." Mathematics Teacher 86, no. 8 (November 1993): 686–89. http://dx.doi.org/10.5951/mt.86.8.0686.

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A goal of the Curriculum and Evaluation Standards for School Mathematics (NCTM 1989) is faci litating “mathematical power” in students. The curriculum standards use problem solving, communication, reasoning, and connections as organizing principles. One way to apply these principles in the classroom is with the use of “project questions.”

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Wadlington, Elizabeth, Joe Bitner, Elizabeth Partridge, and Sue Austin. "Have a Problem? Make the Writing-Mathematics Connection!" Arithmetic Teacher 40, no. 4 (December 1992): 207–9. http://dx.doi.org/10.5951/at.40.4.0207.

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Get out our journals? I don't get it. We just had English!” This is the initial reaction of most elementary school students when asked to keep daily mathematics journals. However, the Curriculum and Evaluation Standards for School Mathematics (NCTM 1989) indicates that mathematics should emphasize the meaningful communication of mathematics. Talking, listening, reading, and writing about mathematical concepts help

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Morrow, Lorna J., and Thomas E. Rowan. "Implementing The Standards: Geometry through the Standards." Arithmetic Teacher 38, no. 8 (April 1991): 21–25. http://dx.doi.org/10.5951/at.38.8.0021.

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An underlying view of mathematics education expressed in the Curriculum and Evaluation Standards (NCTM 1989) is that a student should be actively involved both mentally and physically in constructing his or her own mathematical knowledge: “The K-4 curriculum should actively involve children in doing mathematics. … [They should] explore, justify, represent, solve, construct, discuss, use, investigate, describe, develop, and predict” (NCTM 1989, 17).

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Hirsch, Christian R., Arthur F. Coxford, James T. Fey, and Harold L. Schoen. "Teaching Sensible Mathematics in Sense-Making Ways with the CPMP." Mathematics Teacher 88, no. 8 (November 1995): 694–700. http://dx.doi.org/10.5951/mt.88.8.0694.

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Current policy reports addressing mathematics education in American schools, such as Everybody Counts (NRC 1989), Curriculum and Evaluation Standards for School Mathematics (NCTM 1989), Professional Standards for Teaching Mathematics (NCTM 1991), and Assessment Standards for School Mathematics (NCTM 1995), call for sweeping reform in curricular, instructional, and assessment practices. Implementing the proposed reforms poses new opportunities and challenges for school districts, mathematics departments, and classroom teachers.

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Clarke, David J. "Activating Assessment Alternatives in Mathematics." Arithmetic Teacher 39, no. 6 (February 1992): 24–29. http://dx.doi.org/10.5951/at.39.6.0024.

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The Curriculum and Evaluation Standards for School Mathematics (NCTM 1989, 1, 2) emphasizes the role of evaluation “in gathering information on which teachers can base their subsequent instruction.” This strong sense of assessment's informing instructional practice is also evident in the materials arising from the Australian Mathematics Curriculum and Teaching Program (Clarke 1989: Lovitt and Clarke 1988, 1989). Both projects offer their respective mathematics-education communities a set of goal much broader than those traditionally conceived for mathematics instruction. The adoption of these goals by mathematics teachers and school systems demands the use of new assessment strategies if the restructuring of the mathematics curriculum and mathematics-teaching practice is to be effected. Mathematics education must not restrict itself to those goals that can be assessed only through conventional pencil-and-paper methods.

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Silbey, Robyn. "What Is in the Daily News? Problem-Solving Opportunities!" Teaching Children Mathematics 5, no. 7 (March 1999): 390–94. http://dx.doi.org/10.5951/tcm.5.7.0390.

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In An Agenda for Action, the NCTM asserted that problem solving must be at the heart of school mathematics (1980). Almost ten years later, the NCTM's Curriculum and Evaluation Standards for School Mathematics (1989) stated that the development of each student's ability to solve problems is essential if he or she is to be a productive citizen. The Standards assumed that the mathematics curriculum would emphasize applications of mathematics. If mathematics is to be viewed as a practical, useful subject, students must understand that it can be applied to various real-world problems, since most mathematical ideas arise from the everyday world. Furthermore, the mathematics curriculum should include a broad range of content and an interrelation of that content.

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Cross, Lee, and Michael C. Hynes. "Assessing Mathematics Learning for Students with Learning Differences." Arithmetic Teacher 41, no. 7 (March 1994): 371–77. http://dx.doi.org/10.5951/at.41.7.0371.

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Buschmon, Larry. "Communicating in the Languge of Mathematics." Teaching Children Mathematics 1, no. 6 (February 1995): 324–29. http://dx.doi.org/10.5951/tcm.1.6.0324.

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As the classroom mathematics curriculum expands to encompass the entire range of skills included in the NCTM's Curriculum and Evaluation Standards for School Mathematics (1989), the process by which a student arrives at the answer to a problem becomes as important as the answer itself.

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Rowan, Thomas E., and Hilde Howden. "Implementing The Standards: Patterns, Relationships, and Functions." Arithmetic Teacher 37, no. 3 (November 1989): 18–24. http://dx.doi.org/10.5951/at.37.3.0018.

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In the NCTM's Curriculum and Evaluation Standards for School Mathematics (1989). function is viewed as both a concept and a process. As a concept, it is the study of regularity and quantification of phenomena, which is the essence of mathematics. As a process, students apply the concept to analyze relationships throughout the curriculum by using tables, graphs, verbal and mathematical rules, and models to represent them.

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Whitin, David J. "Exploring Estimation through Children's Literature." Arithmetic Teacher 41, no. 8 (April 1994): 436–41. http://dx.doi.org/10.5951/at.41.8.0436.

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Estimation is a crucial mathematical strategy that can be woven throughout the entire mathematics curriculum. The strategy can certainly foster the development of many of the goals advocated by the NCTM's curriculum and evaluation standards (1989). Since approximately 80 percent of real-world applications of mathematics involve estimation or mental computation, the goal of becoming an “informed electorate” requires us to use and analyze various estimation strategies.

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Malloy, Carol E. "Mathematics Projects Promote Students' Algebraic Thinking." Mathematics Teaching in the Middle School 2, no. 4 (February 1997): 282–88. http://dx.doi.org/10.5951/mtms.2.4.0282.

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Teachers in all curricular areas, especially science, have encouraged students to develop projects to extend their knowledge of specific phenomena. As middle school mathematics teachers grapple with methods to help students enhance algebraic thinking, they should consider the power of the mathematics project. My experiences with students have demonstrated that mathematics projects must be structured as investigations in which students work cooperatively and where the mathematics in the proj-ects is substantial. Projects can provide middle school students with the opportunity to investigate, conjecture, and reach mathematical conclusions that require algebraic thinking, as recommended in the NCTM's Curriculum and Evaluation Standards for School Mathematics (1989). This article describes how various projects helped middle school students harness their experiences and construct mathematical conclusions through algebraic thinking Students employed algebraic thinking as they used number patterns and verbal rules to “explore the interrelationships of these representations” (NCTM 1989, 102) and reach conclusions in their projects.

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Swetz, Frank. "Implementing the Standards: Incorporating Mathematical Modeling into the Curriculum." Mathematics Teacher 84, no. 5 (May 1991): 358–65. http://dx.doi.org/10.5951/mt.84.5.0358.

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In suggesting plans of action for the reform of mathematics education in North America, NCTM reports have focused strongly on the need to improve problem-solving skills and the need to “do” mathematics. Most recently, these goals have been reiterated and clarified in Curriculum and Evaluation Standards for School Mathematics (NCTM 1989). In discussing the impact of Standard 1: Mathematics as Problem Solving on students in grades 9-12, the report notes that students should be able to “apply the process of mathematical modeling to real-world problem situations” (p. 137). By using the phrase “apply the process of mathematical modeling,” the authors of this standard were most precise in their language. Mathematical modeling is a process and must be taught as a process. Certainly mathematical modeling involves problems, but it should not be considered as merely a collection of interesting problems and solution schemes. More important, modeling is a multistage process that evolves from the identification and mathematical articulation of a problem through its eventual solution and the testing of that solution in the original problem situation. The challenge for teachers is to understand this process of mathematical modeling and to apply it effectively in problem solving.

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Flores, Alfinio. "Connections: A Lottery, a Computer, and the Number e." Mathematics Teacher 86, no. 8 (November 1993): 652–55. http://dx.doi.org/10.5951/mt.86.8.0652.

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I mportant mathematical constants, like π and e. which are encountered first in specific contexts, appear throughout different branches of mathematics. Students are surprised to find rr, which they know as the ratio of the circumference to the diameter of a circle, in such a probabilistic context as Buffon's needle problem (Hirsch 1981). This article links Euler's constant e-the base of natural logarithms, which students usuaUy encounter in relation to compound-interest problems-with an experiment simulating a drawing. Establishing mathematical connections among different mathematical fields is one of the standards stressed throughout the K-12 mathematics curriculum in NCTM's Curriculum and Evaluation Standards for School Mathematics (1989).

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Esty, Warren W., and Anne R. Teppo. "Grade Assignment Based on Progressive Improvement." Mathematics Teacher 85, no. 8 (November 1992): 616–18. http://dx.doi.org/10.5951/mt.85.8.0616.

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The NCTM's Curriculum and Evaluation Standards for School Mathematics states, “Evaluation is a tool for implementing the Standards and effecting change systematically” (1989, 189). Tests are one facet of evaluation, and we maintain that mathematics classes are strongly affected by the way in which test scores are used to generate final course grades. In the traditional secondary school mathematics class, current grading practices tend to drive instruction by putting constraints on specific course content and its organization. In turn, content and its organization affect testing and therefore grading. The interaction of these factors is an aspect of assessment that is not specifically discussed by the NCTM's evaluation standards. The purpose of this article is to examine the impact of grading on mathematics instruction and on the implementation of the curriculum and evaluations standards.

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Leitze, Annette Ricks, and Sue Tinsley Mau. "Assessing Problem-Solving Thought." Mathematics Teaching in the Middle School 4, no. 5 (February 1999): 305–11. http://dx.doi.org/10.5951/mtms.4.5.0305.

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Recent reform efforts that are based on the Curriculum and Evaluation Standards for School Mathematics (NCTM 1989) call for an increase in problem solving as part of the mathematics curriculum for students at all levels. Teachers can use problemsolving activities for multiple purposes, such as developing critical-thinking skills, data-organization skills, communication skills, and a risk-taking attitude, as well as making connections among mathematical topics. Regardless of the curriculum goal, teachers face many challenges in finding suitable activities and then assessing the work that students do on these activities. Neither task is easy.

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Romberg, Thomas A. "One Point of View: NCTM's Curriculum and Evaluation Standards: What They Are and Why They Are Needed." Arithmetic Teacher 35, no. 9 (May 1988): 2–3. http://dx.doi.org/10.5951/at.35.9.0002.

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During this past year, NCTM has produced a working draft of a set of curriculum and evaluation Standard for school mathematics (Commission on Standards for School Mathematics of the National Council of Teachers of Mathematic 1987). As chair of the Commission, I have been asked to respond to four questiona.

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Joyner, Jeane M. "One Point of View: Using Manipulatives Successfully." Arithmetic Teacher 38, no. 2 (October 1990): 6–7. http://dx.doi.org/10.5951/at.38.2.0006.

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A curriculum with goals for students of valuing mathematics, being confident in their abilities, making mathematical connections, becoming mathematical problem solvers, and learning to reason and communicate mathematically is a call for classrooms in which students are actively involved in learning. It is a call for teachers to establish environments that encourage the use of manipulatives to assist students in attaining these goals proposed by the NCTM's Curriculum and Evaluation Standards for School Mathematics (Standards) (1989). A major difficulty, however, is how to manage the materials efficiently.

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Shannon, Ann, and Judith S. Zawojewski. "Connecting Research to Teaching: Mathematics Performance Assessment: A New Game for Students." Mathematics Teacher 88, no. 9 (December 1995): 752–57. http://dx.doi.org/10.5951/mt.88.9.0752.

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Schifter, Deborah E., and Deborah Carey O'Brien. "Interpreting the Standards: Translating Principles into Practice." Teaching Children Mathematics 4, no. 4 (December 1997): 202–5. http://dx.doi.org/10.5951/tcm.4.4.0202.

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Since the publication of the Curriculum and Evaluation Standards for School Mathematics (NCTM 1989) and the Professional Standards for Teaching Mathematics (NCTM 1991). such phrases as “mathematics should be taught for understanding.” “teachers should facilitate the construction of mathematical concepts,” and “classrooms should be student centered” have become identified with a reformed mathematics pedagogy.

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Schielack, Jane F. "Reaching Young Pupils With Technology." Arithmetic Teacher 38, no. 6 (February 1991): 51–55. http://dx.doi.org/10.5951/at.38.6.0051.

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Recommendations in such current publications as NCTM's Curriculum and Evaluation Standards for School Mathematics (Standards) (1989) and the National Research Council's Everybody Counts (1989) emphasize the full use of technology in the classroom at all grade levels. But what is the role of technology in the early grades? How can computers best be used to support primary-level mathematics instruction? Where does the use of the calculator fit into the primary-level pupil's development of mathematical concepts? How can we justify the abstract nature of calculator activities in a primary-level mathematics curriculum built on the needs of young pupils to experience concrete representations of mathematical concepts?

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