Principles and Standards: Developing Computational Fluency with Whole Numbers

2000 ◽  
Vol 7 (3) ◽  
pp. 154-158 ◽  
Author(s):  
Susan Jo Russell
Keyword(s):  
Mathematical Reasoning ◽  
Number System ◽  
Basic Number ◽  
School Mathematics ◽  
Evaluation Standards ◽  
Computational Fluency ◽  
Mathematics Program ◽  
Principles And Standards ◽  
Learning To Reason ◽  
Fact Learning

Principles and Standards for School Mathematics (NCTM 2000) emphasizes the goal of computational fluency for all students. It articulates expectations regarding fluency with basic number combinations and the importance of computational facility grounded in understanding (see a summary of key messages regarding computation in Principles and Standards in the sidebar on page 156). Building on the Curriculum and Evaluation Standards for School Mathematics (NCTM 1989) and benefiting from a decade of research and practice, Principles and Standards articulates the need for students to develop procedural competence within a school mathematics program that emphasizes mathematical reasoning and problem solving. In fact, learning about whole-number computation is a key context for learning to reason about the baseten number system and the operations of addition, subtraction, multiplication, and division.

Beyond the Golden Ratio: A Calculator-Based Investigation

2001 ◽  
Vol 94 (2) ◽  
pp. 138-144
Author(s):  
Peter L. Glidden
Keyword(s):  
Problem Solving ◽  
Mathematical Reasoning ◽  
Golden Ratio ◽  
School Mathematics ◽  
Opportunities To Learn ◽  
Mathematical Communication ◽  
Evaluation Standards ◽  
Mathematical Connections ◽  
Principles And Standards ◽  
Classroom Use

NCTM's Curriculum and Evaluation Standards for School Mathematics (1989) calls for increased emphasis on problem solving, mathematical reasoning, mathematical communication, and mathematical connections. This call is reaffirmed in Principles and Standards for School Mathematics (NCTM 2000). A preferred way of achieving these goals is by having students perform mathematical investigations in which they explore mathematics, search for patterns, and use technology when appropriate. In short, students should be given opportunities to learn mathematics by doing mathematics. Of course, if students are to learn mathematics through investigations, teachers must have a ready supply of such investigations available for classroom use.

Implementing The Standards: Evaluation: A New Vision

1991 ◽  
Vol 84 (4) ◽  
pp. 276-284
Author(s):  
Frank K. Lester ◽  
Diana Lambdin Kroll
Keyword(s):  
Instructional Practices ◽  
Evaluation Process ◽  
School Mathematics ◽  
Curriculum Standards ◽  
Evaluation Standards ◽  
Evaluation Program ◽  
Testing Procedures ◽  
Mathematics Program ◽  
New Vision

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.

Call For Manuscripts 2012 Focus Issue: Fostering Mathematical Reasoning

2010 ◽  
Vol 16 (3) ◽  
pp. 187
Keyword(s):  
Real World ◽  
Mathematical Reasoning ◽  
School Mathematics ◽  
Sense Making ◽  
Principles And Standards ◽  
Critical Aspects

Mathematical reasoning and sense making are critical aspects of learning and doing math. “People who reason and think analytically tend to note patterns, structure, or regularities in both real-world situations and symbolic objects; they ask if those patterns are accidental or if they occur for a reason; and they conjecture and prove. Reasoning mathematically is a habit of mind, and like all habits, it must be developed through consistent use in many contexts” (Principles and Standards for School Mathematics, p. 56).

Felix Klein and the NCTM's Standards: A Mathematician Considers Mathematics Education

2000 ◽  
Vol 93 (8) ◽  
pp. 714-717
Author(s):  
Kim Krusen McComas
Keyword(s):  
Mathematics Education ◽  
School Mathematics ◽  
Rote Learning ◽  
German Mathematician ◽  
Evaluation Standards ◽  
10Th Anniversary ◽  
Felix Klein ◽  
Look Back ◽  
Principles And Standards ◽  
Year 2000

The year 1999 marked the 10th anniversary of the NCTM's Curriculum and Evaluation Standards for School Mathematics. It also marked the 150th anniversary of the birth of German mathematician Felix Klein, who lived from 1849 to 1925. Although the relation between these two anniversaries may not be obvious, the connection is that Klein, were he still alive today, would probably support the NCTM's Standards. As the year 2000 brings us NCTM's Principles and Standards for School Mathematics, let us look back to the year 1900 and find Felix Klein at the forefront of a movement to reform mathematics education from rote learning to more meaningful mathematical learning.

Call For Manuscripts 2012 Focus Issue: Fostering Mathematical Reasoning

2010 ◽  
Vol 16 (1) ◽  
pp. 17
Keyword(s):  
Real World ◽  
Mathematical Reasoning ◽  
School Mathematics ◽  
Sense Making ◽  
Principles And Standards ◽  
Critical Aspects

Mathematical reasoning and sense making are critical aspects of learning and doing math. “People who reason and think analytically tend to note patterns, structure, or regularities in both real-world situations and symbolic objects; they ask if those patterns are accidental or if they occur for a reason; and they conjecture and prove. Reasoning mathematically is a habit of mind, and like all habits, it must be developed through consistent use in many contexts” (Principles and Standards for School Mathematics, p. 56).

Call For Manuscripts 2012 Focus Issue: Fostering Mathematical Reasoning

2010 ◽  
Vol 15 (8) ◽  
pp. 457
Keyword(s):  
Real World ◽  
Mathematical Reasoning ◽  
School Mathematics ◽  
Sense Making ◽  
Principles And Standards ◽  
Critical Aspects

Mathematical reasoning and sense making are critical aspects of learning and doing math. “People who reason and think analytically tend to note patterns, structure, or regularities in both real-world situations and symbolic objects; they ask if those patterns are accidental or if they occur for a reason; and they conjecture and prove. Reasoning mathematically is a habit of mind, and like all habits, it must be developed through consistent use in many contexts” (Principles and Standards for School Mathematics, p. 56).

Call For Manuscripts 2012 Focus Issue: Fostering Mathematical Reasoning

2010 ◽  
Vol 15 (7) ◽  
pp. 399
Keyword(s):  
Real World ◽  
Mathematical Reasoning ◽  
School Mathematics ◽  
Sense Making ◽  
Principles And Standards ◽  
Critical Aspects

Mathematical reasoning and sense making are critical aspects of learning and doing math. “People who reason and think analytically tend to note patterns, structure, or regularities in both real-world situations and symbolic objects; they ask if those patterns are accidental or if they occur for a reason; and they conjecture and prove. Reasoning mathematically is a habit of mind, and like all habits, it must be developed through consistent use in many contexts” (Principles and Standards for School Mathematics, p. 56).

Spotlight on the Principles/Standards: Building Mathematically Powerful Students through Connections

2002 ◽  
Vol 7 (9) ◽  
pp. 484-488
Author(s):  
Christine Thomas ◽  
Carmelita Santiago
Keyword(s):  
Mathematics Curriculum ◽  
School Mathematics ◽  
Mathematical Tasks ◽  
Evaluation Standards ◽  
Mathematical Ideas ◽  
Natural Inclination ◽  
Points Of View ◽  
Principles And Standards

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.

Abi, A. M. (2016). Integrasi Etnomatematika Dalam Kurikulum Matematika Sekolah. Jurnal Pendidikan Matematika Indonesia, 1-6. François, K. (2009). The Role of Ethnomathematics within Mathematics Education. Proceedings of CERME 6 (pp. 1517-1526). Lyon France: INRP 2010. Mansur HR. (2015, February). Menciptakan Pembelajaran Efektif melalui Apersepsi. Retrieved from LPMP Sulsel: http://www.lpmpsulsel.net/v2/index.php?option=com_content&view=article&id=327:pembelajaran‐efektif‐ M.Balamurugan. (2015). ETHNOMATHEMATICS; AN APPROACH FOR LEARNING MATHEMATICS FROM MULTICULTURAL PERSPECTIVES. INTERNATIONAL JOURNAL OF MODERN RESEARCH AND REVIEWS, 716-720. NCTM. (1989). Curriculum and Evaluation Standards for School Mathematics. Snipes, V., & Moses, P. (2001). Linking Mathematics and Culture to Teach Geometry Concepts. Retrieved from Semantic Scholar: https://www.semanticscholar.org/paper/Linking-Mathematics-and-Culture-to-Teach-Geometry-Snipes/de16ae98aa72c9eef916e40f2e91dd17deb5a179 Stylianides, A. J., & Stylianides, G. J. (2007). Learning Mathematics with Understanding: A Critical Consideration of the Learning Principle in the Principles and Standards for School Mathematics. The Mathematics Enthusiast, 103-114. Sukayati, & Suharjana, A. (2009). PEMANFAATAN ALAT PERAGA MATEMATIKA DALAM PEMBELAJARAN DI SD. Yogyakarta: PPPPTK Matematika Yogyakarta. Wijaya, A., Heuvel-Panhuizen, M., Doorman, M., & Robitzsch, A. (2014). Difficulties in solving context-based PISA mathematics tasks: An analysis of students’ errors. The Mathematics Enthusiast, 555-584. Yusuf, M. W., Ibrahim Saidu, I., & Halliru, A. (2010). ETHNOMATHEMATICS (A Mathematical Game in Hausa Culture). International Journal of Mathematical Science Education, 36-42. Yvette d’Entremont, Y. (2015). Linking mathematics, culture and community. Procedia - Social and Behavioral Sciences, 2818 – 2824.

2017 ◽  
Vol 3 (2) ◽  
pp. 1928-1941
Author(s):  
Ernawati . ◽  
◽  
Kurniawati . ◽  
Keyword(s):  
School Mathematics ◽  
Mathematical Science ◽  
Evaluation Standards ◽  
Mathematics Tasks ◽  
Learning Mathematics ◽  
Mathematical Game ◽  
Principles And Standards ◽  
Multicultural Perspectives ◽  
Critical Consideration

Call for Manuscripts, 2012 Focus Issue: Fostering Mathematical Reasoning

2010 ◽  
Vol 15 (9) ◽  
pp. 539
Keyword(s):  
Real World ◽  
Mathematical Reasoning ◽  
School Mathematics ◽  
Sense Making ◽  
Principles And Standards ◽  
Critical Aspects

Mathematical reasoning and sense making are critical aspects of learning and doing math. “People who reason and think analytically tend to note patterns, structure, or regularities in both real-world situations and symbolic objects; they ask if those patterns are accidental or if they occur for a reason; and they conjecture and prove. Reasoning mathematically is a habit of mind, and like all habits, it must be developed through consistent use in many contexts” (Principles and Standards for School Mathematics, p. 56).

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