scholarly journals Magnitude, number and school mathematics

2021 ◽  
Vol 62 ◽  
pp. 94-100
Author(s):  
Rimas Norvaiša
Keyword(s):  
Cognitive Complexity ◽  
Mathematical Reasoning ◽  
School Mathematics

Definitions of concepts of magnitude and number used in academic mathematics are not suitable for school mathematics for reasons of their cognitive complexity. We discuss possible ways to treat magnitudes and numbers in school mathematics based on mathematical reasoning.

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).

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).

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).

Ideas for Developing Students’ Reasoning: A Hungarian Perspective

1998 ◽  
Vol 91 (8) ◽  
pp. 677-681
Author(s):  
Anita Szombathelyi ◽  
Tibor Szarvas
Keyword(s):  
Twentieth Century ◽  
Mathematics Education ◽  
Teaching Assistants ◽  
Mathematical Reasoning ◽  
School Mathematics ◽  
Evaluation Standards ◽  
American University ◽  
Graduate Teaching ◽  
Reasoning Skills ◽  
End Results

As the end of the twentieth century approaches, we start to realize again the significance of proof in mathematics education. The NCTM's Curriculum and Evaluation Standards for School Mathematics (1989) cautions against the tendency to completely abandon proofs and focus only on the end results and formulas. In this article, we reemphasize the importance of proofs in teaching by sharing some of our experiences as students and teachers in Hungary, in addition to our experiences as graduate teaching assistants at an American university. We offer examples and ideas that might help educators develop students' mathematical reasoning skills.

Illustrating Mathematical Connections: A Geometric Proof of Euler's Theorem

1996 ◽  
Vol 89 (1) ◽  
pp. 62-65
Author(s):  
Erin K. Frye ◽  
Peter L. Glidden
Keyword(s):  
Mathematical Reasoning ◽  
School Mathematics ◽  
Geometric Proof ◽  
Evaluation Standards ◽  
Mathematical Connections ◽  
Euler’S Theorem ◽  
Problem Solvers

The Curriculum and Evaluation Standards for School Mathematics (NCTM 1989) calls for teachers to emphasize mathematical connections, promote mathematical reasoning, and help students become better problem solvers. If teachers are to achieve these goals, they need compelling examples, problems, and theorems that address all these elements.

Connecting Research to Teaching: Mathematics as Reasoning

1995 ◽  
Vol 88 (5) ◽  
pp. 412-417
Author(s):  
Peter Galbraith
Keyword(s):  
High School ◽  
Mathematical Reasoning ◽  
School Mathematics ◽  
Teaching Mathematics ◽  
Evaluation Standards ◽  
High School Geometry ◽  
School Geometry ◽  
Mathematical Quality

The Curriculum and Evaluation Standards for School Mathematics (NCTM 1989) defines a role for reasoning in school mathematics that is far different from the norm of recent practice. Until recently, the study of mathematical reasoning was largely confined to high school geometry. Further, as Schoenfeld (1988) pointed out, the approach used in geometry was often so rigid that it conveyed the impression that the style of the response—for example, the two-column-proof format—was more important than its mathematical quality. The Standards document notes that reasoning is to have a role in all of mathematics from the earliest grades on up and that the form of justification need not follow a pre scribed format. Indeed, students are encouraged to explain their reasoning in their own words. Teachers are asked to present opportunities for students to refine their own thoughts and language by sharing ideas with their peers and the teacher.

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.

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