scholarly journals The aims of teaching mathematics: mathematical literacy vs mathematical reasoning

2021 ◽  
Vol 61 ◽  
pp. 8-14
Author(s):  
Rimas Norvaiša
Keyword(s):  
Public Opinion ◽  
Real World ◽  
Mathematical Reasoning ◽  
Gifted Students ◽  
School Mathematics ◽  
Teaching Mathematics ◽  
Mathematical Literacy ◽  
The Real ◽  
Alternative Means ◽  
Academic School

We discuss different alternatives of the content of school mathematics. According to the prevalent public opinion in Lithuania school mathematics can be oriented either to the academic mathematics or to the applications of mathematics. In reality the second alternative means lowering of the level of teaching in the hope that school mathematics will be accessible to all students. While the content oriented to the academic school mathematics is accessible only to gifted students. In this article we describe a middle alternative content which we call school mathematics based on mathematical reasoning. We argue that such school mathematics serves all students and makes acquaintance with mathematical reasoning and with applications of mathematics to the real world. Reasoning makes mathematics reasonable for all.

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).

scholarly journals Developing purposeful mathematical thinking: a curious tale of apple trees

2012 ◽  
Vol 6 (3) ◽  
pp. 85-103
Author(s):  
Janet Ainley
Keyword(s):  
Mathematics Education ◽  
Real World ◽  
Mathematical Thinking ◽  
Task Design ◽  
Mathematical Understanding ◽  
School Mathematics ◽  
Apple Trees ◽  
The Real

In this paper I explore aspects of the ways in which school mathematics relates to the “real” world, and argue that this relationship is an uneasy one. Through exploring the causes of this unease, I aim to expose some problems in the ways in which context is used within mathematics education, and argue that the use of context does not ensure that the purposes of mathematics are made transparent. I present and discuss a framework for task design that adopts a different perspective on mathematical understanding, and on purposeful mathematical thinking. Desarrollo de un pensamiento matemático intencionado: un relato curioso de manzanos En este artículo exploro aspectos de las maneras en que las matemáticas escolares se relacionan con el mundo “real” y argumento que esta relación es preocupante. Al explorar las causas de esta preocupación, me propongo exponer algunos problemas que surgen de las formas en que se usa el contexto en Educación Matemática y argumento que el uso del contexto no asegura la transparencia de los propósitos de las matemáticas. Presento y discuto un esquema para el diseño de tareas que adopta una perspectiva diferente sobre la comprensión de las matemáticas y el pensamiento matemático intencionado.Handle: http://hdl.handle.net/10481/19524

Connecting Measurement and Architecture: Building an Inflatable

2007 ◽  
Vol 13 (3) ◽  
pp. 144-149
Author(s):  
Elizabeth D. Gray ◽  
Denise Tullier-Holly
Keyword(s):  
Middle School ◽  
Middle School Students ◽  
Real World ◽  
School Mathematics ◽  
Classroom Experiences ◽  
School Students ◽  
The Real ◽  
Mathematical Connections ◽  
Principles And Standards

Middle school students need to see connections between mathematics and the real world. However, they often learn mathematics as a set of distinct topics or separate strands, because a majority of the available textbooks tends to present it that way, and teachers tend to follow the textbooks. According to Principles and Standards for School Mathematics (NCTM 2000), our students should be made aware of mathematical connections explicitly so that the manner in which topics are connected is obvious. McClain (1996) suggests that if teachers offer classroom experiences in which students can see connections, then “the vibrant discipline of mathematics actively engages students in their own learning” (p. 682).

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).

Projects: Developing Modelers and Modeling Opportunities: The Stepping Stones Project

1997 ◽  
Vol 90 (8) ◽  
pp. 686-688
Keyword(s):  
Mathematical Modeling ◽  
Mathematics Education ◽  
Real World ◽  
Mathematical Knowledge ◽  
School Mathematics ◽  
Stepping Stones ◽  
Evaluation Standards ◽  
The Real ◽  
World Modeling

Mathematical modeling is an emerging theme in mathematics education. In addition to giving students a knowledge of the applications of mathematics and a process for applying mathematics in the “real” world, modeling offers teachers an excellent vehicle for introducing and developing students' mathematical knowledge. For these reasons, modeling occupies a prominent place in the recommendations of the Curriculum and Evaluation Standards for School Mathematics (NCTM 1989).

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.

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