International Mathematical Education: Mathematical Structures and the Role of Algebra in School Mathematics

1969 ◽  
Vol 62 (8) ◽  
pp. 673-678
Author(s):  
Howard F. Fehr ◽  
P. Lefebvre
Keyword(s):  
Mathematics Instruction ◽  
Applied Science ◽  
School Mathematics ◽  
Foreign Languages ◽  
Mathematical Education ◽  
Mathematical Structures ◽  
School Subjects ◽  
Arab States ◽  
And Mathematics

Editor's Note.—In April 1966, at a meeting of ministers of education in the Arab states, held at Tripoli, a resolution was adopted requesting an updating of instruction in school subjects—particularly mathematics, pure and applied science, and foreign languages. In November 1966, the General Conference of UNESCO invited member states to undertake a major program for improvement of science and mathematics instruction and selected the Arab states as an initial place to start because of their April resolution. Mathematics was selected as the initial subject primarily because, worldwide, the reforms in education during the last fifteen years began with mathematics.

Applying Mathematics

2018 ◽  
Author(s):  
Otávio Bueno ◽  
Steven French
Keyword(s):  
Quantum Physics ◽  
Scientific Practice ◽  
Explanatory Role ◽  
Mathematical Structures ◽  
Middle Way ◽  
History Of ◽  
And Mathematics ◽  
History Of Quantum Physics ◽  
Available Information

What has been called ‘the unreasonable effectiveness of mathematics’ sets a challenge for philosophers. Some have responded to that challenge by arguing that mathematics is essentially anthropocentric in character whereas others have pointed to the range of structures that mathematics offers. Here a middle way is offered that focuses on the moves that have to be made in both the mathematics and the relevant physics in order to bring the two into appropriate relation. This relation can be captured via the inferential conception of the applicability of mathematics which is formulated in terms of immersion inference and interpretation. In particular the roles of idealizations and of surplus structure in science and mathematics respectively are brought to the fore and captured via an approach to models and theories that emphasizes the partiality of the available information: the partial structures approach. The discussion as a whole is grounded in a number of case studies drawn from the history of quantum physics and extended to contest recent claims that the explanatory role of certain mathematical structures in scientific practice supports a realist attitude towards them. The overall conclusion is that the effectiveness of mathematics does not seem unreasonable at all once close attention is paid to how it is actually applied in practice.

FEATURES OF STUDYING THE SECTION "MULTIPLIERS. THE ELEMENTS OF LOGIC" IN THE COURSE OF PRIMARY SCHOOL MATHEMATICS ON THE UPDATED CONTENT OF EDUCATION

2021 ◽  
Vol 73 (1) ◽  
pp. 42-49
Author(s):  
M.Zh. Мynzhasarova ◽  
◽  
A.B. Akpaeva ◽  
L.A. Lebedeva ◽  
◽  
...  
Keyword(s):  
Primary School ◽  
School Mathematics ◽  
Educational Goals ◽  
Mathematical Education ◽  
Special Role ◽  
Logical Thinking ◽  
School Students ◽  
Elementary School Mathematics ◽  
Independent Work

This article discusses the features of studying the topics of the section "Set. Elements of Logic" in the course of elementary school mathematics. The analysis of the content of the program and its implementation in the textbook "Mathematics" is given. The article describes the features of the updated content of mathematical education in primary classes. The role of the "Set. Elements of logic" in the development of logical thinking of primary school students. A feature of studying the section "Set. Elements of Logic" is that a system of exercises has been developed that implement the formation of thinking techniques. The analysis of the proposed system of exercises in the implementation of the educational goals of this section is carried out. When developing the system of exercises, the age-specific features of the students ' thinking development were taken into account. In the organization of work with the system of exercises, the ways of increasing the mental activity of students, the development of independent work were considered. A special role in the development of logical thinking of students is also occupied by logical tasks presented in the category "You are a researcher".

Experimental Programs: Textbook difficulty and mathematics achievement in junior high school

1965 ◽  
Vol 58 (8) ◽  
pp. 724-729
Author(s):  
L. Doyal Nelson
Keyword(s):  
Mathematics Achievement ◽  
Junior High School ◽  
School Mathematics ◽  
Mathematics Textbooks ◽  
Considerable Time ◽  
Text Book ◽  
Mathematical Ideas ◽  
Content Organization ◽  
And Mathematics

The importance of the role of the text-book in determining the content, organization, and mode of presentation of school mathematics can hardly be overemphasized. In recent years various groups and individuals have devoted considerable time and effort to the production of school mathematics textbooks with content strikingly different from that found in traditional textbooks. Probably more striking are the changes which have occurred in the methods of organizing and presenting the material. These changes have generated increased interest in the question of whether there is any one method of presenting mathematical ideas which is superior to all others in promoting maximum learning efficiency on the part of students.

Inquiry-Discourse Mathematics Instruction

2007 ◽  
Vol 101 (4) ◽  
pp. 290-300
Author(s):  
Azita Manouchehri
Keyword(s):  
Mathematics Teachers ◽  
Mathematics Instruction ◽  
School Mathematics ◽  
Professional Standards ◽  
Teaching Mathematics ◽  
Mathematical Inquiry ◽  
Mathematical Structures ◽  
Approach To Teaching ◽  
Principles And Standards ◽  
Student Inquiry

Principles and Standards for School Mathematics (NCTM 2000) proposes that mathematics instruction provide opportunities for students to engage in mathematical inquiry and in meaningmaking through discourse. Mathematics teachers are encouraged to build on student discoveries in designing subsequent instruction. Natural consequences of using an inquiry-based approach to teaching include the emergence of unexpected mathematical results and the articulation of novel and different strategies by students. Anticipating the potential for such occurrences, Professional Standards for Teaching Mathematics (NCTM 1991) urges all teachers to remain flexible and responsive to student ideas in their instruction: Help students make connections among various solutions, tie student ideas to important mathematical structures, and extend student inquiry by posing questions and tasks that challenge their initial interpretations of problems or their false generalizations.

Research findings applicable in the classroom

1969 ◽  
Vol 16 (8) ◽  
pp. 640-642
Author(s):  
Marilyn N. Suydam ◽  
C. Alan Riedesel
Keyword(s):  
Elementary School ◽  
Mathematics Instruction ◽  
Elementary Mathematics ◽  
School Mathematics ◽  
Elementary School Mathematics ◽  
Research Findings ◽  
Elementary Mathematics Instruction ◽  
Use Of Research

Teachers, administrators, textbook authors, and textbook editors often discuss the role of research in elementary mathematics instruction. Usually one of two dichotomous views is brought forth. Either they express the view that there has been little or no valid and important researchor they state that the findings of research are being used daily in their work. Probably the actual status of the use of research in the teaching of elementary school mathematics is somewhere between these poles.

The use of models in the teaching of mathematics

1961 ◽  
Vol 8 (1) ◽  
pp. 22-24
Author(s):  
Roger Osborn
Keyword(s):  
Secondary School ◽  
Mathematics Instruction ◽  
School Mathematics ◽  
Instructional Materials ◽  
Effective Teacher ◽  
Secondary School Mathematics ◽  
Teaching Of Mathematics ◽  
Use Of Models

Instructional materials make up an important part of the equipment of the effective teacher of elementary- or secondary- school mathematics. The distinction between number and numeral is being made with increasing consistency and emphasis in programs of mathematics instruction being currently evolved. The development of this concept may, for many teachers, point up a need for new evaluation of the role of instructional materials in the classroom. The importance of the fact that the name of a thing and the thing itself are not the same has become more and more evident in mathematics programs as teachers con ider numerals as symbols we use to denote numbers.

Working Memory and Number Sense as Predictors of Mathematical (Dis-)Ability

2015 ◽  
Vol 223 (2) ◽  
pp. 102-109 ◽  
Author(s):  
Evelyn H. Kroesbergen ◽  
Marloes van Dijk
Keyword(s):  
Working Memory ◽  
Learning Disabilities ◽  
Spatial Working Memory ◽  
Number Sense ◽  
Mathematical Learning ◽  
Visual Spatial ◽  
Mathematical Learning Disabilities ◽  
Visual Spatial Working Memory ◽  
And Mathematics

Recent research has pointed to two possible causes of mathematical (dis-)ability: working memory and number sense, although only few studies have compared the relations between working memory and mathematics and between number sense and mathematics. In this study, both constructs were studied in relation to mathematics in general, and to mathematical learning disabilities (MLD) in particular. The sample consisted of 154 children aged between 6 and 10 years, including 26 children with MLD. Children performing low on either number sense or visual-spatial working memory scored lower on math tests than children without such a weakness. Children with a double weakness scored the lowest. These results confirm the important role of both visual-spatial working memory and number sense in mathematical development.

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