Improving the learning of mathematics

1954 ◽  
Vol 47 (6) ◽  
pp. 393-400
Author(s):  
Kenneth P. Kidd
Keyword(s):  
Mathematics Teacher ◽  
Mathematics Instruction ◽  
Spatial Relationships ◽  
Problem Situations ◽  
Teaching Of Mathematics ◽  
Effective Use ◽  
Clear Conception

Probably every mathematics teacher has asked himself the question, “How can I bring about improvements in the teaching of mathematics?” An answer to this question presupposes a clear conception of the desirable outcomes of mathematics instruction. Let us assume that the test of competence in mathematics is the effective use of the skills and concepts of mathematics in problem situations which involve quantitative and spatial relationships.

HUMANITARIAN-ORIENTED TEACHING OF MATHEMATICS AND NATURAL SCIENCES AT SCHOOL

2021 ◽  
Vol 31 (3) ◽  
pp. 322-330
Author(s):  
R.R. Ismagilova ◽  
G.Kh. Akhmetshina
Keyword(s):  
Science Education ◽  
Natural Science ◽  
Natural Sciences ◽  
Academic Disciplines ◽  
Language History ◽  
Problem Situations ◽  
The World ◽  
History Of ◽  
Teaching Of Mathematics ◽  
Natural Science Education

The humanitarian potential of school mathematics and natural science disciplines for the education of a person who has a unified representation of the modern picture of the world, its scope and content require more and more study. The humanities-oriented teaching of mathematics and natural sciences at school is implemented in the learning process within the framework of traditional academic disciplines and has the full means for the comprehensive and harmonious development of the student's personality. The use of components of literature, language, history of the native land in the implementation of programs of mathematical, natural science education contributes to the development of interest in learning, the formation of personal values of students. Cognitive interest is created and maintained through the design of problem situations in the classroom, through the development of the ability to solve, develop plot problems that form functional (mathematical and natural science) literacy. The combination of natural science and humanitarian approaches in the representation and assessment of the world in the process of mastering the content of educational disciplines will spiritually enrich every student.

It's not how new you make it, but how you make it new

1971 ◽  
Vol 18 (1) ◽  
pp. 7-9
Author(s):  
F. Lynwood Wren
Keyword(s):  
Cultural Heritage ◽  
School Mathematics ◽  
Curriculum Content ◽  
Teaching Techniques ◽  
Problem Situations ◽  
Basic Understanding ◽  
Reser Voirs ◽  
Teaching Of Mathematics ◽  
And Function

Before the “;mathematics revolution” of some fifteen years ago, the emphasis of instruction in school mathematics was almost entirely on the “how” of manipulation. Little or no attention was paid to the “what” and “why” of understanding. Since then the efforts of committees and of individual teachers have effected changes both in curriculum content and in teaching techniques. These cha nges were designed to make basic understanding, as well as significant manipula tion, a fundamental responsibility of all levels of instruction. No longer is the teaching of mathematics designed to result merely in a catalog of rules for mechanical application. Ra ther, it is designed to develop, a long with a facility in use, a comprehe nsion of and an appreciation for bas ic concepts. Further, it is designed to develop an understanding of the purpose and function of opera tional procedures that they may serve as resource reser voirs for intelligent attack on problem situations whenever and however they may occur. Thus the underlying philosophy of this new emphasis in instruction is to present mathematics as an important, logically structured segment of our cultural heritage rather than as a tool kit of rules, formulas, and assorted mnemonics.

One Point of View: Setting Our Sights High

1983 ◽  
Vol 31 (1) ◽  
pp. 4
Author(s):  
Douglas A. Grouws
Keyword(s):  
Young People ◽  
Everyday Life ◽  
Mathematics Instruction ◽  
Point Of View ◽  
Technological Changes ◽  
High Expectations ◽  
The Future ◽  
Teaching Of Mathematics ◽  
Made In

The way mathematics instruction accommodates the large technological changes sweeping society will profoundly affect the ability of young people to adjust to everyday life situations and perform efficiently in the skilled professions of the future. In particular, continued thoughtful attention must be given to the role of microcomputers in all aspects of the teaching of mathematics. Many significant issues in this area will need to be discussed and important decisions made in the months ahead. We need to set high expectations in these discussions and the decisions that follow from them. Settling for what can be done easily or selling short the talents of our students or our colleagues will be a mistake.

Language Connections in Mathematics: A Critical Part of Mathematics Instruction

1993 ◽  
Vol 41 (1) ◽  
pp. 8-12
Author(s):  
Lelon R. Capps ◽  
Jamar Pickreign
Keyword(s):  
Mathematics Instruction ◽  
Mathematical Language ◽  
Critical Part ◽  
Problem Situations

In 1973, Bruner maintained that teachers need clear and correct mathematical words to describe problem situations, to question students' unreasoned statements in mathematics, and to encourage students' further research and reading in mathematics. Bruner insisted that “good mathematical language challenges—relights the flame of curiosity” and further said that people use words to resolve puzzling situations. He suggested, however, that using words correctly in solving problems is not easy. To encourage students to speculate, teachers need to help them to understand the use of the words.

Critiques: Seeking Meaning in Mathematics Instruction: A Response to Gagné

1983 ◽  
Vol 14 (3) ◽  
pp. 210-213
Author(s):  
Leslie P. Steffe ◽  
Rick N. Blake
Keyword(s):  
Problem Solving ◽  
Mathematics Instruction ◽  
Mathematics Learning ◽  
Mathematics Educators ◽  
Teaching Of Mathematics ◽  
Mental Operations

Mathematics educators have for some time been interested in psychological bases for the teaching of mathematics in the schools (Buswell, 1951). They have naturally turned to cognitive theorists in their quest to understand such terms as knowledge, meaning, concepts, mental operations, problem solving, and insight. Gagné's (1983) paper is bur one example of this historical collaboration. His purpose is to “relate what is known about learning, … from the kind of theory [he has] described, to the problem of improving mathematics learning” (p. 10).

Scales for the Study of Children’s Characteristics

1919 ◽  
Vol 12 (1) ◽  
pp. 10-16
Author(s):  
Eugene Randolph Smith
Keyword(s):  
Standardized Tests ◽  
Mathematics Teacher ◽  
Teaching Of Mathematics

Recent issues of The Mathematics Teacher have given considerable attention to standardized tests and their influence on the teaching of mathematics. The authors, Dr. Minnick and Dr. Rogers, while they are convinced of the value of such tests, recognize their limitations, up to this time, in that they test the more routine kinds of work. They, with other investigators, have been trying to develop tests that will gage the fundamental qualities that underlie successful accomplishment in the subjects in question.

A Brief Study in Non-Mathematical Logic

1923 ◽  
Vol 16 (4) ◽  
pp. 242-246
Author(s):  
N. J. Lennes
Keyword(s):  
Mathematical Logic ◽  
Mathematics Teacher ◽  
School Program ◽  
Teaching Of Mathematics ◽  
The Mind

While engaged in taking general stock of the existing literature on the teaching of mathematics the writer came again upon a paper by Ernest C. Moore entitled “Does the study of Mathematics train the mind specially or universally?” which was printed in The Mathematics Teacher Vol. 10 pages 1-18. A cursory reading of Moore's paper revealed certain interesting qualities which led to closer scrutiny. The purpose of the paper, as revealed by its content rather than by the title, is to show that the only reason for studying any subject is the use which the student may reasonably be expected to make in his own life of the matter actually learned. “Every form of skill that we attempt to teach him gets its place in the school program solely because he cannot live a civilized life without practicing it” (op. cit. p. 3). (The italics are mine).

scholarly journals Um estudo sobre o trabalho com resolução de problemas após um curso de formação continuada em Matemática com professores dos anos iniciais do Ensino Fundamental / A Study about Work with Problem Solving after a Course of Continuing Education in Mathematics with Teachers of the Early Years of Elementary School

2015 ◽  
Vol 2 (1) ◽  
Author(s):  
Giovana Pereira Sander ◽  
Nelson Antonio Pirola
Keyword(s):  
Elementary School ◽  
Problem Solving ◽  
Continuing Education ◽  
Sao Paulo ◽  
Early Years ◽  
Teaching Mathematics ◽  
São Paulo ◽  
Problem Situations ◽  
Teaching Of Mathematics ◽  
Concrete Materials

ABSTRACTThis research aimed to investigate the practice of teaching mathematics through problem solving after the completion of the course of the continuing education of Pró-Letramento program. 458 persons participated of the program and they are teachers of the early years of elementary school from districts of the state of São Paulo / Brazil. The instruments used were a questionnaire about possible reflections offered by the course as the teaching of mathematics and recordings of three classes of four teachers of Mathematics. The data indicate that the course contributed to the practice of these teachers regarding the methodology of teaching mathematics, using concrete materials and games; and understanding of the content. In relation to work with problem solving, it was something with little presence in their speech. During the monitoring of lessons was observed that the problem situations are used for the application of previously learned algorithms. Although the course emphasize on teaching mathematical content through problem solving, having a specific time for discussions on this topic, teachers work with problems after the explanation of content, then characterizing it as exercise.RESUMOA presente pesquisa teve como objetivo investigar a prática de ensino da Matemática por meio da resolução de problemas após a realização do curso do programa de formação continuada do Pró-Letramento. Participaram 458 cursistas do programa que são professores dos anos iniciais do Ensino Fundamental de municípios do estado de São Paulo/Brasil. Os instrumentos utilizados foram um questionário sobre as possíveis reflexões propiciadas pelo curso quanto ao ensino da Matemática e gravações de três aulas de Matemática de 4 professores. Os dados apontam que o curso contribuiu com a prática desses professores quanto à metodologia de ensino da Matemática, utilizando materiais concretos e jogos; e à compreensão dos conteúdos. Já o trabalho com a resolução de problemas foi algo pouco presente em suas falas. Durante o acompanhamento das aulas foi possível observar que as situações problema são utilizadas para a aplicação de algoritmos anteriormente aprendidos. Apesar de o curso salientar sobre o ensino de conteúdos matemáticos através da resolução de problemas, tendo um momento específico para discussões sobre essa temática, os professores trabalham com problemas após a explicação de um conteúdo, caracterizando-o, então, como exercícios. Contato principal: [email protected]

scholarly journals Simulation of Teacher Interventions in a Training Course of Mathematics Teacher Educators

Mathematics ◽  
2021 ◽  
Vol 9 (24) ◽  
pp. 3228
Author(s):  
Adriana Breda ◽  
Marcel Pochulu ◽  
Alicia Sánchez ◽  
Vicenç Font
Keyword(s):  
Preservice Teachers ◽  
Mathematics Teacher ◽  
Teacher Educators ◽  
Teacher Interventions ◽  
Mathematics Teacher Educators ◽  
Problem Situations ◽  
Semiotic Approach ◽  
Official Curriculum ◽  
Ecological Suitability ◽  
Patterns Of Interaction

This work aimed to characterize simulated teacher interventions to manage a didactic configuration in which students solve problem situations using an ICT resource. We also aimed to identify patterns of interaction between the teacher and the students that make it possible to characterize styles of interaction and assess both their interactional and their ecological suitability. To do this, we used the tools of the Onto-semiotic Approach to Mathematical Cognition and Instruction to analyze the level of reflection of 102 educators of preservice teachers of mathematics, about hypothetical problem resolutions of their students and the types of interactions simulated by them to manage the students’ learning. The educators were participants of a Teacher Training of the Teacher Specialization in Education and ICT in Argentina. The results show that there are three levels of reflection and four types of interaction (maieutic, falsificationist, dogmatic and paternalistic). We did not find a high interactional suitability in their proposals of dialogues, and participants do not consider aspects of the ecological suitability, such as the adaptation to the official curriculum. We conclude that the type of interventions that teacher educators propose is closely related to their level of reflection about the reasons why their students respond to problems in one manner or another.

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