Teaching and Learning Middle School Algebra: Valuable Lessons from the History of Mathematics

2016 ◽  
pp. 131-154 ◽  
Author(s):  
Mala S. Nataraj ◽  
Mike Thomas
Keyword(s):  
Middle School ◽  
Teaching And Learning ◽  
History Of Mathematics ◽  
History Of

scholarly journals Em Foco a Aritmética do Curso Primário: Um Estudo de Cadernos Escolares e do Manual “Práticas Escolares”

2018 ◽  
Vol 11 (1) ◽  
pp. 47
Author(s):  
Rosimeire Aparecida Soares Borges ◽  
Cristiano José de Oliveira
Keyword(s):  
Primary School ◽  
Cultural History ◽  
Teaching And Learning ◽  
History Of Mathematics ◽  
Historical Study ◽  
School Practices ◽  
New School ◽  
Culture History ◽  
History Of ◽  
Cultura Escolar

Este estudo histórico investigou apropriações das propostas reformistas da Escola Nova no que tange ao ensino da Aritmética para a escola primária em cinco cadernos de um aluno, de terceiro e quarto anos do curso primário, dos anos de 1952 e 1953, respectivamente, e no primeiro volume do manual didático “Práticas Escolares” que teve sua primeira edição em 1940 e décima edição em 1965, de autoria de Antonio D’Ávila. Utiliza-se como base teórico-metodológica a História Cultural na direção de dar significado às apropriações que foram feitas em relação à aritmética da escola primária em tempos da Escola Nova. Há uma predominância da resolução de problemas aritméticos ligados ao cotidiano dos alunos, indicando uma preocupação com a abstração dos conceitos com foco em uma aritmética prática, que tinha por finalidade preparar o aluno para a vida fora da escola após quatro anos de estudo no curso primário. Observa-se uma valorização do aluno como indivíduo, com respeito ao seu ritmo e dificuldades apresentadas na aprendizagem da Aritmética, um dos aspectos marcantes da Escola Nova, o aluno considerado como protagonista do processo de ensino e de aprendizagem, podendo interagir no meio social em uma formação mais humana.Palavras-chave: Aritmética. Ensino Primário. Manual Didático para Professores. Cadernos de aluno. Cultura escolar. História da Educação Matemática.AbstractThis historical study investigated appropriations of the New School for the teaching of Arithmetic for the primary school in five books of a student, of the third and the fourth years of the primary course, of the years of 1952 and 1953, respectively, And in the first Volume of the didactic manual “School Practices” that had its first edition in 1940 and tenth edition in 1965, authored by Antonio D’Ávila. It is used as a theoretical-methodological basis for the Cultural History in the direction of provide meaning the appropriations that were made in relation to the primary school in times of the New School. There is a predominance of solving arithmetic problems related to students’ daily life, indicating a preoccupation with an abstraction of concepts with a focus on an arithmetic practice, whose purpose was to prepare a student for the life outside of school after four years of primary school. It is observed the evaluation of the student as an individual, with respect to its rhythm and difficulties presented in the learning of Arithmetic, one of the markers of the New School, the student considered the protagonist of the process of teaching and learning, being able To interact in the social environment in a more humane formation.Keywords: Arithmetic. Primary school. Didactic Manual for Teachers. Books of a student. School culture. History of Mathematics Education.

The Representational Value of Hats

2008 ◽  
Vol 14 (1) ◽  
pp. 4-10
Author(s):  
Jane M. Watson ◽  
Noleine E. Fitzallen ◽  
Karen G. Wilson ◽  
Julie F. Creed
Keyword(s):  
Middle School ◽  
Middle School Students ◽  
History Of Mathematics ◽  
Graphical Representations ◽  
Data Sets ◽  
School Students ◽  
Mathematical Ideas ◽  
History Of ◽  
The Way

The literature that is available on the topic of representations in mathematics is vast. One commonly discussed item is graphical representations. From the history of mathematics to modern uses of technology, a variety of graphical forms are available for middle school students to use to represent mathematical ideas. The ideas range from algebraic relationships to summaries of data sets. Traditionally, textbooks delineate the rules to be followed in creating conventional graphical forms, and software offers alternatives for attractive presentations. Is there anything new to introduce in the way of graphical representations for middle school students?

scholarly journals Comparison between a Modern-Day Multiplication Method and Two Historical Ones by Trainee Teachers

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 349
Author(s):  
María José Madrid ◽  
Alexander Maz-Machado ◽  
Fernando Almaraz-Menéndez ◽  
Carmen León-Mantero
Keyword(s):  
Comparative Analysis ◽  
Secondary School ◽  
Mathematics Teachers ◽  
Mathematical Knowledge ◽  
Teaching And Learning ◽  
History Of Mathematics ◽  
Trainee Teachers ◽  
Multiplication Algorithm ◽  
History Of ◽  
Different Levels

Different studies consider the possibility of including history of mathematics in the classroom. However, its inclusion in the teaching and learning of mathematics depends on the conceptions of it that teachers have, among other factors. This study displays a comparative analysis between the opinions of primary education teachers-to-be and the opinions of mathematics teachers-to-be at secondary school and A-levels after the realization of an activity related to two historical or unusual multiplication methods. These trainee teachers were asked to identify the differences between these methods and the multiplication algorithm usually used in Spain. We collected these data and conducted an exploratory, descriptive and qualitative study. In order to analyse the information obtained, we used the technique content analysis. The answers given by these trainee teachers show their lack of knowledge about other multiplication methods and the various differences which they observed. These differences are mainly related to the structure of each method, the procedure and application of these methods and the mathematical processes carried out for each method. The comparison between the opinions of the teachers-to-be at different levels shows similarities but also some differences, probably due to the different mathematical knowledge they have.

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