Abstract
The results of this study point out the contributions of the theory of Conceptual Fields to identify the nature of the mistakes made by students of the 6th year of elementary school in solving mathematical questions with ten natural numbers. We ask: What are the concepts and theorems put into action to carry out the operations of addition, subtraction, multiplication and division with natural numbers? The concepts and theorems in action related to the understanding of the decimal numbering system structure are responsible for the errors? The mistakes are due to the understanding of the organization of representation registers (word and Arabic notation)? As a result, we find that students have the addition of errors and subtraction errors by misunderstanding of the structure of the Numbering Decimal Positional System, errors due to lack of meaning assignment to the operations of addition, subtraction, multiplication and division, and also the numbers of Arabic script which induce errors in the handling of algorithms.
Highlights
This text presents the results of a research on the performance of addition, subtraction, multiplication and division with natural numbers of students from 6th grade of elementary school
The answers to questions posed characterized the empirical data, submitted to analysis in the light of the theory of Conceptual Fields of Gérard Vergnaud (1990) to answer the following questions: What are the concepts and theorems put into action to carry out the operations of addition, subtraction, multiplication and division with natural numbers, students from 6th grade of elementary school? The concepts and theorems in action related to the decimal number system structure are responsible for the errors? The errors are due to the understanding of the algorithm structure? The errors are due to the understanding of the organization of representation registers?
With the development of the survey intended to achieve the following objectives: to explain the concepts and theorems put into action to carry out the operations of addition, subtraction, multiplication and division with natural numbers, by students of the 6th grade of primary education; explicit the students’ understanding of the SND, at the time of use of operative algorithms; unveil the chances that students manifest to justify strategies and procedures used to perform addition, subtraction, multiplication and division with natural numbers; point the conceptual field necessary to perform addition, subtraction, multiplication and division operations with natural numbers
Summary
This text presents the results of a research on the performance of addition, subtraction, multiplication and division with natural numbers of students from 6th grade of elementary school. The answers to questions posed characterized the empirical data, submitted to analysis in the light of the theory of Conceptual Fields of Gérard Vergnaud (1990) to answer the following questions: What are the concepts and theorems put into action to carry out the operations of addition, subtraction, multiplication and division with natural numbers, students from 6th grade of elementary school? With the development of the survey intended to achieve the following objectives: to explain the concepts and theorems put into action to carry out the operations of addition, subtraction, multiplication and division with natural numbers, by students of the 6th grade of primary education; explicit the students’ understanding of the SND, at the time of use of operative algorithms; unveil the chances that students manifest to justify strategies and procedures used to perform addition, subtraction, multiplication and division with natural numbers; point the conceptual field (set of situations and set of concepts) necessary to perform addition, subtraction, multiplication and division operations with natural numbers
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