Difficulties of 6th Grade Elementary School Students in Solving the Four Basic Fundamental Operations: Addition, Subtraction, Multiplication and Division of Natural Numbers

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.

Ethnomathematics: Mathematical Concept in the Local Game of Tong Tong Galitong Ji for High School

“…All possible combinations of selected number I, selected operation, and selected number II are presented in Table 5. 10 + 1; 10 + 2; 10 + 3; 10 + 4; … ; 10 + n, nϵℕ Multiplication 10 × 1; 10 × 2; 10 × 3; 10 × 4; … ; 10 × n, nϵℕ Subtraction 10 -1; 10 -2; 10 -3; 10 -4; … ; 10 -n, nϵℕ 4 Addition 4 + 1; 4 + 2; 4 + 3; 4 + 4; … ; 4 + n, nϵℕ Multiplication 4 × 1; 4 × 2; 4 × 3; 4 × 4; … ; 4 × n, nϵℕ Subtraction 4 -1; 4 -2; 4 -3; 4 -4; … ; 4 -n, nϵℕ 7 Addition 7 + 1; 7 + 2; 7 + 3; 7 + 4; … ; 7 + n, nϵℕ Multiplication 7 × 1; 7 × 2; 7 × 3; 7 × 4; … ; 7 × n, nϵℕ Subtraction 7 -1; 7-2; 7-3; 7-4; … ; 7-n, nϵℕ Table 5 shows basic mathematic operations (Brandt, Bassoi, & Baccon, 2016;Rosenberg-Lee, Chang, Young, Wu, & Menon, 2011) of addition, multiplication, and subtraction, but not division. In addition to basic mathematic operations, it also contains arithmetic sequences (Khalid & Embong, 2020;Tohir, Abidin, Dafik, & Hobri, 2018;Zazkis & Liljedahl, 2002).…”