This paper provides a method of the process of computation called the cumulative method, it is based upon repeated cumulative process. The cumulative method is being adapted to the purposes of computation, particularly multiplication and division. The operations of multiplication and division are represented by algebraic formulas. An advantage of the method is that the cumulative process can be performed on decimal numbers. The present paper aims to establish a basic and useful formula valid for the two fundamental arithmetic operations of multiplication and division. The new cumulative method proved to be more flexible and made it possible to extend the multiplication and division based on repeated addition/subtraction to decimal numbers.
References
[1]
Akhter, N. and Akhter, N. (2018) Learning in Mathematics: Difficulties and Perceptions of Students. Journal of Educational Research, 21, 147.
[2]
Fischbein, E., Deri, M., Nello, M.S. and Marino, M.S. (1985) The Role of Implicit Models in Solving Verbal Problems in Multiplication and Division. Journal for Research in Mathematics Education, 16, 3-17. https://doi.org/10.5951/jresematheduc.16.1.0003
[3]
Clark, F.B. and Kamii, C. (1996) Identification of Multiplicative Thinking in Children in Grades 1-5. Journal for Research in Mathematics Education, 27, 41-51. https://doi.org/10.5951/jresematheduc.27.1.0041
[4]
Anghileri, J. (1989) An Investigation of Young Children’s Understanding of Multiplication. Educational Studies in Mathematics, 20, 367-385. https://doi.org/10.1007/BF00315607
[5]
Kaput, J.J. (1985) Multiplicative Word Problems and Intensive Quantities: An Integrated Software Response. Technical Report, 85-19.
[6]
Karlsson, N. and Kilborn, W. (2022) Teaching and Learning the Multiplication Table by Using Multiplicative Structures: Variation and Crucial Patterns. In: Carmo, M., Ed.,Education and New Developments 2022, Vol. 1, inScience Press, Lisboa, 45-49. https://doi.org/10.36315/2022v1end010
[7]
Larsson, K. (2016) Students’ Understandings of Multiplication. Unpublished PhD Thesis, Stockholm University, Stockholm.
[8]
Larsson, K., Pettersson, K. and Andrews, P. (2018) Students’ Conceptualisation of Multiplication as Repeated Addition or Equal Groups in Relation to Multi-Digit and Decimal Numbers. The Journal of Mathematical Behavior, 48, 1-13. https://doi.org/10.1016/j.jmathb.2017.07.003
[9]
Maffia, A. and Mariotti, M.A. (2018) Intuitive and Formal Models of Whole Number Multiplication: Relations and Emerging Structures. For the Learning of Mathematics, 38, 30-36.
[10]
Larsson, K. (2017) Students’ Conceptualisations of Decimal Multiplication. https://www.researchgate.net/publication/319165771_Students'_conceptualisations_of_decimal_multiplication
[11]
Peanark, P., Khamsim, M. and Poonputta, A. (2023) Think-Pair-Share in the Development of Grade 7 Student Multiply and Divide Decimal Mathematical Achievement. International Education Studies, 16, 21-28. https://doi.org/10.5539/ies.v16n4p21
[12]
Greer, B.D. (1992) Multiplication and Division as Models of Situations. In: Grouws, D.A., Ed., Handbook of Research on Mathematics Teaching and Learning, Macmillan Publishing Company, New York, 276-295.
[13]
Young-Loveridge, J., Bicknell, B. and Lelieveld, J. (2013) Introducing Multiplication and Division Contexts in Junior Primary Classes. Teachers and Curriculum, 13. https://doi.org/10.15663/tandc.v13i0.14
[14]
Hulbert, E.T., Petit, M.M., Ebby, C.B., Cunningham, E.P. and Laird, R.E. (2023) A Focus on Multiplication and Division: Bringing Mathematics Education Research to the Classroom. 2nd Edition. Routledge, New York. https://doi.org/10.4324/9781003185529
[15]
Sari, N., Sukmaningthias, N., Nuraeni, Z., Simarmata, R.H., Hasanah U. and Anggraini, K.N. (2021) Developing Mathematical Literacy Task in Multiplication and Division of Algebraic Expression. Proceedings of the International Conference of Mathematics and Mathematics Education (I-CMME 2021), 597, 203-209. https://doi.org/10.2991/assehr.k.211122.028
