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López-Barrientos, José Daniel; Silva, Eliud; Lemus-Rodríguez, Enrique – Teaching Statistics: An International Journal for Teachers, 2023
We take advantage of a combinatorial misconception and the famous paradox of the Chevalier de Méré to present the multiplication rule for independent events; the principle of inclusion and exclusion in the presence of disjoint events; the median of a discrete-type random variable, and a confidence interval for a large sample. Moreover, we pay…
Descriptors: Statistics Education, Mathematical Concepts, Multiplication, Misconceptions
Hurst, Chris; Huntley, Ray – Journal of Research and Advances in Mathematics Education, 2020
Multiplicative thinking underpins much of the mathematics learned beyond the middle primary years. As such, it needs to be understood conceptually to highlight the connections between its many aspects. This paper focuses on one such connection; that is how the array, place value partitioning and the distributive property of multiplication are…
Descriptors: Multiplication, Mathematics Instruction, Teaching Methods, Concept Formation
Lockwood, Elise; Purdy, Branwen – Journal for Research in Mathematics Education, 2019
The multiplication principle (MP) is a fundamental aspect of combinatorial enumeration, serving as an effective tool for solving counting problems and underlying many key combinatorial formulas. In this study, we used guided reinvention to investigate 2 undergraduate students' reasoning about the MP, and we sought to answer the following research…
Descriptors: Undergraduate Students, Multiplication, Mathematical Concepts, Mathematical Logic
Mulligan, Joanne; Oslington, Gabrielle; English, Lyn – ZDM: The International Journal on Mathematics Education, 2020
An Australian longitudinal study of 319 Kindergartners developed, implemented and evaluated an intervention, the Pattern and Structure Mathematics Awareness Program (PASMAP). It comprised of repetitions and growing patterns, structured counting and grouping, grids and shapes, partitioning, additive and multiplicative structures, measurement and…
Descriptors: Foreign Countries, Kindergarten, Mathematical Concepts, Repetition
Lockwood, Elise; Reed, Zackery; Caughman, John S. – International Journal of Research in Undergraduate Mathematics Education, 2017
The multiplication principle serves as a cornerstone in enumerative combinatorics. The principle underpins many basic counting formulas and provides students with a critical element of combinatorial justification. Given its importance, the way in which it is presented in textbooks is surprisingly varied. In this paper, we analyze a number of…
Descriptors: Multiplication, Textbooks, Mathematics Instruction, Mathematical Concepts
Downton, Ann; Russo, James; Hopkins, Sarah – Mathematics Education Research Group of Australasia, 2019
We report on 25 Year 5-6 students' written responses to two items taken from an assessment of mental computation fluency with multiplication, alongside their reasoning of the strategy they had employed, which may or may not have made use of the associative property. Coding of this interview data revealed four distinct levels of conceptual…
Descriptors: Mathematics Instruction, Mathematical Concepts, Concept Formation, Elementary School Mathematics
Makhubele , Yeyisani Evans – International Electronic Journal of Mathematics Education, 2021
This paper presents an analysis of fractions errors displayed by learners due to deficient mastery of prerequisite concepts. Fractions continue to pose a critical challenge for learners. Fractions can be a tricky concept for learners although they often use the concept of sharing in their daily lives. 30 purposefully sampled learners participated…
Descriptors: Foreign Countries, Middle School Students, Secondary School Mathematics, Algebra
Incikabi, Lütfi; Ayanoglu, Perihan; Uysal, Ramazan – International Electronic Journal of Elementary Education, 2020
This study aimed to reveal the conceptual and operational conceptions of sixth-grade students in the process of division. The focus of the study included the strategies used in the division process, the students' understanding of the division algorithm, and their ability to interpret the remainder in a real-life context. Being qualitative in…
Descriptors: Foreign Countries, Middle School Students, Grade 6, Mathematics Skills
Lockwood, Elise; Erickson, Sarah – International Journal of Mathematical Education in Science and Technology, 2017
Counting problems offer rich opportunities for students to engage in mathematical thinking, but they can be difficult for students to solve. In this paper, we present a study that examines student thinking about one concept within counting, factorials, which are a key aspect of many combinatorial ideas. In an effort to better understand students'…
Descriptors: Undergraduate Students, Mathematical Concepts, Computation, Semi Structured Interviews
Hurst, Chris; Huntley, Ray – Mathematics Education Research Group of Australasia, 2017
Multiplicative thinking is a critical stage of mathematical understanding upon which many mathematical ideas are built. The myriad aspects of multiplicative thinking and the connections between them need to be explicitly developed. One such connection is the relationship between place value partitioning and the distributive property of…
Descriptors: Multiplication, Mathematics Skills, Mathematical Logic, Mathematical Concepts
Zaferos, Melanie – Teaching Children Mathematics, 2016
This investigation presents students with the challenge of determining the total number of eggs in a photograph of a stack of egg trays. The perspective of the photograph does not allow students to count all the individual eggs in the top tray but does allow them to see the number of eggs in one row and one column of the top tray. During this…
Descriptors: Mathematics Instruction, Teaching Methods, Photography, Multiplication
Hurst, Chris; Hurrell, Derek – Australian Primary Mathematics Classroom, 2017
A journey into multiplicative thinking by three teachers in a primary school is reported. A description of how the teachers learned to identify gaps in student knowledge is described along with how the teachers assisted students to connect multiplicative ideas in ways that make sense.
Descriptors: Elementary School Teachers, Elementary School Mathematics, Mathematics Instruction, Multiplication
Lockwood, Elise; Reed, Zackery; Caughman, John S., IV – North American Chapter of the International Group for the Psychology of Mathematics Education, 2015
The multiplication principle is a fundamental principle in enumerative combinatorics. It underpins many of the counting formulas students learn, and it provides much-needed justification for why counting works as it does. However, given its importance, the way in which it is presented in textbooks is surprisingly varied. In this paper, we document…
Descriptors: Mathematics Instruction, Multiplication, College Mathematics, Textbooks
Bicknell, Brenda; Young-Loveridge, Jenny; Simpson, Jackie – Australian Primary Mathematics Classroom, 2017
A robust understanding of place value is essential. Using a problem-based approach set within meaningful contexts, students' attention may be drawn to the multiplicative structure of place value. By using quotitive division problems through a concrete-representational-abstract lesson structure, this study showed a powerful strengthening of Year 3…
Descriptors: Number Concepts, Arithmetic, Mathematics Instruction, Young Children
Beckmann, Sybilla; Izsák, Andrew – Journal for Research in Mathematics Education, 2015
In this article, we present a mathematical analysis that distinguishes two distinct quantitative perspectives on ratios and proportional relationships: variable number of fixed quantities and fixed numbers of variable parts. This parallels the distinction between measurement and partitive meanings for division and between two meanings for…
Descriptors: Mathematics Education, Mathematical Concepts, Multiplication, Measurement