The many studies with coin-tossing tasks in literature show that the concept of randomness is challenging for adults as well as children. Systematic errors observed in coin-tossing tasks are often related to the representativeness heuristic, which refers to a mental shortcut that is used to judge randomness by evaluating how well a set of random…

Patterns are a fundamental component of mathematics, and the patterning ability of young children has been well researched; however, this research has largely been conducted with relatively small cohorts (±70) and in an interventionist way (in laboratory settings or with researchers directly intervening in educational contexts). The current study…

This article presents and analyses a didactic proposal based on manipulative material (Knobless Cylinders) used in a Montessori classroom of 3-6-year-old pre-schoolers. Choosing this material is justified in relation to the competencies/strategies/skills used during the development of mathematical patterning. Numerous studies emphasise the…

Pattern is fundamental to mathematical learning yet pattern has been conspicuously low key within early mathematics curriculum guidance in England despite evidence that it predicts later attainment in mathematics overall. Whilst recent curriculum changes have seen pattern afforded enhanced status, this is within a conception of pattern that marks…

This study examined repeating and growing pattern knowledge and their associations with procedural and conceptual arithmetic knowledge in a sample of U.S. children (N = 185; M[subscript age] = 79.5 months; 55% female; 88% White) and adults (N = 93; M[subscript age] = 19.5 years; 62% female; 66% White) from 2019 to 2020. Three key findings emerged:…

This paper examines the relationship between early childhood music and maths. The emphasis is on children as intuitive pattern makers as they explore, categorise and imagine their worlds. We argue for the careful listening of childhood languages and reason that music and maths are expressive languages that young children use to investigate and…

Mathematical language (or the content-specific words in mathematics) has repeatedly shown to be related to mathematical abilities in preschool and in the early grades of primary education. Research in this field has predominantly focused on young children's quantitative and spatial language. At the same time, recent research has discovered that…

While patterning was commonly seen as evidence of mathematical thinking, interdisciplinary interest has recently increased due to pattern-recognition applications in artificial intelligence. Within two empirical studies, we analyze the analogical-transfer capability of primary school students when completing three types of bi-dimensional patterns,…

Research shows that attention to pattern and structure is fundamental to mathematical learning and attainment yet early mathematics curricula in England underplay the importance of patterning. In a critical realist notion of powerful knowledge, pattern teaching has the potential to empower children to notice patterns, mathematise their everyday…

Mathematically gifted students have a potential for understanding and connecting mathematics concept. Pattern generalization as a part of functional thinking becomes one of the benchmarks for gifted students in mathematics. The mathematics curriculum in Indonesia that has not accommodated the functional thinking ability of elementary school…

This study investigates 27 preschool teachers' verbalization of various aspects of pattern structure as well as their knowledge of pattern structure while solving patterning activities. Aspects of structure that are investigated include the unit of repeat, its length and the amount of times it is repeated, and whether or not the pattern ends in a…

This study explored students' mathematics-related beliefs and the relationship between the beliefs and their strategies for solving non-routine mathematical problems. The study was guided by Daskalogianni and Simpson's 2001 belief systems categories and strategies for non-routine mathematical problems. The participants were 625 grade 11 students…

This paper describes kindergarten children's engagement with two patterning activities. The first activity includes two tasks in which children are asked to choose possible ways for extending two different repeating patterns and the second activity calls for comparing different pairs of repeating patterns. Children's recognition of the unit of…

This paper synthesizes research from three separate studies, analysing how different representations of a mathematical concept may affect young children's engagement with mathematical activities. Children between five and seven years old engaged in counting objects, identifying triangles and completing repeating patterns. The implementation of…

This project tested the effects of adding instruction of trios of children in patterning, mathematics, early literacy, or social studies to ongoing instruction in kindergartens. Children were randomly assigned to trios which were randomly assigned to one of four kinds of instruction. A quarter of the trios received patterning instruction with a…