Rationale   

The NSW board of studies syllabus divided the maths children encounter in schools into three strands: Number and algebra, measurement and geometry, and statistics and probability. Here we will look at the strand of number and algebra, in particular the substrand: Patterns and algebra.

Educators in early childhood can sometimes feel like mathematics concepts are best left to primary school teachers when children begin formal schooling (Touhill, 2013).

However as the Early Years Learning Framework states “experiences in early childhood settings build on the range of experiences with language, literacy and numeracy that children have within their families and communities. Positive attitudes and competencies in literacy and numeracy are essential for children’s successful learning. The foundations for these competencies are built in early childhood” (DEEWR, 2009, p.38). Fox (2011) also highlights that much research now provides evidence that children begin to learn early numeracy concepts in early childhood, before they go to school.

Educators should make learning about mathematics relevant to children’s lives and use every day experiences to teach mathematics concepts (DEEWR, 2009; Geist, Geist, & Kuznik, 2012; Lee, 2010).

Pedagogical content knowledge (PCK) 

“Pedagogical content knowledge (PCK) of mathematics has been identified as a critical factor on children’s mathematical achievements” (Lee, 2010, p.28).

Pedagogical content knowledge is a term that refers to teachers’ pedagogical knowledge and their content knowledge, that is, their knowledge of a subject and their knowledge of how to teach that subject to others (Lee, 2010). More specifically it refers to the way these two ideas are linked or related (Koehler & Mishra, 2006).

A teacher can have sound knowledge of content that is to be taught but without pedagogical knowledge of how to teach the content teaching is less effective (Lee, 2010). So having high level of content knowledge and a high level of pedagogical knowledge is needed to supply high quality education programs.

In early childhood mathematics education studies have shown that teachers with high PCK “implement higher quality mathematics instruction in their programs” (Lee, 2010, p.35).

Educators need to have a solid knowledge of pattern in order to teach it to children. To help further this knowledge the following terms are defined: pattern, comparing, sorting, Classifying, and repeating pattern and unit of repeat.

Pedagogical content knowledge (PCK)- Pattern

 

Patterns are an “underlying rule or concept that allow us to predict phenomena” (Saracho & Spodek, 2008, p.51). “Patterns can involve letters, shapes, numbers, sounds, words. There are alternating patterns, alternating patterns with repetition, growing patterns and power patterns” (Saracho & Spodek, 2008, p.52)

The difference between pattern and design is that although a design might be pleasing to the eye, “it is not a pattern unless some kind of regularity is involved” (Saracho & Spodek, 2008, p.52)

Comparing is defined as finding “a relationship between two things or groups of things on the basis of some specific characteristic or attribute” (Charlesworth & Lind, 2013, p.146).

Classifying is the activity of sorting things or separating them, and grouping or joining things for a reason (Charlesworth & Lind, 2013, p.146).

Repeating pattern - Papic and Mulligan (2007) in their study of mathematical patterning skills in young children state that children “developed a sound understanding of pattern as unit of repeat” (Papic & Mulligan, 2007, p.596) and that this “appeared to lead to growth in the abstraction and complexity of patterning skills” (Papic & Mulligan, 2007, p.596).

EYLF outcome 5.4 states that Children begin to recognise patterns and relationships and the connections between them, they begin to sort, categorise, order and compare collections and events and attributes of objects and materials, in their social and natural worlds (DEEWR, 2009, p.43).

“The expectation is that students will order objects by size, number, and other properties; recognise and extend patterns; analyse how patterns are developed. Young children learn repetitive rhymes and songs and hear stories with predictive language. They develop patterns with objects and eventually with numbers. They recognise change, such as in the seasons or in their height as they grow” (Charlesworth & Lind, 2013, p.216).

Suggested pedagogical approaches

A variety of pedagogical approaches should be employed to teach pattern and its underlying concepts to young children. Intentional teaching is “deliberate, purposeful and thoughtful” (DEEWR, 2009, p.15). Educators who use intentional teaching “use strategies such as modelling and demonstrating, open questioning, speculating, explaining, engaging in shared thinking and problem solving to extend children’s thinking and learning” (DEEWR, 2009, p.15). Here the focus will be on demonstrating, and questioning.

When children learn a new skill educators can employ the teaching technique of demonstrating. MacNaughton and Williams (2004) state that “to demonstrate is to show how something is done” (p.55) and can assist children in learning new skills as they learn through observation. This technique can be used to teach new skills or as a reminder of how to do something previously learnt (MacNaughton & Williams, 2004).

Questioning is an essential teaching technique for educators to employ when teaching pattern. Open ended questions engage children’s thinking and require them to share their thoughts on the topic at hand. It is used for much more than just gauging what a child knows but to draw attention to things, and promote sustained shared thinking (DEEWR, 2009; MacNaughton & Williams, 2004).

It is also important to note that “Children learn mathematics more efficiently when using manipulative materials rather than abstract or semi-abstract instructional materials” (Lee, 2010, p.37). This means that when children are learning pattern it is important not to jump too far ahead to symbolic and abstract processes.

Children can have difficulty learning the concept of growing patterns due to “inadequate or inappropriate development of repeating patterns without a sound understanding of the unit of repeat” (Papic & Mulligan, 2007). For this reason it is important that teachers make sure children have a firm understanding of unit of repeat before moving on to more complex patterning.

References

Charlesworth, R. & Lind, K. (2013). Math and science for young children (7^th ed). USA: Wadsworth Cengage Learning.

DEEWR (Australian Government Department of Education, Employment and Workplace Relations). (2009). Belonging, being and becoming: The early years learning framework for Australia. Canberra: Commonwealth of Australia.

Fox, J. (2007). International perspectives on early years mathematics. In J. Watson, & K. Beswick (Eds.), Mathematics: Essential research, essential practice. (Proceedings of the 30th annual conference of the Mathematics Education Research Group of Australasia, Hobart, Vol. 2, pp. 865-869). Adelaide: MERGA.

Geist, K., Geist, E.A., & Kuznik, K. (2012). The patterns of music: Young children learning mathematics through beat, rhythm, and melody. YC: Young Children, 67(1), 74-79

Koehler, M.J., & Mishra, P. (2006). Technological pedagogical content knowledge: A framework for teacher knowledge. Teachers College Record, 108(6), 1017–1054.

Lee, J. (2010). Exploring kindergarten teachers’ pedagogical content knowledge of mathematics. International Journal of Early Childhood, 42(1), 27-41.

MacNaughton, G., & Williams, G. (2004). Techniques for teaching young children: Choices in theory and practice. (2^nd ed.). NSW: Pearson Education

Papic, M., & Mulligan, J. T. (2007). The growth of early mathematical patterning: An intervention study. In J. Watson, & K. Beswick (Eds.), Mathematics: Essential research, essential practice. (Proceedings of the 30th annual conference of the Mathematics Education Research Group of Australasia, Hobart, Vol. 2, pp. 591-600). Adelaide: MERGA.

Saracho, O., & Spodek, B. (Eds.). (2008). Contemporary Perspectives on Mathematics in Early Childhood Education. United States of America: Information Age Publishing.

Touhill, L. (2013). Play based approaches to literacy and numeracy. NQS PLP e-Newslletter no.66. Australian Government Department of Education.