Skip Counting
What does research say about Skip Counting?
HOW IS SKIP COUNTING LEARNT IN THE EARLY YEARS?
In order to teach skip counting, teachers must understand the process of how it is learnt.
Precursors to skip counting
Often teachers find it difficult to determine when it is best to introduce skip counting. For children to develop this skill, they require basic number sense, including counting, and an understanding of number patterns (Reys et al., 2012).
Stages of learning development
Skip counting is a gradual skill that develops as children expand the spectrum of numbers by which they are able to skip count (DEECD, 2015). Children generally learn to skip count by 2s, 5's, 10's and then 3's, however children begin to understand and learn other sequences before the previous one is mastered (Reys et al., 2012). As these skills develop, children become able to skip count by starting at numbers other than zero, which creates less familiar sequences (e.g. 1, 4, 7, 10 rather than 3, 6, 9, 12) (DEECD, 2015).
How we know what students know
The Mathematics Online Interview, developed by the Early Numeracy Research Project outlines three key tasks that illustrate children's existing knowledge relating to skip counting in the early years (DEECD, 2015):
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Question 4 - Counting from 0 by 10s, 5s and 2s
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Question 5 (a) - Counting from 'x' by 10s
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Question 6 - Counting from x by a single digit number
After completing this section you are able to record and develop a greater understanding of where your students are at in terms of mathematical ability and create learning pedagogy to support this information.
Knowledge that children demonstrate through skip counting
As skip counting and multiplication are closely linked it is important children first learn to understand and manipulate 'composite wholes'. This means that students need to build an understanding of 'counting groups of objects' and that each group is made up of multiple objects. For example when students count to a number they don't have to count each individual object in a group they can count using a pattern (Cohen Jones, 2013, p. 229). By developing skip counting as a skill, students begin to demonstrate the awareness of number patterns.
Challenges Of Skip Counting
When teaching skip counting, it's important to acknowledge that children may have difficulty grasping the following concepts:
Counting backwards
Counting backwards when skip counting, can prove to be a challenging task for students (Reys et al., 2012). This may require more practise than skip counting forwards.
Bridging across barriers
Students may find it difficult when counting to bride across barriers of 10, 20, 30 and even 100 for older years (DEECD, 2015). For example when students count backwards by 3's: 30, 27, 24, 21 ... unsure... (DEECD 2015). Students may even show this when counting backwards by 10's leaving out 100: 120, 110, 90, 80.
Starting points
Children man also find it difficult to start skip counting from randomized numbers (DEECD, 2015) For example a child might be ask to start counting from 41 by 2's. When doing this children are likely to skip into a know sequence counting 41, 43, 46, 48, 50.
Skip Counting VS Later Mathematics?
Although skip counting relates to many other mathematical topics its importance is vital to children's development of calculation, fluency, number sense and as the foundation of multiplication and division (DEECD, 2015). It is for this reason that it must be taught explicitly, with sufficient time and dedication.
Number facts
Skip counting allows children to extend from calculating by ones to using number facts. For example, rather then calculating 8 + 4 by counting 8, 9. 10. 11. 12, a child could immediately add by 4 or by 2 twice. "This transition to using fluent number facts is a key to success throughout school" (DEECD, 2015).
Multiplication and division
Skip counting provides the foundation for multiplication facts, for example, when asked to calculate 6 x 6 a child may think in terms of skip counting 6, 12, 18, 24 (Reys et al., 2012). The patterns identified by the child when skip counting from basis for understanding the patterns that exist with basic multiplication facts (Reys et al., 2012).
What key concepts underpin Skip Counting?
Skip counting is an essential skill which is utilized throughout everyday life, as a result of this, basic mathematical concepts must be explored in teaching and learning in order for children to develop an understanding of what it means to skip count (Reys et al, 2012). According to the Australian Curriculum (2015) early years learning students must first "establish understanding of language and processes of counting" before they progress to counting numbers other than one. To achieve this students must develop prenumber experiences, which "provide the basis for building early number concepts and the foundation for later skills" (Reys et al. 2012, p. 142).
Developing an understanding of rational counting along with sequence of numbers will help children develop a greater knowledge of skip counting. Understanding of numeric patterns and conservation of number are also essential skills as it teachers students what they need to skip count (Reys et al. 2012). Children must also have a basic understanding of multiplication, addition, subtraction and grouping in order to understand the meaning behind what is being performed in a skip counting experience.
