Research states that the topic of mathematics is in fact, the study of pattern (Reys et al., 2009). Reys suggests that pattern should not be limited as an isolated idea and instead, it is considered to be based on a number of attributes including the following four: - Geometric (shapes)
- Relational (sequencing)
- Physical (colour, size)
- Affective (like, happiness)
Pattern can be based on these individual attributes but it is also possible and desirable to combine these attributes to help students deepen their understanding. For example, if you ask a child to arrange of a group of coloured shapes in a pattern (see image below), you are combining geometric (shape) and physical (colour) attributes. By creating learning opportunities for students to be exposed to the different attributes of pattern, we as educators will facilitating meaningful learning for children to understand pattern.
Pattern as a foreground in learning
Pattern is the foreground for future mathematical learning. As previously discussed, the overall idea of mathematics is the study of patterns. Pattern is often misunderstood to be an isolated topic when it is put in the context of activities such as ‘what comes next?’ or ‘what is missing from this pattern?’. Although these exercises are useful to introduce the idea of pattern to students in early years, it is important to extend thinking to view pattern as a basis for all mathematical ideas and problems (Hurst, 1997). The key concepts of pattern link to the following 'big ideas': -Problem solving
-Mathematical investigation (worded problems)
-Sense of number
-Manipulation of variables
-Understanding of numerical pattern (skip counting)
A solid knowledge of pattern can enhance student's ability to understand the 'big ideas' that evolve from pattern. The interactive games that can be found under the ‘teaching resources’ tab can be useful to help students develop their understanding and become familiar with pattern. There are also many resources beyond these activities that directly target the idea of pattern. For example, having students count by 2s, 5s or 10s with the aid of a number chart is a great way to broaden their view of what it means to find and complete a pattern (Hurst, 1997). Considering that one of the ‘big ideas’ is that pattern is the foreground of mathematical learning and understanding, there are endless possibilities of how it can be present in activities that are not necessarily directly designed to teach pattern (Coburn, 1992). As teachers, we must educate students to be aware of the importance of pattern and provide opportunities for them in and around the classroom to explore the concept.
Trial and error: let students create pattern
It is no secret that in order to learn, students must make mistakes. Trial and error is a fundamental way to let students actively participate in their own learning and understanding of pattern (Light, E. 2010). We must encourage our students to 'have a go' and not be afraid of getting a different solution to a mathematical problem than the person next to them. As teachers, we sometimes need to take a step back and let students show us their understandings without our guidance. By letting students create their own patterns, it will give us insight into their mathematical thinking (Reys, 2009). It will also allows us to reflect upon concepts that students understanding as well as ideas that need further development. It is through trial and error that we will start to witness 'light bulb moments' and give us clarity in our teaching moving forward (Light, E. 2010).