## Generalising The Pattern Rule For Visual Growth Patterns: Actions That Support 8 Year Olds’ Thinking

**Key points**:

- This article is full of ideas to support my action research with children when the time comes. I intend to use some of the ideas within to help structure my input and form the base and review tasks.
- This article also grabs me as it contains citations of other authors I have read so far – not necessarily the same articles/sources as the Kaput writing I have read is a later date than this article, however the 2008 Kaput source seems to be a development of the 2001 piece used here. These connections confirm to me that my thinking and research is along the right lines and hasn’t been as unfocussed as I first feared.
- “Difficulties occur with adolescent students stem from a lack of early experiences in the elementary school” – relates to functional thinking and how students find it difficult to spot generalisations easily. They lack apporpriate language to describe what’s happening, generally focus on a single data set rather than comparing information and have “an inabilty to visualise spatially or complete patterns.” (Warren, 2000). The researchers found that children had limited experience with visual growth patterns and had rarely used arithmetic for anything other than finding answers.
- It continues to state that recording data in a table inhibited the children’s thinking, encouraging “single variational thinking, finding relationships along the sequence of numbers instead of find the relationship between the pairs.” … “The patterns chosen here were those where links between the pattern and its position were visually explicit…to focus in particular on the relationship between the position number and the pattern.” The article gives examples of the patterns used (shown below) and describes the aims of the questions in detail.

**Main Reference**:

- Warren, E., Cooper, T. (2007) ‘Generalising the pattern rule for visual growth patterns: Actions that support 8 year olds’ thinking’
*Educational Studies in Mathematics*, Vol. 67, No. 2, pp 171-185

**Citations**:

- Kaput, J., Blanton, M. (2001) ‘Algebrafying the elementary mathematics experience’ in Chick, H., Stacey, K., Vincent, J. and Vincent, J. (eds.)
*The future of the teaching and learning of algebra. Proceedings of the 12th ICMI study conference*. Melbourne: ICMI, Vol. 1, pp. 57-94 - Warren, E. (2000) ‘Visualisation and the development of early understanding in algebra’ in Nakahara, T. Koyama, M. (eds.)
*Proceedings of the 24th conference of the International Group for the Psychology of Mathematics Education.*Hiroshima. Vol. 4, pp.273-280