Number Lines & Mental Computation
I found the research completed by Bobis (2007) to be so intriguing. I was almost memorised to reflect upon where I had fallen short within my years of learning maths. A key paragraph that captured my attention the most:
"The worry with an early emphasis on standard algorithms is that students will shift their focus to executing convenient procedures rather than on understanding the mathematics." - Bobis (2007)
Thinking back to when I would be completing maths tasks, I felt so lost and confused which resulted in me writing and using an algorithm, even if wasn't related to that mathematical area. This piece of computational knowledge would have served as a strength throughout the development of my mathematical knowledge (Grover & Pea, 2013; Bobis, 2007). Fortunately, these reflections of my own experiences allow me to realise where I struggled and what key information I missed that lead me to struggle. It allows me to consider how am I providing the right information in the most engaging and mind stimulating way.
Number Line Strategies to Support Mental Computation:
The introduction of strategies such as number lines promotes children's awareness of multiple relationships among numbers, understanding of mathematical procedures, the examination of assumptions and opportunity for visual references for mental computations (Kaminski, 2002; Cheeseman, 2010). Number line strategies include:
Patterns Placement:
Research explains that the development of number sense supports the ability to build upon the mental computation of children (Yadav, Mayfield, Zhou, Hambrusch & Korb, 2014) Through pattern placement, children learn number sense by adding and subtracting numbers through numerical value (Bobis, 2007).
Empty Number Lines:
The procedure of an empty number lines allows for children to access and use conceptual thinking processes, such as logical reasoning, decomposition, a recreation of patterns and abstract thinking (Berry & Csizmadia, 2016). By using an empty number line, children are able to map out visually techniques to build upon sophisticated strategic thinking by using different methods of sequencing by number groups (Cheeseman, 2010).
Number Line Addition and Subtraction:
Number lines can be used to exercise children left-to-right spatial-numerical representations of numbers (Aulet & Lourenco, 2018; Kaminski, 2002). Number lines allow children to map out numbers and the spaces between them when adding or subtracting (Aulet & Lourenco, 2018). Children are able to make a relationship between algorithms and spatial organisation (Aulet & Lourenco, 2018; Kaminski, 2002).
References:
Aulet, L., & Lourenco, S. (2018). The Developing Mental Number Line: Does Its Directionality Relate to 5- to 7-Year-Old Children's Mathematical Abilities? Frontiers in Psychology, 9, 1142.
Bobis, J. (2006). From here to there: The path to computational fluency with multi-digit multiplication. Australian Primary Mathematics Classroom, 12(4), 22- 27. http://ezproxy.acu.edu.au/login?url=http://go.galegroup.com/ps/i.do?&id=GALE|A170817120&v=2.1&u=acuni&it=r&p=AONE&sw=w&authCount=1
Cheeseman, J. (2010). Empty number lines: How can we help children to use them? In J. Mousley, L. Bragg, & C. Campbell (Eds.), Mathematics-Celebrating achievement 100 (Proceedings of the 42nd annual conference of the Mathematical Association of Victoria pp. 49-58) Melbourne, Vic: MAV. http://ezproxy.acu.edu.au/login?url=http://search.informit.com.au/documentSummary;dn=998640761921722;res=IELHSS
Grover, S., & Pea, R. (2013). Computational Thinking in K-12: A Review of the State of the Field. Educational Researcher, 42(1), 38-43.
Kaminski, E. (2002). Promoting mathematical understanding: Number sense in action. Mathematics Education Research Journal, 14(2), 133-149.
Yadav, A., Mayfield, C., Zhou, N., Hambrusch, S., & Korb, J. T. (2014). Computational Thinking in Elementary and Secondary Teacher Education. ACM Transactions on Computing Education, 14(1), 1-16.
