Subitising through the years...
Although subitising is too often a neglected quantifier in educational practice, it has been extensively studied as a critical cognitive process.
If you don't already know the wonder-powers of Subitising (where have you been?!) let me give you a brief intro:
- The critical early number sense concepts of conservation (understanding that a quantity does not have to look the same to be equal) and cardinality (‘trusting the count’) become deeply understood.
- Learners develop the critical understanding that numbers are not merely a series of ones, but that numbers are composed of/decomposed into other numbers in a variety of ways (Grey & Tall, 2007; Ma, 1999).
Here are 3 ways YOU (yes, you!) can EASILY support your learners in their number sense development by using subItising throughout the primary years!
Deliberately and intentionally we can move learners from ‘getting answers’ when simplifying expressions such as 8 + 5 towards teaching learners to use the base-ten system to clump into tens. We don’t want our learners to continue ‘living in a ones world’…
Now Subitising with Multiplication. When learners practice their multiplication facts, they’re expected to move from concrete to abstract too quickly. This takes time!!! Moving too quickly forces memorisation and avoids any possibility of multiplicative thinking. Strategy development is the key underpinning of automaticity.
Using our Multiplication concept cards provides a great opportunity to begin building multiplicative reasoning with children. Even if you have not started formal multiplication with your learners, you are helping them build a sense of multiplicative reasoning when they see groups. Learners see connections and use the structure to build number fluency.
Once your learner is fast with these and can name different FACTORS fluently and with meaning, you are ready to build from there. There is no hurry. Have learners use the language of factors and products accurately.
Subitising can even help learners to have discussions about the different structures of division and to better understand that division is not about ‘making things smaller’ but about considering relationships between parts (Faulkner, 2013; Ma, 1999).
Do you see how valuable these visual representations can be? These are skills that are very hard to teach with a pencil and paper, but when we can help learners see the connections, it can be powerful! I cannot emphasise the value of connections enough.
It is likely learners will need repeated exposure and experience but it really will make a difference to your children's understanding and fluency with numbers. Enjoy working on it. Keep it going!
I’d love to hear your thoughts. Have you tried subitising? What subitising routines do you use? How do you use them? Which ideas resonate with you? What do you disagree with? What questions do you still have? All views are welcome - post in the comments. Maths IS Visual. Let’s teach it that way.
Thank you for all you do to support your children's number journey. Thank you for watching and listening.
Love, Janey x
To further inform your thinking here are some useful links to literature that supports the research and the pedagogy:
Clements, D. (1999). Subitizing: What is it, why teach it. Teaching Children Mathematics, 5(7), 400–405.
Clements, D., & Sarama, J. (2009). Learning and teaching early math: The learning trajectories approach. New York: Routledge.
Cain, C., & Faulkner, V.N., (2011). Teaching number in the early elementary years. Teaching Children Mathematics, 18(5), 288–295.
Faulkner, V.N. (2013). Language, math, and the common core. Phi Delta Kappan, 95(2), 59–63.
Faulkner, V.N., & Cain, C. (2010). The components of number sense: An instructional model for teachers. Paper presented at the Council for Exceptional Children Conference, Nashville, TN.
https://valeriefaulknermathclub.files.wordpress.com/2020/06/faulkner-ainslie-2017-subitising.pdf
https://valeriefaulknermathclub.com/videos/videos-early-math/subitizing-videos-by-level/
Gray, E. & Tall, D. (2007). Abstraction as a natural process of mental compression. Mathematics Education Research Journal 19(2), 23–40.
Ma, L. (2010). Knowing and teaching elementary mathematics: Teachers’ understanding of fundamental mathematics in China and the United States. New York, NY: Routledge.
Ma, L., & Kessel, C. (2003). Knowing mathematics intervention program: Teacher’s guide. Boston: Houghton Mifflin.
Richardson, K. (2012). How children learn number concepts: A guide through the critical learning phases. Math Perspectives