A recent(ish) Twitter conversation with Dr Helen J Williams (@helenjwc) about her wishes for a jigsaw club to exist in schools and our subsequent reasons why this would be a good idea, inspired this blog.
No curriculum can fully capture the range of human activity that supports the learning of a discipline (or at least not one that can be easily digestible by busy teachers). Maths is no exception. Travelling through the maths world in an attempt to gain a more holistic view has led me to discover some surprising activities not necessarily explicitly in the maths curriculum but that can nevertheless benefit the learning of the subject. Now seemed a good time to share some of these.
Developing bat and ball skills
The act of throwing a ball and trying to strike it means that the body must rapidly make estimations about space, speed and time as the ball travels towards the bat. This is called interceptive timing. As with so many aspects of development, the link between the body and mathematics is often crucial, e.g. learning counting words as stairs are climbed or tracking times tables on fingers (as described in this blog). In this case, there is some evidence that being accurate at hitting a ball / tapping a moving object on screen ‘may have a specific relationship with mathematics’ (Giles et al, 2018). So getting children outdoors and helping them to become more accurate when striking a ball could well be doing more than keeping them physically fit.
Doing jigsaws, puzzles and constructing with blocks
This is probably better known than the previous example and there is a plethora of research that underpins our understanding of why doing puzzles and construction are important.
Fitting shapes together into holes helps children to develop their understanding of lines, angles, translation and rotation. Babies are able to deal with horizontal and vertical translation when they reach to slide a cup or toy in one direction or another. Frequently used puzzles help to develop a child’s ability to visualise and predict slides, flips and turns for images and 3d shapes which helps with all areas of learning; not just maths. The ability to ‘hold an image in mind’ and manipulate it helps children with more effective use of short term memory which is beneficial for all areas of learning.
However, what is possibly less well understood is that being great spatially supports number and measures knowledge too. Jigsaws are a numberless part whole model. Whilst, we work hard to help children understand the numbers that live inside other numbers, what we do less of is allow children to experience shapes that live inside other shapes. Doing a jigsaw where we put lots of parts together to make the whole can underpin this thinking. When we take away parts of the puzzle, the area covered reduces and when we add a piece, it increases. This provides children with a representation of the operations of addition and subtraction and also introduces the two dimensions of multiplicative concepts as jigsaws help children to understand the coverage of space – area. Furthermore, they may notice that the smaller the puzzle pieces, the more will be needed to cover the whole space. From my observations of children, this also seems to help with the concept of units of measurement and scale.
If we want our children to be ‘nimble’ with number then I would argue that we need them to be ‘nimble’ with composition and decomposition of shapes too.
If you need further ammunition to provide experiences with shape then consider the UKS2 children who are asked to find the area of compound shapes such as rectilinear shapes or shapes that can be decomposed to find area such as trapezium or triangles. It is easier for children who have had a wealth of experience at constructing and deconstructing to notice the triangles and rectangles that ‘live’ inside these shapes and also therefore make better sense of the rules for finding area.
Tangrams are a fantastic form of mathematical puzzle and easy to find and download from the internet. One of my favourite books, The Tangram Cat, is a beautifully illustrated set of tangram shapes which, helpfully, children can explore using tangram pieces provided at the back.
I also love the book ‘Messy Maths’ for EYFS teachers by Juliet Robertson. One of my go to activities from here is the leaf puzzle. Children can collect large leaves and cut them into several pieces (or an adult can do this), muddle them up and children try to put them back to re-make the leaf. You could also try with a page from a magazine.
Playing snakes and ladders (other board games are available and are to be encouraged)
Research by Siegler and Ramani in 2008 found that the more board games a child was familiar with, the better they were with areas of number sense, such as counting and estimation, as well as comparing quantities. Board games where there is a number track provide children with a sense of magnitude which is also an area that correlates with mathematical ability. Because in snakes and ladders, the 100 is far from the start, it helps children to compare the relative position of numbers – 20 is nearer to me than 100. It takes more moves to get to a number further away from the start than it does to closer numbers.
[This is one of the home maths activities we are sharing with schools currently for Year 1.
Later, children should be asked to estimate a number’s place on a number line as well as to estimate the value of a position on a number line. Placing a paperclip on a strip, providing the start and end number and asking children to estimate what number the paperclip represents creates a brilliant environment for reasoning about estimates. This needs to be with increasing and decreasing scales dependent on the age of the child.
Areas of the curriculum such as mental arithmetic, rounding and measurement are far easier if you understand how near or far numbers are relative to each other.
Games in general boost children’s strategic thinking and you can read Charlie Harber’s recent blog here for more information on that. Sign up to our YouTube Channel here for some fantastic games to play.
It’s fair to say that there are some social justice issues at play here that schools should take into consideration. How many households have and encourage these activities? If not, then how do we ensure that children have access to these activities in schools and highlight their value? This is why a jigsaw club at school seems like a very good idea to me, and a board game club and plenty of opportunities to get outdoors and improve ball skills. It also shows that whether the Early Learning Goals reference spatial concepts or not, the curriculum opportunities must be rich with them, as should the rest of children’s mathematics provision.
Further Professional Development Opportunities
For more information about our KS1 action research project ‘Nimble with Number’ which promotes the value of board games for fluency then please visit our research page here.
Bryant, P. (2007). Key Understandings in mathematics learning. Paper 5: Understanding space and it’s representation in mathematics. Nuffield foundation. Retrieved from https://mk0nuffieldfounpg9ee.kinstacdn.com/wp-content/uploads/2019/12/P5.pdf
Gifford, S. (2019) The case for Space in the early years. British Society for Research into Learning Mathematics website
Giles, O.T., Shire, K.A., Hill, J.B., Mushtaq, F., Waterman, A., Holt, R.J., Culmer, P.R., Williams, J.H.G., Wilkie, R.M., & Mon-Williams, M. (2018). Hitting the target: mathematical attainment in children is related to interceptive-timing ability. Psychological Science, 29(8) 1334 – doi: 10.1177/0956797618772502
Gunderson, E., Ramirez, G., Beilock, S.L. & Levine, S.C. (2012). The relation between spatial skill and early number knowledge: The role of the linear number line. Developmental Psychology, 48(5) 1229-1241. doi:10.1037/a0027433
Ontario Ministry of Education. (2013). Paying attention to spatial reasoning. Toronto, ON: Queen’s Printer for Ontario. Retrieved from www.edu.gov.on.ca/eng/literacynumeracy/lnspayingattention.pdf