Wow, we play maths!

This blog post was contributed by Hilde Stroobants & Tinne Van Camp (UCLL)

“Look,” says Leentje, “the moon has curved lines and I made them beautiful!”
“Tell me about that?”
“I did a gem and a stone.”
“How did you alternate the gems and the stones?”
“First a gem and then a stone and then a gem and then so …” She points out the corresponding stones on the lines. “More than ten!” she adds.
“You made a real pattern! Every time again: first a stone and then a gem. You took care to keep repeating the pattern. More than ten stones?”
She proudly nods: “For a pattern.”

What Leentje does not mention is that she first had to tell Nassim, the Keeper of the Treasure, how many gems she thought she needed for her work. They counted them out loud and playfully before she could get started with her artwork. She even had to go through that process twice before her work was finished. In this one activity, Leentje practised different mathematical skills: estimating, counting, finding out whether the number she estimated would be sufficient, following the curved lines, maintaining the pattern. She is truly proud of her achievement and would like to make a second stone drawing. Preferably right now.

Weigh your words

Understanding key concepts is one of the most important predictors of emergent numeracy. A child needs to hear and use a new word several times – and in different meaningful contexts – before that word becomes part of their active vocabulary . This means that in early childhood education mathematical concepts need to occur on a regular basis and in varied circumstances. (Purpura, 2018) That is why we do more than mere counting, and regularly offer the children brief verbal supports in which we integrate mathematical concepts: curved lines, first, then, pattern, every time, more than … To accomplish this in a natural way, we always link mathematical concepts to concrete actions, so that the abstract concepts are tied to lived experiences and become meaningful for the child.

“You made a real pattern! Every time again: first a stone and then a gem. You took care to keep repeating the pattern. More than ten stones?”

Playing mathematics during the holidays?

Together with nine student teachers we organized a research inspired mathematics holiday camp for a group of twenty  five- and six-year old children from low SES families. For five days they played all sorts of games with the underlying goal of developing a mathematical mindset. As the week progressed, we saw how children’s enthusiasm and focus increased.

Getting rid of mathematics anxiety

Based on the idea that anyone can learn mathematics to a high level, Jo Boaler and her research team looked for ways to develop a growth mindset for mathematics in all children. She translated that approach into what she calls ‘open creative mathematics.’ (Boaler, 2016)
Under the guidance of two lecturers, two pre-service mathematics teachers started from Jo Boaler’s work to find criteria on which to base the choice and design of the maths games. They also assembled a list of mathematics vocabulary to be used in facilitating the children’s learning of mathematical concepts while playing. Six pre-service preschool and physical education teachers made use of those criteria to find and design mathematics games that would not only be used in the mathematics holiday camp, but also translated into lesson plans for kindergarten and first grade.

What is open creative mathematics?

Central to the open creative mathematics approach is the collaborative search for a variety of possible strategies to solve a problem that offers a challenge to all of the children in a group. The search for possible strategies outweighs finding the right solution. Learning to enjoy thinking and searching for a solution is essential to learning to love maths. Speed ​​is less important than in-depth understanding. No worksheets, no tricks, but many open challenges to gain insight through collaboration. In the games package that we developed, we made sure that each game included at least three of the criteria for open creative maths:

1. The problem is presented in different ways (words, drawings, materials).
2. The search for a variety of ways to solve the problem is central, not just the solution.
3. Starting point is what children would do intuitively to tackle the problem.
4. Children present their discoveries in a visual way.
5. The starting level is achievable for many children, and yet the game enhances high levels of thinking (low threshold, high ceiling).
6. The children are coached by articulating their thinking wherever possible.
   

In how many different ways can you make 7?

Karissa raises a full hand with outstretched fingers, looks at it for a moment, and quickly puts the thumb and index finger of her other hand next to it. We check: is it correct? Ben counts all those fingers and concludes that it is right. Mehran draws seven balls in a domino stone: three on one side, four on the other. And again we check if it is correct. Vince writes a large graceful 7. Yes, that’s good too, because that’s what a 7 looks like. Kenny tallies 5 and adds two more lines. Oh yes, that looks like what Karissa did, but it is different. Tanja approaches the problem from a completely different angle: “14 divided by two,” she says. Oops, that’s hard. How can we check that? First place 14 blocks. Divide that fairly over two piles. And then count every pile. Yes, that’s right as well. So you can also create a number by making a larger number smaller. Too difficult for most preschoolers, but Tanja is doing fine.

In this example, preschool children are allowed to look for different ways to make 7. As long as they come to 7, it’s okay. We start from what they spontaneously do with this problem: one adds, the other represents, someone else divides. Strategies are drawn, written down, executed, so that they become visual and concrete. The starting level is a feasible entry level for all of these children. Tanja’s reaction shows that a preschooler who is a bit ahead can still find a challenge in the assignment. The essence of this open math problem is: “in how many different ways …”

Can you make a pattern?

On the table there is a collection of circles and rectangles in different colours. The teacher asks: “Can you make a pattern with shapes and colours?” Children make different patterns:

This open and creative assignment provides opportunities for the children to show different levels of thinking within the same assignment. All of the solutions are correct, but they show different levels of understanding. While the first row shows an alternation of orange circles and orange triangles, the second one makes abstraction of the colour and just goes by shapes. The third pattern is an intricate one where growing patterns of circles and triangles alternate, meanwhile the colours alternate with every new line. Having a conversation about the different ways of reasoning behind each new pattern, gives children a chance to pick up ideas and strategies from one another.

Can we master mathematics through movement?

Another excellent opportunity to practice mathematical concepts with young children are movement games and movement breaks, in which children move around the room or move things around. Through our coaching, we can interweave:

• space concepts such as: above, on, below, behind, fore, beside, over, under, through, between, high, higher, low, lower;
• quantitative and qualitative concepts: little, much, more, less, long longer, big, bigger, small, smaller, faster and slower, …
• and also those hard and abstract concepts such as: almost, about, exactly, completely, …

Physical education teachers should not stop their verbal concept support as soon as children understand and join the game. Rather continue to use those mathematical concepts as the children are playing the movement games. In this way, those basic concepts return in different contexts, which allows for more in-depth understanding. Multilingual children and children in low-SES situations especially, profit from contexts in which concepts regularly occur in authentic situations that they themselves experience (Bailey & Pransky, 2014).

“Wow! We Play Mathematics” came about with the financial support of the King Baudouin Foundation and would not have been possible without the collaboration with Buurtwerk ‘t Lampeke and Kinderwerking Fabota in Leuven.

References:

• Bailey, F., & Pransky, K. (2014). Memory at work in the classroom: Strategies to help underachieving students. Alexandria, VA: ASCD.
• Boaler, J. (2016). Mathematical mindsets: Unleashing students potential through creative math, inspiring messages, and innovative teaching. San Francisco, CA: Jossey-Bass & Pfeiffer Imprints.
• Purpura, D. J., & Reid, E. E. (2016). Mathematics and language: Individual and group differences in mathematical language skills in young children. Early Childhood Research Quarterly, 36, 259-268. doi:10.1016/j.ecresq.2015.12.020
• Purpura, D. J., (2018) The role of mathematical language in early numeracy development. Presentation on Research seminar on children’s early arithmetic development. Centre for Instructional Psychology and Technology, 16 maart 2018, KU Leuven.