# UKEdMag: Developing Thinking Skills in Mathematics by @keran77

With the updated National Curriculum for mathematics in England, three aims were made clear. In brief, all pupils should become fluent in the fundamentals of mathematics, reason mathematically and solve problems by applying their learning. All of these require developing thinking skills. But how do teachers do that with all of the other things that have to be taught?

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I have seen The Thinker (Le Penseur) by Auguste Rodin in the gardens of the Musée Rodin in Paris. Just like the figure, we have to give children the time and space to think deeply. One strategy that works well in our school is to start each day with a thinking challenge. The tasks tend to be open-ended questions designed to engage children in thinking for 15 minutes. At the end of the session some of the ideas are shared. This is an opportunity to celebrate diverse thinking and for children to show off creativity in their approach to thinking. It is a great way to start the day, it wakes up brains!

So now you may be thinking what a great idea, but you need some inspiration. Don’t worry! Look at the following examples and use them to start thinking of your own. That’s the great thing about developing thinking tasks, it makes you think too. With a simple metre stick, children can understand and use the language of comparing lengths. I personally love the ‘how many triangles’ type puzzles and the different variations with other 2d shapes. It is a challenge to count all of the differing sized triangles, but then simply asking how do you know makes children think even more deeply. See an example at bit.ly/uked16oct05.

What maths is involved in this ‘think of a number’ challenge (page 10 bottom)? The ability to think of more than one possible answer for a maths puzzle and also thinking backward, doing the reverse. These types of thinking tasks enable children to make links in different areas of mathematics. Matchsticks are a simple tool for thinking puzzles. I often given pairs of children a set of matchsticks so that they must talk to each other and cooperate. It enables children to think out loud.

Place the numbers 1 to 5 in the bottom row of the pyramid. They can be arranged in any order. What arrangement of the numbers in the bottom row gives the largest total in the top brick of the pyramid? Can you find the smallest total? This type of task develops mathematical thinking as well as fluency.

This type of challenge encourages children to think about more than one possibility. Explaining how a solution was found can be a great way of encouraging children to reason.

Another way of developing thinking skills is to provide an answer and children think of calculations with that answer. Using ‘on this day’ type information also widens general knowledge (image. In Bridge Junior School we “think through the curriculum.” This is double-edged. We encourage children to develop their thinking skills in all subjects and in doing so develop our own thinking skills to provide better learning experiences.

Keranjit Kaur @keran77 is a senior leader in a junior school in the East Midlands. With over 10 years of teaching across Key Stage 2 and a MA in Learning and Teaching she is keen to continue learning. She loves being a mathematics subject leader.