Mathematical Thinking It is central to mathematics learning; the glue that both develops and holds mathematics learning together It involves: Looking for pattern and relationships Logical Reasoning Making Connections This is not new to the maths curriculum at any key stage but I do think we may have ‘lost’ some of this in our drive to ensure coverage and jump through assessment ‘loops’. With a slimmed down curriculum we should be able to explore mathematical reasoning. I have chosen a few examples to think about.

Perhaps we can think of reasoning as systematic thinking. Hundred square has been printed on both sides of a piece of paper one square directly behind the other. What number is on the back of 100? Hundred Square challenge (Nrich) This depends logical thinking to convince ourselves and others which number is behind the other. Think about how you would explain what is on the back of number 23? 28 as 3 from the end.????? On Nrich web set 2 articles focus on Reasoning ideas and progression.

In this task pupils have to use coded jigsaw pieces to complete a hundred square. Making the decision how to tackle the activity involves reasoning. s Coded Hundred Square (Nrich) Another example is a task that can be solved in a number of ways, where there is no starting point

What reasoning is needed here? Amy has a box containing ordinary domino pieces but she does not think it is a complete set. She has 24 dominoes in her box and there are 125 spots on them altogether. Which of her pieces are missing? s Coded Hundred Square (Nrich) First need to know that information is missing. Second use reasoning to work out what we need to know. Third use reasoning to draw on existing knowledge and work out info Need to know 28 dominoes in full set and total is 168 spots. So 4 dominoes missing and 43 spots. Trail & error 6 6 5 5 6 5 6 4 Amy’s Dominoes (Nrich)

Mathematical Coherence mathematical coherence is the idea that all maths subjects are connected to one another basic mathematical concepts can be built upon and related to one another, resulting in a deeper understanding of more complicated mathematical concepts. Coherence is an important part of maths because, when done effectively, it helps students understand mathematical ideas more deeply while also making complex subjects easier to understand. Helping students make sense of why certain mathematical operations work is a key way to a full understanding of what they're doing in class. Teachers can reinforce these concepts by encouraging students ask questions, showing them alternative ways to get the same results and allowing them to defend their answers. This promotes deeper learning, rather than simple memorization, and will help students better understand future math concepts.

The teacher holds the string of a kite and lets it unravel so that the pupils can go their own way to explore and make their own sense of the mathematics, but the teacher must also reel the kite back in on a regular basis, to ensure that all pupils have made the most valuable connections and developed correct understanding of the mathematical ideas.