Many thanks to Nick Hart for this blog post, which takes a look at success criteria in mathematics.
I vividly recall maths lessons as a child. I was in the bottom set and I remember a general feeling of bafflement as it appeared to me that others seemed to know what to do while tasks remained a mystery to me. I don’t remember anything being explained and years later as an NQT, reading the numeracy strategy unit plans, I had a moment of realisation that there were ways of calculating in your head. In your head! All I’d known was formal written methods. For everything! What I needed whilst at school was to be let in to the secret of how to do maths.
When it comes to success criteria in maths lessons, absolute clarity is needed. Teaching children to think mathematically needs structure, explained and modelled expertly, so that the procedures or strategies required are transparent. When there is a lack of clarity, it is our disadvantaged children and children with SEND who suffer the most and gaps between these children and their peers are easily compounded.
To be successful in meeting mathematical lesson objectives, children need either rules or tools. When it comes to developing mathematical fluency, children must first follow tried and tested procedures. To be successful, a number of steps need to be applied correctly. In time, those procedures become more efficient, familiar and eventually automatic.
For example, when adding two two-digit numbers, using the strategy of partitioning, one must follow a few simple steps:
It may be tempting to have tiered success criteria based on the task that children will be doing. For example, lower attaining children might be given one digit numbers to add to two digit numbers. This is a mistake. Work should be scaffolded so that all children can think in the way that the teacher is modelling. Where children are considerably behind their peers, this scaffolding must be supplemented with extra work outside of maths lessons so that they can catch up while still experiencing age appropriate maths and being included in the work that their peers are doing. Anything less is simply low expectations.
Once children become fluent with one method, the teacher may then show children a different method. Again, gaining procedural fluency requires following a series of steps. This time, rounding and adjusting:
At this point, children should be fluent in two strategies for adding pairs of two digit numbers. The teacher may now build some reasoning into the unit of work by modelling how to select the most efficient strategy from those that have been taught. In the first instance, a simple sorting task with associated modelling of the mathematical thinking is appropriate:
In this example, the two calculations are very similar. The only difference is the ones digit of the second number. Adding 23 to 35 requires no crossing of a tens boundary and so partitioning it and adding the parts is quick and easy. On the other hand, rounding 23 to the next multiple of ten and then subtracting 7 seems clunky.
Adding 29 to 35 is slightly trickier as it involves crossing a tens boundary. Rounding 29 to 30, adding 30 to 35 and then subtracting 1 is much more efficient. Through this modelling, explanation and carefully chosen examples to compare, we can come up with some rough guidelines for making a decision on the most efficient strategy. In this case, if the number you’re adding is really close to the next ten, round and adjust. If not, add by partitioning.
Here, children will have developed two strategies to choose from. There could be more, such as using double facts if the two numbers are near doubles. At this stage, when given varied calculations to solve, the success criteria are no longer procedural, no longer a set of rules to follow but a set of tools to choose from which to choose:
Success is now not about simply being correct and fluent, but about efficiency and reasoning. Children must think mathematically to choose and explain the most appropriate strategy. This represents a significant shift in thinking from basic procedural fluency.
Developing a unit of work in this way also gives teachers the opportunity to ensure that children working below age related expectations have time to catch up to their peers. While the vast majority of children are learning a variety of strategies, some children who need more time to master one strategy are afforded that time. They can access extra practice on fluency which would go a long way to preventing gaps widening.
The key is to make the mathematical thinking explicit. Success criteria are a vital first step in planning a sequence of lessons. If teachers get this right, it guides task design, it focuses teachers on their modelling and explanations and sets children up for success.
Thanks again to Nick Hart for this blog post.
Rising Stars has a range of mathematics resources that can help ensure success in mathematics, including Rising Stars Mathematics.