Task design within our maths curriculum
Subject Lead (maths)
Earlier this year, we explained our approach to curriculum and that we have been developing brand new curricula with our partners to provide entirely optional, high-quality curriculum models and adaptable resources.
Here we will give you a behind-the-scenes look at some of the careful thinking and task design that is going into our primary and secondary maths curriculum, one of six subjects with brand new curricula being created for release this Autumn.
Task intent in maths
Pupil practice is an important element of learning mathematics. Giving pupils time with structured tasks can help them understand and develop their ability to solve problems – but it’s important that the tasks we ask pupils to do, align well with what we want them to actually learn.
A simple prompt to test the suitability of a task is to ask ‘what will they be thinking hard about?’. Whilst we know what we want the answer to be, it’s not always clear that the task being attempted serves that purpose effectively and efficiently. There are a few factors to consider:
- What specifically do we want pupils to be confident in understanding?
- What modelling preceded practice?
- What comes next?
- What does success look like?
What do we want pupils to understand?
The key here is specificity. When taking broad topics or objectives, like ‘addition of fractions’, it’s often important that practice is much more precise in order to develop subskills and knowledge that build towards the bigger picture.
Let’s take an example of different cases of fraction addition, which allows us to think more deeply about which subskill(s) practice should be targeting.
⅓ + ⅓ = ⅔
Here we have two unit fractions with the same denominator added together, resulting in a sum that is less than one and requires no reinterpretation (such as converting from an improper fraction to a mixed number, or simplifying). The distinctions are important, and should not be mixed together in practice unless that is the purposefully considered intent.
⅓ + ⅔ =³⁄₃
This example, whilst similar to example 1, potentially requires skills and knowledge that are not needed in example 1. Interpretation of ³⁄₃ as 1 for example – is this a focus of the lesson? Is it prerequisite knowledge? If it’s neither, then this example would require more teacher input and potentially shift focus away from other learning intentions.
Whilst these are just two types of question related to the broader objective of being able to add fractions, there are of course many more, each with their own implications regarding what knowledge and teaching they might require.
The important thing here is that this is considered and informs design. It is unlikely that practice written by a third party will exactly match what is needed in your own classroom, and so the need to be able to identify the implicit task intent of the authors, and compare it with your own, becomes a critical part of lesson planning.
Questions that deviate from your own objectives, or add in too many variables that detract focus from the core skills you’re attempting to develop, can significantly reduce the efficacy of a practice phase in a lesson.
What modelling preceded practice?
Simply put, if the maths that pupils are attempting doesn’t closely match or ‘behave’ in the same ways as the maths that was modelled with the class, then unnecessary difficulties may arise. This doesn’t mean that all practice questions should look like ‘example 1’ on the board, but certainly the first few should not throw in edge cases or unpredictable outcomes whilst pupils are beginning to gain confidence and feel successful in a new area of maths.
For example, if we model the steps and solution to a few one-step equations on the board, and each one requires addition or subtraction to solve, then an opening example in independent practice should not involve multiplication or division.
Similarly where the answers are all natural numbers in our modelling, if the first question in independent practice reveals a fraction or negative number as an answer, it is likely to cause confusion and consequently diminish confidence in pupils.
What comes next?
The next phase of teaching should inform the last part of the preceding practice. A simple way to think about this is: “I want pupils to become confident in these types of problems, so that I can lead them into this next level of complexity, or this new use case”. As such, what would be suitable questions or tasks that lead pupils to a place where they are considering or enabled to think about the next phase of teaching?
Going back to addition of fractions, it might look something like this:
- ⅗ + ⅕ =
- ²⁄₇ + ³⁄₇ =
- ⁴⁄₇ + ²⁄₇=
- ⅜ +⅜ =
- ³⁄₁₂ + ⁵⁄₁₂=
Questions 4 and 5 purposefully lead into discussions and teaching around simplifying answers with a view to that being the next phase of the lesson. Similarly it may be that the questions move from pictorial models towards introducing more abstraction.
The general principle is that the practice is designed to enhance understanding, and create a flow of thought and knowledge development as the lesson progresses.
What does success look like?
Finally, feeling successful within maths lessons is a key element to developing positive classroom cultures and strong foundations for teaching new ideas and concepts.
Success should not be accidental, but should instead be planned for with careful considerations like those outlined above to maximise the chances of pupils being able to answer questions without getting stuck around elements of task design that are superfluous to the lesson objective.
It is easy to imagine a pupil feeling disheartened when they felt they understood a concept, only to attempt their first question on their own and be presented with an ‘unusual’ looking answer at the first hurdle. It’s important to consider the relative difficulty of each question or task, and how that may or may not impact confidence.
Questions should be accessible enough, but there needs to be a suitable challenge to test the depth of pupil understanding and ensure that even the most able pupils are having to think hard for some tasks. These interpretations can only be accurately made by a class teacher, who knows their pupils well, and should always be a consideration when using Oak resources.
The balance between enabling success for pupils, and introducing necessary difficulty and hard thinking is challenging, but is made easier with experience teaching the same group over time to develop a sense of pitch and escalation of challenge within tasks.
We look forward to sharing our new curricula and early-release units with you soon so you can see our thinking in action.
Get updates on our new maths curriculum