Phases of an Inquiry

The easiest way to understand the different phases is to read through this and then look at an example island from the Isles page. The phases ensure that the depth and breadth of an exploration is controlled in an accessible way to allow everyone to access an island in a mixed-ability classroom.

All the tasks use the analogy that maths is like exploring an uninhabited set of islands in search of treasure. The phases represent the scope of the inquiry.

At the start of the inquiry, it is carefully confined to make it as accessible as possible. Preliminary tasks or steps are sequenced thoughtfully and there are constraints in place to ensure that children specialise on specific or a small set of possibilities. This is the Landing Spot of the isle.

Often, inquiry learning is viewed as being where teachers just give children complete freedom and stand back and watch. Nothing could be further from the truth. In this phase, children are generally working on just one case or on a simplified set of ‘what if…?’ questions as a means to hook them in and introduce the main inquiry gradually. It also allows for a shared case or set of cases that they can focus on developing and discussing strategies that they can then utilise as they go deeper within the inquiry.

In terms of the analogy, it is saying that children have only just landed on the island. As such, they have a limited view of the whole situation and need to understand their initial circumstances before exploring in different directions.

In Distinct Digits to 5555, we start by just making any addition to 5,555. This focuses them on this as a goal. Once they have created an addition, they score it.

In Digital Shape Sequences, we all start with 38 as the first number. It ensures they can make chains of a reasonable length before having to think about good starting numbers.

Through changing or reducing the ‘what if…?’ constraints, we can then explore an isle and seek out deeper understanding.

This might mean that we all go off again together with a similar amount of depth to our Landing Spot but in a slight variation in what we are looking at. Equally, children might have some choice over which area they explore in and go in their own direction or in groups.

The Island phase represents the start of the exploration. They have the knowledge required to explore and create data of their own rather than just looking at one specific case or simplified rules. The island as a whole represents all the cases possible in the exploration. Each new case represents a new spot on the island. They are seeking to understand the whole island (all cases) through finding treasure – patterns and discoveries.

In Distinct Digits to 5555, the children now try and create calculations that score all different values. They try and make the lowest and highest scores possible.

In Digital Shape Sequences, the children choose their own starting number. Now that they understand the difficulty in creating a chain of more than a few numbers and the rules involved, they can focus on using their reasoning skills to pick an appropriate starting number.

Through the asking of ‘what if…?’ questions, children can then take things in an entirely new direction.

With the Archipelago phase of the inquiry, children are not just exploring the defined set of rules, creating new cases and seeking to understand them. Instead, they are using their ‘what if…?’ questions to alter the problem in some way creatively to create a new exploration. Each alteration is its own island and warrants a new exploration in search of new treasure.

Through the new rules that are created, they might go in a direction that you haven’t thought of before and become the world’s expert in this island. This is incredibly empowering for the children and what makes them explorers rather than followers.

In Distinct Digits to 5555, we could change the rules to use subtraction rather than addition. This is a significant change to the original rules (rather than just the constraints) and so warrants its own island. It is still related to the original inquiry and shares thinking but will require an exploration of its own.

In Digital Shape Sequences, the children could change the shapes that they use and think about which set of three shapes would produce the longest chains. They could also change the operation, Digital Shape Sequences – Multiplication does this by using multiplication instead.