The *Structure of Observed Learning Outcomes* Taxonomy (SOLO) is a notion that describes the stages of learning that students go through to reach a real depth of understanding on a topic. It outlines the journey from surface to deep learning. SOLO is John Hattie’s taxonomy of choice and is currently being studied in depth at his Visible Learning Labs (Osiris Educational Outstanding Teaching Conference, 2014). It is seen by Hattie and other academics as having many advantages over other taxonomies, in particular that of Benjamin Bloom. Quoted advantages over Bloom’s Taxonomy include:

- The SOLO Taxonomy emerged from in-classroom research whereas Bloom’s Taxonomy was theorised from a proposal by a committee of educators
- SOLO is a taxonomy about teaching and learning vs Bloom’s which is about knowledge
- SOLO is based on progressively more challenging levels of cognitive complexity. It is argued this is less clear within Bloom’s Taxonomy.
- It is claimed that educators and students agree more consistently which level a piece of student work has reached on the SOLO Taxonomy than on Bloom’s Taxonomy
- SOLO is more simple to understand and apply than Bloom’s making it more accessible for students to grasp, even primary phase.

Whilst interesting from a mostly academic perspective, these advantages are unlikely to grab the coal-face busy professional teacher and convince them to go SOLO in their planning. I had the same thought originally until I understood how incredibly simple SOLO is and that it seemed to ‘work’ for a maths classroom a lot better than Bloom’s Taxonomy does. It makes sense to me as a good summarisation of what I have learned from experience as the way students learn in maths.

Image via pamhook.com. Check out her fab website with lots more info on SOLO

SOLO works by students progressing from surface learning to deep. On a particular topic they can be at any of these particular levels:

**Pre-structural**- The student has no understanding of the task. They completely miss the point.

**Uni-structural**- The student has ‘learned’ one aspect of the topic.

**Multi-structural**- The student has ‘learned’ more aspects of the topic. However, they see each of the aspects as independent and unrelated

**Relational**- The student understands the links and relationships between the different aspects of their previous learning *within* the topic.

**Extended abstract**- The relational learning is so well understood students can now start using this to conceptualise further learning outside of the topic domain.

Describing progression within a maths topic such as angle facts this could look like:

**Pre-structural**- The student has heard other people talk about angles.

**Uni-structural**- The student can estimate the size of an angle

**Multi-structural**- The student can estimate the size of an angle, measure the size of angles and has learned the angle facts

**Relational**- The student understands how estimation can be used as a way to check that they’ve read off the correct scale when measuring an angle. They understand how to use angles in parallel lines rules to prove angles in a triangle add up to 180 degree. From this they can then derive the sum of the interior angles in an octagon.

**Extended abstract**- Students can apply their angle fact knowledge to solve geometrical problems where the angles are algebraic expressions and the solution requires the formation and solution of equations.

The pre-structural, uni-structural and multi-structural levels are considered ‘shallow’ learning, relational and extended abstract are ‘deep’ learning. One of the most important things to understand about SOLO is that it describes a journey. **You have to progress through the levels and cannot jump straight to deep learning**. As Hattie put it recently, “you can’t do the deep stuff until you know the shallow stuff.” You can’t link things together until you have things to link together. This is one of the reasons ‘problem-based learning’ strategies score so poorly in his Visible Learning rankings (0.15 ES where 0.4 is mean average). In Visible Learning, he wrote, “…this is a topic where it is important to separate the effects on surface and deep knowledge and understanding. For surface knowledge, problem-based learning can have limited and even negative effects…” You can’t solve problems until you are fluent in the skills required to solve the problem. It’s like trying to solve a jigsaw without having the pieces.

A consequence should be that teachers know it is ok to have some ‘shallow learning’ lessons where students are simply trying to acquire and become more fluent and accurate at the skills. I wonder sometimes, particularly with newer teachers that expectations in *some* schools for formal observations to feature open, higher-order thinking questions and tasks, that those teachers think this is where every lesson should be pitched. Progress should be viewed as successfully moving through-or-between any level in the taxonomy. ‘You need the range of lessons,’ should be the message to new teachers; dedicated skill-and-drill practice has its place as do higher-order thinking lessons. They complement each other.

However, for the remainder of this post I want to focus on the deep learning stages: relational and extended abstract. Rather than getting bogged down with edu-jargon, the message is simple- **deep learning is about links. Firstly, links to other things within the same topic, then to things outside the topic. **

I’ve been trying to think of all the different types of links that we can use to design deep learning resources for a topic. The intention is to produce a prompt-sheet or checklist of things I (or any GMTI readers!) could refer to when planning a deep learning lesson. The following list will not be comprehensive, but is the result of this idea bubbling away in my mind for the last six months. Please feel free to add, build or challenge my thoughts in the comments section. Here goes, first draft!

I think ways we can build ‘deep learning’ into our lesson planning include:

**Link to a concrete representation**- How can the problem be represented using physical equipment? This could also be a kinaesthetic representation using other senses e.g. hearing or touch.
**Link to a visual diagram**- How can the problem be represented using a diagram?
**Link to metaphors**- What different metaphors can be used to describe the concept? What are each metaphor’s limitations?
**Link that helps you understand another part of maths within the same topic better**- How can one idea help in understanding another within the same topic?
**Understand the limitations**- Does it work for all types of numbers? What range of values in the answers would we expect? Where does the maths still theoretically work, but in real life it becomes impossible?
**Understanding ‘dynamic variation’**- What role does each part play? If I double this, what happens to the answer? If I halve that, what happens to the answer? Which part has the largest effect?
**Reverse engineering a question**- Can students create a challenging question that has a specific answer and also meets additional criteria you set them?
**Comparing different solution methods in terms of their efficiency**- What different solution methods are there and when would each one be more efficient that the other?
**Historical links and significance**- Where did this maths come from? Who discovered it? Was it discovered out of necessity to solve a particular problem or just as a curiosity?
**Link to a real life context including other subject areas**- What real life examples and contexts can we ask questions about? What other subjects within school can we link this to?
**Link that helps you understand another area of maths outside of the topic better**- How can one idea help in understanding another within another topic domain in maths?

In the coming weeks I intend to build example resources demonstrating these ideas. I hope to create both the prompt sheet and examples of resources for particular topics in the hope to spark debate. For now, however, I think this is enough to open the discussion. Please do contribute in the comments section below!

Have I missed any ways of forming links? I am working on the assumption that a worksheet resource based on building 11 *different types of links* will develop deeper learning that 11 questions on the same type of link. Is that reasonable? The 11 suggested types of links are in a particular order as I think this reflects the movement from relational to extended abstract. Do you think the order is right?

With thanks to:

http://pamhook.com You should certainly check out her fab website for more detailed info on SOLO.