SOLO mats - a 1 page lesson

It's been ages since I did a blog post about a teaching resource, so here we go...

I was looking to build in SOLO (For more posts on SOLO see here), some independence and also some structure to a lesson that also included an amount of differentiation. I try wherever possible to aim my lessons at the most able in the group, with scaffolding back for lower ability so that the more able aren't always subject to differentiation by just being given more work to do.

I mucked about with various ideas and finally landed on this one page lesson structure to try. The basic idea is that it incorporates a starter, core learning points and extension all in one place. It is possible for the strongest students to progress through the whole sheet with relatively little teacher input with prompts for them to reflect on what they've noticed. Students are given an A3 print of the sheet to work on, but can choose to make other notes or even do all of the work in their books if they want to (and some asked for squared paper for plotting the graph in the extending knowledge section).

Clearly this is a VERY maths based example - but I see no reason why this basic approach couldn't be used for any subject/topic that is looking to build on and combine prior knowledge in new ways.

(I should note that this was done for a very high ability group of year 11 students, it assumes quite a lot of knowledge and is certainly not a "start from scratch" position for this topic)

Powerpoint version available here.


The assumption is that the students start broadly in the top left, progressing down the left hand side, and then the right hand side, finishing off with a RAG123 assessment and comment in the bottom right (for more posts on RAG123 see here). Some got stuck straight in with it and progressed from one box to another fairly independently, others needed more support in lesson (possibly delivered by me or sometimes I would direct them to another student to discuss it), and some needed prompting to move on to the next box or to make links beyond what was immediately in front of them.

At the end of the lesson I collected in the sheets to review and complete the RAG123 comments. In the next lesson I issued the next sheet as follows:

Powerpoint version here.

This second sheet builds on the info I knew they had picked up in the first lesson and then structures some extension.

Reflections on using it
I was really taken with this approach and the majority of the students seemed to find them useful. The more inquisitive students came up with interesting ideas to navigate through it and made links readily, often pooling ideas to find solutions.

The lessons were very much of the form "here's your sheet, off you go" - I did very little discussion at a whole class level, in fact for the second lesson the sheets were already out on the desks and the students just came in and got started as they knew what to do. During the lessons my interactions with students were focused on removing barriers to them making links and progressing with the sheets. Sometimes I would add a line to a diagram to help them spot the right angled triangle, sometimes re-phrase or express what they told me verbally into algebraic form, sometimes it would be asking a question to open the door to the next box on the sheet. For those making most progress independently I would occasionally draw them back to earlier boxes to explore reasoning for answers or particular approaches to make sure they had seen the more general patterns among their specific answers.

The lack of formal instruction in a particular method or rule did expose some weaknesses for students who are otherwise strong performers; for some it was simply their discomfort with working with algebraic variables, for others it's a reluctance or lack of practice linking up different mathematical topics.

The most negative responses tended to come from those students who are diligent in making notes when a method is explained explicitly but tend to then apply this as a procedure to follow rather than understanding the underlying concept. In particular I had a group of girls who will probably get A* grades at GCSE (indeed they have already done so in Mocks), who got stuck at every stage because it was presented in a way that didn't signpost a method to apply, and sometimes there was no single clear answer to give. As a result they were fairly difficult to motivate through the lessons, however I still think it was a worthwhile experience for them.

For maximum benefit across the class I did use a final plenary to draw together all of the central key points with a few more formal notes, and then we spent a lesson applying this knowledge to exam type questions to check security of the concepts in different ways.

Other difficulties come with storing the sheets afterwards - A3 is not a convenient size to tuck into a small exercise book, but that's not a reason to not use them - I'll certainly use this approach again.

The group I was working with are generally well motivated and would get on with much of this independently, and also had a large amount of prior knowledge to work with. To use this approach with a weaker group, or with a group prone to behaviour challenges would need some thought as the lack of structure opens the door to classroom management issues if too many get stuck. I do think it could be used with weaker or more challenging groups, but it would need some more thought.

I think this basic approach could be used with almost any topic, it just needs a bit of thought. You also need to know the class well in order to know what knowledge you can assume. there is also no reason why this approach couldn't be used beyond maths.

So there it is - plan and deliver your lesson on a single page...

All thoughts welcome as always.

Reflecting on reflections

Reflecting is hard, really hard! It requires an honesty with yourself, an ability to take a step back from what you've done (that you have a personal attachment to) and to think deeply about how successful you've been. Ideally it should also involve some diagnosis on why you have/haven't been successful, and what you might do differently the next time you face a similar situation.

Good reflection is really high order thinking
If you consider where the skills required or the type of thinking for reflection lie in Bloom's taxonomy then it's the top end, high order thinking. You have to analyse and evaluate your performance, and then create ideas on how to improve.

Picture from http://en.wikipedia.org/wiki/Bloom's_taxonomy

Some people don't particularly like Blooms and might want to lob rocks at anything that refers to it. If you'd prefer to use an alternative taxonomy like SOLO (see here) then we're still talking the higher end Relational and Extended Abstract type of thinking. Anyone involved in reflection needs to make links between various areas of understanding, and ideally extend this into a what if situation for the future. Basically use whatever taxonomy of thinking you like and reflection/metacognition is right at the top in terms of difficulty.

The reason I am talking about this is that one of the things I keep seeing on twitter and also in observation feedback, work scrutiny evaluations and so on or are comments about poor quality self assessment & reflections from students.

Sometimes this is a teacher getting frustrated when students asked to reflect just end up writing comments like "I understood it," "I didn't get it" or "I did ok." Other times it is someone reviewing books that might suggest that the student's reflections don't indicate that they know what they need to do to improve.

It often crops up, and one of the ways I most often hear about it is when someone is first trying out RAG123 marking (Not heard of RAG123? - see here, here and then any of these). This structure for marking gives so many opportunities for self assessment and dialogue that the teacher sees lots of relatively poor reflective comments in one go and finds it frustrating.

Now having thought about the type of thinking required for good reflection is it a real surprise that a lot of students struggle? To ask a group to reflect is pushing them to a really high level of thought. Asking the question is completely valid, it's good to pose high order questions, but we really shouldn't be surprised if we get low order answers even from very able students, and particularly from weaker students. Some may not yet have the cognitive capacity to make a high quality response, for others it might be a straight vocabulary/literacy issue - students can't talk about something coherently unless they have the appropriate words at their disposal.

Is it just students?
The truth is that many adults struggle to reflect well. Some people struggle to see how good things actually were because they get hung up on the bad things. Others struggle to see the bad bits because they are distracted by the good bits. Even then many will struggle to do the diagnosis side and look for ways to improve. It's difficult to recognise flaws in yourself, and often even harder to come up with an alternative method that will improve things. If we all found it easy then the role of coaches and mentors would be redundant.

As part of thinking about how well our students are reflecting perhaps we should all take a little time to think about how good we are at reflecting on our own practice? How honest are we with ourselves? How objective are we? How constructive are we in terms of making and applying changes as a result of our reflections?

Don't stop just because it's difficult
Vitally just because students struggle to reflect in a coherent or high order way doesn't mean we should stop asking them to reflect. But we shouldn't be foolish enough to expect a spectacularly insightful self assessment from students the first time they try it. As with any cognitive process we should give them support to help them to structure their reflections. This support is the same kind of scaffolding that may be needed for any other learning:

Model it: Show them some examples of good reflection. Perhaps even demonstrate it in front of the class by reflecting on the lesson you've just taught?
Give a foothold: Sentences are easier to finish than to start - perhaps give them a sentence starter, or a choice of sentence starters - the improvement in quality is massive (See this post for some ideas on this)
Give feedback on the reflections: As part of responding to the reflections in marking dialogue give guidance on how they could improve their reflections and not just their work.
Give time for them to improve: A given group of students that have never self assessed before shouldn't be expected to do it perfectly, but we should expect them to get better at it given time and guidance.

As ever I'd be keen to know your thoughts, your experiences and if you've got any other suggestions....

SOLO to open up closed questions

I've been dabbling with SOLO for a while now, it's been part of bits of my practice (see here, here and here) but I've yet to really embed it in all lessons as fully as I would have liked. I have used it as a problem solving tool, or to help structure revision, but not really deployed SOLO on a more day to day basis, and I want to change that.

I recently completed an interview for an Assistant Head position and as part of that was asked to teach a PSE lesson. This took me well out of my Maths comfort zone, so I had to give the planning deeper consideration than a maths lesson might have. After some thought I decided to introduce SOLO as part of the lesson, and it worked really well...

SOLO as a structure for discussion
I was teaching this PSE lesson to a group of year 7 students that I had never taught before and I knew that they had never seen SOLO before. As such a bit of my lesson needed to become an intro to SOLO. Fortunately the symbols are so intuitive that once I'd suggested that a single dot (Prestructural in SOLO terminology) meant you basically knew nothing about a topic, and a single bar (Unistructural) meant you knew something about it, the students were able to develop their own really good working definitions for Multistructural, Relational and Extended Abstract:

Once they had defined this hierarchy I could refer back to it at any point in the lesson and they knew what I was talking about. As such when I asked a question and the student responded with an answer I could categorise their response using the SOLO icons, such as "one bar," "three bar," "linked bar." If the student gave a "one bar" response I then asked them, or asked another student what was needed to make it a "three bar" response, and so on.

I was really pleased with how natural the discussion became, escalating up to really high level answers in a structured way. Similarly the students could use the same method with each other to improve their written answers through peer and self assessment. It even gives an easy way to open up a closed question question... For example:

T: "Name a famous leader"

P: "Nelson Mandela"

T: "What type of answer is that?"

P: "It's just a fact so it's got to be One bar"

T: "How could the answer be improved?"

P: "Give more facts about him, like that he led South Africa, or say why he was famous"

T: "Can you improve that further?"

P: "Maybe make links to other countries or compare him to other leaders"

T: "Fantastic, work on that with your partner..."

Rightly or wrongly I have a feeling that the opportunity for this type of discussion is much more common in a subject like PSE, and the SOLO linkage is much clearer as a result, however it got me thinking about how this approach could be used in the same way for Maths...

SOLO vs closed questions
A constant battle for maths teachers is the old "there is only one right answer in maths." Now of course that may be true in terms of a numerical value, but that ignores the process followed to achieve that answer, and often there are many mathematically correct processes that lead to the same final answer. In more open ended activities there may also be multiple numerical answers that are "right."

In maths we constantly battle to get students to write down more than their final answer and to show their full method. Following my experience of using SOLO for PSE I started thinking about how to use it to break down the closed answers we encounter in maths. As such I've put this together as a starting point...

The pupil response could be something that is seen written down in their working, or something that they say verbally during discussion. The possible teacher response gives a suggestion of how to encourage a higher quality of response to this and future answers. This could be part of a RAG123 type marking (see here for more info on RAG123), verbal feedback, or any other feedback process.

An alternative is to use it for peer/self assessment, again to encourage progress from closed, factual answers, to fuller, clearer answers:

 I realise I may be diluting or slightly misappropriating the SOLO symbols a little, e.g. is the top description above truly Extended Abstract or is it actually only Relational? In truth I don't think that distinction matters in this application - it's about enabling students to improve rather than assigning strict categories.

Proof in the pudding
The assessment ladder is part of a lesson plan for Tuesday, and I am going to try and use the pupil response grid throughout the week to help open up questions and encourage students to think more deeply about the answers - watch this space for updates.

As always - all thoughts & comments welcome.

Using SOLO in a maths classroom

I've blogged on SOLO before (here and here), and it's still very early days in rolling this out beyond a few experiments, but it's working and developing...

Here are a few of the things we've been trying...

SOLO to structure revision:
The hierarchy of understanding that SOLO brings is a natural match to structuring revision. In helping my year 9 middle ability group to prepare for a test I put together some  sheets that tried to help them to collect and organise their knowledge & skills.

I used SOLO to guide them trough it:

• Prestructural - do they remember that we've covered that topic?
• Unistructural - can they remember one fact about it?
• Multistructural - can they remember any more facts about it?
• Relational - can they combine these facts to answer some questions about it?
• Extended Abstract - are there any links to other things that will help them to remember the key points?

I didn't want to guide them too much so I left most of the boxes blank, but gave example questions for them to complete in the Relational box, so they could prove their understanding. A completed sheet looks like this:

I tried this with the class with only a limited explanation of the stages - just presented them with the sheets and encouraged them to use their notes or other resources in the room to help get from Prestructural to Relational, pushing to Extended abstract where possible. The students reacted in a really positive way - they really liked the way they could demonstrate increasing understanding. The weaker students also liked that they could demonstrate some understanding even if they couldn't get all of the way to the bottom of the sheet. They recognised that they needed to find more of the multistructural facts and link them up in order to answer the questions posed. As a result I will definitely be using this approach again with this group.

More advanced revision
I have also started using a similar approach with my year 13 group. Initially this was a relatively informal process, with the SOLO icons scribbled on the board and student lead notes being made in class. Like this:

Following the success of the year 9 sheets, and a good response from the A-level students I've now got to the next step and created some proper A-level revision sheets - like this:

Tried it out with yr 13 on Friday - again a really positive student response, meaning I'll create more.

SOLO as a problem solving tool
I've also used SOLO a few times to help students to solve unfamiliar problems. For example without actually teaching anything about arc length or sector areas I put this slide up on the board:

The class then followed a "Think, Pair, Share" type activity to generate enough facts, individually and as a whole class. They then linked them up to allow the problem to be solved.

The second slide (arc length) needed much less discussion as the class had already accessed the key facts, and reached the solution more quickly.

Form there, without me actually telling the class how to do it at any point in the lesson, they all went on to confidently answer a range of questions relating to arc lengths and sector areas.

SOLO as a starter
We've also looked at using SOLO to collect prior knowledge on a topic at the start of a lesson. This can be really useful with a new group, or when coming across a topic that you've not touched on with a group before. Just put the icons on the board, write the topic name next to the prestructural blob and then see what facts the students can give to you and what links they can make between the facts.

SOLO as a Plenary
Part way through a lesson or at the end - just ask the students where on the SOLO taxonomy they think they are, how they know that and what they need to do to move to the next level - they soon get the hang of the icons and the conversations are great.

How are you using SOLO?
Do you have any comments or suggestions - I'm really keen to know how others are using SOLO in maths and in other areas - please comment or drop me a line on twitter.

Tentative SOLO steps

Got to be brief this week...

Learning curve for SOLO
If you've not heard of it before then look up some background to SOLO on Pam Hook's website here. Also for a quick intro watch this video.

Having stumbled upon SOLO earlier this year and used it to help structure some questioning (see this post) we are now starting to try and spread it across our teaching more widely. Frankly I'm still amazed that SOLO isn't a core part of teacher training - in my opinion it is so much more powerful than Bloom's taxonomy but that's still pushed heavily.

The first step for us was to take our department through the SOLO concept in a departmental meeting last week. We watched the video and discussed the levels. The team rapidly moved from prestructural knowledge of the name only through to relational understanding. Several of the team could identify how the taxonomy links to recent lessons... We're now looking at the extended abstract bit of this - embedding SOLO in our day to day practice. Big tip of the hat to Rob (@robewilliams79) for leading this with the team and for the vast majority of the ideas below.

Small beginnings
We're not trying to run too fast with this... We have two rooms set up with "SOLO" walls - displaying the Icons for the different levels. Further use of these is under development - we have some thoughts on using them to indicate progress through topics but they're not full formed yet.

Selected classes are also being introduced to the terms and symbols. They've been shown the lego video and are starting to get to grips with assessing themselves vs the various levels.

Some lessons have started with an introduction of some facts (unistructural or multistructural level) for example angle facts in triangles and on straight lines Then the objective has been set to solve a question that uses combinations of those facts, e.g. finding compound angles in a diagram or proving rules about angles. This has been reinforced with the students by demonstrating that they are making links between the facts, and hence moving them up the SOLO taxonomy into relational understanding.

So far so good - the groups it's been tried with are really warming to it - and it is certainly not hurting their progress. They see the structure and understand that they need to start with what they know and use that to develop towards what they need to know.

Further steps
More of the same really - continuing to develop the use across more lessons and embedding it further. I'm also keen to use it to structure & guide thinking for 3 act lesson a la Dan Meyer. As I see it Dan's approach effectively presents the extended abstract question and then encourages students to break it down to the multi and unistructural level facts and information that they need to build a solution. I see this as a good approach to breaking down this kind of maths problem, and am keen to use the solo terminology to help the students to frame their problem solving processes.

Watch this space
Realise this isn't the fullest of posts - very much a work in progress, however it signposts the next key direction we are taking and I'm keen to share it and get any feedback. I assure you there will be more posts on this as we progress further.

I'd be really keen to hear from you if you have any SOLO experience that you'd like to share or have any other comments on this.

Leave a comment or find me on twitter... @listerkev

Minding the Gap - Using SOLO to help structure questioning

We're having a real push in our school on the quality of questioning. This sparked various debates across the staff that start along the lines of "our subject is different because..." and frankly these discussions are all a load of hot air. Good questions can be used to extend learning across all subjects. The form that the question may take, and the subject matter it links to will change for obvious reasons, but the core idea of using good questions to assess and extend learning applies regardless of subject, and Maths is no different...

The gap... Closed to open / specific to general
In maths lessons without proper planning we can too often allow students to get caught up with chasing down "the" right answer, and therefore get stuck with apparently closed questioning. However maths is a subject that makes leaps from closed questions to open questions, and from specific cases to general cases with huge regularity.

For example we can step from the specific 3+6=9, to the less specific x+6=9 to the general x+y=9, and beyond into the even more general x+y=z. Sometimes we ask students to make this leap in the space of a single lesson, and too often we do it with students that don't fully understand what the letters represent (for more on levels of understanding of algebra see chapter 8, of this book - it's fairly old, but well worth a read if you've not done so before - can provide a real insight into the barriers to understanding algebra). For those of us with a sound grasp of algebra and who are happy to use letters as variables this step from specific to general is fairly trivial. However for those without that grasp it is too often a step that presents a real challenge, or that can be made only by copying procedures without deeper understanding of the concepts that lie underneath.

Vitally though, if we don't plan and structure it properly our questioning can also make these big leaps from closed and specific all the way up to open and general. There is the potential to leave a huge gap in between, where misconceptions and misunderstandings can sneak through without detection.

It was while I was contemplating this gap that I stumbled upon the SOLO taxonomy and realised that this helps me to explain this issue. In terms of SOLO levels of understanding this gap can require a student to take a leap from Prestructural or Unistructural understanding all the way to Relational or Extended Abstract understanding without making any links on the way. (When I found out about SOLO I was amazed that it wasn't part of my basic teacher training; I think it's really powerful. If you've never heard of SOLO before then take a couple of minutes to have a look at this video as it explains all of the key points - also linked here on youtube if this embedded video doesn't work)

Using existing good practice to help fill the gap
I know from observations that there is a range of excellent practice in terms of questioning within the maths department, but even the best of us do leave this gap open at times in our rush towards generalisation. I thought that with some tweaks we could put something in place to help us to bridge the gap.

To capture examples of the existing good practice I asked each member of the department to send me 2 or 3 examples of questions that they had found effective during a particular week. I then took these questions, added a few more, and tried to align them with the SOLO taxonomy. The result is this sheet:

You can get a PDF version here: LINK

What's the point?
The idea of the sheet is to give us a quick reference sentence starter or framework to build a good question around depending on topic. By aligning the questions with SOLO we can work our way up (or down) the levels of understanding as needed with a particular class or individual. Importantly it structures the questions with several in the Multistructural and Relational areas to help us avoid making jumps too big and losing students in the gap.

Of course those fortunate enough to be really gifted teachers can always from the perfect question at exactly the right time, however for most mortals it can be useful to have the occasional prompt, and there are other uses for a sheet such as this (see below).

Not a definitive list - all about context
This sheet is only intended as a prompt, it's not all encompassing and it should be used with a due level of professional interpretation to judge whether a question is suitable for a given class or student. Similarly the detail of the question can be tweaked as needed, and extended with further questions (ref Pause, pose, pounce, bounce by @TeacherToolkit).

Of course you could debate the location of some of the questions and where I've assigned them in the SOLO taxonomy - this was my first attempt and some are far from clear cut. In fact one of the key points of SOLO is that the response to a question can be at a different level to the question itself. For example the deceptively simple "What is a fraction?" could be Prestructural if we're talking to a student that has only a vague concept of what a fraction is, and it could rise as high as Extended Abstract if we start making links beyond decimals and percentages into algebraic fractions, gradients or differentiation, etc. This is where the context of the question and professional skill/judgement comes into it.

How are we using the sheet?
1) Copies in departmental planners to help form questions at lesson planning stage
2) Copies available in the classroom (soon to be on the wall) to give a quick prompt for the teacher as part of a plenary or mid-lesson review (particularly useful if the lesson hasn't gone exactly as planned so any questions planned in advance can't be used)
3) Whole sheet, or sections of it, given to students as part of a lesson to encourage them to ask challenging questions of themselves or each other as part of group or discussion work.

What's the impact?
Early days really, but having the sheet for reference is undoubtedly useful as part of the planning process. Similarly just asking the department for examples of their good practice provokes reflection and review over and above normal day to day practice. However what is more interesting is where this could take us next...

What next?
The sheet is planned to be kept as a live and developing document. I plan to review it in department meetings over the coming 12 months or so and update it with more questions and refinements to make sure it is as useful as possible to the department both for planning and use during lessons.

I also see a route towards questioning structures linked to schemes of work. This link shows an example that @TeacherToolkit has posted using Bloom's Taxonomy to differentiate questioning for a Design Technology topic, and I see no reason why we can't develop a similar approach in Maths using this SOLO structure.

I am also keen to try to embed this approach alongside our work on establishing a common language for feedback (see this earlier post). If the students can start spotting patterns in our questioning and make links to how this helps to develop understanding then I suspect there is a meta-cognitive benefit to be had. However we've not tried that yet so it's nothing more than speculation for now...

All thoughts welcome
As always I'm keen to know your thoughts. Is this useful? Do you have anything similar? Do you have anything completely different that does the same job? Do you think I'm wasting my time (if so - please say why)?

Thanks for reading. Look me up on twitter... @ListerKev