A simple model for meta-cognition in maths (and all other subjects)

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Having stated on Twitter that I think that maths has it easy in many ways and concurrently ready ‘Making Good Progress‘ and the chapter on using tests, I thought I’d share an adaptation of what I do in GCSE RS and show how it could be used in maths.

The Theory

Getting students to think about what they got right/wrong and why will help them to understand it and learn from it in the future. This process of ‘meta-cognition’ seems to have a high potential impact on learning.

How I do this in GCSE Religious studies

Once students have done a test, they complete an online form about the test. Example, here. It is a record of their marks for each question and a reflection. This collates all their responses and I get a pre-populated spreadsheet of their results and their individual targets. I can quickly analyse which topics/questions the students have done well or struggled on. I’m also an uber-geek and mail merge their results onto a reflection sheet for their next test.

 

 

Possible model for maths

I thought the same could be done in maths but with a reflection for each question after a test.

In order to support the process, you could add a box below each question for them to comment whilst doing the test. This might be particularly useful if they don’t answer a question.

maths-4

 

The teacher then needs to create a form that has the questions and the possible pitfalls. It is also a record of what answer they all put.

Here is a sample part of a form.

 

maths-5

You have to go through the test with them in some way before they input their data to help them understand why they got things right/wrong.

Alternatives to this might be to not give them options but require them to explain in their own words or only focus on particular questions for feedback.

You might also put the correct and the common incorrect answers as a drop down on the form for them to select. Google forms then has the ability to ‘mark’ the correct answers so your spreadsheet would also have marks e.g 14/20.

They make time to construct but there are ways to save time. Maths teams tend to be quite big; share the load. Or, commit to writing the form as they sit the test. 1 hour test = 1 hour to write the quiz. You can also, to some extent copy and edit these in Google forms. Other platforms have the opportunity to have tagged question banks so you could make generic responses that can easily be reused. Or only get them to reflect on specific questions based on your judgement on what might be useful.

You will need access to electric devices during the lesson for them to access the form. If this is problematical you can get them take turns in class with the devices you do have, whilst the others do their corrections or to do it for homework on their own devices. ( you just need to give them the URL link). I prefer it to be done in class.

Once you’ve established this routine with the students then it becomes easier and second nature to them. They know they will do this after each test.

Potential activities after this are:

  • make corrections in class showing an understanding from where they went wrong
  • to redo the exact same test at a later date (then you can compare outcomes)
  • focus on their incorrect answers for homework and use a programme such as My Maths to watch how they should be done, then re-do the questions

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The power of these forms are they  are useful for info on:

  • how they answered each question ( you get a copy of their answer as they’ve inputted it
  • how the class did on each question
  • what they need to ‘revise’/ do further practice
  • what you may need to re-teach
  • their thought process as they answered
  • common misconceptions
  • misconceptions that you might not have thought of

Overall, these forms make tests even more valuable in terms of their formative use.

As you can see I do a similar thing in Religious Studies, so this idea can be adapted fairly simply across all subjects.

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Teaching to the test vs Teaching for the test (and beyond)

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These thoughts are from an INSET day a few weeks ago when I wanted to focus in our department on ‘What is learning?’. We had some good discussions and one of them was about key stage 4 and GCSE teaching.

I have blogged before on how I ‘Teach to the test‘ by arguing that students need to see exam papers well before they’re faced with one in their final exam.

Our discussions focussed more on the teaching that takes place over the 2/3 years. We came up with two potential models for teaching for GCSE? (For ease I will use hand drawn diagrams – apologies for the presentation/quality)

Model 1 – Teaching to the test

 

This model is when a teacher only teaches the content of the GCSE. Everything that a student needs to know as a potential exam question is taught. It is often taught in the ‘units’ or ‘modules’ that the exam follows, so student know that today’s lesson on ‘Islam and marriage’ will be in Paper 1, unit 3. They are taught the correct amount and level of knowledge and understanding needed to be able to answer any exam question asked on the topic. In my current spec that is four different teachings. These two elements, subject knowledge and exam structure, fit together neatly.

All students need to know is a minimum of four correct answers to the question. Their notes can follow this format. Revision can be done in nice chunks.

However, if you then asked a student, a question about Islam and divorce, rather than considering the teachings behind these beliefs, they would go to their notes on Islam and divorce and find the four correct points. Whilst there are important connections in teachings between these two, they’d been learnt as a separate ‘chunk’ that few students can transfer knowledge from one to another.

Similarly, if you asked them to compare Christian and Muslim teachings on marriage, they wouldn’t be able to. It’s not an exam question they’ll be asked so they don’t know how to do it. They have no skills beyond what they’ve been taught for the exam.

This is how I’ve taught for a lot of my career. I used to teach compulsory GCSE RS short course on one lesson a fortnight. Imagine if a students was off ill, then it was the Easter holiday. I wouldn’t see them for potential 6 or 8 weeks. It was the only way to teach. They needed to know what could be on the exam. There wasn’t time for anything else.

But most subjects are not in this position. Whilst many teachers will always say they need more time (yet some are happy to waste time on the last day of each term…..) there is enough time to teach. And if you consider secondary school as a 5 year learning process (NOT a 5 year GCSE) then there is time not to resort to ‘teaching to the test’.

Importantly, model 1 works. If they know all the possible questions and all the correct answers, they can do well on an exam.

Model 2 Teaching for the test (and beyond)


I’m not sure this diagram truly depicts this model so hopefully my explanation will do it better.

If we consider our subject to be a minimum of 5 years learning, we can begin to teach beyond the test.

Instead of teaching for what is needed directly for the test, we can teach what is essential for students to understand in our subject to have the ability to answer any question on any topic. (I think some might call this ‘mastery’).

To help explain, I will take the new GCSE RS course. In a bizarre decision, students have to study Christianity, yet there is no requirement for them all to know and understand the Bible. There won’t be any questions in the exam about the Bible. If we were to follow the model above, they would never have a lesson about the Bible. They would have to reference it for its teachings in moral and ethical areas, even know about some miracles but not what it is, how it is formed, and how it is interpreted by different Christians.

So I decided, that I would sacrifice time to do a few lessons on this with them. From this it helped them understand: Biblical interpretations, Christian denominations and crucially why there is not agreement amongst Christians on key moral and ethical issues. Of course, when I get to teach abortion, I would then have to teach them the differing opinions amongst Christians and the biblical references they use to justify their position. But I would then have to do this again for Euthanasia, and war and capital punishment etc etc Instead, giving them a foundation in Biblical interpretations means they can apply it to anything, even topics beyond the GCSE. We’ve given them the foundations to answer any, not just the four possible answers for an exam answer.


This diagram attempts to show this. They may well have the same exam question as in model 1, but because they’ve learnt all the foundations in Islam, they have an array of sources to pull from to write an answer. The focus in this model is learning the essentials in order to be able to apply to all situations. The second circle shows that the same foundations are there for a completely different question, that wouldn’t even be in the exam, but they would be able to have a go at it from their foundation knowledge.

We do, of course, teach them what the exam questions will look like and how to do well in them but in theory, they could take a different exam board specification and equally be able to answer those questions as the basics and foundations are the same for Islam.

The other benefit of this is there is less ‘unit’ or ‘module’ learning. Students don’t learn an answer for unit 3, they apply their knowledge to unit 3. I’ve heard teachers criticise interleaving because their students would get ‘confused’. I’ve even heard stories of their students writing about the wrong concepts in an answer because they had got confused. I strongly believe that in this model, that wouldn’t happen. My students wouldn’t confuse Muhammad’s last speech with what Jesus said on the cross. They know both so well it won’t be confused. Yet they can apply both of these to any context and to any moral/ethical issue. I’ve been interleaving all this academic year and thus far I haven’t had any confusion between key concepts.

This model teaches outside and beyond the exam. It prepares them for A level and beyond, if they choose to.

My students have learnt some Arabic; it’s certainly not in the exam but now they know the root s_l_m they have range of applications in their exam. And they remember it. They remember the core stuff because it’s ‘deep’ and helps to explain some of the unexplainable.

Skeptics of this model will always claim the time issue will prevent them from doing it. There are four responses to this:

1) It doesn’t take up the time you think it does. Because you focus on the core ‘stuff’, it’s the foundations that are needed. No foundation, no independent application.

2) It will work better in the long run. Learn a few things in-depth that apply across the syllabus or lots of things that can only answer one or two questions?

3) You can start students on these core issues before GCSE. I certainly don’t believe we should teach the GCSE in key stage 3 but we can start those foundations.
Using model 2 has changed how I teach GCSE and I also think it makes them better students of religious studies. I know they’ll be going into key stage 5 with a much better grounding of studying religions.

4) Be brave. Change your mindset.

This model can work in any subject but it takes a mind shift away from what is needed for the exam to what learning is needed to understand topic X, that can be applied in any exam.

Oh and I think that model 2 will work….better than model 1.

Recall, recall, recall – how to get students to learn quotes in Religious Studies (and any subject)

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As the RS specs have changed, students need more than ever to remember quotes. I thought I’d help colleagues by sharing ideas based on what research suggests is the best way; recall, recall, recall.

  1. Make quote cards from index cards. They can write various things on each side. For example side A ‘give a quote that supports incarnation’ and side B ‘The word was made flesh – John 1’
  2. Make online quizzes – quizlet, google form or if you really have to kahoot (not a fan!) Google example here
  3. Quick quiz 1-5 – ask them 5 quote questions. An easy starter.
  4. Longer quiz – see this fab example that could be adapted from Dave Grimmett. It’s essential that it’s done but individuals, not teams.
  5. Pairs – give a set of pre made cards. Matching pairs. Either match quote and reference or topic and quote or all three!
  6. Songs or rhymes or (ewwww!) raps – as long as they can all ‘sing’ it. It counts as recall.
  7. Wall display memory – I have loads of quotes on my walls. The students look at them and reference them all the time. They look at the wall during tests (here is why I don’t care) They then ‘visualise’ this when in the exam hall and recall the quotes
  8. Student response expectation – when a student is discussing a topic or giving an answer in class, always follow it with “What quote might back that up?”.
  9. Memory palaces – I don’t know much about these except for Sherlock Holmes using them For an explanation see here
  10. Imagine the scene – this could be used well for the narrative parts of the religions  Think what the most important things that were said at that time and imagine how people reacted. Link that to a concept. When it’s time to remember, think of the reaction, then what they were reacting to. e.g Imagine the crowd at Muhammad’s final speech. He told them “Treat your women well”. Some might have been shocked as this hadn’t been the case. So when questioned on an important quote from Muhammad’s speech, it may be easier to remember this quote.


Sample ways of structuring questions:

  • Fill in the blanks – “In the beginning the ________of God hovered over the waters” Genesis 1
  • Link to a paragraph– give a paragraph on a topic – give a question “Which of these 4 quotes could be used to best support it?”
  • Reference question – “what does John 1 say?”
  • Topic link – give them a topic ‘e.g Incarnation’ and they must write down a quote that would support it e.g “The Word was made flesh”
  • Image link – link a concept to an image and they must recall a quote that supports this point e.g picture of Jesus being crucified = “Today you will be with me in paradise”
  • Scene link – as above, “Give a quote from Muhammad’s speech”

When to do the recall?
Any time! Setting quizzes for homework is especially effective as, if you get them to auto mark online, there is no marking for you.

TIPS

In my opinion, any activity where only one student has to do it is a waste of student time e.g a quiz where one person answers or something like hangman where only person can ‘get it right’. All the class need to be engaging in all the tasks.

When teaching the content in the first instance, make a big thing of the key quote/s. Get them to either have their own quote sheet or highlight in a specific colour so all quotes stand out in their notes.

Identify one juicy quote per concept. E.g incarnation, salvation, predestination. Where possible choose a quote that covers multiple concepts.

Remember to interleave the quotes, don’t just test them on quote recently covered. Mix up with those learnt from the start of the course.

Get the students to create all of these activities. It saves you time but also forces them to all engage with the quotes again.
Leaving it to revision isn’t a good idea. Embed these techniques from lesson 1……in year 7.

High expectations – what they look like in my classroom

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I regularly waffle on about ‘high expectations’ yet don’t define what I mean. This blog will attempt to explain how you might see it in my classroom. It’s a long list.

Firstly, I need to make it clear that high expectations at key stage 3 is not starting GCSE in year 7 nor is it getting them to do ‘more work’. 

I think the following shows how I have high expectations in my classroom:

Learning behaviours 

  • If I ask the class to do something, everyone in the class should do it, if not this will be pointed out to the individual
  • I expect them to have independence. All classes make notes and as a minimum make the notes I tell them. Most will write over and above.
  • I expect students to behave, if not they are choosing to have the sanction as set by the school policy. I give them plenty of chances to choose (two in class warnings, time out and then they are taken out of class)
  • I expect students to have manners, patience and respect me and others in the room. This includes listening, not talking when others are talking and being kind in what they say.
  • I expect them to ask for help when needed, if they don’t understand they should ask another student or me
  • I expect them to contribute in class discussion and structure this so there are no ‘I don’t knows’ to shirk giving an answer
  • I expect them to stay on task 
  • I expect them to come to my class. 
  • I expect them to come equipped (I do lend pens where necessary)
  • I expect them to look to the front, put pens down and stop talking when asked. I will wait for them all to do this and will name those that don’t manage one of them. I don’t talk when others are.
  • I expect them to know the school rules and to follow them and to expect a consequence if not

My classroom 

  • My room will be kept tidy. Everything has its place. If a child uses something, I expect them to put it back where they got it from.
  • I expect them to come in and out of my classroom sensibly.

Their work

  • I expect them to complete an appropriate amount of work for the time they’re given. Again with support where needed. If one student writes a page and another two lines, and hasn’t asked for help, I question their attitude to learning and will make them complete more in their own time. If they need further support I will do this 1-2-1.
  • I check all their work regularly. If it isn’t a good enough standard or quality of presentation, they have to edit or re-do
  • I expect them to complete their homework as specified when set. Every single bit I asked them should be done. I expect it to be in on time.
  • I give KS4 core RE clear expectations on what I need to see in their work by the end of the lesson. Almost a checklist. If not done, they will come at break to do it.

Level of work

  • I expect them to produce their best work, otherwise they’ll do it again
  • I ‘teach to the top’ which means I set the ‘highest’ task for all students to work on and expect them to try their best. Where needed, I will scaffold and put support in.
  • I expect the same of all students. I do not ‘differentiate’ for any student except for where scaffolding is needed to achieve the top level of work. I do not do anything special for pupil premium, SEN, LAC, boys, girls, black, white, tall, small children unless they need the scaffolding to achieve. 
  • You will never see in my classroom ‘must/could/should’ type activities 
  • You won’t hear me referring to levels, marks or grades on any piece of work (except in year July year 10 mock, December year 11 mock when a grade is calculated for the data collection. This is 5 minute activity for the students)
  • I don’t discuss ‘target grades’ except when I give the sticker to them to put on their book/folder as directed. I never reference it.
  • I expect a good standard of literacy (individual to a student) and where I’ve pointed out errors expect them to correct them (with support where needed)

Books/folders

  • All GCSE students use folders. I train them and expect them to be organised.
  • I expect their book/folder to be neat and tidy. I personally hate pieces of paper sticking out of books and make it clear to students. I support those that need it.
  • I expect them to add the title and date and underline them (as per school policy, as per key stage)
  • I expect them to take ownership of their book/folder and be proud of it.
  • I expect them to make corrections to their work wherever I have highlighted, ideally without asking or minimum when asked.
  • I expect them to complete the trackers in their book as instructed (or independently)

Overall I expect them to learn. That is my job to ensure I put in everything possible to support them in this (my other blogs outline how). So I plan for learning not for fun or for any other whim or gimmick.

You’ve probably read this and think my classroom sounds awful. It’s not! Children want structure; they get that in my classroom.

 However I have just presented one aspect of my teaching, what I expect from students. I could just as easily write about what they can expect from me, how I teach, how students perform in my classes but that’s not the point of the blog.

I’ve probably missed loads of stuff out but I think it works; of course I do, it’s my classroom.