Summer Institute highlight: An amazing day on number

I’m posting a series on the highlights as I saw them from the Teach First Summer Institute at Warwick. One of these was the first day we devoted to studying how to teach number. Diana Spurr and Marcus Shepheard covered a wonderfully rich variety of content in impressive depth – it was a really valuable day. Highlights include:

More highlights to come in a few days…


The wonderful world of the empty number line

Screen Shot 2013-08-11 at 09.36.44

How interesting can an empty number line be? Not very, I assumed. I’d read before about teachers raving about the concept. I’d always thought they were a little funny in the head. I am now officially a convert.

It turns out the empty number line can be used in a whole range of ways. Most simply, it can be a great mental tool for students’ addition and subtraction, by using multiples of 10, counting on etc.

For example, 12+13 becomes:

Screen Shot 2013-08-11 at 09.36.51

25-12 becomes:

Screen Shot 2013-08-11 at 09.36.56

So far so good, but it was what Diana and Marcus did next that was so exciting…using empty number lines to visually represent linear equations. (I’m aware there are many other ways to represent linear equations – this just feels like a particularly powerful one)

For example, taking the equation 3x+8=23:

Screen Shot 2013-08-11 at 09.37.02


Screen Shot 2013-08-11 at 09.37.11

so x=5


You can even use the empty number line to explore relationships between fractions, decimals and percentages:

Screen Shot 2013-08-11 at 09.37.18

What could A be?

Summer Institute highlight: IWBs and technology in the classroom

This is part of a series blogging the highlights (as I saw them) from the Teach First Summer Institute 2013.

Hannah Tuffnell and Joe Ambrose hosted a great session on IWBs and technology in the classroom. It was brilliant partly because of the content but also partly because, on the penultimate day of the Summer Institute, in a boiling hot room, at 7:30 they kept 20 or so exhausted participants engaged and learning for an hour.

The new technologies they promoted were:

  • Prezi: Most of us knew this one – a more engaging version of powerpoint. It’s time-consuming, though, so best for the occasional lesson e.g. introducing a new topic.
  • Powtoon: Use to easily create animations up to 5 minutes long – students can make them too.
  • Padlet: An online noticeboard where students can write on a wall (you can moderate comments!). Could be great for homework.
  • Edmodo: A safer version of facebook. You can use it to set up assignments, polls, resources etc.
    • Useful for homework setting
    • Marks multiple choice answers
    • Students can download an app that lets them do homework on their phone.
  • Google Forms: (find via Google Drive) Create a questionnaire to give to students. Useful for feedback on you as a teacher.
  • Poll everywhere: allows students to text into polls in real-time, and can embed within powerpoint.

In terms of IWBs themselves, some specific tricks:

  • Revealer tool: pull down a box to reveal specific parts of the board
  • Infinite cloner tool allows you to create duplicates of e.g. a coin
  • Layering can be used to allow some things into a box and not others
  • Using two colours can allow you to magically ‘reveal’ an answer
  • It is possible to lock things into place.
  • Shape recognition and text recognition tools are available
  • The magic pen allows you to:
    • Write in text that slowly fades
    • Circle (everything else goes dark)
    • Zoom in by drawing a square
  • You can create a random name generator with a hat (this allows you to differentiate by having different names in different areas of the hat)

SMART exchange/SMART world is the source of more information and training.

These IWB ideas are great, but have made me realise what I really need is a bit of time with the board to play around with creating and using things. I can already see how I could use these tools to sort shapes, or to reveal the correct answer to factorising problems.

A great series of problem-solving lessons on Pythagoras

Problem-solving lessons on Pythag

This article offers good insights into how to design a series of interlinked lessons and homework tasks in order to teach Pythagoras’ theorem in a problem-solving approach. It contains good AfL, lots of group work and carefully thought-through homework.

I can refer back to this when seeking to design a series of lessons on another topic.

Behaviour4Learning Resources

The (now defunct) Behaviour4Learning website has a set of 26 scenarios for behaviour – it’s really useful to think through each situation and what I can do to manage/prevent it.

Scenario 1: Starting a lesson in an orderly way

  • Key message: establish routines to settle the class – don’t just expect it to happen.
  • How to apply it in practice: devote time in the first class to establishing a routine that works for me and for the students, and then reinforce this in every class.

Scenario 2: Gaining attention in a noisy class

  • Key message: have an established, fun routine for gaining quiet, and then focus attention. These aren’t the same thing!
  • How to apply it in practice: Have a musical instrument to gain attention. Plan for a quick review of learning and AfL before moving on.

Scenario 3: Including pupils with special needs

  • Key message: Regular planning with a TA supporting a pupil is vital in order to help their learning progress.
  • How to apply it in practice: Meet my TAs early on, and find a time to meet them over coffee/lunch once every couple of weeks.

Scenario 4: Identifying behaviour hotspots

  • Key message: the classroom layout may cause behaviour problems, and it may be hard to predict what these will be in advance
  • How to apply it in practice: Remain vigilant for behaviour problems associated with a layout, and act on any problems to (a) change the layout and/or (b) establish routines for the movement and activity associated with the area that’s causing a problem.

Scenario 5: Setting classroom standards

  • Key message: Keep the code of conduct short and positive
  • How to apply it in practice: Distil down the ground rules I think are important, but also be prepared to negotiate with each class to get ‘buy-in’, then reinforce with ‘catch you being good’.

Scenario 6: Maintaining classroom standards

  • Key message: sanctions do not change behaviour; they just limit it for long enough to reward good behaviour.
  • How to apply it in practice: Have a behaviour target for each lesson based on the code of conduct, and reward students for meeting the target.

Scenario 7: Establishing your authority

  • Key message: constant development of professional relationships is how you gain respect – it isn’t a one-off thing or a thing you can demand.
  • How to apply it in practice: Maintain an attitude of respect all the time, and consciously manage my emotions. Use a raised voice or anger rarely.

Scenario 8: Setting learning intentions and success criteria for behaviour

  • Key message: The reason for focusing on behaviour is to improve learning. Help students to appreciate this.
  • How to apply it in practice: Devote some time or a lesson to discussing behaviour for learning approaches – how can we maximise each other’s learning through our behaviour? Agree targets and then focus on one each lesson.

Scenario 9: Responding to a pupil who refuses an instruction

  • Key message: I am likely to feel an emotional reaction to the situation, but clear procedures will help me to ignore that reaction.
  • How to apply it in practice: Practice! Practice using language of limited consequences whenever these situations arise. Always follow-through on consequences.

Scenario 10: Defusing a conflict between pupils

  • Key message: It is a complex situation which requires quick thinking, with safety as the clear priority.
  • How to apply it in practice: Work on establishing and building authority so that when something like this occurs you’re more likely to be listened to.

Scenario 11: Dealing with a late arrival to class

  • Key message: When a pupil is late, don’t make a fuss – acknowledge them and get on with the class, then follow it up where others can see but perhaps not hear.
  • How to apply it in practice: I’m clear on the approach needed here, I just need to practice it once I’m in school.

Scenario 12: Dealing with unacceptable language

  • Key message: It’s important always to be able to explain why a rule is in place e.g. that some people will be offended by swearing.
  • How to apply it in practice: I will say to pupils that they can always ask me the reason why I’ve done something, after the lesson/by email etc.

Scenario 13: Enforcing a school rule

  • Key message: When multiple students are involved in a contravention of the rules, it is far better to keep your response low-intervention and focus on the learning. Inject humour if you can!
  • How to apply it in practice: Practice a range of low-intervention methods with my classes and see which works best, then perfect it.

Scenario 14: Giving praise and reward

  • Key message: Praise and rewards can be small, short-term things and pupils may respond better than something long-term.
  • How to apply it in practice: Plan carefully how to find ways to praise those who may not receive much. Make it genuine and understated.

Scenario 15: Managing a pupil who is angry

  • Key message: If any students have individual education plans I need to know these thoroughly in order to be able to react well ‘in the moment’.
  • How to apply it in practice: Ask to see any IEPs for my pupils, and follow-up if I think one is needed.

Scenario 16: Effective sanctions

  • Key message: Sanctions are effective when used sparingly, and focused on restoration, or pupils taking responsibility for their behaviour and discipline.
  • How to apply it in practice: Try to praise as much as I can, and get a balance between being consistent with school rules, but not applying sanctions too often.

Scenario 17: Physical intervention

  • Key message: Physical intervention should always be a last resort, and should be applied only if strictly necessary.
  • How to apply it in practice: Find and practice ways to defuse tensions before they arise, or once they are manifest.

Scenario 18: Giving instructions

  • Key message: Developing the ability to give precise, clear instructions is really important.
  • How to apply it in practice: Plan my instructions, and practice with others in giving clear instructions. Ask my mentor to focus on this.

Scenario 19: Managing transition in a lesson

  • Key message: Managing transitions is all about understanding why pupils are acting in the way they are acting – are they deep in the task, or are they gossiping? An authoritative response to the latter is important.
  • How to apply it in practice: Plan transitions, but also be flexible and explore whether my timings are right.

Scenario 20: Finishing a lesson in an orderly way

  • Key message: Planning time at the end of the lesson to review learnng, and set and discuss homework, is really important to establish an orderly end.
  • How to apply it in practice: Plan carefully, and leave enough time to discuss homework propery. Establish a routine for the end of the lesson.

Scenario 21: Restorative approaches (A)

  • Key message: restorative approaches rely on a non-judgemental atmosphere, but can still evoke deep feelings.
  • How to apply it in practice: Put it into practice as much as I can in my day-to-day meetings with pupils. Investigate whether the school has a formal process in place.

Scenario 22: Restorative approaches (B)

  • Key message: For restorative approaches to work, both parties must want to resolve things, and the process must be voluntary.
  • How to apply it in practice: Ask restorative questions at every opportunity, that give a pupil a chance to explain, and that ask them to explore the impact on others. Model this behaviour myself.

Scenario 23 and 24: Conflict resolution (A) Conflict resolution (B)

  • Key message: Understanding the reasons for conflict is essential, as is giving responsibility to the pupils to take the decision to act differently.
  • How to apply it in practice: When I see conflict, encourage both sides to reflect on their actions and feelings, and then ask them to think of alternative solutions. Ask them for a decision.

Scenario 25: Peer mentoring

  • Key message: Can be a very valuable approach, but needs careful monitoring and strong pupil ownership.
  • How to apply it in practice: If I can see that some pupils are struggling, explore with senior management and then raise with my tutor group or similar. Ask them what they think about bullying and how to help those who are unhappy.

Scenario 26: Circle time

  • Key message: This is a form of school-based facilitation allowing pupils to explore and resolve issues, but the ground rules are very important and there is a lot of trust involved.
  • How to apply it in practice: Read more about it first, and observe others doing it.

Encouraging patient problem-solving

The ever-reliable TED talks have produced another one – how to encourage students to delve into maths problems more patiently and with greater focus and interest.

The video gives five pointers:

  1. Use multimedia.
  2. Encourage student intuition.
  3. Ask the shortest question you can.
  4. Let students build the problem.
  5. Be less helpful.

This chimes perfectly with my aims to get more students to see the relevance of maths to their everyday lives – I reckon I can get everyday problems about just about any topic, and use this approach to turn them into meaty maths.