Sunlight on a gremlin

Before starting the Teach First Summer Institute I’ve read quite a bit about maths teaching. One thing that I’ve really struggled to make sense of is how to map progression in key mathematical topics. In particular, being able to track back from what I see as the key learning outcome of a particular topic to the simplest building blocks of that topic is a real struggle for me.

This post, then, is a bit of a celebration. If progression in maths feels like a bit of a gremlin, at the end of the first week of the Summer Institute I feel as though I’ve found the string that’ll let me pull back the blind and expose the gremlin to the sunlight (excuse the awful analogy!)

Taking advantage of some excellent subject studies sessions this week, and using the example of linear equations, I am starting to grasp what progression means in practice, and most importantly how to plan for progression.

It is surprisingly simple in practice really. Taking examples of linear equations, I worked with fellow trainee maths teachers to write all the linear equations we could think of, and then number them according to our perception of their increasing complexity.

Focusing particularly on finding the simplest linear equation we could, this process allowed us to look at equations at several National Curriculum levels. Most valuably, it means that when we come to teach solving linear equations and try to judge the level of the class, we will know where to go if pupils find the content either too easy or too difficult.

Just as important, going through this process is helping me to formulate a strategy for planning for progression in other topics too. Brainstorming all aspects of the topic, and the assumptions that underpin each of those aspects, before ranking these in order of increasing complexity will help me to know where to go when students find a topic too easy of difficult. The result is that I will be better able to help all students learn in every lesson, which is the point of it all after all!

After a busy first week of the Summer Institute, this nugget of progress stands out as the most exciting for me.


Cold Call

Teach Like a Champion Technique 22: Cold Call

In order to make engaged participation the expectation, call on students regardless of whether they have raised their hands.

  • This allows you to better check for understanding, increases pace, and distributes work more broadly and more authoritatively.
  • Make it predictable, systematic (with a chart?), positive (prepare questions in advance!), scaffolded (break questions into simpler and harder for the same student).
  • Using cold-call to follow-up on previous questions, another student’s comment or the student’s own earlier comment is particularly effective.
  • Explain cold call the first time you use it.

Stretch It

Teach Like a Champion Technique 3: Stretch It.

The sequence of learning does not end with a right answer; reward right answers with follow-up questions that extend knowledge and test for reliability of knowledge. This technique is especially important for differentiating instruction.

  • Ask how or why.
  • Ask for another way to answer.
  • Ask for a better word.
  • Ask for evidence.
  • Ask students to integrate a related skill.
  • Ask students to apply the same skill in a new setting.

The Lazy Teacher’s Handbook: Ch 8 Differentiation

Three golden rules:

  • Differentiate for all through variety in your lessons over the term
  • Ask others (professionals, learners) what differentiation they feel is needed
  • Make differentiated strategies clear to the class so that they can differentiate for themselves.


Ways to differentiate the classroom experience:

  • Have plants that the students look after
  • Cultivate wonder through having weird props (regularly changed)

[These are great ideas but they aren’t differentiation as I understand it]


Ways to differentiate tasks:

  • Get students to design the task
  • Share Bloom’s Taxonomy with the class and make clear that you will be asking questions at different levels.
  • Have low access-high challenge tasks, and open questions
  • Get students to start the challenge just before it is getting difficult for them.
  • Make it clear where students can find help other than from you.
  • Matching learners
  • Ask learners what they need to learn better
  • Get a panel of students to review your intended tasks for the forthcoming lessons, suggest amendments and then surprise them by asking them to teach it.
  • Allow students to produce work in a variety of formats
  • Model how the task might look at different stages (perhaps by asking another group to do so?)
  • Think about what can be recorded that the students can refer back to.
  • Use what you know about the class.
  • Have high expectations of everyone.

The Lazy Teacher’s Handbook: Ch 6 IT

Six principles for technology:

  1. It should be used to switch on learners
    1. Fast and slow music to create a different mood in the classroom.
    2. Having a clip on loop at the start of the class with an open question next to it.
  2. It should be used to keep them engaged
    • E.g. Random name generators
    • Take pictures of a lesson and review them to recall learning
    • Record jingles to make transition easier
    • Have key messages as ‘advertising’ when not using the projector [But doesn’t that go completely against the idea of extending concentration spans?]
  3. It should be used to review what has learnt
    • Have a machine available to review video clips for those who need it
    • Get groups to record what they have done and play it back
  4. It should be used to empower learners
    • Get one group to work on a PC with the work projected onto the IWB to show that you value process as well as outcome
    • Make videos to explain difficult concepts that students can use in lessons on their mobile phones
    • Give students online access to all resources that you create to help them – this will be a bank they can return to
    • Get music from pupils’ mp3 players to play in class [this could be a reward?]
    • Get students to design and deliver lessons using technology
    • Get students to record a journal/blog online
  5. It should be used to link the learning process together
    • Use 63336 to text any question, to which students must try and beat the answer.
    • Use the IWB for ongoing AfL such as ClassDojo
  6. It should be used to link learners together
    • Using web conferencing software

The Lazy Teacher’s Handbook: Ch 4 Great ideas for lazy lessons

As I read through this book I realise the ‘lazy’ moniker is simply a marketing ploy – this is a book on how to teach much like any other. There are some good ideas in here all the same, based on the principle that some of the best lessons occur when you are forced to think on your feet, rather than having planned in depth. The key idea in this chapter is to apply that principle, but in a systematic way i.e. planned spontaneity. Ideas that can allow you to achieve this include:

  • Quick ideas:
    • Arrest me! Tell a pupil to imagine they have been arrested for being an outstanding mathematician. What evidence would be used? What evidence might be used in 4 weeks’ time? [To me this is a slightly forced way to achieve meta-cognition goals – I feel as though there might be more effective ways to achieve the same outcome by being more straight with pupils]
    • Choose a letter/number and come up with the specified number of mathematical words starting with that letter.
    • Just a minute [Love this idea!]
    • Thunks (get students to create their own)
    • Killer questions on a topic being studied – with someone in the hot spot.
    • Get students to create questions that keep them awake at night [I could have got these already from the first lesson questionnaire]
    • What if…ask odd questions and see what creativity it sparks in pupils
  • Chunkier ideas:
    • 5-3-1: Think up five ideas – pick the top three – justify one
    • Link two items together in five steps
    • Create a presentation of exactly 60 seconds to prove they know something
    • Pick the odd one out
    • Create your own report (then post it to them a month later) [I really like this]
    • Plot quirky variables on a graph e.g. happiness of a water molecule throughout the water cycle [another great idea!]
  • Huge ideas:
    • Circle time to discuss emotive topics such as dreams or ambitions.
    • Get students to think up the most unbelievable way to teach a topic, and then come up with more reasons why it could happen rather than couldn’t, covering all areas of project management.
    • Set up a trial for a controversial historical (or present) mathematical figure [I adapted this one a bit]
    • Create a crime scene in your classroom and get pupils to solve it.
    • Rewrite history – imagine what might have happened if oil had never been discovered, or the computer hadn’t been invented?
    • Predict future events, and the likelihood of these
    • ‘Resign’ and get pupils to plan the next five lessons (great for revision!)
    • Get pupils to present a topic they have learnt in the style of a TV show.
    • Evidence hunt in the textbook.
    • How could they improve the textbook?
    • Tell students they have the lesson to do something that would help them be a better learner, mathematician, or person.


I really like these ideas, but I think an important criterion for each is what the objective and outcome will be, and how this is related either to improving mathematical learning, or assisting pupils in building agency, self-esteem and an internal locus of control.


The Lazy Teacher’s Handbook: Ch 3 Structuring the lazy lesson

  • Prepare – do – review “learning loops” allow flexibility in lesson planning rather than sticking to a ‘three part lesson’ or similar.
    • By reviewing what you are doing throughout the lesson, this allows students to develop their abilities as autonomous learners.
  • In the Prepare phase, you need a good starter, clear outcomes and task introduction. All of these can be student-led.
    • At this stage it is worth having a discussion about the learning you will do in the lesson; if you are asking students to learn differently, you need to prime them to do so by e.g. asking them what they want to learn, where they have learnt something similar etc.
  • In the Do phase, let the students work! Don’t interrupt or try to lead.
    • Use strategies such as 3B4ME: use three strategies (brain, book, buddy, boss) before putting your hand up and asking the teacher.
    • FAQs whiteboard – students write questions, the teacher tells only them the answer and others must ask them.
    • Set up a ‘help desk’ with useful info/an email contact.
    • Use meta-questions: what are you currently thinking about?; what are you stuck on?; what do you need to answer the question?; what connections have you made?; what progress have you made?; have you seen anything like this before? Etc.
    • Again in the Do phase you can have a ‘meta-discussion’ about students’ learning.
  • In the Review phase (not necessarily the end of the lesson but the end of a learning loop):
    • Use a plenary to review the learning or reflect on progress so far
    • Again have a ‘meta-discussion’: how are you going to remember this learning?; what is the key point you will remember?; what has this lesson reminded you of/what connections have you made?; what did you learn that you didn’t know before?; where can you use this learning?
  • At the end of the lesson, hook them into the next lesson by introducing a teaser, and also dismiss them with praise and encouragement.