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.
Teach Like a Champion Ch 8: Improving your pacing
- Pacing is the skill of creating the perception that you are moving quickly, when necessary.
- Six techniques:
- Change the Pace: through different activities with the same objective, with nothing longer than 10 minutes.
- Brighten lines: make activities begin and end clearly and crisply, by setting clear, unexpected time limits, and having a clear signal for the end e.g. clapping hands.
- All hands: if an activity is extended, create markers by involving lots of different pupils for short periods.
- Every minute matters: keep a series of short learning activities ready so you’re prepared when a 2-minute opportunity arises.
- Look forward: create purpose by e.g. putting an agenda up with a ‘mystery activity’ on it or by talking about what students will be able to do by the end of class.
- Work the clock: use countdowns in class and set timings for activities.
Teach Like a Champion Technique 20: Exit ticket
Set a single question or short sequence of problems to solve at the end of the lesson, and analyse the results.
- Keep them simple – if students get them wrong you need to know why.
Teach Like a Champion Technique 13: Name the steps
Subdivide complex skills into component parts and build knowledge up systematically.
- Give each step a name so that it can easily be recalled.
- Key components of naming the steps:
- Identify the (fewer than 7) steps with clear and crisp language and post on the wall.
- Make them sticky by naming them and perhaps creating a mnemonic.
- Build the steps with students.
- Use two stairways – discussing both the current problem and a generalised form (both the problem and the process of solving these sorts of problems).
Teach Like a Champion Technique 12: The Hook
Have a short introductory moment that captures what’s interesting and engaging about the material and highlights it
- Possible techniques include:
- Telling a story
- An interesting and useful analogy
- A prop
- Short use of media
- Give the topic status
- Set students a challenge c.f. Pepper
- A good hook is typically:
- Quickly yielding to the lesson proper
- Energetic and optimistic
- You don’t need a hook for every lesson; perhaps the first of a set of three or four when a new topic is introduced.
From Teach Like a Champion:
Progress from I to We to You i.e. move from direct instruction to guided practice to more independent practice.
- For ‘I’:
- use both modelling and explanation
- include student interaction
- anticipate misconceptions and share these with students.
- For ‘You’:
- repetition matters
- keep going until they can do it on their own
- use multiple variations and formats
- grab opportunities for enrichment and differentiation
Teach Like a Champion Technique 11: Draw the Map
Always consider how the layout of the room impacts on the learning goal.
- Aisles and alleys are as important as desks.
- Walls should reinforce the tools and learning goals recently covered in class.