Seductive Problems

My trainee maths teachers love setting students challenging, interesting problems. I see students scribbling away trying to be first to solve it, or staring at the table, or scribbling away pretending not to stare at the table.

The feeling that the trainees (and I) get when the first couple of students solve it is great. That’s the seduction, but it’s important to take a wider view.

Adam and Eve, Seduction and the Tree of Knowledge

First, the students who solve it may benefit. I am uncertain. Cognitive Load Theory shows that working with a high cognitive load inhibits learning. Continue reading “Seductive Problems”


Retrieval Practice and Sentence Practice All In One!

Retrieval practice is in the air. The latest blog by Alex Laney on the Teach Like a Champion blog (here) is very useful.

We’ve been developing retrieval practice DoNows with the trainee teachers at Paradigm Trust, but we’re also keen on practising sentence types. Hochman and Wexler’s The Writing Revolution is full of great sentence practice activities. We’re using: ButBecauseSo and Expand-a-Sentence, both of which work well with factual knowledge recall.


This activity not only uses retrieval practice, but elaboration as well. Your students are taking a single idea and strengthening its links to other ideas, developing the relationships between them.

  • Squealer called a meeting, but…
  • Squealer called a meeting, because…
  • Squealer called a meeting, so…


  • Magnetic north poles repel, but…
  • Magnetic north poles repel, because…
  • Magnetic north poles repel, so…


  • 2 is the only even prime number, but…
  • 2 is the only even prime, because…
  • 2 is the only even prime number, so…

TopTip: always try these out before you give them to students in case they aren’t possible (I struggled with “2 is the only even prime number, but… ) – if you can’t do it, your students probably can’t either.


Give your students a very simple sentence. E.g. “Magnesium is an element,” or “The Weimar Republic was unsuccessful.”

The retrieval practice comes in the next stage. Students have to give short answers to as many of the following as possible:

  • Who __________
  • What _________
  • Where _________
  • When _________
  • Why _________
  • How _________

The final step is to expand the original sentence. E.g.

Magnesium Expand-a-Sentence DoNow

In practice, the DoNow looks like this:

Weimar expand-a-sentence DoNow

So, use your DoNows for retrieval practice, but think about the sentences too.



Check Out, Check In, Check Up

She is very confident in her decision, but subjective confidence is a poor index of accuracy of a judgement.”

Kahneman, Thinking Fast and Slow p.244.

I have been re-reading Daniel Kahneman’s Thinking Fast and Slow because I am interested in expertise – specifically, expertise in the classroom.

In chapter x, Kahneman writes about the differences between experts and novices, and whether intuition can be developed. I want to know whether I can trust my intuition about whether students are learning. Kahneman says I probably can’t, unless I’ve had clear, quick and accurate feedback.

Like most of us, I use proxies to tell in the classroom who is getting it and who isn’t: nodding, smiles, on-taskness. And then I take in the books….

According to Kahneman, experts in any field are generally overconfident in their judgements. Expert teachers generally over-estimate the amount their students are learning. This problem is worst for novice teachers. If they rely on their intuition about whether their students are learning, they can be badly misled.

Did he really have an opportunity to learn? How quick and how clear was the feedback he received from his judgements?

Kahneman, Thinking Fast and Slow p.244.

Novice teachers need quick, clear and accurate feedback. Feedback from mentors or evidence in books is too late. They need feedback on learning immediately to tell whether their class is getting-it.

But they also need to develop their intuition about long-term retention. They need feedback the next lesson and feedback a month later.

In Teach Like A Champion 2.0, Doug Lemov describes a strategy called the “Exit-Ticket”. We call it a check-out or a plenary. It is common-place. A well designed check-out gives the teacher feedback on the lesson faster than any mentor. By well designed, I mean:

  • It focusses on assessing the most important learning from the lesson.
  • It allows students to demonstrate whether they have understood or not.
  • It allows you to quickly walk round the class and see who can do it and who can’t.

But don’t forget about forgetting. Can you say it was an effective lesson if your students have forgotten it by the next lesson? How can find out how much has been remembered?

The check-in checks the same learning as the check-out. It may even be the same task. We do the check-in as part of the starter activity of the lesson. The teacher can quickly and clearly see whether the previous lesson was as effective as she thought.

But remembering and forgetting is a long, slow process, so you need a check-up.  A check-up takes place weeks and months later. It assesses again whether the learning you thought happened is still there.

All of this assessing gives excellent feedback to the novice teacher, allowing her to develop more accurate intuition. Luckily it is good for the learner too: retrieval practice, spaced practice, and if you add together various check-ins and check-ups, you have interleaving too.

But for trainee teachers, it’s the feedback that’s most important. Your intuition is built on fast, clear and accurate feedback – the fastest way to become an expert.

A Teacher Is the Sum of All of the Problems She Can Solve

Teacher = sum of problemsOver the past year and a half I have been writing a handbook for novice physics teachers. The book is about using cognitive science to help novice physicists into experts. In it I wrote the line:

A physicist is the sum of the problems she can solve.

Now my mind has turned to training teachers, I realise that a teacher too is the sum of the problems she can solve. Teaching is about solving problems: how to explain something quickly and clearly; how to assess it; how to break down sequence the ideas; how to get students into the class quickly; how to manage a Q&A…. The list is very long.

An expert teacher knows how to solve thousands of problems, some outside the classroom, but many of them live, in front of demanding students.

In my physics book, I used Cognitive Load Theory (CLT) to help understand how we learn to solve problems. One of the key findings of CLT is that we learn how to solve problems best when the cognitive load is low. That means, distractions should be kept to a minimum. The classroom is a terrible place to learn to teach.

At Paradigm Trust, we are addressing this problem by rehearsing solutions to classroom problems outside of the classroom. We are using Paul Bambrick’s Get Better Faster programme alongside Doug Lemov’s Teach Like a Champion 2.0 strategies. When these strategies become automatic, the cognitive load of the classroom is reduced, meaning teachers are able to learn to solve new problems faster.

The next blog discusses automaticity and Lemov’s Teach Like a Champion strategies. 

1. I have allowed for everything else that makes a teacher by adding a correction factor ‘X’. I am aware of how wrong-headed this is.


Cognitive Psychology and Initial Teacher Education

The question is not whether these experts are well trained. It is whether their world is predictable.”

Daniel Kahneman, Thinking Fast and Slow p.221

This is the first in a series of blogs I am writing about initial teacher education (ITE). Since July, I have been developing a programme for novice teachers, with the aim of using cognitive science to help them become experts faster.

For a new teacher, a classroom is a place of exceptionally high cognitive load. Hundreds of small decisions adding up to a successful lesson or an unsuccessful one.

Reducing the cognitive load allows new teachers to learn more quickly. One way to do this is to practice in a simplified, predictable environment – a training room. We are using Paul Bambrick’s  “Get Better Faster” programme, combined with Lemov’s “Teach Like a Champion” strategies to practise out of the classroom.

The idea is to make the classroom predictable: the solutions to everyday problems like getting students into the classroom and ready to learn become automatic, so that a teacher can learn faster.

The next blog is about solvign problems in the classroom.

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