Going Goal-Free to Learn How to Solve Physics Problems

In previous posts, I have been writing about teaching problem solving (here, here and here). This post describes a strategy that appears counter-intuitive, until you think about what you really want your students to learn.

AQA Phy Jun16
from AQA Jun 16 Physics A-Level Unit 2 Paper

When you use this question in class, which of the following learning goals is most important to you:

A: learning how to solve this type of problem

B: finding out how much vertical supporting force the rock really supplies.

I’m assuming that you don’t really care about the answer to the question.

When you set this question, any student who can’t solve it is actually less likely to solve it or a similar one next time (Hattie and Yates. 2011 – Visible Learning and the Science of How We Learn. p151). Your student is so caught up in the goal (solving the problem) that she has no working memory left to reflect on learning the strategy.

This blog describes the strategy that prompted John Sweller to develop Cognitive Load Theory (CLT) – the Goal-Free strategy (read more about its history here).

Reducing the cognitive load allows the learner to learn. In the question above, simply cut off the bottom line. You then have a situation to explore with your students – the boy on the plank.

I like to go cooperative at this stage, asking students to discuss the situation in turns. I use a strategy I learned from Jakob Werdelin, a cooperative learning specialist, called Word-Round. In groups of four, students have 20 seconds to talk about the situation in the question. After 20s, the next team member speaks. The teacher listens in to pick up any useful and interesting points to share with the class after the Word-Round is finished. (Another cooperative strategy that works well in this situation is Think-Pair-Share).

A considerable amount of learning has happened by this stage, especially if your learners recognise the situation as a familiar one involving beams with two supports. It is possible that your students are now ready to tackle the problem. You may wish to demonstrate the working yourself or you might prefer to give a partial solution and allow your students to complete it.

Going Goal-Free might sound directionless, but it is the fast route to problem solving.




Using Worked Examples to Reduce Cognitive Load in Physics

Screenshot from 2017-04-29 11-12-05
from Cognitive Load Theory – Sweller, Ayrea, Kalyuga 2011 (art by @@olivercavigliol – https://teachinghow2s.com/docs/CLT_chapter_summaries.pdf)

Learning how to solve problems is the key to becoming a physicist (here and here). The problem with problem solving is that you need to be pretty knowledgeable before you can make a good go at it. And we tend to teach new information and then put it into a problem in the same lesson. This doesn’t work for most learners.

The science of learning – cognitive load theory – has found the best way to to teach problem solving: worked examples.  Hattie puts the effect size of worked examples at 0.57 – 7 months extra progress per year.

Screenshot 2017-04-29 at 13.40.24
from Story of a Research Program by John Sweller

When a teacher models how to solve a problem, she is giving the guidance that novice physicists need. She will make the hidden process of solving the problem visible. It is a way in.

But then what? The jump from seeing someone do it to being able to do it yourself is still big.: “novice learners reach apoint of working memory overloadvery quickly” Hattie, Yates. 2014). Learners need a bridge.

One method is to give learners partially completed problems – this method is called problem completion. This reduces the cognitive load, allowing the learner to focus his working memory on fewer aspects of the problem.

Here is an example:

Worked Example

Terminal Velocity Q AQA 2016

AQA June 2016

Teacher’s explanation

Imagine you are standing at the board – ideally the question is projected adjacent to where you are explaining and making notes for the class:

  1. The weight of the ball is independent of the ball’s speed – it doesn’t change.
  2. The drag on the ball increases as the ball accelerates.
  3. The ball stops accelerating when the drag matches the weight – it has reached terminal velocity.

Completion Problems…

Going straight from worked example to whole questions is very challenging for most learners. Sentence starters reduce the cognitive load:

On 14 October 2012, Felix Baumgartner created a new world record when he jumped from a stationary balloon at a height of 39km. Above the Earth’s surface. 42s after jumping, her reached a terminal velocity of 373 m/s. Explain in terms of weight and drag how terminal velocity is reached.


  1. The weight ________________________________________________________________________
  2. The drag __________________________________________________________________________
  3. When the drag has increased _____________________________________________________

One completion problem will not be enough. You will need lots. There are plenty available in past papers, however, there is a cognitive advantage in including individuals in the class:

When his balloon experiment began to go wrong, Mr Rogers knew he had to jump. He was 5km high. Explain in terms of weight and drag why he reached terminal velocity as he fell.


  1. The weight ______________________________________________________________________
  2. The drag ________________________________________________________________________
  3. When the drag has increased ____________________________________________________.

Other insights from cognitative psychology include spacing out the practice and interleaving. I suggest revisiting these problems regularly and mixing them up with other questions. Aim for success – there are benefits for students getting it right. Optimum challenge is great, but getting answers wrong makes it more challening next time.

In my next blog, I will describe another strategy for reducing the cognitive load for novice physicists – cooperative learning.
I found @olivercavigiol teachinghow2s.com helpful in writing this blog.

What I Think About When I Think About Energy

Occult, mysterious and ad-hoc, energy should have no place in modern physics. Newton had no use for it. Motion, in the form of momentum, was enough for him.

Momentum keeps the universe moving. But what causes the planets to orbit the sun and the moons orbit their planets? What is the watch-spring of the universe?

Leibniz believed momentum was not enough. He wanted something to explain what made the ball roll down the hill; the arrow leap from the bow; the wind begin to blow on a still day. He wanted to find the force that gave life to motion.

Leibniz 1646 – 1716

So Leibniz created a new quantity – something that could move from the spring to the cog; from the bow to the arrow. He created double-entry accounting for the universe: energy. Continue reading “What I Think About When I Think About Energy”

Haven’t We Got Enough To Do Already? Why Science Teachers Should Teach Vocabulary and How to Make it Stick


There are words in the English language that science teachers wish the English department would teach – words like process, appropriate and monitor. We don’t expect anyone else to teach scientific vocabulary such as photosynthesis and nucleus, but if someone (English teachers?) could teach all of the rest, that would be great.

bitesize sankey
Tier 2 words: summarise, process, involved, x rather than y. http://www.bbc.co.uk/schools/gcsebitesize/science/aqa_pre_2011/energy/heatrev5.shtml

Worse luck – it doesn’t work that way. If you want your students to be able to read science textbooks and understand exam questions, teaching this sophisticated, but non-specialist vocabulary is down to you.

Specialists call these words tier 2. Here is my strategy for teaching tier 2 words in science. Continue reading “Haven’t We Got Enough To Do Already? Why Science Teachers Should Teach Vocabulary and How to Make it Stick”

Cooperative Reading

I started thinking about cooperative learning in 2010 and have made slow punctuated progress since. I know enough to write about it.

Back in 2010, I read and reread John Hattie’s Visible Learning. Among other strategies, I was drawn to cooperative learning.

Following a trail of references, I bought Graham Nuthall’s book: The Hidden Lives of Learners which confirms that students learn more from their peers than they do from their teachers.

Any teacher would be crazy not to make use of this. Continue reading “Cooperative Reading”

How Practical Work in Physics Supports Knowledge

Back in 1994, I began by PGCE at Oxford University. I was lucky to have a brilliant tutor, Brian Woolnough. He was an important academic: with Terry Allsop he wrote the key text Practical Work in Science. We respected him enormously.

The book was a review and analysis of science teacher’ practice – why we use practical work in science. My super-short summary is that we use practical work to:

  • develop practical skills and techniques;
  • be a problem-solving scientist;
  • get a ‘feel for phenomena’.

It was obvious that Brian was excellent in the classroom too. He was a showman and had an irreverant, maverick touch. In a full lecture hall, he solomnly picked up a copy of the National Curriculum and tossed it on the floor.

I also remember we caught him cheating demonstrating a physics practical that wasn’t working. He gave us a cheeky grin and said, “Well, it doesn’t matter if they learn it, does it?”

It is noticible that the summary list does not include “learn science knowledge” – practical work is pretty poor at helping learners master exam content. But it does support the learning of knowledge, by providing a concrete structure to build a schema around.

The more abstract and theoretical the concept, the more we need something concrete to attach the learning to. A practical activity provides a concrete experience that a skilled science teacher can build upon.

But it doesn’t happen automatically. The leap from concrete to abstract is generally too far for most learners to make solo. The gap needs to be bridged.

Recently, I have used Lemov’s Write/Rewrite to help my students link abstract concepts to concrete, practical work. I refer to the same practical experiences over and over again, spaced over weeks, to help my students make permanent memories, linking to abstract ideas. If the practical can’t be set up repeatedly, I bring in a key piece of equipment and photos to remind them and I set writing tasks (in a carefuly written sentence, explain….).

write rewrite chronometer

When I am confident that the have made a reliable connection between the abstract and concrete idea, I go about building on it. I ask them to make novel comparisons using a worksheet like the one below (see The Learning Scientists on Elaboration).

Elaboration (making inflexible knowlegde flexible)

As Brian said back in 1994 -“Well, it doesn’t matter if they learn it, does it?”

How to Teach Problems…

Physics is all about the problems.

In my last post, I picked apart the knowledge I needed to solve this physics problem:

A bottle of water is suspended from a fixed point by a inextensible rope. The bottle is set in motion and the system swings as a pendulum. However, the bottle leaks and the water slowly flows out of the bottom of it. How does the period of the swinging motion change as the water is lost?

200 Puzzling Physics Problems (with hints and solutions) by Gnadig, Honyek and Riley (2001)

The Role of Problems in Physics 1

The knowledge included:

  • knowledge about pendulums
  • knowledge about how physics questions are asked
  • knowledge of useful strategies to use
  • knowledge about what makes an acceptable answer in physics.

But I didn’t go into how you teach someone to solve problems. This post is about teaching problems. Continue reading “How to Teach Problems…”

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