By year 6, pupils are skilled mathematical problem solvers. They can solve multi-step questions involving abstract concepts. This sounds like GCSE physics. Many year 6 pupils are taught to use visual representations to facilitate their problem solving. I wondered whether this would work in physics. I think it does.
I have put together a booklet containing problems and model answers using the Singapore Maths visualisation method: the bar-model. My goal is to carry out research to demonstrate whether bar-model in physics facilitates long-term learning.
In the meantime – I thought I would share the booklet to get feedback. The link is below. If you use it, please give me feedback.
With thanks to Jonathan Wragg, Lyndsay Sawyer, Ryan Doney and Anand Chauhan of Paradigm Trust for their knowledge, support and enthusiasm for this project (and @ollie_lovell for spotting embarrassing mistake!)
I was convinced by the Singapore bar-model when I invigilated the 2016 Key Stage 2 maths reasoning exam. One of my pupils, who I’d come to realise wasn’t going to score well, was faced with this problem:
A few weeks ago I observed an English teacher pull a sentence apart. A line from Romeo and Juliette was on the board and the class spent ten minutes together identifying the parts of speech (verb/noun/particle etc); the effect of words on the reader (to connote is a verb – I didn’t know that) and language techniques (repetition, alliteration, rhyme, personification etc). They marked it all up on the board. The students were practising marking-up the same sentence on paper (board=paper from Teach Like a Champion 2.0).
I thought it was like looking at a diagram goal free . Without worrying about the question at first, students were laying down all of the information they could about the line.
Then, as a class, they began to add the context. The result was an exploded sentence, with all of the bones exposed.
They answered questions about the line.
I wondered whether I could do something similar with a physics sentence – specifically an exam question. Instead of looking at the language techniques, I would pull apart the vocabulary and knowledge.
So I took some exam papers and chose a couple of questions to try.
The first obvious thing is that for GCSE physics questions (especially higher tier), single sentence questions are rare. Also, many questions have diagrams:
So I split the task into several parts. First, we went ‘goal-free’ on the diagram, which took 5 minutes using a think-pair-share.
(AQA Physics Unit 1 June 2016)
We did a mini control-the-game (Reading Reconsidered) on the opening line (you can see the mark-up we did on vacuum below).
Finally, we got to the close-reading of the question line. I think the student’s marked-up sheet explains what we did as well as I could write it. It was a collaborative effort – I asked students to do this in pairs and then we shared. I was modelling on the board.
Then they answered the question.
We shared and read the mark scheme and the students did a rewrite.
The whole task took 20 minutes, which is a big investment for one question. But I recommend doing it regularly because it does three things:
It exposes students to both technical and non-specialist vocabulary, in a physics context, over and over again. You don’t need to plan and track the high mileage non-specialist words – they come up naturally. Technical words are also experienced, in context, over and over again, building understanding.
It teaches student how to read a question.
It teaches students how to write a good answer.
This sequence is an effective and simple way to develop literacy in physics lessons. It does several jobs pretty well. With practice, you might be able to get the whole sequence down to 10/15 minutes – but I’m not there yet. I’d be interested to hear if anyone else tries it or does something similar.
Reading is a physics problem that doesn’t receive much attention in class. I think it should. Science professionals read a lot:
It turns out that the people who responded to the survey read a lot. Almost 85% of them read professional texts for more than 5 hours per week and 20% of them read for more than 15 hours per week. And they read to learn…
But most weren’t taught to do it at school.
This last chart troubles me. I know STEM texts (exams, textbooks, papers) are different to other texts. They use different vocabulary; follow different conventions and have a different purpose. Either learning to read these texts is so easy, it doesn’t require teaching, or it is hard and we are letting learners down.
How many capable young scientists and engineers are dropping out because they can’t access the information in texts? I worry about this a lot.
Cognitive Load Theory explains why reading is difficult and tells us how to make it easier. All three memories are in use:
long-term memory – the knowledge you already have. Commit as much to memory as possible – use quizzes every lesson.
working memory – where we compare what we’ve read to what we know and try to make meaning. There isn’t much we can do to boost this, though a good night’s sleep always helps me.
external memory – the text, and any scribbles you’ve added to it. This is a skill and we should teach it.
Comprehension depends most on what you already know. The two most important things for reading are in your long term memory (or they need to be). They are vocabulary and knowledge. Readers who are equipped with these are equipped to understand texts.
Science teachers are good at teaching science vocabulary. We explain clearly; we use example sentences; we revisit; we match words to diagrams. We use every trick we know.
But we ignore key non-specialist vocabulary. Words like: determine, suggest, establish and system (I took these from a couple of recent GCSE papers).
These words should be taken as seriously as technical vocabulary. It is hard to choose words to focus on. I tend to teach words as I come across them in textbooks and exam papers (especially if I think they could come up again).
Along with vocabulary, the most important part of understanding is what you already know: your schemata. As we read, the information in the text is held in your working memory to be presented to knowledge from your long-term memory like a debutante or a novice speed-dater. If sense can be made, great. If not, the reader has work to do.
Skills get tough press – but there are a few reading skills (or habits) which make a difference. These are the four that expert science readers (like us) use most often.
I Wonder…. Expert readers ask questions of the text. Often these questions are related to meaning, but they can be “I wonder what that word means?” or, “I wonder why the writer said that…”
In other words…. Paraphrasing (rewording, often making clearer) is a powerful comprehension checking skill/habit.
I predict…. Asking readers to predict what comes next in a test is a useful way of drawing attention to the structure and conventions of scientific texts – it is extremely useful when scanning a text for the information you want to be able to predict whether the information might be in a nearby section.
So far… Summarising is a habit which encourages prioritisation of information.
If these activities can be practiced enough (several times over a few weeks, with occasional top-ups) they quickly become part of a reader’s reading schema, increasing your students’ ability to learn from texts.
This blog is a development of the blog I wrote in 2015 for the Royal Society of Chemistry – here. I am reassured to find that I still agree with most of what I wrote then. Thank you if you’ve stuck with me all this time!
In my mental lesson control booth, I have three sliders I try to get right.
The first slider is ratio. I learnt this idea from Teach Like a Champion by @Doug_Lemov, who got it from Dave Levin from Kipp.
Ratio is the amount individual students spend actively thinking in class compared to the total lesson time. For example, in a teacher-to-one Q+A session, the ratio is low for every child who isn’t asked the question – most children don’t think much in those circumstances. You can increase the ratio by asking a question to the class and then getting them to answer it in pairs.
I used to worry that increasing ratio meant that direct instruction and teacher- modelling were low ratio. But pushing the ratio slider up a little in these activities means the teacher says what she needs to say as clearly and succinctly as possible, before the learners get active. That’s a good thing.
By load, I mean cognitive load. I want to bring this as low as I can so that my students are thinking about the thing I want them to learn. I reduce all of the extraneous ‘noise’ – especially for novices.
This week I have been working on direct speech with my class. There are many loads on a novice with writing direct speech: paragraphs, capital letters, commas, question marks, inside the speech marks or out. Added to that, they wanted to write their own dialogue.
I pulled the load slider as low as I could – we used goal free to look at speech from a book. They wrote their dialogues as playscripts first before converting to direct speech. Each element was difficult, but I reduced the load.
When I first learnt about cognitive load, I thought it meant make the thinking easy. It doesn’t. Cognitive load theory simply says take out the extraneous thinking – the undesirable difficulties and make the thinking about the thing you want to achieve. And that thing can (and should) be difficult.
There is an optimum difficulty for tasks – Bjorn calls them desirabledifficulties (see here). He makes a terribly important point – one that I missed for many years – performing well in class is not the same as learning well. The struggle is important.
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.
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:
AQA June 2016
Imagine you are standing at the board – ideally the question is projected adjacent to where you are explaining and making notes for the class:
The weight of the ball is independent of the ball’s speed – it doesn’t change.
The drag on the ball increases as the ball accelerates.
The ball stops accelerating when the drag matches the weight – it has reached terminal velocity.
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.
The weight ________________________________________________________________________
The drag __________________________________________________________________________
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.
The weight ______________________________________________________________________
The drag ________________________________________________________________________
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.