September 2, 2013 by dragonflytraining
What are the answers to these three questions? Try to solve them before reading further:
1.(1) A bat and a ball cost $1.10 in total. The bat costs $1.00 more than the ball. How much does the ball cost? _____ cents
2.(2) If it takes 5 machines 5 minutes to make 5 widgets, how long would it take 100 machines to make 100 widgets? _____ minutes
3.(3) In a lake, there is a patch of lily pads. Every day, the patch doubles in size. If it takes 48 days for the patch to cover the entire lake, how long would it take for the patch to cover half of the lake? _____ days
These are taken from S Frederick Cognitive Reflection and Decision Making (2005) . Each question has a compelling answer that is wrong. Intuitively we assume the ball costs 10 cents, 100 machines would take 100 minutes and half the lake would be covered in 24 days. Correct answers at the bottom of the post. In tests 65% of students made at least one mistake. When the questions were then made hard to read by greying out the writing, performance improved dramatically with now only 35% making mistakes. The full research paper is here.
This seems counter intuitive, performance was improved by adding a difficulty?
Another piece of research that seems to support this was the following:
Line 1 is easier to read, but that lines 2, 3, and 4 are easier to remember and may help learning new material.
Researchers at Princeton University and Indiana University conducted two experiments to determine if changing the font of material would improve memory and learning. In the first study, people (18 to 40 years old) were given 90 seconds to memorize information written in different fonts. They were given a memory test 15 minutes after they memorized the information. The subjects scored 72.8% correct when they memorized information in the easy- to-read text (Arial font, line 1 above), but the scored significantly better (86.5% correct) when they memorized information written in the difficult-to-read font (Comic Sans MS font, line 2 above).
This also seems to fly in the face of the fundamentals of teaching. Surely the simpler we can explain things and the easier students can access information, the better their learning will be? Evidence seems to suggest this is not the case.
Dr Derek Muller, who has a brilliant physics videofeed under the name of Veritasium, looked at using multimedia to support learning. His full PhD thesis is available here but a useful summary is:
It would appear that simply giving the information to students, even if it is to us clearly at odds to their prior beliefs, can often just lead to them misinterpreting it and instead using it to confirm their own bias. We have many biases, an overview is here, one of the most powerful is probably Bias Blind Spot – the tendency to ignore our biases!
Teaching would be a very simple process if humans were rational and eager to learn from us. In his superb book Predictably Irrational – Dan Ariely outlines some of our bizarre behaviour patterns. The chapter on how arousal affects our decision making processes is particularly frightening, for example 5% of the respondents said they would consider using a date rape drug in a non aroused state – this rose to 26% in an aroused state.
The advent of online courses such as MOOCs and Flipped Lessons might to some start signalling the end of teachers. Those who believe this are missing the point. Teaching is a two way process and cannot be reduced to it’s tools. This has been nicely outlined in Aaron Barlow’s blog here. A skilled teacher can never be replaced by technology as they understand that giving information is only the starting point and that whatever your teaching style you adapt to the needs and responses of your students. More importantly we have to challenge our students assumptions and force them to make a mental effort and to move away from spoon feeding. This involves forcing them to go beyond the shallow and immediate response into deeper thought. This is not something most will welcome. Safety is a more powerful driver than exploration to many. A nice maths blog by John Smith – Penny Drop Teaching makes a great point – Are we simply rewarding those who make the least mistakes or developing the best mathematicians? this applies to every subject.
I am a huge fan of the 3 Act Maths approach by Dan Meyer which I have blogged about before and supporting it with technology and have started developing the science of it.
The idea is that students are shown a video/demo of something and asked for what questions it makes them think of then an intuitive response, the students build their own problems then delve deeper into it. It makes them question their automatic response before leading them to the ‘reveal’ e.g. what the answer might be.
Is there any theory which supports 3 acts? To me this takes students into the realms of dual process theory and the work of Daniel Kahneman starting with system 1 and then forcing system 2 into action but using the students own motivation to do so.
In his book ‘Thinking Fast and Slow’ Nobel Prizewinner Daniel Kahneman splits the brain into 2 systems.
“System 1 operates automatically and quickly, with little or no effort and no sense of voluntary control”
“System 2 allocates attention to the effortful mental activities that demand it, including complex computations”
So system 1 is fast, intuitive and emotional, while System 2 is slower, more deliberative and logical. System 1 thinking is for example recognising a teacher or answering the question what does 2+2 equal, while an example of System 2 thinking is finding your way to a new classroom or what is 27 multiplied by 43.
When system 2 is in action, for example in trying to solve the 27 multiplied by 43 problem you may have to stop other things that we are doing (it wouldn’t be sensible to try and solve this when overtaking in a car for example) The harder you find maths , the bigger the load on your brain and you may enter the realms of cognitive overload if other things are competing for your attention. This is clear to any parent who tries to have an in depth conversation when looking after a toddler, it is next to impossible.
Whilst engaged in system 2 thinking our pupils will dilate (could this be a use for Google glasses – to analyse the level of our student’s thinking?) and our blood pressure and heart rate rise. It is a conscious action, heavy on resources; glucose consumption rises rapidly and we soon feel tired. Many people have a reluctance to use system 2 so System 1 is the one that usually deals with things.
Our sense of who we are is based on System 2, “the conscious, reasoning self that has beliefs, makes choices and decides what to think about and what to do”. But our self that is most apparent to others is System1 as it “effortlessly originates impressions and feelings that are the main sources of the explicit beliefs and deliberate choices of System 2”. System 2 is portrayed by Kahneman as the supporting actor who considers themselves to be the lead which is usually taken by System 1. If we used the slow System 2 all the time we would scarcely get things done. Consider the mental effort the first time you ever drove a car to being an experienced driver. But in order to learn something new we have to have System 2 working and this is where a skilful teacher comes in. We have to find a way of getting past the guards that are System 1 and a powerpoint or video designed to transmit information is unlikely to help you .
The average pause time for a teacher between asking a question and getting a response is too short to invoke System 2 so we tend to get an automatic System 1 response from those who already know the answer. This has very little purpose as it is unlikely to influence those who don’t know the answer and is simply a way of those who already know showing knowledge. An interesting alternative to this question- response , new question – response that Dylan William likens to playing table tennis with one student, reducing the rest to passive observers, is to involve all by employing a more basketball like Pose, Pause, Pounce, Bounce as outlined by @teachertoolkit.
Technology now has the potential to give teachers unparalleled insight into our student’s prior knowledge with the likes of Socrative and the promising looking Answerpad if used as part of an effective Assessment for Learning strategy so we can see their starting point. We can track student thinking with the likes of educreations, Explain Everything or iMovie. This means we are no longer simply presented with just an answer we can also track the students learning journey and give feedback along the way Showbie is particularly good for this. I’ve outlined a lesson using these here.
By teaching students to pass tests, we can equip them with simple, or even quite sophisticated Pavlovian System 1 responses that will get them a good grade. They can answer the questions because they have practiced many similar questions so know how to decode the exam paper. This strategy leaves them vulnerable to any slight change in the style of the exam question. We can be guilty of giving them fish, rather than teaching them how to fish due to the pressures of the current system that encourages risk aversion. Are we preparing our young people perfectly for a world that no longer exists, highly qualified, but poorly educated ?
To me the 3 part Maths or Science clearly uses System 1 and System 2 very effectively. Possibly most importantly it also gets our students to question whether their intuition gives them the best answer and encourages deeper thinking that will equip them with the challenges for life.
Of course the 3 acts are a supplement to other teaching methods and tools and they lead to improvement in performance as well as learning
At this point it may be useful to consider performance separate to learning:
It is possible to have improved performance without deep learning.
If you’re after rapid improvement (performance) then you make your teaching predictable, give students clear cues about the answers you’re looking for, and do a whole load of massed practice. If you watch that lesson it looks great! The teacher is happy, the students are happy and the observer can tick delightedly away at their clipboard. Come back and text them next week, next month, next year and the situation is a little more bleak. David Didau
Finally we can look at the culture of our classroom to promote thinking . There is evidence that focussing purely on performance and particularly comparing the performance of classmates leads to a reduction on thinking about the task and an increase in thinking about the outcome. In this great video Alfie Kohn argues in the video below passionately and (to my bias) compellingly for change. He says that in performance orientated cultures students choose the easy route not because they are lazy, but because they are rational. I will give you what you want with the least effort possible. Looking at the work of Carol Dweck we want our students to see their success or failure as something they have control over not – I succeeded because I am clever/was lucky/it was easy turns into at some point I failed because I am not clever/was unlucky/it was hard – something that makes them powerless to do anything about. A fuller and more eloquent review by Alex Quigley @huntingenglish is here.
So before you teach next please consider how you are going to challenge your students to really think and to engage System 2.
Answers to questions: 5 cents, 5 minutes and 47 days