A response to the recent NCCA discussion document on Applied Maths

The NCCA have produced a discussion document entitled Draft Background Paper and Brief for the Review of Applied Mathematics. Link

ncca discussion documentThe syllabus hasn’t been reviewed since it came into existence 40 years ago so a review seems reasonable.

Two key messages feature in the report

1. The exam is so predictable in nature that it’s just regurgitation of material learnt off in class.

2. The subject needs to be removed from the curriculum and replaced with one that is more relevant.

I want to respond to the first point.
From the document:
[Students’] experience of learning in Applied Mathematics is often reduced to exam preparation with the examination regarded as predictable.
Supporting evidence:
“Almost every question which appeared in recent years was similar to at least one other question on an older paper – the natural conclusion being that if you cover all the old papers along with the recent ones you really should see very little new material in the leaving cert exam.”
The Physics Teacher website

Let’s leave aside the dismal referencing system (the quote wasn’t taken from my website – it’s from an old blog post)

As I mention in the post, I had been teaching Applied Maths for a few years using a textbook when I came across some old exam papers left by my predecessor in the school. I spotted that there was a resemblance between these and more recent questions.

It certainly did change how I teach the subject in that when looking for questions I now go to past exam questions rather than a textbook.

I wanted to pass this message on to other teachers of the subject, many of whom teach Applied Maths in complete isolation.
I have now incorporated all 40 years worth of questions from past papers from both higher and ordinary level into my class notes such that there is now an excellent scaffolding of the work from a gentle introduction using ordinary level questions right up to the most difficult of the higher level questions.

I ‘sell’ this notion that I have ‘cracked’ the system to the students. It helps create the sense that we are a team working against the system. It’s a fun idea and quite simpIy I will try try anything if it helps to make the subject easier to teach and easier to learn.

I penned that particular post deliberately to increase the uptake of students choosing the subject and to let other teachers know of the resource itself (complemented by a bank of solutions to all questions) which are freely available on my website also.

But now let’s add some context:
We’re talking about 40 years worth of questions, at higher and ordinary level, most or which are sub-divided into a part (a) and a part (b) which are completely independent of each other.
If we get through half the questions on any given topic in class we’re doing well.

Secondly, while there is a pattern to many of the questions, there is often a twist at the end of the question and there is an infinite number of ‘twists’ that can be asked, so learning off one won’t necessarily help you with the next one.

So it’s a ruse. And anyone who thinks otherwise has never taught the subject. Using the quote above out of context will create a very misleading impression of how I view Applied Maths. Doing questions from past paper can help significantly in your study but you simply cannot get an A just by doing past papers, no matter how many you do.
Anyone who thinks otherwise does not teach Applied Maths.

Now let’s compare this to Leaving Cert Physics.
Physics (and as far as I can tell, Chemistry) are subjects where you can get an A grade by learning everything off by heart. Biology even more so. There is almost no problem-solving in these subjects and there is quite a lot of choice on the paper so if you don’t like a question that requires you to think, you can always skip it and pick a different question instead.

This is not the case in Applied Maths. Thinking/ problem-solving is the name of the game and you simply cannot get an A grade by learning past questions off by heart.

I go to great pains to warn students of this from the first week in September (and even before then when I am giving a few taster classes in Transition Year). In particular I am conscious of the student who is interested in Science, is a great worker and wants to do very well in all leaving cert subjects. I tell them that hard work will most likely get them the A grade in Physics, but not in Applied Maths. To get an A in Applied Maths you need to be good at solving problems (see extract from TY booklet below).

Let’s also consider that you only need to cover past-paper questions in physics for the past twelve years (the course was introduced in 2002) to be practically guaranteed a replica question next June. In Applied Maths you have to go back forty years and the most you’re likely to see is a question similar in context, but which may well have a completely different ending, one which will cost you your A-grade if you can’t solve it.

I was aware at the time that the post caused a little stir, but was happy to leave it as it was because it helped stoke a debate which we very much need in this country about the purpose of education.

If the author of this report had taken the time and effort to see what I really thought he would have gone to thephysicsteaacher.ie website itself where he would have read the following advice which I give to interested TY students (the link to this document is on the homepage).

Who shouldn’t study Applied Maths?
This subject doesn’t suit students who just like learning things off by heart.
In fact the questions are designed to catch out those very students and whether that is fair or not is a moot point – you are being warned about it now so if you don’t like it you know what to do. You cannot come out of an Applied Maths exam and say to your teacher ‘we never did that question before –you never covered it with us in class’. It is my job to ‘train’ you to tackle problems which you haven’t come across before.

So Applied Maths suits people who like solving puzzles (we like to make it sound more impressive so we call it ‘problem solving’). This means being able to think for yourself, and because almost all of your secondary-school education encourages you to ‘learn the right answer off by heart’ it can make a lot of students uncomfortable. The ability to problem-solve is however a very important skill and is highly-valued by many employers. It is one of the reasons why you often see politicians and business people on the news saying that the country needs more scientists and engineers.
Link

The NCCA report is scathing in its dismissal of teachers’ claims that we are teaching problem-solving skills.
From the document:
Leaving Certificate Applied Mathematics is also promoted as a subject that enhances students’ problem solving skills. However, with its emphasis on content as opposed to the development of skills and mathematical reasoning students’ [sic] are not problem solving per se but rather, learning to solve particular problem types in mathematical physics.

Where to start?
My mantra when telling students about this subject is as follows:

“Applied Maths is the one subject which teaches you what to do when you don’t know what to do.”

In other words, rather than put down your pen because you don’t know how to proceed, we teach you to look at all available information and choose the next step as if your life depended on it. You may not be 100% confident that it is the correct step, but chances are it will lead to an opening which contains a signpost which will lead you to your destination.
Yes we will instil in you an appreciation of knowing the procedure which you will need to follow for each topic, but this will only get you so far and is not to be confused with a solution which you learn off by heart like an essay you buy from The Institute. You will need to think for yourself.
Now I regard this as teaching problem-solving skills. This report thinks otherwise.

Of course there’s a problem in transferring skills learnt in one context into another area. But that’s not unique to Applied Maths. That applies everywhere in education and is a problem we have yet to find a solution to (the problem is compounded by our current mode(s) of assessment). But we get closer to real problem solving in Applied Maths than we do in any other leaving cert science subject. So if you want to develop higher order thinking it would seem strange that you choose Applied Maths as the one to criticise.

Again I refer you to just about every other subject on the curriculum in both the Junior Cert and Leaving Cert curriculums. Find me another subject that demands a similar level of analysing rather than parroting information (the new Project Maths course may indeed be an exception, but it’s still early days with that one).

I can’t for the life of me figure out who would have been responsible for compiling this report.
The assumptions made about the subject are so ridiculous that I can’t believe it was written by a teacher who ever taught the subject. But why would the NCCA ask somebody who never taught the subject to produce a report on it?
No matter what way I look at it, it doesn’t make sense.

But then I have often found the workings of the NCCA to be a mystery.

Coming back to the point made above that
“with its emphasis on content as opposed to the development of skills and mathematical reasoning students’ [sic] are not problem solving per se but rather, learning to solve particular problem types in mathematical physics.”
The author is obviously referring to the students’ lack of ability to transfer problem-solving skills. For some reason he chooses to bolster his argument with the following:
Chief examiner reports on state examinations in mathematics over a number of years have consistently pointed to the over-reliance by candidates on rote-learned procedures and the lack of deeper understanding of basic mathematics concepts. There is evidence that students are not able to apply and transfer mathematical knowledge and skills, except in the most practised way and in familiar contexts.

That’s all very well, but this is from a Chief Examiner’s report on Maths, not Applied Maths. There have been four Chief Examiner reports in Applied Maths over the years (2000, 2004, 2007 and 2012) and nowhere in any of these does it refer to a lack of problem-solving skills or an inability to ‘apply and transfer mathematical knowledge and skills’.
To imply otherwise is mischievous at the very least.

For what it’s worth, these are some of the comments/ recommendations made in those reports over the years:

2012
The overall standard of answering was quite good, particularly in questions [. . . ] and it was similar to previous years’ standards.
“Candidates appeared to understand each question and there was little or no confusion as to what was required. “

2007
“The regular practice of examples is an essential part of preparation for this examination.”

2004
“Practising problems regularly is an essential part of preparation for this examination.”

2000
“Practising problems regularly is an essential part of preparation for this examination.”

2000
“Overall, candidates’ answering was satisfactory. In general, candidates showed a good level of ability to extract from the text of the given problems the mathematical equations necessary to lead to successful solutions.”

I regard that last comment as a vindication of our belief that we teach problem-solving. The fact that students leave the subject not being completely proficient at transferring mathematical knowledge and skills from one subject area to another may have less to do with it being redundant as a subject and more to do with the fact that this mode of learning is at odds with just about every other subject in the school. Having a go at Applied Maths in this respect is a cheap shot.
Think that’s a bit harsh? Well so’s this (taken from the Introduction):

With its emphasis on content and in the absence of any aim or rationale, it is difficult to ascertain what group of students’ needs the syllabus aims to meet.

Eric Mazur is a professor of Physics and Applied Physics in Harvard University.
He knows the difference between ‘school’ problem-solving and ‘real’ problem solving better than almost anyone. But to go from the former to the latter he didn’t so much change the subject material as how he taught it. The problem in our schools today is also not what we teach – it’s how we teach it. Replacing Applied Maths with a different subject would be a step backwards, not forwards.

“Even now, if I give my students a problem on an exam that they have not seen before, there will be complaints: ‘We’ve never done a problem of this kind.’ I tell them, ‘If you had done a problem of this kind, then by definition, this would not be a problem.’ We have to train people to tackle situations they have not encountered before. Most instructors avoid this like the plague, because the students dislike it. Even at Harvard, we tend to keep students in their comfort zone. The first step in developing those skills is stepping into unknown territory.”
Link

Recent exam papers
In the past two years the leaving cert exam simply went too far and the test ended up being too difficult for the average student. Applied Maths is a numbers game in more ways than one and we need to balance noble aspirations against the possibility of alienating potential students (who have little if any experience of thinking for themselves and may well be fearful of the prospect) from coming in the door in the first place.
And exam papers need to bear this in mind.

Already the subject is seen as ‘elitist’ by many and I suppose I have the option of using that to just attract the top students.
I choose not to.
In sixth year I have 20 students, in fifth year I have 26.

WIN_20141117_091356From the word go I make them familiar with my mantra: “Applied Maths teaches you what to do when you don’t know what to do”.

To emphasise this idea in fourth year I give students the following challenge: using only 30 paper straws and 1 metre of tape, build a free-standing tower as tall as possible such that it can hold up a marble for at least 5 seconds.
And that’s it. No other rules. There are limited resources, limited time and not necessarily any one best way. They have a ball. And then I tell them that Applied Maths is the mathematical equivalent of this.

IMG_6498This needs to be a fully thought-out discussion, listening to all interested parties, not a hatchet-job.

It may well be the case that we need other subjects on the curriculum; it’s hard to argue against the inclusion of proposed options such as computer programming, business mathematics and game theory. I’m just not sure that Applied Maths is the subject which needs to make way for this.

But whatever decision is made, let it be for the right reasons, and let that decision be made on the basis of evidence, not ignorance.

While I am a member of the Irish Applied Maths Teachers’ Association (IAMTA), all views are my own and are not necessarily representative of anyone else or any organisation.
Tomorrow the IAMTA hold their annual conference and the discussion document is on the agenda on the day.
iamta website

Hope to see some of you there.

A quick reminder of how to study effectively: advice to parents

I was putting this together for parents and thought I might as well stick it up here in the hope that it may be useful to others.

With Christmas exams just around the corner for most students, it’s time to issue a reminder that when it comes to studying, most of us do not spend our time effectively.
I am putting together a document listing the key aspects of effective study (and just as importantly, what doesn’t work) and will forward it on when complete.

In the meantime I just want to stress what doesn’t work: rewriting notes of any description should not be confused with learning; it may be first step, but then you need to follow up with a technique that does work.
I say this because most of the homework we set simply requires students to find the relevant information from their textbook and then write this information into their copy.
And then we put a tick beside their correct answer, implying that this has been a worthwhile exercise.
It has not.
Information has merely been copied from one page to another, bypassing (in the main) the brain en route.
This is the single greatest waste of time that we as teachers tacitly encourage.
The funny thing is, if a student is found copying another student’s work they get in trouble, yet in effect this is all they are doing when using the textbook anyway – so why do we bother? Much more effective would be for us to give students much fewer questions, but to have to learn the information rather than just write it down.

The single greatest way to learn is by testing yourself.
There are a myriad number of different ways this can be achieved, but chances are that if you’re not testing yourself then you’re not engaged in committing the information to long-term memory.

Not all school-work is about memorisation; a lot of it is about learning new skills, and how to do that effectively depends on the skill, but the bottom line is still the same; if you’re not testing yourself then you’re not likely to remember it.

Secondly, a student has no business studying for more than about 20 minutes at a go. After this they need to take a short break.
At the beginning of the session they need to clearly lay out what they hope to accomplish during that session.
And at the end of that 20 minutes they need to review their work and determine whether or not they have learnt anything during that time.
How do they do this? Test themselves.

If you are allowed to be part of this process, you don’t need to be an expert in the subject area. Just discuss with the student what the objective for the next 20 minutes is, and then help with testing the student at the end.

The student then gets a short break to check de facebuks or whatever, then gets back to work (all distractions once again removed).

Simples.

Much more on what does (and doesn’t) constitute effective study is to be found on my betterteaching.ie site:

http://www.betterteaching.ie/studentlearning.html

2014 Applied Maths paper: ‘disgraceful’ or simply ‘testing’?

Update: A number of students have taken the time to write a considered responses in the ‘Comments’ section below, so please take the time to read it to get a student’s perspective.

You might also want to look at the relevant page on the boards.ie site where there is an ongoing debate about the fairness of the exam.

The leaving cert Applied Maths syllabus is just one page long. For each topic it’s not at all clear how to prepare students properly other than by looking at past questions. Therefore when a paper comes out that varies considerably from the usual format, it’s not surprising that students end up struggling to deal with it.

This is exactly what happened in June 2013. And again in June 2014.

But maybe Applied Maths isn’t meant to be a subject where students rely on past papers as a guide. Perhaps it should an ‘anything is fair game to appear on the paper’ approach. If that’s the case the only people it will suit will be the elite students. In which case it completely goes against the DES promotion of STEM subjects in recent years.

The real killer punch here is that this is the second year in a row where the Exams Commission has produced a nasty paper. Once is (just about) understandable; twice is a disgrace.

Giving feedback on these papers is difficult.
First impressions can be quite deceptive; it’s only when you sit down to do out the questions that you get a feel for their true level of difficulty. It doesn’t help that Applied Maths is the last exam on the Leaving Cert and many teachers will no longer be in the school to meet the students in person to get immediate feedback. I personally didn’t realise how bad last year’s paper was until I gave it out as revision to this year’s sixth years after Christmas. It was a bit late then to make any complaints. I’m not going to make the same mistake twice.
Apparently there is a new person setting the paper and perhaps he wishes to ‘put his own stamp’ on the paper. That would be understandable, but if only if it was done very gradually. The change in the Applied Maths paper over the past two years has been anything but gradual.

It is not outside the bounds of possibility that one person has the power to kill this subject completely. The numbers taking the subject have always been quite low; many teachers are teaching it outside normal school hours to no more than two or three students. Others who are teaching it in a school timetable have perhaps ten students and while a school could allow for this ‘luxury’ in the past, the insidious increase in the pupil-teacher ratio over the last few years has resulted in schools being forced to withdraw the subject from the normal timetable.
My own numbers are normally between ten and fifteen. In the last couple of years I have made a big effort to promote the subject including running ‘taster classes’ during lunchtime and coming in to their normal maths classes. This year 24 students have signed up to take the subject in fifth year. I’m now going to speak to all of them in the first week and ask them to think very carefully about going ahead with the subject. From a personal point of view it’s nice to say that I have a full class of students, but I’m not going to play with their futures just to massage my ego. In the past I have told interested students that they don’t need to be a genius at Maths to do Applied Maths; I’m now going to have to roll back on that one also.

Over the past two years the paper has been referred to as ‘challenging for the brighter students’. This is surely a euphemism. If the top students found it difficult then the C/B students would find it nothing short of a disaster. And as a colleague reminded me recently, when reviewing these papers there’s no point looking at it from the perspective of the A student – chances are they’ll still come out with an A regardless. But for the average student the consequences are likely to be much worse. For example two of my students (one a C student, the other a B student) simply gave up half way through. It was their seventh subject and they realised that it was going to end up as their worst result by a long shot. I could never condone a student leaving an exam early, and certainly not the Leaving Cert exam, but these are both conscientious students and I understand completely their frustration. I have contact details for each student and their parents and have sent them all an email apologising for the paper. While I didn’t set the paper, and nobody would ever think of blaming me, I do somehow feel responsible; should I have seen this coming? Should I have warned them in advance? Should I have discussed worse-case scenario with them? I certainly will do all this next year – it’s just unfortunate that it will have been a year too late for this year’s cohort.

I will also need to speak to my sixth years at the beginning of the year. Many of them do eight subjects in fifth year and drop one at the beginning of sixth year. I’d love to tell them that this year’s exam was ridiculously difficult and that the Exam Commission would never make the mistake of doing this twice. The fact of course is that they just have done it twice. And it has coincided with a new guy setting the paper. And there’s no indication that it will be any different next year. And then I’ll get them to review the evidence for themselves. At this stage we would have 5 questions covered to Leaving Cert Higher Level standard. The students simply need to look at the questions over the past ten years and see how the questions in 2013 and 2014 compare. I may be wrong, but my guess is that it won’t be pretty.
Again, it would be very dishonest to try and keep them in my class just to play the numbers game. I’ve no doubt I’ll lose some of them as a result. I can only hope that the number of students who jump ship won’t be too great.

A few years ago we set up a discussion forum to help the many Applied Maths teachers who were working in almost complete isolation.
These are comments from three of those teachers (included with their permission):

Luckily I didn’t have a class doing the Applied Maths exam this year but this paper was an awful advertisement for students to do such a specialist subject. How many students would have got one full question correct or would have thought they got one correct?. Could the answers have been more uninspiring?

It was my first year teaching a highly motivated student applied maths in one year (repeat lc student). A massive effort was put in to preparing for the exam and my student is very diligent and hardworking. How is it then that she can get no reward when faced with a paper like that? In my opinion I thought it was a disgrace and my student came out visibly upset at the thought that her work throughout the year has gone to waste. Whilst the applied maths book is great it has no resemblance to 70 per cent of the questions asked in the 2014 paper. I’m raging to say the least.

I agree fully with the comments below. This was my first applied maths exam class and what a baptism of fire! I am very disappointed with the paper and my students were very upset with it. This negative reaction will filter through and our numbers will be adversely affected by this paper.

This was the report from The Irish Times:

Unfortunately for applied maths students, who were also sitting a morning paper, they were presented with a real challenge. “Strong students were really tested,” said Hilary Dorgan of the Institute of Education. “Students expecting a C grade may have left the exam thinking they had done very badly.”
The exam required a great deal of knowledge, aptitude, calmness and an ability to get through large amounts of data, according to Dorgan. The length of the paper may not have given students a chance to think about how to approach questions.

I don’t know Hilary Dorgan but his comments repeat what I alluded to earlier; if the strong students were really tested, how must the C grade students feel?

In contrast, this was the report in The Irish Examiner:

[The] subject spokesperson for the Association of Secondary Teachers Ireland (ASTI), said the higher level exam had some new features but the style and content were all welcome, with the opening question on linear motion featuring no underlying problems.

He said students might have been unnerved by the appearance of the more challenging elements in the first, rather than the second parts of questions on projectiles, particle dynamics and differential equations.

He said a question on collisions was set out in a way not seen before but students should have progressed well on it, and most should have been familiar with issues in a relative velocity question that looked very long at first.

I don’t know the ASTI spokesman either but it’s not likely that we’re going  to meet up anytime soon; we appear to inhabit different planets. Either that or he was guilty of the same offense as me – a quick browse through the paper giving the impression that it wasn’t too bad, whereas a more detailed analyses would reveal that it was anything but.

 

Due an upgrade? Speak to the ‘loyalty team’

This is a copy of my conversation this afternoon. Think I’ll be looking for the ‘loyalty team’ from now on.

021

022028

024

025

026

027Update
That was on the Wednesday.
On Friday I went to collect said iPhone.
The conversation went something like this:

Saleswoman: Sorry, but we have no record here of any of that. We can only offer you the €35 contract and it will still cost you €160
Me: But I just had the conversation two days ago and they assured me that they would update my contract details accordingly.
Saleswoman: I’m sorry, they mustn’t have updated your account yet – perhaps if you call back in a few days.
Me: Do you have the doubleyadoubleyadoubleya system on your computer?
Saleswoman: Excuse me?
Me: Would you mind opening up thinkforyourself.ie and just browsing through the last post there?
Saleswoman: Pause
Saleswoman: Just bear with me one minute please while I make a phonecall

Act Two

Saleswoman: It seems we were able to confirm your updated contracted. And we can now offer you the phone for €69 instead of €119, on an 18 month contract instead of the 24 month contract, and still keep your €20 a month price plan.
Me: Seriously?
Saleswoman: Seriously.
Pause.
Saleswoman: Just enter your pin there. Would you like to take out insurance with that?
Me: Most definitely not

You’ve messed up one of your exams. What happens now?

You’ve sat the exam. You’ve messed it up.
What happens next?

Contrary to what you feel at the time, messing up in one or two questions isn’t going to make much, if any, difference to your overall set of results. How you respond to the setback will however say a lot about your approach to overcoming adversity, not just now but in life in general.

What you’ve got to remember is that almost nobody is going to excel in every exam. So your ‘competition’ is the other students (the fact that we can use the words competition and education in the same context is an absolutely terrible indictment on what we do, but for now it is what it is). And they’re going to make mistakes too.

If you allow yourself to dwell on mistakes then it is going to adversely affect your ability to concentrate for later exams. You’ve simply got to put it behind you.
I like to use sporting analogies.
If you’re a footballer and you miss a penalty in a crucial game then you want nothing more than for the ground to open up and swallow you.
But that’s not an option.

So you pick yourself up, hold your head up high and get on with the game – no matter how difficult that seems at the time.

You see nobody goes a whole match without making mistakes – it’s how you respond that determines whether or not you are a success.

So try to avoid the post-mortems, particularly if you’re not an optimist to begin with.

For what it’s worth, this also applies on a large scale. Reading about the anniversary of the Normandy Landings, a comment from one of the veterans resonated with me. In war, the side that wins is usually the side that makes the fewer mistakes.
So don’t compound one by making another.

Welcome to life.

 

 

Why do we remove Wonder from Science Education?

If it’s possible to dedicate blogposts to individuals then I choose to dedicate this to my aunt; Sr Cathy. Like many religious folk I know, her passion for Science may well surpass her passion for her religion. Or maybe she’s just passionate about everything. Either way, I’m looking forward to meeting up with her over the Easter break as part of a big extended family celebration.

Wonder is a theme we return to again in again in this blog. More specifically the theme is one of frustration that we have deliberately removed all reference in our science textbooks and syllabi to concepts that evoke a sense of wonder. And it doesn’t help that it seems to bother so few other people. Which is why every time I come across somebody else expressing the same frustration I move to wrap the up in cotton wool and store in away in s0 that I can return to it anytime I need reassurance that it’s not just me. And where better to store it than here?

Students today are often immersed in an environment where what they learn is subjects that have truth and beauty embedded in them but the way they’re taught is compartmentalised and it’s drawn down to the point where the truth and beauty are not always evident.
It’s almost like that old recipe for chicken soup where you boil the chicken until the flavour is just . . . gone.

The speaker, David Bolinsky, is famous for having created an incredible animation on the private life of cells. I have watched that video many, many times (it’s a beauty in it’s own right) but it was only when I watched its Bolinsky talk about it on TED that I zoned in on his quote above.

I devour popular science, finding its history and its wonder a constant delight. . . . It is a mystery how so many science teachers can be so bad at their jobs that most children of my acquaintance cannot wait to get shot of the subject. I am tempted to conclude that maths and science teachers want only clones of themselves, like monks in a Roman Catholic seminary.

That was from Simon Jenkins in the Guardian

We are deprived by our stupid schooling system of most of the wonders of the world, of the skills and knowledge required to navigate it, above all of the ability to understand each other. Our narrow, antiquated education is forcing us apart like the characters in a Francis Bacon painting, each locked in our boxes, unable to communicate.

That was courtesy of well known columnist George Monbiot

We educators take this incredibly exotic jungle of knowledge called Science and distil it again and again until all the wonder has been removed! We are left with nothing but a heap of dry shavings. We then pour this drivel into our syllabus and textbooks and make our students learn it off by heart so that it can all get vomited back up come exam time.
And then we wonder why so many young people don’t like science.

That one’s mine.

It’s really such a shame that the wonder of Science only seems to be spoken about by artists, poets and writers. Why do scientists (and science teachers, and in particular those who are responsible for drafting the science syllabi) hide from it so much?

Anyway, the reason for this particular post is that it’s time to add the opinion of the author of what is for me the greatest book ever written in the Popular Science genre; Bill Bryson, author of A Short History of Nearly Everything.
I’ll paste in the short quote first, but to understand the context it deserves to be read in its entirety so I’ll follow with that (and anyway, reading Bryson could hardly be termed a chore).

It was as if he [a science textbook author] wanted to keep the good stuff secret by making all of it soberly unfathomable. As the years passed, I began to suspect that this was not altogether a private impulse. There seemed to be a mystifying universal conspiracy among textbook authors to make certain the material they dealt with never strayed too near the realm of the mildly interesting and was always at least a long-distance phone call from the frankly interesting.

Here is the full context:

My own starting point, for what it is worth, was a school science book that I had when I was in fourth or fifth grade. The book was a standard-issue 1950s schoolbook – battered, unloved, grimly hefty – but near the front it had an illustration that just captivated me: a cutaway diagram showing the Earth’s interior as it would look if you cut into the planet with a large knife and carefully withdrew a wedge representing about a quarter of its bulk.

It’s hard to believe that there was ever a time when I had not seen such an illustration before, but evidently I had not for I clearly remember being transfixed. I suspect, in  honesty, my initial interest was based on a private image of streams of unsuspecting eastbound motorists in the American plains states plunging over the edge of a sudden four-thousand-mile-high cliff running between Central America and the North Pole, but gradually my attention did turn in a more scholarly manner to the scientific import of the drawing and the realization that the Earth consisted of discrete layers, ending in the centre with a glowing sphere of iron and nickel, which was as hot as the surface of the Sun, according to the caption, and I remember thinking with real wonder: ‘How do they know that?’
I didn’t doubt the correctness of the information for an instant – I still tend to trust the pronouncements of scientists in the way I trust those of surgeons, plumbers, and other possessors of arcane and ¬ privileged information – but I couldn’t for the life of me conceive how any human mind could work out what spaces thousands of miles below us, that no eye had ever seen and no X-ray could penetrate, could look like and be made of. To me that was just a ¬ miracle. That has been my position with science ever since.

Excited, I took the book home that night and opened it before ¬ dinner – an action that I expect prompted my mother to feel my forehead and ask if I was all right – and, starting with the first page, I read.

And here’s the thing. It wasn’t exciting at all. It wasn’t actually altogether comprehensible. Above all, it didn’t answer any of the questions that the illustration stirred up in a normal enquiring mind: How did we end up with a Sun in the ¬ middle of our planet and how do they know how hot it is? And if it is burning away down there, why isn’t the ground under our feet hot to the touch? And why isn’t the rest of the interior melting – or is it? And when the core at last burns itself out, will some of the Earth slump into the void, leaving a giant sinkhole on the surface? And how do you know this? How did you figure it out?
But the author was strangely silent on such details – indeed, silent on everything but anticlines, synclines, axial faults and the like. It was as if he wanted to keep the good stuff secret by making all of it soberly unfathomable. As the years passed, I began to suspect that this was not altogether a private impulse. There seemed to be a mystifying – universal conspiracy among textbook authors to make certain the material they dealt with never strayed too near the realm of the mildly interesting and was always at least a long-distance phone call from the frankly interesting.

I now know that there is a happy abundance of science writers who pen the most lucid and thrilling prose – Timothy Ferris, Richard Fortey and Tim Flannery are three that jump out from a single station of the alphabet (and that’s not even to mention the late but godlike Richard Feynman) – but, sadly, none of them wrote any textbook I ever used. All mine were written by men (it was always men) who held the interesting notion that everything became clear when expressed as a formula and the amusingly deluded belief that the  children of America would appreciate having chapters end with a  section of questions they could mull over in their own time. So I grew up convinced that science was supremely dull, but suspecting that it needn’t be, and not really thinking about it at all if I could help it. This, too, became my position for a long time.

 

Why should a teacher care about Mindsets?

This post acts as an introduction to the webpage betterteaching.ie/mindsets and is also the first link on that page.

Why will this post help to make me be a better teacher in my classroom?
Students of low academic ability often have a low opinion of themselves and believe that they will remain academically weak no matter how hard they try. This then becomes a self-fulfilling prophecy. To counter this, students need to develop a Growth rather than a Fixed Mindset. But it is important for students of all abilities. Developing a Growth Mindset is only likely to happen if teachers are aware of the issue and are prepared to work to encourage change.

Nobody rises to low expectations
Calvin Lloyd

One of the more generous things we can do for another person: believe in their capacity to change.
@alaindebotton

Teachers’ beliefs and commitments are the greatest influence on student achievement over which we can have some control.
John Hattie

Recent scientific evidence demonstrates both the incredible potential of the brain to grow and change and the powerful impact of growth mindset messages upon students’ attainment. Schooling practices, however, particularly in England, are based upon notions of fixed ability thinking which limits students’ attainment and increases inequality.
Link

 

What is a Fixed Mindset?
People with a Fixed Mindset tend to believe that intelligence, personality and character are all carved in stone; potential is determined at birth.

What is a Growth Mindset?
People (including students and teachers) who have a Growth Mindset tend to believe that intelligence, personality and character can be developed and that a person’s true potential is unknown and unknowable.
Those with a Fixed Mindset tend to allow failure (or success) to dictate who they are, while those with a Growth Mindset tend to see setbacks as opportunities to grow and improve themselves. These people fully appreciate that to reach their potential takes practice and perseverance.
We have a choice as to which view we adopt for ourselves and it’s never too late to change.

As teachers we are constantly communicating messages to students about their ability and learning, whether we realise it or not. If we (consciously or subconsciously) subscribe to the Fixed Mindset view then we are imparting a message to our students that they are limited in what they can achieve and how much they can improve. If however we believe in a Growth Mindset we are much more likely to push our students and they in turn may be more likely to respond positively.

Put simply, if you focus on praising the student for an impressive result rather than instead praising the effort put in, you are – bizarre though it may seem – encouraging a Fixed Mindset. And that’s not good.

 

How to go from a Fixed to a Growth Mindset
There is a lot of online information on Fixed versus Growth mindsets but not so much on how to go from one to the other. The following pointers are worth bearing in mind if you do want to go down this road:

1. A Growth Mindset is not something you can develop overnight; it is an attitude you cultivate over an extended period of time.

2. The first step in changing is to recognise that you have a fixed mindset

3. You then need to accept that it is possible to change; you do have a choice

4. Finally, ask yourself how would someone with a growth mindset respond to the challenge at hand.

Much of the research on Mindset Theory comes from Carol Dweck; here is her advice on how a whole school approach might work

First, the students learn about the brain and all the wonderful things it does. How it’s involved in everything they do and everything they care about. Then they learn that they can grow their brains. Every time they stretch out of their comfort zone, do hard things, stick to hard things, their brains form stronger and stronger connections and over time their abilities can grow. And then we show them how they can apply it to their schoolwork.
Link

Implications for STEM subjects
The Fixed Mindset view seems to be more of a challenge to girls than boys. It’s not that girls necessarily subscribe to it more than boys; but boys with a Fixed Mindset are more likely to assume that they are naturally good at these subjects while girls with a Fixed Mindset are more likely to assume that they’re not. The end result is that girls are more likely to avoid these subjects when it comes time to making a choice. I wonder if all those organisations who want to promote girls doing STEM subjects are aware of this, and if not how would it shape their programs?

Implications for Teachers as professionals
This post focuses on recognising Fixed or Growth Mindsets in our students, and encouraging them to go from one to the other.
But what about if we have a Fixed Mindset in relation to our own teaching ability? How could we recognise it, what consequences might it have and how could we change?
For another day perhaps, but if you’re interested in finding our more about it now I suggest you read some of the related blogposts on the Mindsets page of betterteaching.ie

Alternatively check out this YouTube link to a keynote lecture given by Carol Dweck in 2012. It’s 46 minutes long but it may just change how you interact with your students from now on. Unless, of course, you subscribe to a Fixed Mindset in relation to your own teaching. But if that was the case you probably wouldn’t be reading this in the first place.

Posts related to this are
Fail Better
Praise the effort, not the student (still in draft form)

Finally, below is a link to a Word document I put together to help students identify what mindset they subscribe to. It may or may not be fit for purpose, but if nothing else it will hopefully help to raise awareness of the issue with the students themselves.
Link