Design

Several people have mentioned that white type on a black background is a bit of a mission to read.  I'm going to try a few new design ideas.  The current one is temporary - but should be easier to read.

Actually, this purple thing going on is giving me a headache.

Anxiety - why smart people crumple under pressure

Big toe - shoe - rub.

The other day I wrote a post about some of reasons smart people perform poorly.  We looked at the 'stereo-type effect' and in particular 'self threat' and 'group threat' and how smart people perform worse in maths tests when they know their scores will be made public and represent a group they associate with.  

The final point of the post was that the 'meaning' you place on your performance will determine part of your result, positive or negative. 

However, the way these things negatively impact you is through one mechanism -Anxiety.  Anxiety is your enemy.   

So what is anxiety, how does it impair performance and how do you stop it?

What is it?

Hard to define but essentially it is a physiological response to an anticipation of harm.  There are two things happening.  First, you sense potential harm.  This may be harm to your body, or harm to your reputation, self-identity or self-image.  Then the second part is that your body responds physically to prepare you for action.

How does it mess you up?

Your brains ability to think can be divided up into working memory and long term memory.  The working memory is used to accesses information from the long term memory, hold the information, move it around, and think about it.  Working memory has several parts including a specialized part for imaging and another for sound buffering and an episodic buffer.  The working memory is limited.  It can only do so much before it is running at full capacity (say the alphabet backwards while adding random numbers).  Anxiety erodes your working memory.  The more anxious you get, the more erosion occurs - Ultimately it reduces you to a state of pure reaction and zero planned strategic action.  You lose the ability to access information and use it to make decisions.

If you need to run away from a mugger - it is perfect - just let that body react.  If you need to win a game of cards - you are doomed.

What else?

 There are two types of anxiety.  Both reduce your mental resources dramatically.  It happens via two separate yet interrelated domains.  One through your affective domain (feelings) and through the cognitive domain (thinking).  Within the affective domain (usually associated with math anxiety) a person has an affective reaction to stimulus (emotional).  That is they 'feel' unpleasant feelings and subsequently incur an erosion of working memory (sometimes likened to a panic attack, but often mild).

Math anxiety erodes working memory which makes thinking difficult which leads to failure which leads to an increased focus on the unpleasant feelings and hey presto - they are a quivering mess. This is common for people who fear looking less smart than their managed self-image (losing status).  Ironic because it becomes a self-fulfilling prophecy.

The other aspect of anxiety is cognitive and is associated with test anxiety.  This causes people to think about the consequences of their failure.  They begin to focus on this, they engage in self-ruminating thoughts and subsequently pull precious resources from the task to thoughts of the consequences.  This is common in smart people doing high stakes testing.

The double whammy of feeling anxiety and thinking about what will happen if you fail - destroys people.

Lets mess with Larry

So let reduce Larry (a trainee teacher) to a quivering mess.  Here is how will we do it.

Get a classroom full of trainee teachers.  Tell them that they must be good at maths to teach children.  Lay it on think how poor teachers produce children who are bad at maths etc.  Don't let the teachers speak to each other.  Larry is not so good at maths so the last thing he wants is his colleagues to know this.  Larry is desperate to not be labeled bad at maths.  He is now thinking about his performance and wondering if he really is good or bad at maths (we have turned his attention onto himself).

Next the lecturer writes a maths problem on the board.  It is hard and Larry is not sure of the answer.  Lecturer says,"We'll start with an easy one.  This is a maths question that most 12 year olds will be able to work through.  I want one of you to come up the front and solve it".

There are the two things happening to Larry.  First his body temperature has risen, as has his heart rate, chemicals are being released in his brain that limit his working memory as they divert resources to reactive processes.  Second thing, Larry is thinking about what will happen if it is him that gets picked.  What will happen if they all find out he is no good at maths.  What will it feel like when he can't solve the problem with all those people watching him?  What new career will he get now he can't be a teacher?  How stupid and pathetic is he going to look?

The lecturer looks over the class and ... points to Larry.  "Larry, come and do this one, show us how you would solve this on the board".      
Someone else in the class says "Lucky you got the first easy one Larry, the next person will get the hard one".

Larry realises that he is about to be exposed.

Poor old Larry has two problems.  First his brain is preparing him for physical danger.  He has lost the ability to access information and use it to solve anything.  Second, what is left of his thinking ability is consumed with thoughts about what is going to happen.  If you haven't noticed, Larry has not even really thought about the problem on the board.  It could be 55 + 55 for all he knows.  But it doesn't matter because Larry gets to the front of the board and can't even think anything except how to get out of here and save some face.

 Later that night Larry sits in his room and looks at the same maths problem and solves it easily.

We turned Larry's brain around so that instead of focusing on the maths problem he focused on himself.

The truth is we can do this to anyone we want - no matter how confident they are.  We just need to find the right situation and stimuli.  Worse yet, the more it happens to you, the more it becomes an model , a pattern and an expectation, and remember anxiety begins with an expectation of harm.  If it happens twice, it'll happen three times.

The anxiety response is entirely predictable and therefore NO educator should be putting anyone in this position.

Next post - Beating anxiety

Most of the information on beating anxiety is rubbish written by people who have never felt it.  I'll give you the real secret in the next post.


Think about what happened to Larry and think about how you could interrupt the process.

Final note:  Bruce Banner turns into the Hulk when he senses danger.  Anxiety is a trigger - Yes in true scientific fashion Bruce's body interprets anxiety (and its precursors) as danger.  Who's brain would you rather have if you were playing chess, the Hulks, or Bruce Banners?

big toe - shoe - rub

Bearapocalypse final

A week ago I posted a numeracy problem in which a water tank needed to be filled by two people.  It was imperative that the tank be filled within two hours or less or the world would essentially end.  You can read the post here and have a go at the problem.

One person could fill the tank in three hours (Karl).  The second person could fill it in five hours (Larry).  The question was:  If they work together how long will it take them?

This is a TOUGH question.  But here are some tips.

1. If fractions freak you out just don't use them.  Turn them into decimals immediately by dividing the top number by the bottom on a calculator.  Easy.
2. If you want to keep fractions but hate adding them - just type the sum into into Google and you get your answer!  Yes, Google does add fractions.  Just type, 'one-third plus one-eighth'.  Cool huh.

Okay - the problem solved my way -  Think about how much of the water tank Karl and Larry will fill in one hour.

Here is how I approached it.

1.  In one hour how much of the tank does Karl fill?.  Answer one/third (or .333)
2.  In one hour how much of the tank does Larry fill?.  Answer one/fifth. (or .2)

So if these two chaps work together, then in one hour the tank has one/third plus one/fifth in it (or .333 + .2 = .533).

The answer in fraction language is eight-fifteenths or if you want to turn it into decimals = 0.533.

Okay, so in one hour Karl and Larry have it a little over half full.  So there you have it - if they can fill it above halfway in one hour then it is definitely full in two.  Don't over think it.  Will they be back in two hours? Yes.

If you want to be a genius you may want to work out exactly how many minutes it will take them to fill the tank.  Well, it took one hour (60 min) to fill eight-fifteenths.  So how long to fill up seven-fifteenths?

I guess we have to work out how many minutes each of those eighths took?  60 divided by 8 = 7.5.  So 7.5 minutes to fill one-fifteenth.  How many minutes to fill fifteen-fifteenths?  15 times 7.5 = 112.5 min.

Okay, clearly this is a tough one. But keep in mind - the future of the human race depended on it.  So when the apocalypse happens are we all going to look at each other and say 'Who's good at maths?'.

I know in every movie there is always that one geeky guy who can do the math - but what if the job falls to you?

Side projects...

As you know, as well as working to complete a PhD I also deliver workshops to educators across the country.  But I also have a few little side projects on the go. One in particular, is the development of a revolutionary type of resource designed to engage people of all ages in mathematics - so that anyone can taste the joy of maths - and come back for more.

Recently. I have tested the materials on the toughest most disengaged adult learners - And they loved it.  I have tested it on children of various ages and they loved it.  Last week, I ran another little test and used one of the resources in a workshop with tutors.  Again - they loved it.

I might be on to something here.  It does appear that your average person does enjoy maths if it is presented in certain ways.

Anyway, today I am off to Palmerston North.  I may try out another resource with this group and see how it goes down.  (Update - it went very well).

The paradigm of the resource is different from other maths resources I've seen or used.  Basically four key features dominate 1. Identity shift. 2. Fun, 3. Engagement, 4. Satisfaction.  Who you'da thunk it'd be so successful?

People like math.

Funny

So this clip just cracks me up.  A group of parents get their kids pretend to be various things or scenarios (in this case a maths class).  They record it and then act it out using the same recording.  What you get is how kids see the world, acted out by adults.

Why I like this clip is because I have actually seen many, many lessons go like this!  I kid you not.  As you watch, understand that this really happens between teachers and students.

Gotta love it.  Anyway enjoy.

Hat tip - Graeme Smith 
 

Why smart people perform poorly in some situations

One of my interests is understanding why smart people show impaired performance under certain conditions, particularly in maths or numeracy.

A quick example is when you sat your driving test.  The presence of the driving assessor and the fact that they were judging you impacted your driving.  The cool confident you went away for a while and was replaced by a bunny-hopping, sign missing, break slamming fool.  When you got back into the car by yourself, the cool confident driver returned!  Hopefully your inept self was still good enough to pass the test.

Below are a couple of really interesting lines of research that demonstrate how simply raising or changing the stakes impacts performance.  My point as we move through this is that the 'meaning' you place on your performance in any situation dramatically changes the nature of your results.

These are quite complicated and I'm suffering a cold - so bear with me.

Stereotype effect

Research shows that if people associate with a group that suffers from a negative stereotype then they will perform poorly in tasks in which their inclusion in the group is made salient.  For example, a generation or so ago, it was a stereotype in many countries that men were better than women at maths.  Today, we have a stereotype that Asians are better at math than most other ethnicities.

How might this be used to lower performance?  Lets look at one example and see if we can spot what is happening.  If you tell a group of Asian women that they stereo-typically struggle with the English language (a common stereotype), they will perform lower than a control group of Asian women in an immediate vocabulary test.  But, if you tell Asian women that they are stereo-typically good at maths, and then get them to do a maths test - they will score higher than a control group of Asian women who were not told.  This effect is not only found within ethnicity or gender studies (although they are the best IMHO) but also found within socioeconomic groups and class groups.

The question is why?  Why do people perform lower than they are really capable of?

Let's look at an experiment that demonstrates the effect.

To test our hypothesis we have four groups: A = women (individually anonymous); B = women (identifiable) , C = Men, D = control group of women

• Make it known to women in group A & B that women stereo-typically score lower than men in maths.
• Make the women identify themselves as women (they fill in a survey regarding being a woman)
• Tell them that their combined scores will be compared to a group of men.
• Group A are told that all the women's and men's scores will be averaged - no individual scores will be known
• Group B are told that scores will be individually compared to the men's.  Everyone will see your score.

Control group of women not told anything, just taking a maths test.

Group-threat - Group A

'Group-threat' is the idea that a group you identify with will look bad if you under-perform.  It is most often seen in gender studies with women but found in a wide variety of groups.    

In the scenario above we see the effect of group-threat.  The women in group A (even though they are individually anonymous) feel they are representing their entire gender.  Guess what - they perform lower than the control group.

The threat of being responsible for confirming a negative stereotype of a group to which they belong raises anxiety levels which lowers performance.

But not as much as the next concept - self-reputation threat.

Self-reputation threat - Group B

Group B - this time their individual results will be made public.  Yip, their name will be on their score (yuck). So not only would a low score confirm the negative stereotype of women as not as good as men, but also the score would be traced back to the individual.  So how would women perform under these conditions?  The answer - they performed significantly lower than the control group and worse than the 'group threat' (group A) group above.   

These results have been replicated across different contexts and groups including ethnicity, socioeconomic groups and gender.  Yes, men get hit just as much.

In short - both groups A and B performed lower in maths simply because their results were linked to confirming negative stereotypes.  Interesting huh?

Note:  The stereotype effect above is only one of MANY such phenomenon.  The research on anxiety (test and math) shows its effect is so extreme that it has been called a learning disability by many (more on anxiety in a later post).

Thoughts about level one and two tertiary sector numeracy testing

 If I tell a group of lower socioeconomic youth in a class that their maths scores are stereo-typically lower than another higher socioeconomic class and that their scores will be compared, and that they will be individually identified, their performance will drop significantly.  And guess what - I don't even have to tell them, I just have to make their group identity 'salient'.  It doesn't even have to be explicit.

Likewise, the other group will show a 'lift'.  I didn't mention it but a similar effect is found in the opposite direction.  Groups stereo-typically better at maths, will score higher if the individuals self identify with that group.  Eg, tell the men in the experiment above that they out perform women and that their scores will be compared to the women - and they will score even higher than if they were told nothing.

The good will score even higher - and the poor will score even lower.  Makes me think about the bootstrapping effect over time of the Assessment Tool.

We become what we think we are.

What this means for you

What stops you performing less well than you should is anxiety.  Anxiety is complex - it has an affective dimension and a cognitive dimension.  That means you feel it and think about it.  A double whammy, so to speak.

But the cause of this anxiety relates to what you believe your results 'mean'.  If I add meaning to your maths results - for example, that they mean you are 'less' than others, that you are part of a 'lesser' group or that the results may 'mean' you are wrong about your ability - then you will operate under anxiety and perform lower.
If you think failing to master chess at the first few games MEANS you are no good at chess you are vulnerable.  If you think (or thought) that being bad at board games MEANS you are not smart as others you are vulnerable.

We become what we think we are.  This is worrying because so many of us carry secret little doubts about ourselves.  Certain situations can pull on these doubts and mess with your head.  As educators, parents and friends, we have the power to help people frame themselves and set people up for success.

Remember, you are a miracle, you are super smart and you are going places!

More on this later.  If you want to read more about this check out:

Zhang, S., Schmader, T., & Hall, W.  (2013).  L'eggo my ego: Reducing the gender gap in math by unlinking the self from performance.  Self and Identity, 12, (4), 400-412.

How much money has the TEC invested in the literacy and numeracy infrastructure?

Graeme Smith, the talent behind ALEC, has written a post that I found very interesting.  There are many in the literacy and numeracy world that would like to roll back the infrastructure that has grown up around Learning Progressions in the tertiary sector.  And there is always the game of trying to predict what changes are going to occur in the sector in the short term.  If you are not too keen on the Learning Progressions the question is often one of two:

1. Is it time to embrace the Learning Progressions and get with the programme?
2. Do I keep the LPs at arms length until the TEC relaxes its' position on them?

Graeme's article made me think about the level of TEC's commitment to the infrastructure and whether number two above is an option.

You can follow Graemes' blog here.  But I'm going to post it here in its entirety here as well.

How much money has the TEC invested in the literacy and numeracy infrastructure…?

Posted on June 9, 2014

It’s a lot of money… I just changed my original title as I don’t have a good reference for the exact amount. Let’s just say it might have 9 figures.

That’s how invested the Tertiary Education Commission (TEC) is in the infrastructure that we now have for literacy and numeracy in New Zealand. That infrastructure now includes:

• the Learning Progressions for Adult Literacy and Adult Numeracy
• the Literacy and Numeracy for Adults Assessment Tool
• Pathways Awarua

Keep in mind the following:

• the TEC’s Assessment Tool is a massively scalable automated assessment machine generating massive amounts of data on learners literacy and numeracy abilities.
• And Pathways Awarua, is a massively scalable and automated delivery platform.

Software is going to eat education. And it’s going to do that mainly via massively scalable and mostly automated processes that will get increasingly cheap to run.

But… we’re still going to need skilled human tutors (middle management is another story). At least for another 20 years.

So I would also argue that this infrastructure also means having specific adult literacy and numeracy education qualifications including for trades and vocational trainers, as well as for specialists. This includes:

• NCALNE (Voc)
• NCALNE (Ed)
• DipALNE

And that $120 million dollar investment probably means these things are not going to go away any time soon.

So if you’re still wondering about whether you should have a go at trying to get your head around the Learning Progressions, or whether there is any value in the Assessment Tool, or whether you should upskill yourself or your staff in these areas then it’s time to stop wondering.

What action will you take…?