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…?

Teacher lust... Not what you think.

I came home last night at about 9:00, to find the house quiet and dark.  Now I have four sons, so this is strange.  Was it an ambush?  I made my presence known by knocking on the door and stumbling around with my suitcase.  And what did I find as I wandered through the house?

Three boys sitting at the table, playing Chess, with a candle as a light.  Lovely.  They were immersed in the game.  I came over and quickly sized up the game (after saying hello and hugs and everything).  I could see hundreds of potential moves, awesome moves, profound moves, moves that would marvel and amaze.  I was just bursting to tell them what they each should do.

The boys haven't played much chess, and I want them to love it.  If you have played chess the following experience may hit a cord (yes, yes, we will get to teacher lust).  You are playing a game with a friend and over come a couple of people who are pretty good at chess.  They suddenly start offering advice.  "Watch out for the Bishop", "You should bring the Rook down", "Take his Knight".  Of course their advice is correct, and it would be stupid not to follow it.  They then inject themselves into the game and 'hey presto' now it is their game - but you have the privilege of moving the pieces.  

This sucks.  The only way you get good at chess is to play, and to make all those dumb mistakes.  You MUST lose your Queen because you didn't see the Bishop!  This causes you to be fully on guard next time.  In other words, there is a progression everyone goes through, and there are a series of mistakes you will make, and must make, to improve.  You must be allowed to make mistakes.

When the expert prevents you from making those mistakes he/she is robbing the learner from learning.  Even though the learner may win.  But here is the thing - when people watch chess they just can't seem to stop their mouths from moving and telling people things.  This is called teacher lust.  It is fueled by the need to tell others what to do, the need to show others what you know, the inability to shut up and let people make mistakes.  It is rampant in the adult education sector.  And it is the destroyer of the natural learning curve.

Teacher lust has been identified as one of the biggest problems with mathematics education.  The over zealous teacher cannot, or does not, let students make, and learn, from mistakes.  They coach and prompt and hint and TELL learners what to do - just like in chess.  At the expense of learning.  This is often a result of insecurities and the need to be known as the expert.  If you want to be known as the expert - you never pass up an opportunity to show what you know, or that you know more than the others.

Teachers often micro-correct learners.  Even in macro problem-solving tasks teachers will correct learners' small mistakes - essentially rendering the learning from problem-solving useless!  Teacher lust has been attributed as one reason problem-solving based curriculum's have not delivered the results they promise.

The wise, mature, and good teacher lets students make mistakes.  AND lets them identify their own mistakes via natural feedback.  They know that if you tell the student anything - they rob the student of a powerful learning experience.  Good teachers shut up.  And good learners learn from mistakes.

Good educators are worth more than their weight in gold.  They are not people who know lots of information.  People who know lots can do more harm than good.

So, let your students make mistakes and learn from the naturally occurring feedback (like losing your Queen to a pawn!) - it is essential to their development.  Don't rob them of the opportunity to learn a real lesson.

Teacher lust - Rampant!     

Enforced conformity and the role of home educators 

John Stuart Mill is one of my heroes.  He formulated the greatest defense of freedom every written.  His book 'On liberty' has shaped my thinking ever since I first read it. I have read the first chapter many, many times and come away richer every time.  The rest of the book is pretty good too (in fact it's awesome).


In one section Mill talks about 'eccentrics' and how they are vital to our survival.  Here is why:

Eccentrics are defined as people who do not do things in the accepted way.  They are the odd bods, they are the square pegs in round holes, they are the strange, the different, the weird.  They live their lives by different rules and norms.  Mill loves them - so do I.


Now why Mill says they are so important is because in a free world in which eccentrics can do as they wish, we can watch the outcomes of the eccentric's life choices.  We can use their outcomes as empirical evidence for our choices.  Or as empirical evidence for our error.  

For example, if the common societal belief is that washing in water is unhealthy and some guy comes along and starts washing regularly and doesn't die - then this shows the population that they may be misguided.

Let me give you another recent example.  The accepted social norm is to send children to school.  An 'education' is considered a right in NZ, and every child MUST be educated.  NZ society has barely deviated from this for 100 years.  It is such a social norm that for most people not sending children to school is inconceivable .  NZ being a semi-free country, parents are allowed to educate their children at home.  That is, parents with no educational experience, are allowed to home educate their children.  Yes, they do have to meet some criteria.

Back to Mill.  Mill said that without eccentrics conducting 'experiments in living' we have no evidence to support our choices, our choices are in fact not choices but simple compliance with social pressure.  In other words - we think we are right because everyone else thinks we are right.  We could just as well have been complicit with any society that condoned evil behaviour because it was socially acceptable (insert any society that endorsed evil practices).  Ours just happens to be less evil, but only through luck, not moral strength.

Without evidence that your choices are good, they are simply biases.  Mill says we need more unique and challenging individuals rather than a society in which we all slowly conform to one another.

Home educators 

So, we have some people in society that fly in the face of a persistent social norm.  Home educators are the eccentrics.  They are doing something different and against the 'common sense' of society.  How could parents, without the resources of a school, and without educational training, educate their child?  How would their child compare with those in school?  What will become of the poor retch?

And here is where Mill's argument is so powerful - sometimes the eccentrics demonstrate that the accepted way of doing things is wrong, wrong, wrong.

The few studies that try to compare the home educated with school educated graduates are in favour of the home educated.  Home educated kids appear to be academically ahead of their schooled peers.  Not because they are socially challenged - they are just as weird as the kids at school.

Because of this surprising outcome, that home educated kids do better than those in school, according to Mill, we (society) should be examining our beliefs about education, big time. Teachers being out performed by parents, in less time, with less money, with less education, is strange.

Summary

Some families are eccentric - they have home educated their children in an age when this is not a social norm and often looked down on. And their exercise of freedom has paid off.  We should be asking some questions of our education system and social norms.


I dare you to read chapter one of 'On liberty'.

Why maths counts - part two of three...

If you have engaged in the bearapocalypse scenario in the previous post, you may be interested in this clip. What makes the problem so darn  hard is that it requires one of two types of proportional reasoning.

Check out the baseball players having a go at the same problem.   Now if you want a challenge stop this clip before the explanation begins and work out how long it takes the two painters to paint the house.  Here is a tip - forget the way the guy does it at the end.  Do it your own way - draw pictures whatever.

By the way - the 'take me out to the ball game' song that intros and exits this clip makes me angry.  What were they thinking? It's like finger nails on a blackboard.  Doesn't last long though.

This type of thinking is called 'proportional reasoning'.  Lamon (2006) suggests that up to 90% of the adult population are NOT proportional thinkers.  If that's true, then it is a serious problem because to master algebra one needs to reason proportionally and mastering algebra is essential to almost every other mathematical domain.  

Here's the kicker though - you should have mastered proportional thinking by year 10/11.  Notice the age of the kid in the clip.  Yip, you should have learned it by age 12/13.  Actually, a growing group of researchers believe that the main cause of student math failure in high school is due to a lack of proportional reasoning.    If you don't learn it in intermediate School you won't learn it in high school.

Well, you can relax- nine out of ten adults act just like the baseball players in the clip (even in education).  

Have a go at the problem.  

I'll work through it in a day or so.  

Why maths counts - part two

You have survived the apocalypse and find yourself the reluctant leader of a group of ragtag survivors.

Due to the situation in which you find yourself, your group has to collect its drinking water from a river a distance from your base.  How it works is this - A person sneaks (quietly) to the river and fills containers with water and carries them back and tips them into a tank.  The tank is outside of your base but connected to your base by a pipe and tap.  So long as the tank gets filled daily, your people are fine.  Here is the issue - If the tank is not completely filled, your group will suffer extreme dehydration - and probably die.

This filling job is dangerous, so only one person is sent. Unfortunately it takes ages to fill the tank, and your growing group is using the water at an increasing rate.

You don't want to send two people because you need all the people you can to guard the base.

The person who collects the water is named Karl.  Now Karl is fast, smart and strong (salt of the earth kind of guy).  It takes him 3 hours to fill the tank.  Karl is fast, but clearly he needs help from a second 'filler'.  Every moment he is outside the camp the more likely 'they' will get him.

You pick another person, 'Larry'.  Larry is a bit slower, but he is keen.  So you decide to let Larry fill the tank by himself to see how long it takes.

It takes Larry exactly five hours to fill the tank.

You decide to have Larry and Karl fill the tank together.  It'll get done quicker.

The -I slept through maths in school scenario

You send Karl and Larry out together first thing in the morning (7:00).  Just as they disappear into the distance you hear the alarm.  Someone yells out "The bad guys will be here in two hours exactly. If Larry and Karl are not back we will be overrun.  We either all abandon our base and run for the hills or hope they get back in time.  If they're not back in two hours - we are dead!"

You think to yourself 'If it takes Karl three hours and Larry five hours to fill the tank then working together they should fill it in about three and a half hours?  Maybe? Let me think, 5 plus 3 is 8 and 8 is half of 16...   Oh forget it, Lets get out of here!  RUN!!'.

You tell the group to open the gates and run for it.  You are all eaten by bears later that night (it's a bearapocolyps).

The - I learned all about proportional reasoning in school scenario.

Will Larry and Karl be back in two hours?  Let's work this out...

Karl takes three hours, Larry takes five so that means in one hour each fills the tank...

Conclusion, you work out exactly when they will have the tank full of water and plan accordingly. You all live and you become the leader of the new world.

Maths has saved your life - again.

The challenge

Have go at this problem:  It takes Karl three hours to fill the tank.  It takes Larry five hours to fill the tank. How long will it take them if they work together?

I'll post the answer in a few days.

Don't be a Nicholas Cage.





  

Heading to Dunedin

I have a workshop tomorrow with the good people of Dunedin.  There are some fantastic tutors and organisations down there.  Whenever I am there I come away impressed.

Tomorrow will be a mix of:

• A wonderful insight into Pacifika learners and the L&N opportunities 
• Enhancing literacy skills (Reading comprehension)
• Formative assessment
• Enhancing numeracy development 

Interesting note on point one - all the Pacifika people I have meet are awesome, smart, big hearted, sharp and well ahead of the curve in every area (social and academic). Makes me wonder what other forces are at play?  Why is the Pacifika community (unfortunately grouped together by the Government) over represented in the ALL numeracy statistics?  Is this another consequence of the government grouping large numbers of people under one heading who are in fact wonderfully diverse.  

There is a concept called 'mathematization', which refers to inducting students into a certain 'way of thinking'.  It has nothing to do with being smart or not, but everything to do with 'habitus'.  Look up the term, it certainly gets you thinking.  I relate it to 'knowing the explicit and implicit rules of the game'.

Zevenbergen wrote a great little article about a retail position that required the applicant to pass a numeracy assessment to qualify (shop assistance's in a grocery store I think).  The job itself required nothing more than some basic arithmetic skill. Zevenbergen suggested the numeracy test was designed to prevent a certain group from making the application.  The adults who passed the test were those that were used to numeracy assessments - they knew the rules of the game - they were familiar with the habitus.  Mathematics is well known as a doorway subject, keeping out more than it lets in. And, its on the increase.

Okay, running late...

More on habitus soon...