Are you a numeracy expert?  

In 2006 a numeracy survey was conducted in NZ (and around the world) to determine the distribution of numeracy skills in the adult population.

We didn't do so well...

Anyway, below is the toughest question in the survey.  If you got this (and a few others) you were likely to be placed in the 'expert' level (level five to the L&N folks).

Good luck!

Problem

You deposit $1000 into a term deposit that gives a rate of 7% interest per year, and you leave it for ten years.  Assuming nothing else changes, will your money double?

Well, guess what - only about 5% of the population actually managed to get this one.

Solution 

Here is what you need.

Where 'x' is the total and 'p' is the principle, 'i' is the interest rate and 'n' is the years.

x = p (i + 1)^n      

Here is a little project for you.  Write this as an excel formula into excel and make it work.  Plug in the numbers above and see if it doubles (right now someones is saying, 'just give me the ----- answer').

UPDATE: 

Okay, here is how you solve it.  

Remember Bodmas/bedmas?  Well lets just plug the numbers into the formula and use a calculator.

p = $1000

i = 7% = .07

n = 10

1.  So, brackets first = (i + 1) = 1.07

2.  Then exponents = 1.07^n = 1.07^10 = 1.97 

3.  Then p x 1.07 = 1000 x 1.97 = $1970

Now most folk get stuck on step 2.  Remember that with exponents you are multiplying the number by itself.  You do this ten times (once for each year).

1.07 x 1.07 x 1.07 x 1.07 x 1.07 x 1.07 x 1.07 x 1.07 x 1.07 x 1.07.  DO NOT do this on paper or in your head.  Grab a scientific calculator and use the  x to the power of y button.  All your phones have this. 

Just enter 1.07, then push the button, then enter 10, and hey presto!  You have your answer.  

Does $1000 double in ten years at 7% interest?

Adult numeracy

Now, this is the type of skills that we each need to cut it in the information age.  It's not just about being able to solve this one task, but rather possessing the skills and the courage to actually have a go at it. 

If you are happy to just let others do it for you, or to use an existing formula calculator - haven't you given up some of your independence as an adult? 

You don't have to know all this perfectly, but do you have the skills to work it out if you want?

Final question:  At what percentage interest point does your money double in ten years?    

Dale Williams - the Mayor of Otorohanga and general legend

I have had the pleasure of hanging out with Dale for a short time.  The man is an inspiration, and is a driver of a great story about turning around Otorohanga.   Just watch it.

To those other people involved (a long list of wonderful people - Marlene, Ray etc...), you guys have done something really amazing and have set a benchmark for the rest of us.

What is School for? (and is it killing dreams?)

Graeme Smith has a thought provoking post on Seth Godin's talk on why we send kids to school.  It seems no one is too sure!

The post and the TED talk are really interesting.  Click below to go.

Graeme' post includes a link to the TED talk.  

How to get smarter, and solve problems - Part one

In the movie limitless, a bumbling, forgetful man starts taking a pill that makes him increasingly intelligent.  It plays into the fantasy of intelligence providing some sort of super advantage.
The truth is we all want to get smarter.  But can we do it?  Yes we can!  There is no limit to your intellect, if you work ... so strap in.

Problems come in all shapes and sizes but the truth is there are only certain 'types' of problems.  This post and a following one discuss how to get better at all of them - and ultimately GET SMARTER.

Here are two examples - the first measures 'functional fixedness' and was designed by Duncker and tests how 'in the box' people are.

Problem one: 'functional fixedness'

Using only the pictured objects figure out how to mount the candle on a wall.


Functional fixedness relates to how you view various objects and what they can be used for.  What do you 'see' when you look at his picture?  If you want the answer - you will have to ask in the comments section.

Problem two: 'negative set' problems ('drinking glasses').

Six drinking glasses are lined up in a row.  The first three are full of water, the last three are empty. By handling and moving only one glass, change the arrangement so that no full glass is next to another full one, and no empty glass is next to another empty one.

Negative set problems have to do with the human tendency to only think in terms of one solution strategy. In a sense you get tunnel vision and become unable to see other solution types.  There is a theory that all of life's problems can be broken down into these types of problems (but that is another post!).  Getting smarter, and solving these, will have real benefits in other parts of your life.

You can improve your ability to solve problems and get smarter by doing some very basic things.  So if you want to get better at problem solving read on.

Crystalised and fluid intelligence

Your intellect can be divided up into two domains - crystalised intellect (CI) and fluid intellect (FI). Crystalised intellect is all the stuff you know.  Fluid intelligence is your ability to manipulate the information.

Example:  If I was to ask you to spell a large word that you don't use much but know (such as 'transparent'), you would be using crystallized intelligence.  Basically, the word is in your memory and you just access it.

If I asked you to spell a word you hadn't heard (such as 'coarticulation'), you would spell it based on your knowledge of word sounds, and word spellings.  You would construct it perhaps like this: co- articulate - ion, [then remember to drop the 'e' and add 'ion'].  The point is you use both your knowledge of words (CI) and some thinking (FI) to spell new words.  Young people tend to have better FI and older people better CI.  (Note: young people are better at spelling new words, old people are better at spelling known words)

1.  Improve your world knowledge (Domain knowledge)

Your great advantage as an older learner is this CI.  Build it - keep building it.  The more CI you have the better the problem solver you will be.  This is the number one thing you can do to get smarter.

Why?
The way you make sense of the world (and hence learn) is by making connections between it and what you already know.  The more life experience you have, the more connections you can make and the more knowledge you can draw on to make sense of new information.

The more you know about the world, the more you can learn and solve problems through induction or deduction.  You need wide knowledge , that is, knowledge of very diverse things.  The broader your knowledge the better.  Second you need deep knowledge.  Become a specialist and learn everything there is to know about a topic.

A really good place to start would be to learn the '100 words everybody should know' list.  

Otherwise here are two hints:  Read, read and read.  Not only will you increase your world knowledge but you will also experience a multitude of perspectives - you will 'see' the world through different characters eyes.  Click here for the best summary of reading information freely available on the net.

Be curious and interested in things and never stop learning.

2. Automate what you can!

Your FI is limited.  It can only think about so much before it red-lines and starts to break down.  This is called 'excessive memory load' and causes people to fail to solve problems.   But your CI can work all day! That is because when you remember something from the CI it is automatic and therefore puts no load on your FI. So, the second step to being a better problem solver is to move as much information as possible to the CI.

Example:  Solve two problems below in your head.

7 x 8 + 9 x 6 =

6 x 6 + 8 x 8 =

Which one was harder?  If you know all your times-tables, they are about the same.  But if you don't, the top one is much harder.  If you have to work out what 7 x 8 is by adding, then this uses up your FI.  But if you know the tables by heart, you can access the multiplication answers automatically and then use your FI to add them together.

Second, you can memorise the 'rules' also, so that by following procedures you free up your FI to think strategically.

So number 2 is to automate as much information as possible by memorising it.  This frees up the FI to think about other things.  When looking at a problem, work out if memorising any part of a process will help you, and then invest the time in doing this.  It will help.  Click here for the tower of Hanoi challenge to see what I mean.  But do increase the discs to seven at least.  Memorising the pattern will allow you the mental space to monitor your progress and stop you losing track half way through.

Final challenge for today - who is better at the tower problem, you or your children?

That's it for now, tomorrow we cover the really good ones:

• Use systematic plans
• Develop sub-goals
• Draw inferences
• Work backwards
• Change the representation

Remember - in the film limitless Bradley Cooper got smart, real smart, by taking a pill.  The truth is, your brain is a learning machine, it doesn't need a pill - it needs you to feed it and learn how to use it.

A quick 'health check' of your organisations embedded literacy and numeracy process.

Here is a quick way to check on the health of your organisation's embedding of literacy and numeracy if you are not present during actual class time.  It is based on 'expectancy theory' and personally, it never fails to give an instant insight into the priorities of a course or wider institution.  

If you happen to meet a learner in the corridor or wherever, simply ask them this question:

"How well do you think you will do next time you complete the numeracy assessment?"

There are several categories of answers you will receive:

1. "What assessment?"
2. "Which one was that again?"  
3. "Oh that, it was hard"
4. "Good!  I think I've improved quite a bit since I've been here".
5. "Awesome.  I can't wait to see how the new strategies I've learned are going to pay off".

Now, they may seem a little contrived (they are!) but you get the general idea.
If the response to your question is similar to the first three - it likely indicates that the learner has no awareness that their current course is designed to develop their numeracy skills.  This means it is either not happening or the tutor is struggling to implement new numeracy support into their practice.  There may be numeracy being taught but it likely not linked in to the learners own goals or the needs highlighted by the assessment.

Moreover, these types of responses suggest that there is not a coherent plan or system in place.  The learner may not realise that the assessment is a SUPPORT mechanism and part of a broader plan to develop their skills.  Rather, the assessment is viewed as a test.

Number four is okay, but not great.  It suggests that the learner understands why they sat the assessment and is feeling confident about their progress.  However, it also suggests that there has been no emphasis on actual progressive development.  Progress is made as a consequence of the normal content delivery, not targeted, explicit ELN.

Number six is fantastic.  The learner has a personal expectation of success and progress.  They have taken ownership, and perhaps are developing their own pro-active learning strategies.

To sum up:  The worst responses are when the learner barley remembers the assessment or has very negative associations with it.  This suggests it is done simply as a criteria of funding, and that there are no support systems in place around the assessment.  Responses in which the learner thinks they have improved due to the natural progression of learning course content are okay but not great.

What we want are learners who have sat the assessment, had the results used to identify priority areas of need, and then have implemented a plan to purposefully work on those areas.  A learner who has taken responsibility for this will be keen to repeat the assessment because they will be confident of improvement. The plan will be a combination of tutor interventions, a personal learning plan, and strategies.  Its a two part process - directly taught skills by the tutor and development of learning strategies by the learner (a tool box of strategies so to speak).

If your learners are not confident of improvement - perhaps think about what could help this situation at a systems level.

HULK SMASH - Getting STRONG in numeracy

This post infuses numeracy with getting strong.

I visited three different sport and rec courses last year.  Each was full of talented 16 to 19 year old guys and gals.  They were into sport, coaching and generally psyched about getting fit and strong.  However - they needed to learn about percentages, fractions and decimals - and were less excited about this. So as a part of a new series called:

How would I teach it? 

Here is how I would, and have taught percentages to sports and rec students.

Fun scenarios

Maths and numeracy doesn't have to be taught in a sensible scenario - and it doesn't have to be immediately contextualized either.  It does have to be 'relatable' and interesting however.  With that being said - here is how I did it and would do it again.

Scenario:

In 9 weeks from today you are going to participate in a MMA bout (cage fighting competition).  To have a hope you will need to increase your strength and power as much as possible (this pushes all the guys buttons - less so the girls, but many girls right into it).

Group discussion:  How would you increase your strength in 9 weeks?  

Then listen to all the ideas and theories about weight training, running up hills, kettle bell training etc.  While the scenario is not great, it generates a massive amount of interest from this crowd.  Suddenly, they bring their knowledge to the table and they know lots.

The solution:

I have a powerlifting peaking routine designed to maximise strength and power over nine weeks.  It is used by the strongest men in the world and has stood the test of time.  If you follow this routine, you will be able to out power and out muscle your opponent.  The first time I used it I gained 15% on my deadlift, and 12% on my squat and 9% in the bench.  Not bad for a guy who hadn't made any gains in ages.

The routine

Three workouts per week on non consecutive days.

Number one: Squats - legs, shoulders

Number two: Bench Press - chest, triceps

Number three: Deadlift, back, biceps

Work out your current maximum lift for each of the above movements and the supplementary exercises.

Then follow this workout schedule for squats, bench press and deadlift.

Week one:  55%     -  3 sets   8 reps
Week two: 60%      -  3 sets   8 reps
Week three:  65%   -  3 sets   6 reps
Week four:  70%    -   3 sets  6 reps
Week five:  75%     -   3 sets  5 reps
Week six:  80%      -   3 sets  5 reps
Week seven:  85%  -   3 sets  4 reps
Week eight: 90%     -  2 sets   3 reps
Week nine: rest

 Keep the weights of the supplementary exercises to the same percentages.  After week six begin to drop them from your workouts.  For example, if you do deadlifts, chin-ups and bent rows for the back drop chin-ups in week six and bent rows in week seven.  The week eight workout is just two sets at 90%, no other exercises.

This is a peaking routine, and boy does it work.  You just have to have faith - first few weeks seem a bit easy but its all part of gearing up the body.

I would show his routine to the class and have them write down the eight week routine with their actual weights.  This means the will be working out percentages for all their lifts.  At the end of this, get them to estimate their strength increase.  Then work this out as a percentage increase - Amount gained divided by previous max.

The doing

The classes I have seen are right into this.  Most would probably have a go at the routine.  This would allow for an actual big gym session where students went for their maximum lifts in week nine.  It would be great to see how they did.  You could also see  who gained the most strength based on body weight and percentage increase.

• Is a 100kg guy squating 150kg better than a 50 Kg guy squating 100 kg?  How would you decide? 
• Is moving from a 92kg bench max to a 102 kg bench max , better than a 100kg to 110kg bench?

These routines would also qualify for 'naturally occurring evidence' needed for numeracy units.  Make copies of the eight week routine and file them.

You could do the same for running, time, distance, recovery time etc.  In fact whatever sport they are into.

So getting strong in body and percentages!  Horaa!  Sport and fitness classes learning about percentages should be easy.

Tutors- plan your work and work your plan.  Inspire your students.

Sport and rec students will spend a good part of their lives in the gym and on the field.  Give them a reason to learn about percentages.  Once they have this, you can begin to develop their conceptual understanding of percentages and their relationship to fractions and decimals.  This is coming up in a further post.

Managing and beating anxiety

Anxiety destroys people, is crippling, dangerous and contagious - this post is to help shed light on how to overcome performance anxiety.

'Performance anxiety' might conjure up certain images - but there are many types of performance anxiety - we are talking here about 'intellectual performance anxiety' such as you might experience if you have to solve a maths problem in front of a group.   Unless you have experienced true anxiety in a socially important environment, it is hard to relate.  For those who have - you will understand.

Performance anxiety relates to experiencing anxiety under conditions in which you are being, or will be, observed and judged by others.  It also usually includes a lack of control.  In other words it is anxiety caused by  potential harm to your social-image, that you cannot avoid.  This is in contrast to the anxiety you feel when about to ride a wild bull.  That type of anxiety relates to physical harm rather than social-image harm.

We have already discussed why you may suffer from anxiety - go here if you haven't.

There are two ways to try and stop anxiety.  One is effectively useless without the other, and the other, unfortunately ... takes a long time implement.  The truth is that you will have to learn to 'manage' anxiety until you finally wrestle it into submission.

States and Traits

There are two things going on with anxiety.  States and traits.  When you are asked to come up to the front of the class and solve a maths problem you 'feel' anxious.  Your heartbeat increases, temperature rises, pupils dilate etc and your brain releases hormones and chemicals that destroy your ability to access and use information from your memory.  You are in a 'state' of anxiety.  The fact that this has happened to you before and is likely to again in a similar situation is a 'trait'.  You have a trait of experiencing anxiety but right now you are not in a state of anxiety.  Traits have a genetic aspect to them.

A trait of Bruce Banner is that he turns into the Hulk, but he is not always the Hulk.

The bad news is that the more you fall apart in a situation due to anxiety the more it will happen - unless you take action! Lets go!

Two strategies

There are two main strategies to help you with anxiety.  The first deals with the state and the second the trait.
The first seeks to deal with anxiety symptoms as they occur by refocusing your mind on something that isn't your impending failure.  Here is how the theory works.

You get called up to solve a maths problem.  And your brain goes "Oh heck I'm gonna look like I shouldn't be in this job.  They're all going to see that I am in fact useless, my reputation is finished, this is going to be horrible.  My life is over... Bla bla bla"  Your brain subsequently pumps chemicals into your body that prime physical action - not thought.  Strategy one is to refocus your thoughts and stop this response by using up conscious attention.

So you think positive and attention filling thoughts.  If you use up all your mental attention on other thoughts there is no mental room to be left for the negative thoughts causing you anxiety.

"I am good at maths.  It's not going to be hard.  The sky looks beautiful today.  I'm going to nail this and show them how smart I am.  I am valuable.  I CAN do this".  Then oxygenate - breath those nasty little chemicals out of your brain.  BREATH!!

The problem with this stuff is... You know its all bluff.  Your deep 'id' and the 'ego' know what is going on! You know it's a strategy.  But as you get closer to the whiteboard, you realise its not working!  "Oh no, I'm still freaking out, it's not working!  I'm gonna look terrible - BREATH!!  Hopefully by the time you get to the board you have hyper-ventilated and pass out before looking stupid (the final strategy!)

Also - the task you are meant to be doing requires all that mental space you are using to focus on positive thoughts - you have to shut this down to do the maths, and now your trait for anxiety kicks in - and anxiety is back with a vengeance.

I'm not knocking these strategies, they can help support you with the other strategies - but having experienced the above I can tell you that once anxiety gets you it really gets you.  These strategies are supplemental to a plan that focuses on the trait.

Strategy two - the long road of truth

Ah, this will never sell a book - but it seems to be the truth, at least mostly.  The way to not be so inclined to become anxious is to change the underlying beliefs that support it.  You need to build up an immunity to the trait.

What causes anxiety is the public exposing of the 'You' that really lives in your body rather than the public image 'you' that you pretend to be.  The forced exposure of the discrepancies between the two is interpreted by you as harm to your social image and thus is to be feared (the research calls this 'shame').  The response is anxiety.

We all present ourselves in a light that reflects how we want others to see us.  I want you to think of me as smart, intelligent, competent, and confident so I present myself in ways that achieve this.  I show my strengths and hide my weaknesses.  Thus I pick the times and environments that best suit me to do things.  Where it goes wrong is when my power to do this is removed and my weaknesses are exposed - destroying the strawman I have put so much hope in.

Three strategies to work on the anxiety trait 

One:  The way to beat anxiety is to kill the strawman, the public image, the fake 'you'.  And that is why it is so damn hard.  Stop engaging in 'image-management' and let be what will be.  Give the world what you are - a real person with strengths and weaknesses.

Two: You have to actually believe that not being able to answer maths questions on the board (or whatever your unique weakness is) doesn't matter.  You have to believe that when 20 people laugh at you for getting an easy answer wrong (or that one person who's approval you so seek) - that it doesn't matter because they are wrong.  You must believe that you are okay regardless of the thoughts and opinions of the pack.  That you are learning, and learning begins with truth.

The doing of this takes time.  Next time you are becoming anxious because you are put on the spot, remember 'it doesn't matter what these people think'.  Believe it.  Next - getting it wrong doesn't mean you are unintelligent.  It really doesn't.  You need to believe this - it is true.  When you believe it your brain will not interpret potential failure as a threat to self.

Once you are working on one and two you must continue to cultivate these beliefs.  Because anxiety is a trait it is like a weakened muscle.  You need to beef up the supporting muscles which are the co-workers confidence and practice.

Third:  Manage the situations that evoke anxiety in order to develop confidence.  Identify the situations that produce anxiety and begin to play/experiment with them.  You are experimenting with your own responses. For this you need control over the situations.  Be prepared to say no to people (like the teacher asking you to solve the maths problem).

Example:

I'll give you an example.  I have a friend who had problems spelling and as a tutor hated writing on the whiteboard in front of other tutors.  During workshops if he was asked to write on the board he would experience anxiety and spell the easy words incorrectly.  Then he would dissolve into an emotional wreak for the rest of the day.   He felt they were judging him - tutors have to be able to spell of you can't teach right?


To beat this- he confessed to his class of learners (not the other tutors) that he was bad at spelling.  It wasn't that bad, and over a year his honesty allowed him to get in hours and hours of practice spelling on the board and experiencing what it was like to spell words right.  And wrong.  Not so bad.  His confidence grew, and grew. When he went to the tutor workshop he DID NOT write on the board.  He declined politely but firmly (don't set yourself up).  He told them 'no I won't be writing on the board, get someone else'.  But later he did offer to write a few words on the flip chart -a nice safe constrained job.  (Being a jerk for a while may be the price you pay for beating anxiety - I'd rather be assertive that a jibbering mess).

Slowly he began volunteering to write on the board, but he would stop when he wanted.  It was on his terms - he had control.  Second, he admitted once to a group that he didn't know how to spell a word.  It was no big deal.  Someone told him the word and he wrote it down.

It has taken years but he can now stand up in front of hundreds of tutors and take notes on the board and he feels confident and in charge.  He writes on that board like a boss.  If he can't spell a word he just says 'how do you spell such n such'.  His worth is not tied up with his spelling, he knows who he is.  He doesn't care what others think.  He is free.

It didn't happen fast - it took about four-five years.  It required a combination of trait and state strategies, awareness of self, knowledge of triggers, knowledge and control of situations, and truth.

The end

So there it is.  Not what you thought?  No quick solutions - but the results are real.  Keep in mind that you are not worth what you can do.  You are infinitely valuable regardless of any performance task.  If the ignorant folk around you want to judge you on your performance - then you don't care... Cause you rock.

Public speaking - How to nail it.

I am not a good public speaker.  I do it and I get good feedback but that is because I try, try and try.  It is not natural.  However, last year I came runner up in a University speech competition for PhD students. Part of why I entered is because it is a weakness of mine, hence represented a real challenge for me personally. Participating required mastering several personal weaknesses.

What most people don't know is that I froze during the heats.  Yip, I had that moment when the mental lights go out and you just stare at the crowd.  Absolutely horrible - the brain was switched off/blank.  The crowd stared back, because they were just as nervous as I was and our combined nervousness just ground the proceedings to a halt.   It was possibly one of the worst moments of my life.  I had worked so hard, only to fail due to nerves.

Somehow I made the finals.  I knew than that I HAD to nail the final speech in order to get my confidence back or else live with the fear of freezing forever.  Here is how I did it.

The basics in order of importance:

1.  Connection.
You must talk 'with' your audience not 'at' your audience.  Doesn't matter how good the rest is - this is EVERYTHING.  A speech, presentation, talk, or whatever, is a dialogue, not a monologue - master this and you will never fail.

2.  No notes
Do not use notes.  They disconnect you from the audience.  Better to forget some content than lose the connection.  You may mess up your first few talks without notes but you will quickly master it.

3.  Vary your voice.
Pitch, tone, pace, volume,  rhythm. These are the tools of the trade.  Think of the audience like a toy car that needs to be pushed along the floor.  You need to give a big push to get it going, it coasts on momentum, but then slows, then you push again and off it goes, then slows.  This is what is happening to your audience's concentration.  They need regular pushes (surprises), your voice is part of this.

4.  Clear message
Structure the talk, know where you are in it and what points you must make.  Think about how the audience will hear and comprehend your content.  The message should include heart, information, and data.  Get the order right (heart first always).

5.  Move your body
Movements must be discernible - we live in a visual world - move when you practice. Face the crowd always, but move, move, move.  But, Do NOT, ever, turn your back to the crowd, even to look at a data show - its like hanging up the phone.  Point and gesture, but do not break the connection.

The stuff they never tell you

1.  Don't sit with the nervous people.  Fear spreads, nerves spread.  Emotional energy is contagious.  Do not go near nervous people before performing - isolate yourself physically if possible, mentally at all costs.

2. Dominate
Be the ego.  Does Kanye West get nervous?  Nope- in fact you are darn lucky he even showed up. Cultivate this attitude, don't advertise it, but get this attitude.  Your audience will appreciate it.  They want the ego, they want confidence, they want a show.  Give it to them.  Don't be Uriah Heap - a creepy David Copperfield character who pretends to be humble.

3.  It is a cultivated skill not a gift
You have to work at it.  Sometimes you will nail it, other times it'll be terrible - the main thing is to review and always think about how to improve.

4.  Chin - keep it up, figuratively and literally.  Literally - Stand tall and look out, never down.  Figuratively -You are never as good as people tell you and never as bad as you think you were.

5.  Memorise the beginning part of your talk and use this time to engage your audience.  Use the spare mental space to connect.   Move from monologue to dialogue as fast as humanly possible. Use a 'hook' to make this happen - a hook is a speech device designed to capture and engage the audience.

6.  Find three people in the crowd, right-side, middle, left-side and talk to each of them equally.  This gives the impression of addressing your whole audience.

I hate this picture, but it is proof that I conquered some demons that day.

The best blog on adult education 

There is a distinct lack of blogs on adult-education and learning in NZ.  At the end of this post are some links to a fantastic blog that meets the needs of two audiences.  The first is the adult who just wants to learn something, anything, just because it is interesting.  The second is for people who work within education and want to know what's going to happen before it happens to them - an ear to the ground so to speak.    

But first a tiny intro to set the scene.

The war in education

There are two competing paradigms of education currently fighting each other across the world.  The first is the paradigm of life-long learning.  In this paradigm of education you are never 'finished' with education, you simply continue to develop specific and diverse skills in response to ever changing demands.  In this paradigm you continue to learn for your entire life.  Your education never ends.  You will never have 'all' the skills because of constant change.  And that's normal- and no problem, because you just go get them.  Life is one big learning journey.

The second, and older, paradigm is that of 'meritocracy' in which you become 'complete' when you graduate from school (or University).  In this paradigm you learn as much as your ability will enable.  Those with more ability or intellect will travel further up the educational pathway.  Those with less will drop out earlier.  If you don't have certain skills in this paradigm it suggests you lack the ability.  For example, if you are struggling with maths in 5th form the advice may be:

"Well, just drop it, you're clearly not going to be a mathematician right?"

In other words - you have reached your limit, so no point pressing on.

Within this paradigm some people are actively encouraged to learn: "You should continue to take maths next year- you are really good at it", while others are actively discouraged from continuing; "Perhaps this academic thing is not for you, why don't you train for a trade or get a job and start making some money?"

Educational zombies

Here is the kicker - The second paradigm is dead, dead, dead.  Yet like a zombie that continues to move after death, this paradigm continues to wander the land looking for victims.  In fact, it may be more dangerous in the short term because you can no longer reason with it.

In fact the Governments' own policies confuse the paradigms and end up feeding the zombies while investing in new adult growth.  What we get in the educational environment is a bit of a zombie wasteland - Lots of zombie institutions barely functioning based on hard wired habit and limbic system response - just zombieing (new word?) through well rehearsed movements.  Meanwhile the new and worthwhile players scurry around trying to survive long enough to grow and establish themselves.

The awesome news for you

The good news is this, as the first paradigm declines, your schooling less and less defines who you are. It does not define your potential, your skills, your intellect, or anything at all.  Go and learn the stuff you are interested in - if you have never studied - go and do it!  Do it for the fun of it.  You are never too old.  There is a 70 year old man in NZ who left school at 14, and has just finished his second PhD.  He re-entered study at 65.  He just loves it for its own sake.

Graeme Smith and ALEC

The point of this post is to point you toward the best blog on adult education in NZ.  Written by Graeme Smith who runs a successful and innovative adult education business (the first paradigm).  The blog is inspiring and interesting - and doesn't stick to the old model of education.  I find Graeme refreshing.  He operates within and around the educational zombies and as such views things with a unique and insightful perspective.  If you want an insight into the future of education, his blog is a must.

If you are an adult or parent, and interested in learning check this site out.  Or, if you work in education, this site is like having your ear to the ground.

This link takes you to the site:

These are some of my favorite Graeme posts in no particular order.

If you are interested in writing short stories (note:  the competition will be back next year).

Checking on burnout (Designed for working in education but applicable to any job working with people)

Minecraft taught my kids everything they needed to know about life

Will software eat teachers?

Graeme's take on lifelong learning

Apogee

We should dream audacious dreams.  We choose them not because they are easy, but because they are hard .

I love the word 'audacity'.  8 worthwhile minutes.

Vihart

I don't know much about V Hart.  But I think she is the best thing since sliced bread.  It's not that she is clever, although clearly she is a brain, and it's not that she is quirky, although she is quirky.

What I love about her is her non-conformity.  She is a true free-thinker - a true mathematician.  She optimizes the idea of 'critical' thinking.  She tries to look behind the information she is meant to learn to find deeper truths.  She has a different way of thinking to that of the child in the picture - but in a very positive way.

Her view of things is always from a different angle.  I love how she dares to go beyond the 'official lesson'.

Anyway, if you haven't heard of her - here are a few of her You Tube clips on various things.  If you watch try to pick out her general attitude toward the 'official message'.

Whatever it is that she has - we need to bottle it and feed it to our kids.

I think she rocks - hope she reads this.

How far is the island?

A week or so ago I posed the following problem:  You are stuck on an island inhabited by man-eating crabs. Unless you swim to another island you will be eaten.  The problem is, you can't tell how far away the island is.  Is it two kilometers or five?  Knowing the distance with reasonable accuracy may be the difference between making it or not.

 How do you determine how far away an object is when you are unable to directly measure it?

Well this is where maths is so cool.  Maths allows you to reach beyond the mortal coil, to see into the future and stretch beyond your physical limitations.

I asked my children how they would work out how far the island was.  One said you could observe how fast the shadow of a cloud moved, and time it, as it traveled the distance.  Awesome.  My second eldest said you could use the sun traveling across the sky as a sort of timer and convert it to distance.  Very nice idea also.

There is another way.  It involves a right angled, 45 degree triangle.  That's a square folded in half for the uninitiated.  A VERY useful shape.  I cannot be bothered  writing down how I would do it - however I do want to amaze you with my brilliance so I'm going to have another go at a video.

A note:  I am a poor student.  I don't have ANY high-tech gadgetry.  This clip is raw.  But I have filmed in shaky cam style to provide some realism.  Think 'Blair Witch project' or 'The Borne Identity'.  In other words- sorry about the quality.  Also- I can only upload 2 minute clips (Errr), so it is in two two minutes blocks.

So there you have it - I hope that gives you an idea anyway.  If we know the length of one side of a right angled triangle and one of other angles we can determine the length of any side.  The 45 degree triangle rocks.  You can use it to work out how high cliffs are, trees etc.

This is essentially the system the navigators on ships would use.  They had Sextants that would work better than my bamboo square - but the same fundamental idea.

My question to you is this... What kind of scenarios might get your children/adult learners (or you) interested in exploring this concept of distance estimation further?

I may put up a learning plan in coming weeks as to how I begin to develop interest and knowledge of trigonometry with learners.

Why maths counts part three

Due to some unexpected circumstances you and your work mate find yourselves on a deserted island. Unfortunately, the island is covered in deep holes that look much like rabbit holes.  You have peered down them but are a bit chicken to go poking sticks down there.

Alarmingly, you find out the first night that the holes are occupied by man-eating crabs.  The crabs emerge, attack on mass and drag your fellow companion down the holes - In bits.  Brian paid the ultimate price for you to have one extra day alive.  However, tonight they are coming for you.

You must get off the island before dark.

As you stand on the shore you notice an island off in the distance.  It looks beautiful and safe.  You wonder how far it is?  Could you swim to it?  How far is too far?  Very hard to judge distances on the sea.

The non-maths scenario

You find the of idea avoiding being eaten by crabs quite motivating.  Yet, it's hard to tell how far that island it.  It could by one kilometer or it could be four.  It would suck to get halfway and run out of gas.

You hope for the best and start swimming....

It turns out your distance estimation was quite wrong.  The island never seems to get any closer while your own island gets smaller every second.  Lets just say, it doesn't end well.

The 'I'm pretty awesome at problem solving scenario'.

Actually, I'm not going to describe this one.  I'm going to ask you instead - Is it possible to work out how far away the island is?  Is it possible to work it out within a reasonable range of accuracy?

I think it is possible.  My technique involves fashioning a 45° ruler (which you could make from sticks right?) and applying a bit of creative thinking.  With a little MacGyver'ing' you could do it.

I would love your ideas or your kids ideas - especially the older kids.  Please ask you kids (show them the picture) and see what they say.  It may surprise you.

This might help to get the juices flowing - can you work out how high a tree is from the ground - without climbing it?  (Yes you can).


Think trigonometry.  But even if you don't know trig you can still work it out.

I would love to know how people would work out far away the island is.

Good luck - I'll post my answer in a day or two.