Invitation

Quite amazing that what we are doing and learning here in NZ is highly relevant to the rest of the world.

PhD tips

Your methodology needs to be your baby.  Love it and nurture it.  Look after it frequently.  Constantly work on it.  It is central to all that you do.

Hamburg - Here we come!

Well, it would appear we'll be heading to Hamburg Germany to attend and present a paper at the ICME 'Mathematics in and for Work' conference.  I have to say I'm pretty excited.  I've never been to Europe so it's a new experience for me.  

The article is fairly simple, it's looking at learner engagement patterns within a particular classroom. It doesn't address a whole lot of theory and hence does little in the way of answering either why learners engage in different ways, or what we can do about it.  I sometimes wonder if I'm making everything more difficult by making classroom interactions so much more complex.  But I quickly think of the quote attributed to Einstein: If I had one hour to solve a problem, I would spend the first 55 thinking about the problem and five about the solution.  

I think my research is part of the 55 minute problem-exploration component.  Without which, we may offer trite solutions to problems we don't really understand.  

A brief example can be found in the fact that many mathematics research articles on reform-or constructivist-based mathematics often end with a list of recommendations for teachers such as; value and promote discussion, value conjectures and justifications, draw on classroom knowledge and so on.  But HOW do you do this in a class of adults who do not want to make conjectures, but simply want you to show them how to solve the darn problem.

"Just show me how to do it!" he screamed at the tutor, who up to now had refused to do so.  The tutor ignoring the growing frustration kept repeating "Tell me how you have been trying to solve it?"  

Clang! - goes the clash of beliefs about how maths ought to be learned.

The issue of poor learner engagement is not purely a pedagogical issue, yet that is usually how it is framed.   It's complex baby!  And we'll be discussing it in Germany!

   

Statistics resources

Statistics are fun.  I'm not even kidding - it is the most fun of all the mathematical domains.  I was asked to put together five resources that taught statistics.  Unfortunately, I was unable to present the fun stuff, because we needed to provide content - rather than activities. Anyway, here is an example clips that presented the concept of chance.  Keep in mind, they are designed for learners with no experience at all of statistics.

The editing is a little clunky, but I've managed to sort this out now, so the newer versions have smoother transitions, better filming and placement of me, and better graphics.

Learning curves

This year I have been adding to my skill-set the 'art' of making video clips.  It requires know-how, technical skills, editing skills, patience, cunning and content.  Anyway, here is a sample of some of the content.  The process is very long, but the hardest part by far is generating and sequencing content so that the audience is engaged and able to learn from the clip.  It's a new medium for me but I see huge potential.

I think we are heading in the right direction, but lots of room for improvement.  The clips were designed for tutors of learners with low literacy skills, and covered a variety of topics.  This one addresses writing 'personal profiles'.  

This one here is about the basics of conversations.  You may think it is rather simple, but believe me, it is needed.

Mathematics and Moral Courage

I have been preparing a paper for a conference in Hamburg Germany with the support of my supervisors - Professor Diana Coben and Assoc Professor Jenny Young-Loveridge.  The paper is pulled from data I collected as part of the PhD but has not made it into the thesis.  The data set is a full audio recording of a vocational mathematics class which included Youth Guarantee learners and older adult learners.  

The paper contrasts three engagement patterns found within the class.  There are actually as many engagement patterns as there are learners but when limited to 8 pages it is not possible to include more.  I called the three: resistant, defensive and engaged. 

What I found is that some learners are very hesitant, or resistant to engage with mathematics because it presents danger to their social-selves.  They are even more resistant to engaging in a discussion because of the social aspect. Some are defensive, in fact they are aggressive about their non-engagement.  Obviously, this is going to have an impact on the class dynamic, and it certainly has a constraining effect on the others.

Finally, there are those that engage fully, and make new understandings.  Quite amazing to watch.   In summary, in a class of 15 learners, five engaged at a meaningful level, and of these five, two made new meanings out of the content presented.

Many mathematics researchers insist that discussing mathematics is the only way to learn.  Some even suggest that you are only doing mathematics when you are arguing about it (Lakatos for example).  Polya argues that doing mathematics requires moral courage above all else.  You must be able to generate an idea that might be wrong, share it with others, and then work toward a better idea. Your idea will likely be wrong, but you have to be brave enough to do it anyway - that's the courage part.  You have to accept that it might be wrong, and be graceful when others point that out, and then move forward - that is the moral part.

This raises real challenges for the Tertiary sector.  How do we better engage and support learners who have had poor school experiences?  Or those who begin to feel small when they make mistakes with maths? Or those who are terrified their friends will think they are dumb? How do we get learners to take risks and engage - how do we cultivate moral courage?

I'll be very interested to see what the international community makes of it all.  Not sure whether the paper has been accepted but will find out over Christmas.

Reading and the mind

Reading quantity may be related to IQ.  That is, the more you read, the smarter you get.  The relationship is somewhat complicated, and not the least bit controversial, but there is some evidence. For a good, although somewhat dated summary, check out this article.

I personally think that the quality of the reading material (aside from vocabulary level) is also important, and hence why the map below interested me.  It is far harder to find evidence to support this, but generally the books that have more 'life on the page' as Ray Bradbury would say, have more themes - and themes give you more to think about.  Being introduced to new themes makes you a better informed, deeper and more reflective person.

The map below shows the most read book by High School seniors in the USA.  Firstly, great!  Young people are reading!  Second, they are reading some good material.  
























Now, there are good books, bad books and ugly books.  The graph above adds an extra category - recently advertised books (i.e huge publicity push, usually with movie).  I see some absolutely life changing books on the chart.  Namely: Night, Animal Farm, Macbeth, and maybe Frankenstein (barely, but with great themes).  It would be enlightening to see the top five most read books.  It may be that those who read the Fault in our Stars also read all the others, but who knows.

The Fault in our Stars is neither ugly nor is it bad.  One way to look at it is, does it play on the emotions of teenagers, or in contrast, expand their paradigms of human experience?  In my opinion it definitely does the first, and perhaps the second a little.  It's an okay book (IMHO), but clearly the teenagers love it.  And why wouldn't they?  It's carefully designed to appeal to them.    

'Night' on the other hand is not.  'Night' is a recount by Elie Wiesel who was sent to the concentration camps in Nazi Germany when he was 14.  You cannot read that book and not be changed.  And yet, it is not designed for anyone, no market research went into it, it is simply a chunk of real life.  If you read 'Fault in our Stars' you will 'feel' (loss, pain, anger, love) but you may not be changed.

Anyway, its great to see young people reading - and not all of them are falling for the commercialization of books and are reading material that is old but powerful, rather than new, glossy and popular.  How much of these are required reading for school we don't know either.  I suspect all the older ones are.  However, any young person who gets through Animal Farm or Night is going to be an educated and interesting person.    

Long live the book.

My STAR WARS - How it all started.

Yip, I was the kid that played Star Wars out on the farm by myself.  The big old Macrocarpa tree was the Millennium Falcon, and Chewie and I use to fly from planet to planet smuggling goods.  I made a blaster, strapped it to my leg in a home sown holster and hit the skies.  Times were never so good.

I got given a Star Wars colouring book - on one page it had a picture of Luke in an X-wing fighter and on the screen it had a code.  Oh boy, Star Wars language!  Turns out it was the code 'pig pen', which doesn't sound that great but is actually a pretty cool code and - STAR WARS!

It got me interested in codes and then ciphers.  Its great for kids to use, and it's also great for parents to use to send messages to them.  The idea is to cultivate an interest in alternative message systems.

The real fun, and learning, occurs when you begin to change the relationship between the two codes.  For example, the most common structure is that below.

However, you can change the letter relationship to create a challenge for the reader.  Just be sure the letter placement is not random and the reader will be able to use a letter frequency strategy to solve the puzzle.  In other words, because 'e' is usually the most common letter, by identifying the most common symbol, it can be solved pretty quickly.  For example, in the code below, if you did not have the key, you could identify the most common symbol (an 'L' looking shape) and determine that it represents an 'e'.  From here you could deduce the position of the other letters.

I might write another post on this - called 'Code busting - turning your kids into analytical code breaking machines - and how this will help them conquer the world'.

Anyway, I've included a variation of the code below.  This version is used in Assassins Creed.  It's a little more complex, but still fun.  Good luck.

A bit rough - but you get the idea.

Pythagoras theorem puzzles

A friend of mine was talking to me about how boring maths is to teach.  He is working on trigonometry and reviewing the Pythagoras theorem.  There are so many great ways to make both of these topics fun, interesting and engaging.

Anyway, fresh from the NCLANA here are a couple of ideas that can be adapted.  The main idea is to use problem situations to engage learners and to get them thinking mathematically, before giving them a procedural solution.

 


One more:

Do we need a meta-literacy?

I'm experimenting with some video clips.  The clip below is a trial - repeat - a trail.  Unfortunately the sound is terrible (but I'm not redoing it) and the lights are too bright.  But it is heading in the right direction.

I would like to provide a forum for others in the field to have their say on various things.  I think it would be cool to have a bunch of these 'idea' clips to stimulate thought and discussion.

Youth Guarantee

Now, I know I mentioned in the comments that the next post would offer some solutions instead of presenting a slightly negative view.  The positive post is on the way.  But, a recent report has been released giving a view of New Zealand's position.

Link: Profile and Trends 2014: New Zealand's Annual Tertiary Education Enrolments

The results are mixed.  The positive points are framed in terms of sitting students in front of tutors (see point one).  If you are familiar with my study you will know that this means little in terms of real learning outcomes.

Point two is meaningless at this point.  We simply don't know about the opportunity loss.

Point three is difficult to determine whether positive or not.  Getting students to attain NCEA level 2, is good.  Unless it turns out that these results are due to an emphasis on tutors pushing credits.  Note the quote below.

Quote:  Policy-makers have confounded the acquisition and award of certificates with substantive skill improvement (Wolf & Jenkins, 2014)

NCEA does NOT equal learning outcomes.  It just doesn't.

Number four is VERY positive.  Great work here by the organisations and tutors involved.  Quality tutors are responsible for these good outcomes.  Boy, we have some fantastic tutors who are inspiring and mentoring young learners.  Simply put, a great tutor is worth their weight in gold.  I have met many, and think how lucky the learners, and organisations, are to have them.  I know of one tutor here in Hamilton for example, who is taking lost young people and making them successful, confident and positive members of society.  In fact, I know several teams here in Hamilton that are amazing -great managers and great tutors.

As for the fifth point?  Well, I'll let you make up your mind on that one.  But the questions is -Why?

Anyway, here are the talking points.      

Monitoring the Youth Guarantee policy 2013

This report focuses on the effectiveness of fees-free places and secondary-tertiary programmes at keeping young people in education, assisting them to attain NCEA Level 2 or equivalent and promoting higher level study in tertiary education. It also includes new information on employment and other destinations. It covers the period from 2010, when fees-free places were first set up, to 2013.

The key findings in the report include:

• Youth Guarantee programmes have reached around 14% of young people by the age of 18
• The programmes were effective in retaining young people in education in the year they started, who would not otherwise have been in education
• The major effect of the programmes has been to increase the attainment of NCEA Level 2 or equivalent
• There is some evidence that the programmes are providing a more effective pathway to employment, particularly to full employment
• So far, neither progarmme has had any effect on increasing the proportion of young people with NCEA Level 2 or equivalent who progress to further study at Level 4 and above.

Agree or disagree with this headline?

The headline below comes from the UK.  Apart from the atrocious grammar, do you agree?  The discussion pertains to raising the school leaving age.

More staying in school longer should lead to fewer adults with basic skills needs.

The landslide

For many years I have become more concerned that the lower tiers of the Tertiary system are largely useless.  I don't mean NZ in particular, nor do I discount the amazing work of educators in the field, but the outcomes, despite Government endorsement and spin, are by and large horrific.  Yes, learners get qualifications, but the courses in many cases DO NOT change the trajectory of learners' lives.

Quote: Policy-makers have confounded the acquisition and award of certificates with substantive skill improvement (Wolf & Jenkins, 2014)

My specialty is on the micro-aspects of education.  I.e - what happens in the moment by moment experience of the learner.  I can tell you with some certainty - the learning outcomes, in terms of 'skills and knowledge' of learners in NZ is poor.  And it has been poor for a long time.

It's not a question of fault - as everybody involved is working hard, it is something else entirely.

Anyway, I can't post the whole article because of copyright issues - but the UK is actually starting to talk about it.  Education Journal, issue 227, 2015

16-19 education and training failing to reduce skills inequality

England's post-16 education and training system is failing dismally to reduce literacy and numeracy skills inequality, according to new research from the UCL Institute of Education. Previous research studies have shown that England has very high levels of skills inequality by age 15 in comparison with other developed countries. But 16-19 education and training, only adds to the problem.   


Did you catch the last phrase?  "Only adds to the problem".

'The authors found that the high rate of early school leavers in England and some other English speaking countries led to too many young people taking short, low quality vocational courses that give too little dedicated time to improving their English and mathematics skills.'

Hmmm, that puts the cat among the pigeons.  Would love anyone's thoughts out there.  Agree/disagree?

A quick problem for tutors and learners

You find yourself in a weird situation (let's leave it at that).  You have to measure out exact amounts of petrol to travelers in a post-apocalyptic NZ environment.

You are going to tip one litre of petrol into the first car, two in the second, and three into the third car and so on.  This will continue until car number nine who will get nine liters.

The problem is that the petrol comes out of a hose attached to a large tank, and you have no measurement devices.

What you do have is a four litre and a nine litre container.

How do you measure out exact amounts using only these two containers?

Here is a start: Measuring eight litres

Fill the four litre and tip it into the 9 litre.  Do this again.  You now have eight litres in the nine litre container.

That's eight done. Can you work out how to measure all the others?

 

The fundamental attribution error

Have just read a very interesting and quite frankly disturbing article on the above mentioned hypothesis.  No time to edit this tonight but posting it anyway!

Sabini, Siempann and Stein (2001) question three 'taken as given' assumptions of social psychology and question them - in particular the fundamental attribution error (FAE).

The FAE is when a person acts in a certain way and 'you' then attribute this behaviour to an internal disposition, rather than to an external situational factor.  In other words we tend to underestimate the effect of the situation and over estimate internal factors.  

For example, in the Milgram experiments, people acted against their consciences because they were told to by a person in authority.  Despite not wanting to shock someone, they still did so.  In the Asch experiments people folded to peer pressure, and lied about how long a line was in order to conform to other group members.  And, in the Darley and Latane experiments people would not intervene in a bad situation if more than three bystanders were also not intervening.  E.g. a woman is being beaten up by a little guy (so no fear of you being hurt) but 'you' will not stop it as long as at least three people do not move to help.  Basically, all this research suggests that we (people) fold waaay quicker than we think we do.  The situation dictates not the internal disposition.

Now, if you are like me, you hate the idea of being lumped in with the participants of these experiements.  If it was us, we wouldn't have shocked the guy!  We would step in and help a person who needed it etc.  But, unless you have read Milgram's book this is ignorance.  Because every single other person thought the same thing and then FOLDED.  Actually, not everyone but way too many for use to be getting cocky about our own behaviour.  

But Sabini et al have a different interpretation and one I tend to agree with due to my studies.  They suggest that all these behaviours can be explained by internal dispositions.  In particular, the need to avoid embarrassment and to avoid losing face.  Sabini et al unpack the research and place this internal factor at the centre of each one, and make a case that this internal factor is the real key.  The internal factor is - Fear of embarrassment and of losing face. 

They conclude that Americans, known as the most non-mitigating people, are in fact more prone to embarrassment and fear of losing face than we have thought.

My thoughts are - heaven help the Kiwis then because we are way down the scale from the Americans.  

Study tip three: Test yourself, don't wreck yourself.


Rather than re-reading a text to retain information - test yourself on what you've already read.  It's a better use of your time.

This leads to deeper processing - more can be seen here in the most boring webinair that I did many years ago.  DON'T JUDGE ME. - it was my first one!  If you need some sleep this is the one.  Skip to 16:30 for a brief overview of Owens (2008) model for more on deep processing.  While my presentation is not great, the model is one I've continued to use for years in literacy.  And you only need to listen for about 60 seconds.

This testing yourself strategy really links with the literature on reading comprehension.  In fact, cognition and reading comprehension research domains are a classic example of two domains that overlap but very rarely cite each other.

Graeme Smith has a great overview here - well worth checking out.

The main point is - if you want to learn, you have to THINK, and thinking is a cognitive action - running your eyes over text doesn't count.  You have to actually do something with the content - testing yourself requires you engage in several mental actions.  Actually, ALL the comprehension strategies are simply codified ways of creating mental action.  The comprehension crowd get a bit pedantic about them being taught as distinct strategies - but for us meta-learners we know better.

Study tips - from cognitive research 

My sister is currently studying psychology and one of her papers is about cognition.  I have done a little work in this area and have found it sooo interesting and helpful in the area of learning and my particular domain - literacy and numeracy.

Anyway, she is deep into it and is sending me brief summaries of study tips fresh off the research train.  They are great so I'll post them here.  Thanks sis.

Study tip one: Memory pegging 
Memory pegging is a surface level learning technique that rocks.  Remember that the best learners select whether to engage in deep learning or surface learning based on a cost/benefit ratio.  If it's worth learning - go deep, elaborate and connect - if you need to recall facts either for recall or to elaborate on later, then attach target information to sequential mental objects.


Study tip two: free up working memory

Write down your worries before an exam, test, attending a meeting etc.  It frees up working memory for better recall.

Working memory is like your work table - if its all cluttered with other stuff there's no room for you to work.  Clear it.

Are you smarter than a 6 year old?

Gotta love these questions...  Apparently this problem is giving adults' headaches right across the internet.  It's an entry leveled child's question.  That should be the clue right there...  Good luck.  Oh - you only have 20 seconds :)

The question is - What is the number of the parking spot the car is parked in?


If you struggle go here.  It explains what may be the problem. 

Why it matters...

Into the deep. 

I spent 10 years tutoring adult learners in literacy and numeracy.  In that time, I can tell you, I witnessed some tragedies.  Stories and situations that break your heart.  

The tragedy usually comes down to a single theme.  People with dreams, ambitions and hopes that are snuffed away because they don't have the basic skills to either complete the qualifications or meet the demands of the workplace.

Many of us know the academic version - stats on a power point.  But how about the real face to face level.

For example:  

Imagine this real scenario I have experienced.  You have a meeting with a 22 year old woman, who since she was 14 has dreamed of working with children, and tell her that she will not be able to meet the basic demands of the ECE programme. Therefore, she is not being accepted onto the course,  She cries, and argues, gets mad, and blames you, and you feel like dirt.  But you know she would not have lasted the first round of assessments and would have wasted thousands of her dollars.

But, you set her on an interim literacy programme.  A pathway.  A hope.  She will spend six months improving her skills and then return.  Then with new skills she will get onto the programme.  

But I know, its probably not true.  She probably won't dramatically improve her skills.  Because the instruction will not be good enough, intense enough, or diagnostic enough.  And in the last 20 cases, the improvements weren't enough.  But there is nowhere else to send her. 

What about a young male learner - who comes to me after class with tears in his eyes because of the utter frustration at not being able to learn the algebra necessary for aspects of the course.  I know what he needs; one-on-one instruction, one hour a day for two months - I know that I could help him.  But I don't have time.  

Instead I introduce him to websites, resources and literacy services.  But I know, that that won't really help him, in this immediate point in time - which is when it counts.  He needs the knowledge now.

He leaves the course.

I have hundreds of these.  I could go on and on and on.  Piles of people unable to continue on their journey toward self fulfillment, reaching their potential - happiness?  And the bodies continue to pile up.

Here is a positive one:  A young chap in my class had just been released from prison (20 years old).  A likable guy, who was easily led.  He had never read a book, and never had a book read to him.  Could not read a word.  A friend of mine committed to working with him everyday.  Every day.

One day he looked particularly happy.  I asked what had been happening.  He said, that my friend and him (together) were reading 'Wild pork and watercress'.  "It's really good", this was the first thing I think he had ever 'really liked' that wasn't artificial.  The two of them spent weeks in that book.  They became good friends, and he made progress on his reading.  In fact they ended up going hunting together.

He learned to read.  He got a job.  Today he has a family - who he makes sure does their homework.  It happened because of buckets and buckets of help from people, but particularly one special guy who committed.  It took time, but damn if I don't look back and feel encouraged at that.

Unfortunately, if I add calculate the stories, one side outweighs the other.  And on the wrong side of the ledger.  

Soon, the Government, the TEC, and the Tertiary Sector are going to discuss the outcomes of international surveys, assessment results, economic inputs and outputs and make some decisions. Part of the decision will be made based on 'how it looks to the public', part by economics and part by a misinformed cost to benefit ratio.  The decision will be made by good people, but people who have never seen the tears - or understood the problem in the first place. 

But it doesn't actually matter because they all missed the point.

You see this is a very personal human problem, and the solution is personal and human.  Poor literacy and numeracy is no respecter of ethnicity, or of social class, or of gender, or of age.  It's equally damaging to all.    

It's a case by case personal issue.  The thinking from above is to improve systems, assess, fund, not fund, fund on performance, fund on credits, fund on assessment.  Never in my now 18 years in the sector, has this been the difference that made the difference.

No matter what happens however, the pile of bodies on one side of the ledger will keep growing. Because the answer is real people, making real relationships, with real commitment.  This cannot be produced by any funding model - and today; funding rules all.  What we need are people who care, and then train them until they are world class.  We need to pay them enough to allow them to stay doing what they are doing, as most leave to make up for the financial loss they have taken to do the work.         

So, in conclusion, why does literacy and numeracy matter?  Because it constrains an individual's ability to take part in the great human endevour - self determination and self improvement. To prevent this leads to a degradation of the human spirit.  

The slow death of literacy and numeracy

Haven't been posting much simply due to a lack of time.  I'm in the final stages of a PhD and a little under the gun.  However, I did think it was worth putting this out there following listening to a conversation between tutors and managers, and observing some worrying trends.

I'm worried that the adult literacy and numeracy domain is being nibbled away.  In a 'death by one thousand cuts' kind of way.

Literacy and numeracy is morphing into policy decrees, assessment, and qualifications.  One would think that gaining credits is the goal, rather than developing the ability to use literacy and numeracy to further one's agency in the world.

Question:  What will happen if this continues?

In my mind, four substantial changes will occur.  At which point L&N will be indistinguishable from general education.  To appear in part two!

Hhmmm.

A poor perspective of mathematics

I collected 120 written responses from adult learners in entry level vocational and literacy courses.  I asked them:
"What is maths?"
And
"If a new student started your course and wanted to learn numeracy, what advice would you give them?"

Below is the word map of frequently concurring words.  What does it tell us?  It tells me that numeracy and maths are seen as boring subjects.  I wonder if we gave these questions to mathematicians what the responses would be?

What do they mean by 'socialized'?

Power and Authority

Parents choosing to home educate their children are asked one question more frequently than any other:

How do you make sure your child is socialised?

It's a bit of a running joke in the homeschool community, as we hear it often.  I imagine this question is rooted in the stereotype of homeschooling.  That is, little 'Johnny no friends' (except for his mum) working at the kitchen table from 7:00 am until 5:00, reading only the classics and never going out into the world.  Except to Sunday dinner with his Granny.  Subsequently, Johnny has no social skills, unlike all the 'normal' children who learned their social skills from the other kids in a classroom.

Its stupid, but when has that had anything to do with anything.  

There are three ways to look at the question of socialisation.  I may explore these in further posts (hoping that someone with more time may pick up on and expand the idea).  However, today I am going to use the lens of Foucault. This lens addresses the issue of POWER and AUTHORITY.

How does the notion of 'socialisation' relate to power?

If we attack the idea of socialisation from the stand point of power, we might discuss the notion of a 'hidden curriculum'.  The hidden curriculum is what children in a class learn tacitly, in addition to the overt curriculum.  While engaging in normal school activities such as learning maths and science, they are also learning lessons about the framework of social interactions.  In fact, the framework is probably at the heart of what most people mean by socialisation.

So what tacit lessons are they learning about the social framework?

Example:
Imagine a group of children sitting on the mat at school.  The teacher sits on a stool in front of them and begins to read and discuss a story book.  The teacher directs the children to sit, quiet down, and get ready for the story.  Then the teacher reads a page and begins a conversation by asking questions about the page.

There are lots of areas we could investigate but for now let's look at the use of questions.

Questions

The questions that you and I are used to are requests for information.

"What have you been doing today?"
"Can you tell me how to get to Straight Street?"
"What are you doing?"
"What did you think of the movie?"

The questions the teacher asks are not 'real' in this sense, because the teacher already knows the answer. The questions are tools designed to control the children's attention, and subsequent thoughts, by directing them to specific ideas.  Secondly, the questions are designed to elicit information that the teacher evaluates, to see if they are 'seeing' what the teacher wants them to see.  The structure will be like this:

Teacher initiates question /Child responds/ Teacher evaluates answer

Teacher: What is the dog doing Sally?
Sally: It's sleeping
Teacher: Yes, its sleeping on the mat.

This pattern is the initiate/respond/evaluate pattern (IRE)

Here it is in an adult class:

Tutor: Okay, so what is the square root of 16?  (Initiation)
Learner: Ah, nine. No four. (Response)
Tutor: Yip, not nine, four.  You got it. (Evaluation)


Back to the children.  Secondly, while the teacher is reading to the children, Johnny interrupts this pattern by initiating a statement.

Johnny: But he might wake up, and run. [the dog might get up and run around] 

The teacher kindly stops him, and brings the class back to the topic.

Teacher: No.  The dog is sleeping.  Now, what is the cat doing?

Johnny departed from the pattern by initiating a new idea.  It was not initiated by the teacher and threatens to take the class into an alternative narrative.  The teacher gently brings Johnny back to the task and the class's attention is drawn to the cat.

These examples are real.  It is worth appreciating that almost ALL of the discourse patterns in classrooms follow this pattern - even adult classes.  Some have called it - "The pedagogy of the question".  IRE rules in school, it is the substructure of almost all teacher to learner talk.

What is happening at the hidden level?

The children are learning about authority and power.  The teacher knows validated information, therefore the children must align their thinking and their answers with the teachers.  When they are wrong, the teacher kindly sets them straight by re-articulating the answers he or she wants.  When a child moves out of this pattern, the teacher brings them back through use of discourse.  The children learn that the teacher sets the topic, controls the discourse, already knows all the answers, and will be judging and evaluating all responses.  This is very different to any discourse the child will encounter in the real world.

The children learn the rules of the game.  They learn a multitude of power relationships in a variety of ways.

Now, I am not saying there is anything wrong with this, yet.  But let's see what happens when you don't know the rules of power.  Or in other words, when you are un-socialised.


An example of non-socialised behaviour

Let me give you an example of my son, not knowing the conventions of school.  My son was aged 8 and had never been to school.  My son is smart, polite, interested in learning and is at ease in any social environment.  We went to a camp and all the children were asked to sit on the mat while the leader went over the rules.  I watched with interest as my son copied those around him, sitting and conforming to the pattern.  This was his first time in such an environment.

When the leader started talking to the group, he talked to them like he was talking to an individual.  He began with an introduction and then moved to talking about the rules of the camp.  He made frequent use of rhetorical questions.  By this I mean, he looked right at the group and asked "Now what's going to happen if you don't clean your rooms in the morning?"

My son answered him aloud with a rational answer, "We won't be able to have breakfast?" [this had just been stated by the leader].  The leader did not answer or acknowledge him but kept on speaking, answering his own question.  Clearly, the children were not meant to answer the question.  All the other kids knew this.  I watched as my son struggled with this strange response, and then continued to answer the questions as you would in a conversation.  In his whole life experience when he was spoken to by anyone, who asked him a direct question, he would answer.  It was a dialogue.  When spoken to by an adult he would answer.

[Now, I could see that the other parents were wondering why my son was talking, and whether he was going to be a behavioral problem during the week!  To be fair I probably would have suspected this too had I not known my son.]

My son continued to answer a few more times before looking around and seeing that the other boys were remaining quiet, and that he was completely ignored by the leader despite being heard.  Then the leader asked another question and several boys raised their hands.  The leader waited a moment and then pointed to one lad with his hand up.  The boy gave an answer, and the leader said 'yes' and then off we went back into the talk.  Lesson learned.

The other strange thing, was that the leader rewarded the group for being quiet (the quietest boy got a t-shirt!) and berated them for making noise.  In fact they had to demonstrate sitting quietly before being allowed to move to an activity.  In our house you are encouraged to talk, and the idea of not being allowed to talk is just weird.  I watched as my son quickly became socialised into the framework by learning the rules of the game.

The social norms (rules)

To be socialised means to know, and obey, the rules of the game.  In this case, the rules were as follows.  Do not talk.  Do not answer questions, unless the question is said with a certain tone and intonation - then put up your hand and wait to be selected.  Sitting up straight, with your arms and legs folded will help you get selected.  And do not speak at anytime, if you want to be picked to answer a question, (and clearly being picked to answer a question was a privilege).  Be quiet and don't engage with the speaker, just watch.  Raise your hand when you are want to demonstrate your obedience.  Theses are the rules in this environment.  Becoming socialised is learning, AND obeying, these rules.  

Of course, all of these classroom norms (rules) are designed to limit the disruptive influence of impulsive children.  But all children, impulsive or not, are subject to them.

To my distress the normal relationship my son was used to having with adults would not be happening at the camp.  A new framework was in place that impacted his relationship with others.  It was now hierarchical.

But here is the thing.  In all my sons previous experience he would engage in equal discourse with others, adults and children alike.  But now he was not allowed to talk, or respond except within controlled rules.  He had been demoted, he had relegated to a sub-category of people.  A group spoken to, but unable to speak back.  A group that had a set of rules that the adults did not have to obey.

Moreover, the leader had not raised himself up to a position of authority, but rather my son was demoted from the status of an equal, to a follower of abnormal social rules.  Welcome to camp!

Again, I am not saying this is bad.  I know and appreciate that we all have to learn about staying quiet in certain environments to facilitate the communication of information.  But to see it in all its starkness was actually quite confronting.  And no, I am not a hippie who does not believe in authority (the opposite in fact).  I saw my son being ignored and treated as a lesser, and I saw his confusion.  He didn't fight it, within a day he had picked up the rules.  He no longer tried to talk to the speaker when in a group.  It took my son about 5 minutes to become socialised to the rule system because he desperately wanted to get on and have fun.

So, what does it mean to be socialised in regard to school norms?  In one sense it means accepting, accommodating and conforming to power hierarchies.


Here is a question though.  Is there a down-side to being immersed in these hierarchies?

Definitely.

If you do not have strong enough contrasting models in your life then 'yes' there is a huge down-side. To be immersed in a sociocultural environment that establishes this pattern for the first ten years of your life is hard to escape, even with good role models.  I have worked with hundreds of adults who remain trapped within this framework.  I have worked with hundreds of employees who also remain trapped.

This experience touches on crime, welfare, education and self-determination.  It concerns how one takes action, seeking either to circumvent authority, to align with power, or to usurp and re-establish power.  I could talk for much longer on this, but would be interested in others thoughts.

Home Schooling report indicates high vocabulary skills but average to low maths skills

Why do home schoolers have good vocabularies but average to *low numeracy skills?  Well, it's all to do with bootstrapping.  A brief summary:


Bootstrapping refers to pulling yourself up by your own bootstraps.  In education it refers to a self-teaching process that occurs when engaging in activities that have reciprocal feedback systems.  One such system is reading.

For example, learning to read is almost a pure process of bootstrapping. Once a child has a system for decoding words, the very process of reading facilitates learning.  By sounding out words they strengthen all letter sound connections, and as the frequency of exposure to words increases they create connections between whole words, their sound and their meaning (graphaphonic, phonological and semantic systems).  The reciprocal effect occurs between these systems and comprehension. Comprehension is a product of the first three, plus prior knowledge and strategies, which increases the motivation to read, which keeps the cycle going.  In short, reading develops reading skill.  Once decoding is learnt, the system is self-constructive; hence bootstrapping.  It is not taught.  Hence, most reading difficulties can be traced upstream to decoding.

Secondly, there is a sociocultural effect.  Children in households that read, will be highly likely to become good readers.  Children who grow up with books in the house, who are read to, and see Mum and Dad reading, are more likely to read themselves.  High reading levels influence vocabulary (you develop your higher vocabulary from reading, not listening to speech), and thus home schooling kids have good vocabularies.  This is great by the way, as vocabulary is associated with many great outcomes.

Finally, the amount of reading a child does relates to their vocabulary level.  While there are caveats, basically the more they read, the better their vocab.

The problem with maths

There is no bootstrapping effect in mathematics if it is taught in a certain way (read here and here for more).  Unlike reading, children in houses in which the parents are good at maths do not necessarily become good at math.  Whatever positive sociocultural effect occurs with reading, doesn't seem to occur with maths.

Maths is generally taught by an external person all the way, all the time (be it a teacher or computer software).  This means the child's opportunities to get better at math are restricted to occasions of direct instruction.  Research suggests the total time doesn't add up to much no matter how you look at it.   Second, much of the time doing maths is spent on worksheets, and almost all the worksheets children work on are a repetition of known content (you learn to add double digit numbers and then do a sheet of double digit equations). Very rarely do they encourage the user to engage in non-routine exploration of ideas and concepts.  Completing worksheets in a routine manner is a poor version of learning, (rehearsal strategies are the least effective of almost all strategies), and they certainly do not encourage bootstrapping.  More of the opposite actually, they tend to teach the child to return to the parent to get help when stuck, at which point the parent tells them what to do.

Think of the difference between time spent reading per day, versus time spent doing maths.  The reason is that reading is used as a tool to do stuff.  Maths, in contrast, is simply a task to be completed.  Imagine if we used maths as a tool to solve real problems everyday.  Then, the bootstrapping effect might take effect.


As an experiment compare your child's time reading versus actual engagement in maths (not just staring at the page like I tend to do).  Be sure to include all reading, such as that done while watching TV, reading signs and so on.  Add to this all the reading they do for other subjects. Once you have the number, extrapolate that to a yearly difference. One piece of NZ research found that NZ primary school children did only 10 minutes of maths a day on average (and this was with a compulsory 1 hour of maths a day rule!).

So, in summary, the benefits many children get from homeschooling are a consequence of family values (we read and enjoy books) and the bootstrapping effect this has on learning.

But, it may be that we need to make maths as much a part of our family culture as reading. Then, I have no doubt, we will be producing avid users of mathematics ready to take on the world.

Tip: Hang a white board in the kitchen and every morning write a maths problem for the kids to solve.  Make it reasonably easy so as to cultivate a culture of success and fun.  Maths should be fun, not hard- so don't make it hard - make it fun.  The kids can chew on it all day, and write the answer on the board.  At a time convenient have them explain what they did and then share how others did it too.  I'll do a post that includes a bunch of starter problems - watch this space.

*Note: The school results for maths and numeracy are also average to below average.  This is not unique to home schooling.  It would be interesting to compare the home school results directly to school results but methodology issues (as noted in the report) make this difficult.  

Staff attrition rates

I would love to see the data on tutor attrition rates in educational organisations.  I wonder if we would see patterns?  Do tutors leave in packs, two or three at a time? (Or more!?) Do they tend to leave in the latter part of the year?  What programmes do they leave, and what was happening in the months prior to this?

What do you think, are high staff attrition rates indicative of highly effective or ineffective organisations.  Is the impact on learners positive or negative?

Here is something to think about regarding replacing these tutors:  Is a new tutor as effective as an experienced one?

Some people think that new tutors bring new energy and that this makes up for a lack of experience.

If I was in an arguing mood I might say that I would rather have an inexperienced new energetic tutor rather than a tired old experience tutor.  But I would be mostly wrong.


What happens if we consistently swap experience for energy?

The post below expresses some concerns and solutions if you are interested.

A big thank you to VARDA for a lovely evening last night.

Varda is the new name for The Waikato School of Hairdressing.  I have had the privilege of working with their tutors occasionally over the last few years (maybe longer!).

The Varda team is fantastic.  From the owners, to the managers, to the tutors, they not only design 'a look', but students too, building confidence, skills, and artistry.  They take young people with few skills, and mold them into amazing hair designers with ambitious dreams.  But it is not only that.  The students possess a confidence and professionalism about them that is a direct response to the ethos of Varda.  The place hums with energy.  And the thing that strikes me the most when talking to the Varda staff, is how much they care about their students.  They are invested in their success, at a personal and professional level.


Having talked with their students, it's pretty clear VARDA has had a huge impact on them.  It has broadened their horizons, introducing them to new opportunities that many hadn't had access to.  I spoke with students who's early school years were less than positive, in fact darn right tragic in some cases.  And as we know, these beginnings often end with poor life outcomes.  Yet, for these students the programmes they were on, had changed that trajectory, setting them on a path toward achievement and success.  The stories are an encouragement for anyone working with young people and wondering if any of it makes a difference.  Yes it does.

Varda is a success story.  The students are evidence.

Check out their site here: VARDA

Emmy Noether - 133rd Birthday

Today is Emmy Noether's birthday.  Albert Einstein described her as:

"The most significant creative mathematical genius thus far produced".

An interesting fact about Emmy.  She was going to be an ESOL teacher, but saw the error of her ways and shifted to mathematics.  Not that I'm tribal or anything ;)


On another note, what do you think Einstein meant by 'produced'?

A new maths?

I attended a workshop run by Associate Professor Joanne Mulligan from Australia.  She was discussing a new 'type' of assessment that will be up and running this year.

The area being discussed was 'pattern and structure' in contrast to 'number' which is what we usually are exposed to.  Although, actually the Learning Progressions do a pretty good job of covering a broad range, although not not so much the above.

The assessment deals with how children perceive, make sense of, and recall visual images (one part anyway).  An interesting piece of information was the fact that learners can score fairly highly in number, yet have significant difficulties with pattern and structure.

The assessment tasks and learner responses really got me thinking about adult learners.

For example, I have noticed that learners often struggle with the idea of 'area' being measured in equal sized squares (not to mention when the area includes a decimal).  I have also noticed that some learners often struggle to copy the 'dice of fortune' grid when copying from the board.  These, and other areas of difficulty, may represent weaknesses in pattern and structure.  If a learner cannot 'see' the pattern as a pattern, but rather see it as random lines and dots, then their working memory is really up against it.  A bit like someone partitioning without automaticity in basic number.  Eventually, they fall behind.  

If these skills are undeveloped it will manifest as difficulties in number at some point, but particularly in space and shape.

The assessment is still confidential, but will be released in Australia later this year.  It would be well worth the adult sector having a look at it.

On tutor turnover

Due to an interesting conversation I had with a tutor this week I am re-posting this post.  All the issues are as relevant as ever.  And with a new TE Strategy about to hit the scene, probably worth another look.

We have some great things happening in the entry level of the tertiary sector.  We work with learners who have the high needs and learners who are very demanding.  We work with learners who have experienced failure and without our help will repeat those patterns of failure.  We work in a tough environment and do it well.

We also have some systemic problems that continue to limit the kinds of success we all want.  One of our biggest problems is high tutor turnover.  This is compounded by poor organisational knowledge management.  In other words, tutors leave often, and when they do, they take large chunks of knowledge and experience with them.

Why is high turnover a problem?  Isn't it feeding us new blood?

Schoenfeld's recent work with teachers provides some troubling findings.  He found that teachers up until the fourth year of teaching were primarily focused on mastering classroom management.  The actual educational gains of students were low, because the teacher was attempting to master the demands of running a class and learning the system.

The next four years of a teachers' career was focused on learning content.  They needed to master what they were teaching.  Let's call this subject knowledge.  Again, the learner gains were very limited.  The teacher's attention is split.

The next four years were spent mastering pedagogical knowledge - actual teaching to students.

Consequently, it takes 12 years for a fully trained teacher to begin to teach students really well.  And this is with a teaching degree, support and constant PD.  Not to mention regular pay rises and a supportive organisation (we assume).

Our sector has about a three year turnover period for tutors.  Several years ago it appeared to be less. There is little hard data so this is based on my observations.  At the time I asked every group (at workshops) that year how long they had been in their jobs and took note of the results.  One quarter had been in their job less than six months (sample was about 1000 tutors) in 2012.

It is not hard to see that tutors are occupied with mastering classroom management, developing content knowledge, and administration knowledge (NZQA, Assessment Tool etc) in their first few years, rather than developing great pedagogical knowledge.  To be blunt - Tutors are struggling to get a handle on the job and leave before developing high quality skills.  Consequently learners (the most demanding across all spheres of education) are not receiving the quality they require.  I don't say this in a judgmental way, I tutored for eight years straight (25 hours face to face contact 49 weeks every year) And STILL struggled.  I tutored a programme last year and STILL struggled with the competing tensions.

The turnover erodes learner progress,  tutor development and institutional progress.

Why do tutors leave? 

I believe the reason tutors leave is twofold:  First is the growing discrepancy between their actual work outcomes and the demanded work outcomes.  Most tutors enter the sector because they want to help people get more out of life.  This is the real reason they are in the job, or at least a large part.  This can be called the 'actual' outcome.

Actual tutor outcomes:

• Positively impact people who need support
• Build confidence
• Work with and encourage young people 
• Developing real skills that will pay off in the real world
• Minimising negative behaviours and maximising positive ones
• Demonstrate to people what can be achieved

Demanded Organisational outcomes

• NZQA Unit & Credit achievements
• Movement on L&N assessment tool
• Attendance
• Completion rates
• Learner employment

Now I know it is not as easy as all that.  But my suspicion is that the tutor role no longer reflects the values that attracted people to the role in the first place.  Hence, the downside of the role is no longer equally balanced by the positive side - and people simply leave (actually, the people with options leave).  All jobs have aspects that we struggle with, but those tensions are balanced by other positive factors.  The tutoring role is out of kilter.

Solutions:  

Many years ago during my degree I did a case-study of an organisation that was having difficulty with staff. Upon investigation it was clear that the staff had gotten themselves into a cycle of complaining and this cycle was now self-perpetuating.  The staff worked hard and well.  But when they got together the conversation always gravitated toward how bad things were getting.  Any negative thing that did happen tended to be taken as evidence that the whole organisation was negative. Management was largely absent but because the staff were highly committed they continued to perform at their very best.  The management were unaware but the staff as a group were on a downward trajectory.

Long story short, I interviewed staff and came up with some solutions based on some theories I was using (mostly motivational theory). The main solution had to do with the personality, traits and motivational make-up of the tutors.  The tutors were short term task oriented, yet highly relational.  They were motivated to make a difference for their students - not motivated by money and  not by achievement.  What did they need most?

Affirmation

I designed a plan based on the make-up of the staff and also drawing on Herzberg's two factor motivation-hygiene theory.  To my mind this is one of the most valuable ways of looking at the PTO sector. Look it up if you don't know it.

As a part of the plan I designed a meeting every two weeks with each staff member.  This would I believe have interrupted the cycle.  But it had to be personal and face to face.  Group rewards were ineffective with this group.  For example, a group trip away as a thank you to everyone would not be effective (this turned out to be a hygiene factor rather than a motivational factor).  They needed individual affirmation.  It had to be real and specific.  Any hint of in-authenticity would blow it. It didn't require money, it required genuine appreciation of a job well done from a senior.

The managers did not do this.  They had their reasons.  However key staff members dominoed out the door. Once one person left, they all went.  I have seen this happen about five times now in the same situation and sector.  The organisation then has to recover and this takes time and hurts learners.

Career pathways

The second way to begin to slow down turnover is to do some thinking around progression plans.  Tutoring has become a terminal job.  That means no pathway of progression.  It means anyone with aspirations must leave to get ahead.  Anyone who needs to save money must leave to get ahead.  As part of an annual review the organisation MUST build in a progression for the tutor.

You can also choose, as many do, to simply let tutors leave and train new ones. But in truth we are kidding ourselves if we think this is a sustainable strategy.  This simply places huge strain on the new tutor (see issue one) and on supporting staff.  But here is the kicker:  The learners will not learn.  You may get them through units, but these skills will be gone within 2 months.  You may get them jobs (great) but you will not have improved their skills.  You may have inducted them into a way of behaving, but you have not improved their skills.

Your organisation needs to be improving every year, year on year on year.  You can't do this if organisational knowledge is rolled back to zero every few years.

Tough talk

The pressure will be coming on soon for PTEs to produce 'real' learning outcomes.  There is a cull coming (we have already seen the start of it) and those organisations that don't begin the transition to become real education organisations will not make the grade.  Mastering the art of moving learners through Unit standards will not be preparation for the next wave.  Those credits will have to reflect authentic skills development. That means if you re-assess any learner in 6 months they should easily pass the assessment.  Ask yourself, what if you reassessed all your learners right now on the units they have passed, with no teaching or support, would they easily pass the units?

We need professional tutors, who want to do this for a career.  This may require an entirely different business model in order for current funding streams to make this possible.  I have some ideas - would love to hear others.

Updated:  Graeme Smith has some great thoughts here.

Exactly why we need better maths resources!

The zombie apocalypse is here

I have been working on a book/resource designed to transition learners' knowledge and skills with angles to trigonometry. A part of this is the Pythagoras theorem.  A couple of years ago I developed the sheet below to promote discussion and thinking around the hypotenuse.  It's rough, (I repeat - it's rough) but I have a new and improved version so the older conceptual model is below.

The idea is to just let people try to work out what needs to be done and how it might be done.  Confusion is okay (avoid the need to explain it).  This will lead to a conversation about Pythagoras - which presents an opportunity to play with the concept.   Two versions below, the first with more scaffolding.  Yes, they are rough - just concept stuff at this stage.

Would love to know if it works though!

Books you must read 

A friend of mine is on a mission to read books that make him smarter and has asked for some recommendations.  He mentioned that the shallow nature of Facebook has eroded his ability to really think deeply.

Reading books to make you smarter does not mean reading books you agree with. It means reading books that expand your current perspectives and ideas.  They should also provoke you to think more, and put you in contact with the smartest minds in various areas.

I remember doing a study on B.F Skinner and thinking that since behaviorism had largely died in educational thinking there would be little of value in his books.  How wrong I was.  In fact, I ended up reading every single book Skinner ever wrote.  I think I understand his ideas and now have an informed view of what I agree with and the limitations of this ideas.  It also helped me understand the emergence of constructivisim and all its variants.

So I am putting together a list for educators.  Now - these are not all books I agree with, but books that have made me think differently.  They are all very different, but if you read them, you will be better educated and a better educator.  I recommend them all and will update the list over the next month.

The books are grist for the mill.  The first four are a slightly skewed balance between competing views of education.  A good project would be to identify the competing themes.

On liberty - John Stuart Mill
The Advancement of learning - Bacon
Atlas shrugged - Ayn Rand
Pedagogy of the Oppressed - Paulo Friere

The problem of engagement

There is a line of thought in the numeracy discourse that goes like this: A learner's motivation in a certain area can be used to piggyback numeracy content.

An example is a learner who loves cars, and is on an automotive engineering course.  The theory states that they will engage to a greater degree with numeracy if it is presented in the context of car specs, and if the content is relevant to their needs.

It sounds true.  And there is some self-report data to support the idea.  Learners who believe that numeracy is useful tend to achieve better than those who don't.

But, I'm not so sure about all this.

Engagement in 'numeracy tasks' at a micro level is how numeracy skills are developed. Does the relevance of the situation context improve micro engagement?  Not from what I am seeing.

Here are some questions for numeracy tutors:

• Do your learners engage more in numeracy tasks that are fun or important?
• Do your learners engage more in numeracy tasks that have clear performance goals (how many can I get right) or conceptual understanding goals (a new way of thinking about an idea)?
• Do your learners engage in different ways depending on the time of day, or the day of the week?
• Are your learners motivated by passing assessments, or developing meaningful understandings of numeracy concepts that will be useful in their lives?

Finally, do your learners actually believe that the numeracy content they are learning on the programme is relevant to their needs?  And how would you know?

Question

I got asked this question the other day.  I'd like you to think about how you would answer a skeptic.

Has the emphasis on literacy and numeracy in vocational courses improved learners' literacy and numeracy over the last five years?




What would you say?

My reply was;

Yes, but not in the way we expected or to the degree expected.

My research findings are a little less positive regarding 'actual' learner gains than many other studies, yet indicate that programmes and tutors make a huge difference in many (but not all) learners' lives.  Embedded L&N is a big part of this.

What needs to change?

The paradox

Many years ago, myself and a friend, who worked for the TEC, attended a numeracy training course. The course was on 'how to teach numeracy' and we were drilled in constructivist approaches. However, during one part we were informed that tutors were no longer teachers, tutors, educationalists or trainers, but rather - facilitators.

Now my TEC colleague took exception to this, and proceeded to exclaim loudly that this was rubbish ("You mean we can't teach them anything!"), and thus started a class debate through which the 'facilitator' lost all control.    

I remained quiet, because I actually agreed with both of them.  I had been immersed in constructivist thinking and was a believer, and still am (a Jo Boaler convert). BUT, I did not like the Orwellian attempt to reduce my chosen vocation to that of facilitator (it simply does not impress at functions)!

This has come up many times since that workshop, and the conversation always misses the deeper issues at hand.  At best, the discussion situates on how much we can 'tell' students versus how much we should expect them to 'construct' understanding.  And all the opinions in between, like the much quoted, "it would take too much time to let them figure it out by themselves" to "if you just tell them they just forget it all anyway".  Part of the real issue regarding numeracy, and why the answer is anything but easy, is discussed below.

The paradox

The conflict is actually situated in the middle of an educational paradox.  Here is the issue - to develop an adult's numeracy skill several things must happen.  One, they must learn content, and two, they must develop agency.  Agency is the learners ability to take action independently for their own purposes.  Third, they must be able to apply their knowledge with agency to unique and novel situations.  Numeracy skill is the ability to take what you know and apply it to situations you have never seen before, and in ways never done before (rather than the reproduction of memorised methods).

Now here is the paradox.  To enable learners to use numeracy in unique, novel, and self-directed ways, the tutor can only ever create conditions in which this MAY happen.  If the tutor shows, tells, explains, scaffolds or models to the learner what to do, then they prevent the learner of autonomously using their skills in unique ways.  And the learner never becomes autonomous or self-directed!  

Do you see it?  You cannot make someone autonomous!  Everything the tutor does to produce the behaviour in the learner they want, deprives the learner of the necessary conditions to do so!  In fact, according to Brousseau and Sarrazy, (2002) the only learner who develops these skills, is the one who actively rejects the teacher (in favour of their own methods).

This is one of several educational paradoxes that settles down around the role of the tutor.  It requires some real thinking about how we balance the numeracy instruction so as to meet both content and agency needs.

So, back to the argument.  Both my friend and the facilitator were right, but they both failed to appreciate the depth of the issue.

However, one thing I do know, the term 'facilitator' is demeaning of someone attempting to create the conditions in which a learner may develop agency and autonomy.  That role is more closely aligned with 'master designer' or 'situational engineer' or... 'grandmaster'.

Love your thoughts.