Early models 

I'm giving a presentation next week and was looking through some old material to prepare. I came across some early attempts to model the factors that might extend between school and adult experiences with mathematics. There is some explanatory use in the diagrams but they need to be re-worked and represented better.  

Here is the original.  I'll post these so I can track the progression of the new versions.

What my findings suggest is that the four interrelated beliefs are developed during school and go on to create a beliefs system (perhaps schema) which frames how tertiary mathematics is experienced by the learner. This extends into real world tasks also. Essentially, the belief system acts either as an affordance, or as a constraint. Unfortunately, for many learners it acts as a constraint and in many cases perpetuates cycles of mathematical failure.   

Learned helplessness

Learned helplessness is one of the biggest problems in adult literacy and numeracy.  It is the creeping, silent, invisible enemy of educators (and parents).  Unfortunately  educators or parents rarely recognize its' impact and they rarely know what they are up against.  They just know that their children or their learners are not learning.

Let me begin be describing what learned helplessness is and how it began.

Story of two dogs

Once upon a time there were two dogs.  The first was hung up in a harness and subjected to a series of mild/medium electric shocks.  However, the harness was configured in such a way that if the dog touched a plate in front of its nose, the electrical current stopped.  The dog figured this out and when it was shocked it touched the plate.  It learned that it could stop the shocks.

The second dog was hung in the harness and also subjected to the same treatment.  However, this time there was no plate and no way for the dog to stop the electric shocks. This dog learned that it couldn't stop the shocks.  They continued this for some time with both dogs.

Now they took these two dogs and ran an experiment to see if they behaved differently under certain conditions.  They made a container with a small wall dividing it into two parts. The dogs could easily step back and forth over the wall, but could not escape the container. The floor on one side of the container was a steel plate allowing electricity run through it. Any dog standing on this side would receive electric shocks.  However, before the shock was administered a light would begin to dim warning the dog of the shock.

When the first dog entered the container it stood on the steel plate and received a shock.  It immediately jumped to the other side of the container and stayed there.  It quickly recognised that the shocks were preceded by the dimming of the light and moved as the light began to dim, therefore avoiding the shocks.  It repeated this behaviour in a variety of different containers - always responding to the dimming light and moving to avoid it.

The second dog however, was very different.  When this dog received a shock, it did not move.  It just hunkered down and continued to receive the shock - always, even when safety was one step away.  It did not respond to the warning (the dimming light).  It did not believe it could make a difference.

You see, the point is, they trained the second dog to be helpless.  They trained it to believe that it would get shocked no matter what it did - so it did nothing.

The question then turned to this: - Can the same thing happen to people?  Yes

Learned helplessness and maths 

Mathematics classes actually recreate the conditions necessary to develop learned helplessness.  The way they do this is complex.  However here is a simplified example, a learner begins to fall behind in a class, he stops understanding most content but does answer some questions correctly here and there.  The learner takes some action to improve.  They may ask a friend for help, ask the teacher to repeat the problem, go home and repeat the classroom problems and so on.  However, if the learner still continues to struggle they begin to get the sense that nothing they do actually makes any difference.  They sit in class and become bamboozled by the content, occasionally getting some things correct but generally failing repeatedly.   When they do get questions correct they attribute it to the work being easy, and when they struggle they attribute it to being too hard.

Sustained failure cultivates learned helplessness until it becomes self-perpetuating - at which point they are lost.  

The end result is that these learners stop trying the moment things get a bit tough.  They will give up trying in the face of any difficulty and relegate the content as too hard.

Key characteristics are expressed by this advertisement.

Anyway, I didn't want so much to describe LH but rather to give you a checklist.  The list below will describe it better than I can.  I have stolen it from a wonderful researcher named Shirley Yates (2009), who tested it to see how reliable and valid it is.  Use it to think about your learners, children, or self.  I am going to write this in the masculine to save time (no sexism intended!)  Think about your learner while they are doing maths.

1. The student gives up when you correct or find a mistake in his work.
2. The student takes little independent initiative; you must help him to get started and keep going on an assignment.
3. When he fails one part of a task he looks discouraged - says he is certain to fail entire task.
4. Tries to finish assignments, even when they are difficult (reversed).
5. Does not respond with enthusiasm and pride when asked how he is doing on an academic task.
6. When experiencing difficulty he persists for a while before asking for help (reversed).
7. Says things like "I can't do it" when he has trouble with his work.
8. When he receives a poor grade, says he will try harder next time (reversed).
9. Prefers new and challenging problems over easy ones.
10. Prefers to do easy problems rather than hard ones. 

The idea of these items is that you rate each one on a five point scale (1 = not true - 5 = very true).  The higher the score the more indicative the learner has LH.   However, I think that if any of these ring slightly true for you (regarding your learners) you need to act immediately.  Once LH is established the consequences are serious and persistent.

Look at the reversed statements (numbers 4, 6, 8).  These are what you want to cultivate in your learners/children.  In fact if you do - it is the greatest gift you can give your child.

If you would like to know more about learned helplessness - make a comment below.


Yates, S. (2009). Teacher identification of student learned helplessness.  Mathematics Education Research Journal, 21 (3), 86-106

For parents of high-achieving girls

Girls are consistently out performing boys across almost all areas of education.  The advantage that boys had in mathematics has largely vanished. 

However, one area that girls do have difficulty with is at the higher levels of education, particularly high-achieving girls. What seems to be happening is that girls achieve well, and expect to achieve well. However, the constant success may not have developed the tenacity, or grit, that is required at higher levels of education, particularly in maths. Hence, when the learner fails, and they are not used to it, it hurts.  Often it damages, or collapses, the learner's self-belief about their ability to be successful in the given field. 

Some of these learners have not experienced 'fighting out of the hole', and instead feel defeated and as thought they have reached their limit.  Many brilliant people quit.

Here is a sentence from Carroll Dweck that should get your attention:

"What we found was that bright girls didn’t cope at all well with this confusion. In fact, the higher the girl’s IQ, the worse she did."

Contrast this with the average achieving learner who has scratched and clawed their way through, constantly fighting to stay in the game.  They may have developed resilience, persistence and grit -which count for so much at higher levels of education.

Of particular note, is the impact of beliefs on how learners interpret and respond to failure.  Your beliefs as a parent will strongly influence your children, positively or negatively.

Anyway, the link below is to a great article by Carol Dweck.  If you are a parent of daughters, it is well worth a look.

Click here for - Is math a gift? by Carol Dweck

If you are too lazy to read, here is a TED talk by Duckworth about grit.  A great message.

Drug taking, learning, and vocational education

The article below reveals what those of us in the sector know - Marijuana is a huge problem in the vocational sector, and no one except the tutors ever talk about or acknowledge it. I have had many experiences with students who are as high as a kite in my classes.  It is very difficult to deal with for several reasons.  

Number one: The learners don't retain ANY of the content they engage with while stoned. It's often back to square one - again.  

Number two: If you expel the learners you have ended their last opportunity for success. The stakes are VERY high. The argument about them taking responsibility for their actions breaks down when you realise the Government took responsibility for their actions long ago. That train has left the station.  Think through what the outcome is and comment if you want me to add to this.     

Number three:  In certain sectors (see horticulture and agriculture below) it is not restricted to several learners but typically the majority. 

Waiariki appear to be doing a GREAT job, with their tough but supportive approach.  Way to go guys.

Read the article below or click the title.

Waiariki drug testing a positive

DRUG testing at Waiariki Institute of Technology has encouraged a student to give up drugs.

Tristin Te Pou, 20, is an automotive student at the Whakatane campus and was the only person to fail the compulsory drug test at the beginning of the semester in June.

As a regular cannabis smoker, Miss Te Pou was eager to quit when she enrolled at Waiariki.

“I wasn’t aware of the drug test but when I was accepted three days after I enrolled, I was keen to give up.”

She had been drug-free for two weeks before she was tested and when the result came back positive for drugs she wasn’t shocked or surprised, but eager to produce a clean test in a week’s time.

“It was a realisation. I knew it was going to be like that because of the amount I smoked. But I had time to get rid of everything.”

She was given a week to re-do the test and in that time she did all she could to “sweat it out”.

“I did exercise, skipping and walked over town to my friend’s house on a really hot day. I did anything to get it out of my system.”

She said it was emotional for her because she really wanted to continue the course and was relieved when the next test was clear.

Miss Te Pou said it was fair that Waiariki made students take drug tests because some industry positions required them to be unsupervised and being drug-free would mean “they were on”.

Waiariki automotive tutor David Ball said he was proud of Miss Te Pou and her effort to become drug-free to continue the course.

Mr Ball, a tertiary tutor who has been at Waiariki for three months, said he thought the compulsory drug testing was a positive for many reasons – for potential employers and the students themselves.

He said potential employers were more open to offering work experience and for the students it was a sense of pride that they could accomplish something and work toward a higher goal.

The institute began compulsory drug testing of all trades programme applicants earlier this year.

Waiariki regional development manager Greg Brimmer said at Whakatane those trade programmes were in the automotive, construction, agriculture and horticulture fields.

Of 17 students enrolled in the horticulture course for semester one, only two were clean, Mr Brimmer said.

He said none of those students wanted to re-take the drug test, which meant the class had to be cancelled that semester. In semester two 16 students are enrolled and will take the drug test this week. Mr Brimmer expected most would pass.

He said in the construction course three out of 17 students failed, but two resat two weeks later and passed.

Five agriculture students failed the compulsory drug test.

“To pass the next, they attended a boot camp run by the tutor and passed two weeks later.

“If you want to work, you have to be drug free.

“It’s a good move for this area because it’s been a high usage location, particularly for marijuana,” Mr Brimmer said.

He said there had been no drop in enrolments at the Whakatane campus. The year-to-date roll was 545 students.

In the full 2015 year, 798 students were enrolled at the Whakatane campus, in 2014 there were 758 and in 2013 736.