Wednesday, 20 February 2019

Statistics and critical thinking


Some quick thoughts on statistics, critical thinking, and foundation-level learners. 


Type one statistical thinking – Understanding how data is collected

Mark Twain noted ‘There are three kinds of lies: Lies, damned lies, and statistics’. He seemed to be implying that statistics were a tool used to manipulate the truth. Perhaps he was suggesting that politicians, advertisers, and others use statistics to mislead the public? What a concept.     

When teaching statistics to foundation-level learners it is useful to think of statistical critical thinking skills as two skills. The first is to understand ‘how data was collected’ and the second ‘how the statistics are represented’ to the reader. The first is closely related to typical critical skills, and the second more mathematically oriented. Foundation-level learners often enjoy the first and are not so familiar with the second.   

Understanding ‘how the data was collected’ is useful when presented with information such as this old advertisement for smoking.





Critical questions here might include:

Did they ask every single Doctor whether they smoked? How many did they ask, where were they from, how many answered, and how didn’t smoke and how many did? Of those who did smoke how many smoked Camel? Why did they smoke Camel? Were the Doctors given any incentives to promote Camel?

Question: Based on the evidence in the advertisement above is this scenario possible.
The researchers asked 50 Doctors whether they smoked. Five said they smoked. Three of these smoked Camels.

Could this be true based on the advertisements claims?

An old ‘good boy’ dog food scam.
A large company sold a popular brand of dogfood called ‘good boy’. The company was putting together a new advertisement and wanted some statistics to use in the advertising.






Here is how they produced the statistics.

An employee rang ten people and asked them what dog food they used to feed their dog. They recorded the amount of people out of ten who named the company.
They then rang another group of ten people. Then another. Then another. After doing this they simply selected the group of ten in which the highest number had selected their dog food. 

The statistic used was ‘six out of ten dog owners use good boy’. It was true, one of the groups of ten people had six members who used Good Boy. What wasn’t mentioned was that this was the highest of the ten groups. Some of the groups included only one or two people who used the dog food, others three, four or five. If the groups were combined the statistics would have read ’36 out of 100 dog owners use Good Boy’, or ’66 out of 100 dog owners do not use Good Boy’. Quite different. Yet the statistics are accurate – it’s the method needs to be critiqued.

However, be careful...
Despite these dubious methods of generating data, don’t allow learners to become cynical of all data. Most data collection methods are very good; understanding the strengths and limitations of the methods is the goal. Critical thinking when taken to the extreme means you can never know anything.  Don’t teach learners to be cynics, teach them to be critical evaluators.


Type two statistical thinking: Understand how statistics are represented to support certain ideas.     
Adults also need to know what statistical data analysis methods have been used and how the approach produces and represent findings. For example, if the term ‘average’ is used, does it refer to the mean, median or mode? Is the average even relevant? The ‘average NZ house price’ is frequently used in the NZ Herald. Would it not be better to know how many houses were sold in various price brackets? If two houses are for sale in a neighbourhood, one for 100,000 and one for 1,000,000, does the average of $550,000 fairly represent the situation? I don’t think so because an average of $550,000 suggests that people with one fifth of this amount cannot buy a house – and it isn’t true based on the situation.    

For example, the classic statistical scenario: There are two buckets, one full of boiling water and one full of freezing water. Stand with a foot in each. Stop screaming, because on average you feel warm.

Image result for red  bucketsImage result for red  buckets




If you only know the average, you don’t know enough to form an opinion.  

In sum, adults are bombarded with statistical information through politics, advertising, workplace statistics, dietary recommendations, safety courses, sports and health advice. In order to make sense of the information, adults require some knowledge of how data can be collected and how it is represented.

Wednesday, 12 December 2018

Petrol Maths

Stolen from David Farrar. 

"So when petrol prices are around $2.50 a litre, how much money does the Government get from you to fill up a 50 litre car?

  • National Land Transport Fund $31.51
  • GST $16.31 (on a $2.50 retail price)
  • Regional Fuel Tax (in Auckland) $5.00
  • ACC Levy $3.00
  • Local Authorities Fuel Tax $0.33
  • Engine Fuel Monitoring Levy $0.15

But that isn’t all. To pay for the $125 petrol bill, you need to (if top tax rate) earn $186.57 which means there was also income tax of $61.57.
So every-time you spend $125 filling up the car with petrol, the Government will have got $117.86 as you will have had to have earned almost $190 to pay for it!"


Note from Damon: This might not be the content to use in a financial literacy class as it may just make the students angry.

Tuesday, 4 December 2018


Good teachers/tutors make the difference

Note: The quality of teacher/tutors is directly related to outcomes.

Chauvel (2014) notes:


New Zealand research conducted over the last 10 years has consistently highlighted that the quality of teaching and the effectiveness of the learning environments facilitated by teaching staff is crucial to Pasifika and Māori learner engagement in tertiary education. As stated by Alton-Lee (2003): “…high achievement for diverse groups of learners is an outcome of the skilled and cumulative pedagogical actions of teaching in creating and optimising an effective learning environment… Quality teaching influences the quality of student participation, involvement and achievement (including social outcomes)” (p.1-2).


Supporting teachers and tutors is pivotal to improving learning outcomes. Not sure why this is argued?

Monday, 24 September 2018


Yes - this blog is ALIVE!!!!



And we're back online... The PhD is done and dusted, and all systems are go. 

This blog was designed to present the process and findings of the PhD in a usable way to the sector. I started uploading lesson plans, activities, ideas, strategies and so on and then it sort of puttered out as life got busy.

I'm going to be developing more content and this blog will be where I test ideas in a risk free environment.  I need an outlet that is low stakes to try things out. So if you are interested, I'll be dumping all sorts of stuff here to do with adult education. It'll be pretty raw, but fun, and I hope highly interesting and useful.



Thursday, 26 July 2018

Last few days of the PhD


Well, this is it - five years of work nearly over. Expect lots of content soon!


Tuesday, 8 May 2018

Cheap and nasty?  No way! 

It's all about engagement!


Some people may wonder why I do not use better materials than paper and dice to develop numeracy skills.  Well, I do.  But only when they improve learner thinking. 

My philosophy to teaching mathematics and numeracy is to focus entirely on student thinking.  Student thinking (which I call 'engagement') is a moment in time when the student stops thinking about everything except the task at hand (some call it 'flow')- they are absorbed fully in the moment as they struggle to make sense or meaning out of the information at hand.  It is in these rare moments that the learner 'constructs understanding'. And hence these are the most precious moments in a teacher or tutors day.  

Everything else is superfluous.  Everything else is killing time.  Everything else distracts.  

So, because I believe that it is only 'what happens in the head' that results in learning I am very utilitarian about my gear.  

My only question when using material is:  does this facilitate learner thinking?

To sum up the wise HULK below: Fancy resources look good but you do what you must do to get the job done. 

Image result for linked hulk smash

Self-regulated learning


The single biggest factor in learner success is a learners ability to self-regulate their learning.  It is the exact opposite to 'learned helplessness' that you should read about here.  Learn about it, understand it, and you will become a better educator.

Of course, self-regulated learning (SRL) is not easy to develop in learners particularly learners who have been beaten around by the educational sector.  Also SRL can be broken down into many sub-skills and dispositions that are generally developed separately but used cohesively.

I used to think that SRL was the secret to developing the potential of adult learners with problematic learning histories.  I used to think it was the answer to the literacy and numeracy problem.  No more embedded ELN, no more literacy or numeracy provision - just SRL.

I now realise that sitting below SRL are belief systems that dictate SRL - beliefs are the mainspring of downstream effects.


As such the form below is no good on its own, even with an extensive PD package that was almost developed and ready to go.

Moving on.