Numeracy wins again

This week’s finding is from analysis of the PIAAC data.  Here is the money shot, 'On average, one standard-deviation increase in numeracy skill is associated with an 18% wage increase.'  That means you pop up two standard-deviations and you are suddenly earning a whole lot more.  

It doesn't prove that being better at numeracy means you will earn more. This is because numeracy skill correlates with other things such as socio-economic status, employment and health.  Also, you may very well learn the numeracy skills 'on the job', which would also explain much of the findings. However, it is very compelling.  No such findings were found for literacy.  

Note that the increase in wages are not as large in countries with denser union numbers. I guess this is because there is less opportunity to leverage your individual numeracy skills.  

Returns to Skills around the World: Evidence from PIAAC

Eric A. Hanushek, Guido Schwerdt, Simon Wiederhold, Ludger Woessmann

NBER Working Paper No. 19762
Issued in December 2013
NBER Program(s):   ED   LS   PE 

Existing estimates of the labor-market returns to human capital give a distorted picture of the role of skills across different economies. International comparisons of earnings analyses rely almost exclusively on school attainment measures of human capital, and evidence incorporating direct measures of cognitive skills is mostly restricted to early-career workers in the United States. Analysis of the new PIAAC survey of adult skills over the full lifecycle in 22 countries shows that the focus on early-career earnings leads to underestimating the lifetime returns to skills by about one quarter. On average, a one-standard- deviation increase in numeracy skills is associated with an 18 percent wage increase among prime-age workers. But this masks considerable heterogeneity across countries. Eight countries, including all Nordic countries, have returns between 12 and 15 percent, while six are above 21 percent with the largest return being 28 percent in the United States. Estimates are remarkably robust to different earnings and skill measures, additional controls, and various subgroups. Intriguingly, returns to skills are systematically lower in countries with higher union density, stricter employment protection, and larger public-sector shares.

Adult numeracy - is there a problem?

I am in the process of updating my literature review and am finding all sorts of interesting things.  The statements below are taken from Professor Diana Coben's presentation found here:

http://www.alice.ch/fileadmin/user_upload/alicech/dokumente/sveb/projekte/Pr%C3%A4sentation_Coben.pdf

She notes:

Use value and exchange value are both necessary.

50% of employers are dissatisfied with the basic numeracy of UK school leavers.

Many firms see a grade C or above in maths and English at GCSE as a benchmark of employability. But this year barely half (55.2%) hit that standard in maths (CBI, 2007)

I'd love to see some New Zealand research. I wonder what we would find?

References.

CBI (2007) CBI applauds GCSE students but gaps in basic skills remain nightmare for firms. Press Release, 23 August, 2007. http://www.cbi.org.uk/ndbs/press.nsf/0363c1f07c6ca12a8025671c00381cc7/ bc6e9d1d3b30a71f80257340003830ad?OpenDocument

Whiteboard problems - Pythagoras theorem 

If you are working on the Pythagoras Theorem these three problems may be good fun.

Wednesdays Whiteboard Puzzle

Below is one of the best puzzles I have ever come across.  The clip below embeds it within a communication context, but you can just copy it straight to the whiteboard.  My advice is to try and solve the puzzle before watching the entire clip.

It's a little long winded I know. Endure.

Good luck.

Does school reduce your ability to apply maths to the world?

The 'suspension of sense-making' has always fascinated me.  I hope this clip creates some interest and discussion among those of us in the adult sector.

Some of you will think I'm being a little heavy handed. Perhaps. But I do think its an issue that receives very little attention here in the NZ tertiary sector. 

The key point is to think about 'embedding numeracy into tasks, not resources'.

Alacaci, C., & Pasztor, A. (2002). Effects of flawed assessment preparation materials on students’ mathematical reasoning: a study. Journal of Mathematical Behavior, 21, 225-253.

Reusser, K. (2000). Success and failure in school mathematics: effects of instruction and school environment. European Child and Adolescent Psychiatry, 9, 17-26.

Reusser, K., & Stebler, R. (1997). Every word problem has a solution – the social rationality of

            mathematical modelling in schools. Learning and Instruction 7(4), 309-327.

Reusser, K., & Stebler, R. (1998). Realistic mathematical modelling through the solving of performance tasks. 
             Paper presented at the 7th European conference for Research on Learning and Instruction (EARLI),                    Athens, Greece. University of Zurich, Institute of Education. 

Teaching old dogs new tricks

The first draft of Chapter Eight addresses the toughest of questions in adult numeracy: How do we teach old dogs new tricks?

The quote directly below the title: "So how you gonna teach a old dog new tricks?" comes from an adult learner discussing his frustration with the mathematical demands of his programme.

The experiences of 'old dogs' (adult learners) who have developed negative beliefs about mathematics are devastating. The cuts run deep. When a 46 year old man can recount unpleasant conversations he had with a maths teacher when aged 10, you know those early experiences matter. Being positioned by your peers and significant others as 'not good at maths', and then coming to accepting this as fact, does not just change. It sticks.

Learning mathematics is entirely to do with how you engage with it. Do the beliefs, developed during early experiences, influence how 'old dogs' engage? Undoubtedly.    

As a nation we invest large sums of money predicated on the notion that an adult who struggled to learn mathematics during school, and developed negative beliefs, will re-engage and learn in a vocational setting.

How did we arrive at our conclusion?
And what do we do if we were wrong?

The answers are far more complex than I ever guessed at the beginning of this journey.  The stakes are also higher for the learners than I ever imagined.

The Magic Square

The magic square can be used to generate great thinking.  The trick again, is not to try to get it done as quickly as possible, but to use it to generate thought.

Here is how

You have engaged in analysing how many ways certain numbers can be produced using two dice. This activity builds on this.

The magic square has 9 squares.  The numbers 1-9 need to be entered so that they equal 15, horizontally, vertically and diagonally.

Before launching in and beginning to guess, have a go at this instead.

Task one

First think about how many equations each individual square will be involved in. For example, the top right square will be involved in 3 equations.

How about the middle right square? It'll be involved in only 2 equations.

Now work out and put in order which will be involved in how many equations.

Task two

Now work out and order the quantity of 3 number equations that equal 15, that each number is included in. For example:

The number 1 is only able to be in two equations that equal 15. 1+8+6=15 and 1+5+9=15.

Therefore, the number 1 can only go into a square that is involved in two equations.  You also know the numbers (8, 6, 5, 9) that must be in the equations with the 1. Read this again if you're not getting it.  

This is how mathematicians solve problems. They deduce their answers - like Batman. They do not go random. Try not to succumb to the temptation to guess.  Use those deductive reasoning skills.

You can do it!

Next challenge

Once you have nailed the three by three square use your new powers of deduction to solve the four-by-four square.  This one is a beast, and well worth taking a deductive approach.

Enter the numbers 1-16 so that horizontally, vertically and diagonally each row and column, and diagonal equals 34.



Good luck.

The joy is in the struggle.