Stolen from Tim Ferris

“Inspiration is for amateurs — the rest of us just show up and get to work. And the belief that things will grow out of the activity itself and that you will, through work, bump into other possibilities and kick open other doors that you would never have dreamt of if you were just sitting around looking for a great ‘art idea’.”-Chuck Close, American artist who achieved fame as a photorealist through massive-scale portraits

How to get the most out of mathematical problems

I had the privilege of speaking at the He Taunga Waka Wananga/Fono last week. It was a fantastically run conference attended by a great group of people and included plenty of thought provoking speakers. Boy, there are a lot of talented people out there. 

Well done to the team who put it together. Thanks for your hard work.

A few people have asked for a run down on a problem I used as an example in the presentation. It is covered pretty thoroughly in the clip below which I've edited. The problem starts at 2:15. 

Additionally, all the conference presentations will be made available on the He Taunga Waka website. 

They are not up yet but will be soon. The clip is below. 

A recent talk at Skills Highway

I was asked to make a brief presentation to the workplace literacy and numeracy sector several weeks ago. This was organised by the amazing team at Skills Highway. A big thank you for inviting me. It was attended by a great group of people, and boy, what amazing work they are all doing. 

All attendees were passionate, smart, and very up-to-speed on current initiatives. In fact, the workplace literacy sector tend to be the most effective, experienced and robust communities in the adult sector. I think this reflects the challenging nature of workplace literacy. In my mind, the most challenging training environment available.   

To give you an example, the table I was sitting at was populated by Gary Sharpe the winner of the 2016 Literacy and Numeracy Leadership Award, Di Boss, literacy and numeracy specialist at ServiceIQ, Claire Matheson (Boss lady at Coffee educators), Jan Eyre of NZCER fame and a wonderful researcher, and several others of equal impressiveness. Quite the crowd.

As for the presentation, it was okay. The clip below starts 15 minutes into the presentation. For some reason I got off to a rushed start and stayed that way. The tone is a little harsher than usual.  

I'm didn't quite make my points particularly well either. However, I received a lot of feedback about the difference between rehearsal and elaboration strategies. I also received feedback about improving the 'needs analysis' process to include learners' conceptions and workplace representations of concepts, and how these could be 'unpacked' to improve trainee outcomes.

Here are some links to previous posts if you are interested: 

Learning strategies

The dangers of being too kind to learners 

Example of a workplace analysis 

They are only blog posts so if you would like a higher quality research-based review perhaps leave a message. 

Teaching/learning maths at home

Someone asked if I would post this again.  A little long but probably still worth a look.

A spelling version is in the works. Might take a while due to workload but it'll be worth it when it finally hits the screens!

The difference in maths achievement scores can be attributed to strategy use

We in New Zealand have a growing mathematics problem. We are not getting better, and by the best measures, getting worse. Poor mathematical performance correlates with limited life outcomes, so its important to get it right.  While there are a range of reasons for the lacklustre performance, there is one that no one talks about yet is potentially a prime reason for our troubles.  

The problem  

We don't teach, or use, appropriate learning strategies. Literacy (reading, writing, speaking and listening) has a bootstrapping effect, this is less so in maths. Therefore, you might get away with poor strategies in literacy, but poor strategy use in maths is unforgiving.  

Strategies

There are three categories of learning strategies: Memorisation strategies, elaboration strategies, and control strategies.  

Memorisation strategies are based on the idea that you want to be able to recall the relevant information when you need it. Sound reasonable? It shouldn't. This approach correlates not only with lower performance, but negative performance. Did you catch that? Negative performance. 

Elaboration strategies are strategies designed to elaborate knowledge. Control strategies are related to organising and managing yourself. Both relate to high performance.

Memorisation strategies are passive, and therefore cognitively simple, resulting in little long-term cognitive change. In contrast, elaboration and control strategies result in cognitive complex activity that results in learning.

How does NZ perform in regard to the strategies we teach and use?

Last year the OECD issued a report that looked at the different strategies used and taught by different countries. Drawing on PISA results the authors found that the high-performing countries teach and use elaboration and control strategies, the lower-performing countries use memorisation.  Guess where NZ sits? Unfortunately, nearer the bottom than the top.

Also note, that the researchers did not ask the teachers - who would argue that they do not rely on memorisation. Rather they asked the students. Student feedback reveals that they have not been taught to use elaboration or control strategies. Despite what teachers might suggest, the fact is that the students’ beliefs are oriented toward memorisation.  Click the title of the paper to go directly to the paper.  

How teachers teach and students learn

Echazarra,A., et al.  (2016), "How teachers teach and students learn: Successful strategies for school", OECD Education Working Papers, No. 130, OECD Publishing, Paris.

Abstract:

Fewer 15-year-olds in Hong Kong-China, Japan, Korea, Macao-China, Chinese Taipei and Viet Nam reported that they use memorisation as a learning strategy than did 15-year-olds in some of the English speaking countries to which they are often compared (Purdie and Hattie, 1996). For instance, 12% of students in Japan and 17% in Korea said they learn as much as they can by heart when they study for a mathematics test. By contrast, 26% of students in Canada, 28% in Ireland, 29% in the United States, 35% in Australia and New Zealand, and 37% in the United Kingdom reported so (Figure 4.1). This may sound surprising to many but mathematics instruction has changed considerably in many of these countries (OECD, 2011). Students in Ireland, the Netherlands, Spain, the United Kingdom and Uruguay reported the most frequent use of memorisation strategies, while those in Albania, Macao-China, the Russian Federation, Serbia and the Slovak Republic reported the least frequent use. [END]

I should note that the statements below are typical of those used to identify memorisation strategies: 

• I go over some problems in mathematics so often that I feel as if I could solve them in my sleep (sleep).
• When I study for mathematics, I try to learn the answers to problems off by heart (heart).
• In order to remember the method for solving a mathematics problem, I go through the examples again and again (examples).
• To learn mathematics, I try to remember every step in a procedure (procedure).

Seems reasonable, right?  Perhaps what you were taught?  Well it isn't! Agreeing with these statements relates to lower performance.

Note that NZ and Australia had the second highest memorisation responses (35%). The myth that the Asian countries follow a drill and skill approach is wrong.  We are closer to that description!  Their learners appear more self-sufficient and able to learn.  Not so NZ learners. We seem to have bought into rehearsal strategies, despite the rhetoric from the MoE.

This study raises serious questions about what is really happening in classes at a social level. We need to start teaching learners to elaborate and control, otherwise we will continue to drop in the world rankings, and it’s getting pretty damn embarrassing!

Mythologysing the 'Aha' moment

I've spent the last few weeks working through some data I collected on learners' beliefs about quick learning.  Here is a brief summary:


Learners tend to believe that 'understanding' occurs in a single moment, usually in response to listening or watching a tutor demonstrate or explain some aspect of numeracy. They say things like, "Some people just 'get it', but I usually don't", or "I love it when I get it". This notion of 'getting it' permeates their thinking around mathematics and numeracy.

And it's all bad.

If a learner believes that understanding happens in a 'moment', then when they do not 'get it', they may begin to doubt their ability to understand it at all.  Often, they will ask the tutor to repeat the content, example or demonstration, or they may just ask the tutor to 'show us again'.  They hope, and expect, to 'just get it' and believe that they ought to be able to do so.  When they cannot (and see others getting it) they often use this as evidence of inability.

The truth is that understanding can on occasion happen quickly, but only when a foundation for understanding has been laid.   Understanding is a 'process', not a 'state'.  It takes time and effort. Often it emerges from an extended period of confusion.  True mathematical understanding develops over time, not in response to someone telling you something.  Yes, there are moments of insight, but these are the conscious outcome of temporal subconscious processes.

If learners believe that understanding ought to happen quickly, then they are set up for failure and negative affective responses.  For example, if Kelly believes that she should understand the concept of ratios as the tutor tells her (in that moment), and she doesn't, then she may believe that she has a mathematics problem.  She may then give up, and reaffirm her belief that she is no good at mathematics.

Compounding this, learners' lack strategic learning repertoires, subsequently they depend on tutors because, as it becomes clear that for these learners, listening to the tutor and hoping to 'get it' is the only option.  This means learners who do not 'get it' have to report back to the tutor which limits their learning opportunities to periods of tutor instruction.  In an adult numeracy classroom in NZ, tutor responses to learners questions are abysmally small. I found that learners don't ask for the tutor to repeat information because it reveals to the rest that they don't understand.  And that noisy learner?  You know the one that asks all the questions, all the time?  Well that learner isn't asking the right questions, and yet tends to dominate the tutor/learner discourse.  We have the conditions for a perfect storm.














Finally, and to the point.  How many tutors talk about the 'aha' moment. In particular, how we feel good about our roles when learners suddenly 'get it'.  We may in fact be mythologizing a negative meme. The 'aha' moment is a passive response to a usually accidental delivery of content.  Instead, we should be talking about the learners we motivated to go home, and spend hour after difficult hour, working on that confusing concept until they finally began to make sense of it.  That would be a real inspiration.

Mathematical understanding is the result of hard work, time, effort and often confusion. Learners who think that this experience means they are dumb, are not going to persist for long.  It's a bit like a hopeful marathon runner who interprets discomfort as a signal that they are no good, - because all the good runners do it so easily.

Questions:
Do you think understanding happens quickly?  Or gradually over time?
Does it make a difference?