Tuesday 30 May 2017

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.  

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.  

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

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!

Friday 26 May 2017

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.

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

Thursday 11 May 2017

Does reading make people kind? 

No, but it might make you more empathetic, and possibly a mind reader. 

The NZ Herald has an article stating that research has found that reading makes you kind. Some vague reference to the research is made, but no links are provided. In fact, the entire article looks like a copy and paste from a UK paper.  

Intrigued, I dug a little. It turns out that the research is not about being 'kind' but rather whether reading is conducive to developing empathy. 

For the record, empathy is a superpower (see 'Speaker for the Dead' etc ;)). It is the ability to take another being's perspective, and hence understand and communicate with them. 

Image result for speaker for the dead and xeno

So, does reading make you kinder or more empathetic, and are readers better people?

Well, Hitler was incredibly well read. He was also very kind to certain people. This shows you that 'kindness' is not a great measure for success, nor a superlative goal. The Herald article implies it is the ideal end goal for us and our children. They should all be kind and reading is the way to do it. In response to the Herald: No, reading does not make you kind. No such research exists.

Perhaps a moral framework with which to make decisions is a more mature approach. However, I digress. 

'Empathy' is a better construct than kindness, and there is a body of related research.   

Does reading increase empathy? Possibly. Check out the research below.   

McCreary, J. J., & Marchant, G. J. (2017). Reading and Empathy. Reading Psychology, 38(2), 182-202. 

The relationship between reading and empathy was explored. Controlling for GPA and gender, reading variables were hypothesized as related to empathy; the relationship was expected to differ for males and females. For the complete sample, affective components were related to GPA but not reading. Perspective taking was related to reading appreciation but not GPA. For females, reading appreciation was related to perspective taking and empathic concern. For males, GPA and non-fiction reading were positively related, but both were negatively related to empathic concern. Results suggest reading may promote both academic achievement and social development. Findings and social implications are discussed. 

Neuman, Y. (2010). Empathy: From Mind Reading to the Reading of a Distant Text. Integrative Psychological & Behavioral Science, 44(3), 235-244. doi:10.1007/s12124-010-9118-7

In the psychoanalytic literature empathy is commonly discussed as a form of 'mind reading', which is deeply associated with the capacity to mirror the other's mental state. In this paper, I propose an alternative perspective on empathy as the process of reading a distant text. This perspective is illustrated through a Talmudic story and by weaving a thread between Bakhtin, Bion and Lacan. The paper concludes by pointing to the danger of empathy as a hidden form of projective identification that provides the reader with a false sense of control rather than with negative capability for otherness. 

Ah ha! Empathy may simply be the projection of our own identities?  I personally think this is minimised as you read, and hence partake in, others lives and experiences. To me this suggests a shallow empathic is still shallow. 


Junker, C. R., & Jacquemin, S. J. (2017). How Does Literature Affect Empathy in Students? College Teaching, 65(2), 79. doi:10.1080/87567555.2016.1255583

Scholars have suggested that reading literature can foster empathy. However, learning empathy through literature in the classroom is understudied. The primary objective of this study was to assess whether affective and cognitive empathy, as demonstrated in student writing, relates to textual attributes, the style of writing prompt, student writing ability, and whether it changes over time. Students in a college literature classroom were asked to assess texts according to a series of attributes related to engagement and textual difficulty, followed by a series of analytical and creative writing prompts. These responses were scored on a comparative scale according to metrics of empathy and compared with textual attributes, strength of writing, and time using a general linear model. Textual difficulty was identified as the greatest predictor of empathy (inverse relationship) followed by assignment grade (positive relationship). These results indicate that textual attributes, strength of writing ability, and style of writing response play a central role in explaining empathetic responses in students. The furthest-reaching implications of this study may, however, rest in the findings that empathy didn't change over the short time period and that textual accessibility may trump all other aspects in facilitating empathetic responses. 

So, how does reading help develop empathy? 

It seems to provide a richer perspective of humanity with which to make judgments, and it allows you to 'step into' the feelings of others. 
However, there is a pseudo-empathy. This is when you simply project your own identity onto others. Reading widely may minimise this. 

My summary - reading is one way to expose yourself to a wide array of experiences and perspectives, which is essential 'but not sufficient' to develop empathetic superpowers (not just empathy). The more widely you read, and enter into the lives of others, the deeper your reservoir of experiences. Books that get more 'life on the page' (such as good literature) are better at developing such a reservoir.