Saturday, 2 November 2013

Talk : Mathematic­s, from failure to functionality

Cafe Sci hosted an interesting talk recently entitled "Mathematic­s : from failure to functionality?", and presented by UoN researcher Diane Dalby. This post is based loosley on the contents of the talk, with some added reference material thrown in.

Background
Diane described how she had progressed from O-Levels, to A-Levels, to a Mathematics degree and then to secondary school maths teaching - a academic route in which Diane commented that she "didn't have to know much about the rest of the world".

After a career break she restarted teaching in a college environment, firstly part time, then full time. The classes were for vocational courses in the beauty, construction and public service careers. Diane commented on her surprise at some of the course titles, such as "maths and physics for beauty therapists"

Then an opportunity came up to undertake a research project in an area that Diane was interested - what do we do with the students who are in a vocational courses and need a degree of maths ability, but who have been put off maths and have not achieved the magic "Grade C or above" at GCSE level.

Constuction Workers in 1932

More background
Diane pointed out that the UK does not perform well in international rankings of maths ability (see the OECD PISA study here).

2009 OECD PISA study. Selected numeracy scores
China(Shanghai)600
Korea546
Japan529
Germany513
OECD AVE496
UK492
Poland495
USA487
Turkey445
Indonesia371

The first international comparison that the UK participated in was the 1996 IALS (literacy) survey of 20 countries, in which the UK performed very poorly. This prompted a UK government to commission the Moser report in 1999, whose summary started with the emphatic comments that :
"Something like one adult in five in this country is not functionally literate and far more people have problems with numeracy. This is a shocking situation and a sad reflection on past decades of schooling. It is one of the reasons for relatively low productivity in our economy, and it cramps the lives of millions of people. We owe it to them to remedy at public expense the shortcomings of the past. To do so should be a priority for Government, and for all those, in the business world or elsewhere, who can help."
The Moser report prompted the Skills for Life strategy in 2001, as well as the Skills for Life surveys of the working age population in 2003 and 2011. During the interval between 2003 and 2011, billions of pounds of government money was spent on advertising campaigns

A BBC report on the Skills for Life research describes how the differning ethnicities in the UK had very different levels of adult numeracy:

%age of aged 16–65 at Entry 2 or below in England
All21%
White British19%
Asian Indian25%
Pakistani British43%
Black Caribbean54%
Black African49%


The Department of Business, Innovation and Skills (BIS) definitions for the various levels of competency in literacy and numeracy :

Entry Level 1 is the expected school attainment at age 5-7. Adults below this level may not be able to write short messages to family or select floor numbers in lifts.

Entry Level 2 is the expected school attainment at age 7-9. Adults below this level may not be able to describe a child’s symptoms to a doctor or use a cash point to withdraw cash.

Entry Level 3 is the expected school attainment at age 9-11. Adults below this level may not be able to understand price labels on pre-packaged food or pay household bills.

Level 1 is equivalent to GCSE grades D-G. Adults below this level may not be able to read bus or train timetables or check the pay and deductions on a wage slip.

Level 2 is equivalent to GCSE grades A*-C. Adults below this level may not be able to compare products and services for the best buy, or work out a household budget.

The 2011 Skills for Life follow on survey showed, disappointingly, that, despite all those billions of pounds of spending, the proportion of adults with low levels of numeracy had actually increased:

Numeracy Levels in 2003 and 2011 (%)
Entry 2 or below : 200321%
Entry 2 or below : 201124%

A NIACE report (which you really should have a look at, dear reader), considered what lessons could be learned from the efforts that had been made and made a number of recommendations, many of which relate to the fact there is a conflict between wanting to help those with the least skills, and measuring success of that effort by exam results:

"Evidence of ‘what works’ included flexible, individualised approaches within small groups, which offer friendly, fun, informal and small steps to learning.

Equally, respondents were clear about what is not working. They suggested that learning driven by qualifications rather than the learners can distort who is included in learning. (37.94 per cent of all 2006/7 Skills for Life qualifications were awarded to 16–18-year-olds who are not necessarily a priority target group).

Other learners may have been excluded because they are not at the ‘right’ level of learning (i.e. within easy access of gaining a level 1 or 2 qualification).

Many reported they are unable to use ICTs due to lack of training and equipment or technical support.

Contributors were very concerned about funding reductions which will remove ‘weighting’ for adult literacy from August 2011, and lead to large groups, reduced provision and less responsive teaching and learning."


Extreme hairdressing on the International Stace Station

The Research
The research Diane undertook looked at students studying vocational subjects (hairdressing, construction etc) at college. As part of these courses, students who had not performed well at maths in secondary school had to study maths to at least a "functional" level before proceeding with the rest of their vocational course.

Diane performed some 17 case studies, with comprehensive interviews and observations being made of students and teachers in each case.

The results showed a number of clear themes :

a) Attitudes were most postive towards maths at college (even in the first term) than they had been at secondary school, many gave as a reason the fact that college was a place where you were treated as an adult, and that college was a step closer to employment and therefore responsibility

b) The most successful teachers taught maths as a valuable life skill and engaged with the students on topics of relevance to them, such as the costs of alcohol consumption or the relative value of pensions today compared to historical levels.

c) Above all, the students reported that they liked their college maths teachers more that they liked their school maths teachers

Diane wondered what was an appropriate technical level of maths that these students should receive, so that they were had "enough to get by and sufficient to get on"

Diane Dalby

The Q&A
As is often the case at Cafe Sci, the Q&A session was just as interesting as the initial talk..

In response to a question about the benefits or otherwise of streaming, Diane commented that the available research suggested that it did not make a significant difference to outcomes. On the one hand it allowed bighter students to achieve more, but on the other, it left lower achieveing pupils disenchanted and feeling inferior. Diane commented that shw had once talked to a girl who was in the top set for maths but, because she was at the lower end of that set, felt she was "no good at maths". You can read more about the pros and cons for streaming (or tracking as it is known in the US) here , here, here and here.

There was also quite a bit of discussion about whether the teaching of maths in secondary schools was fit for purpose in terms of giving young people the skills to critically evaluate the data and statistics that is put before them by companies and politicians - and whether there should be a greater focus in that than, say, trigonometry (which is rarely of use in combating misleading statistics and government spin).

Pythagoras, yesterday


Image Sources: Pythagoras, ISS haircut, Lunch, Olympic Stadium

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