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Through measurement to knowledge

By John Ridd - posted Tuesday, 21 February 2012


Nobel Prize winning Dutch physicist Kamerlingh Onnes used the phrase ‘through measurement to knowledge’. This article will present hard data, measurements, to show that the condition of maths and science in Australia, in particular in Queensland, is very poor; and, aware of the impending State election calls on politicians of all persuasions to take drastic action to rectify matters.

Much of the basic data will be drawn from Trends in International Maths and Science Study TIMSS (or analyses thereof) which is an international sequence of tests held every four years. They test the various ‘domains’ (eduspeak for areas of work).  For example, for Year 8/9 maths they test Number, Algebra, Geometry, data and chance in the ‘Content domain’ and Knowing, Applying and Reasoning in the ‘Cognitive domain’.  The number of countries is substantial. In 2007, the most recent test for which data is available, 36 countries took the Year 4 tests and 49 took the Year8.

 The relative condition of Australian maths/science shown in the 2007 results is summarised below by showing the average from (a) the highest scoring country, (b) US, (c) England and (d) Australia. For each of US, England and Australia the country’s rank order is also given. In both subjects and both grades case the TIMSS average overall was 500.

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Maths 4th grade                      

Maths 8th grade 

Science 4th grade

Science 8th grade

Hong Kong 607

Taiwan 598

Singapore 587

Singapore 567

US 529

US 508

US 539

US 520

UK 541

UK 513

UK 542

UK 542

Australia 516

Australia 496

Australia 527

Australia 515

 

The TIMSS data also enables trends over time to be assessed.  For mathematics the bedrock for subsequent mathematics, numerical sciences and engineering, the changes from 1995 to 2007 were:

Grade 4: US increase11 points, England increase 57 points, Australia increase 22 points

Grade 8: US increase 17points, England increase 16 points, Australia decrease 13 points

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All of the increases or decreases were statistically significant.

The TIMSS tests also place student results in categories according to how well they have performed.  Each student is placed into one of the categories ‘Advanced’, (reached the) ‘High Benchmark’, ‘Intermediate Benchmark’, ‘Low Benchmark’ or, for the very poorest achievers ‘Not at low benchmark’. Below are the results for Grade 4 and Grade 8 students for both maths and science across Australia and, for comparison purposes, for the highest scoring country and the international median.

Tables below show the maths results for Years 4 and 8.

Only those students achieving ‘Advanced’ or, at an extreme pinch ‘High’ in maths at Grade 8 will have any real chance of success in Year 11/12 higher levels of maths. 

Algebra is correctly described as the ‘gateway to further mathematics’.  Weak algebra in lower secondary school leads to trouble later.  TIMSS subdivides the results into categories one of which is algebra in Grade 8.   Algebra outcomes: (TIMSS scale average 500)

Taiwan

617

USA

501

UK

492

Australia

471

All of the top five performing countries were East Asian (>558). The only European countries to reach the 500 mean were Armenia 532, Russia 518, Hungary 503 and Serbia 500. The weak performance of the three English speaking countries is noticeable. US managed to be average, England, despite the better performance overall noted earlier is algebraically weak and Australia’s performance is frankly embarrassing. 

Similar data analyses for science at Years 4 and 8 are:

 

TIMSS also sub-divides science content into four groups: Biology, Chemistry, Physics and Earth Science. The results below all have a TIMSS scale average of 500 as usual;                      

 

Biology

Chemistry

Physics

Earth Science

Singapore

564

560

575

541

USA

530

510

503

525

UK

541

534

545

529

Australia

518

505

508

519

The relative weakness of the physical/numerical sciences is clear but not yet desperate. However when combined with very weak performance in maths especially algebra the later problems in numerical science and engineering are understandable and inevitable.

The Australian Council for Educational Research ACER examined the condition of education in Queensland.  The outcome was ‘A Shared Challenge’. (ACER 2009)  As a part of that work ACER examined comparative performance of the various States and Territories over time for maths and science at Year 4.

           Figure 2.9 Trends in Year 4 mean scores in mathematics

          TIMSS 1995 to 2007

          Figure 2.10 Trends in Year 4 mean scores in science

         TIMSS 1995 to 2007

The two summary paragraphs below are direct quotations from ACER’s A Shared Challenge:

‘Not shown here are the trend lines for the Year 8 mathematics and science. At this level also, the absolute performances of Queensland students were unchanged or declined non-significantly between 1995 and 2007.’

‘…….Australian primary school students, and particularly students in Queensland, perform well below world-best standards in mathematics and science. It is clear from performances in some other countries that much higher levels of mathematics and science achievement are possible in primary schools.’

In summary, there has been a decline in the relative performance of Queensland students in mathematics and science over a period of several decades. In the period 1964 to 1995,the absolute decline inlower secondary mathematics achievement appears to have been greater than in any other state, and to have been the equivalent of about two years of schooling.

Apologists for Queensland students’ weak performance frequently use the fact that Queensland’s students in any given year are about 6 months younger than in other States. Clearly that fact has always been true.  The Tables below from ACER show that Queensland students were once the best in the country – even though they were the youngest. The strength of Secondary Maths up to about 1980 is most noticeable.

The NAPLAN results also showed Queensland as the weakest performer. Those results stimulated the Bligh government to ask ACER to examine the situation. The result was ‘A Shared Challenge’ quoted often in this article. The ACER document exists solely because the NAPLAN data showed up the awful problems.

Summary comments from the authoritative A Shared Challenge are:

‘International studies show that relatively few Australian primary school students reach high standards of mathematics and science achievement. Only three per cent of Queensland Year 4 students reach an ‘advanced’ standard in mathematics, compared with 40 per cent of students in Hong Kong. Only four per cent of Queensland Year 4 students reach an ‘advanced’ standard in science, compared with 36 per cent of students in Singapore. Performances in other countries demonstrate that much higher levels of primary school achievement are possible.’

‘International studies also reveal a long-term decline in the absolute mathematics (and possibly science) achievements of Queensland students. In the mid-1960s, Queensland junior secondary students outperformed students in all other Australian states in mathematics. ….From the late 1970s, there was a significant decline in levels of junior secondary mathematics performance in Queensland.

So, what is to be done? 

Some pointers are available from A Shared Challenge and also from a paper Measuring what Matters: student progress by Dr Ben Jensen of the Grattan Institute.

From ‘A Shared Challenge’ in no special order.  In some cases with comment:

·         ‘All top performing schools recognise that they cannot improve that which they do not measure’.  (Shade of Kamerlingh Onnes! Totally obvious of course)

·         ‘Top performing schools are relentless in their focus on improving the quality of classroom instruction’

·         ‘All of the top performing and rapidly improving systems have curriculum standards which set clear and high expectations of what students should achieve.’

·         (Need for) ‘well developed systems for evaluating and monitoring performances.’

·         (A recommendation) ‘That all aspiring primary teachers be required to demonstrate through test performance, as a condition of registration, that they meet threshold levels of knowledge about the teaching of literacy, numeracy and science and have sound levels of content knowledge in these areas.’ 

·         (A recommendation) ‘That standard science tests be introduced at Years 4,6,8 and 10 for school use in identifying students who are not meeting year-level expectations and for monitoring student progress over time.’ (ACER propose this because Queensland Year 4 students were ranked last in NAPLAN)

·         (In high performing Victorian schools) ‘Each of the schools has been particularly active in identifying tests and other assessments which contribute to an objective picture of student achievement and to the determination of the value that the school itself adds, through analysis of trends over time.’

Note that all of the above are direct or indirect criticisms of syllabi/curricula and assessments or lack thereof, or tertiary teacher training.

From Jensen’s Measuring what matters: student progress:

‘The ‘My School’ website is considerably better than having no information published on school performance. However, problems still exist because the school performance measures published on the ‘My School’ website may not be accurate. Comparisons of schools’ average test scores, even within like school groups, are prone to mismeasurement and can produce biased results for schools in low socio-economic areas.’ (I agree with the advantages and also with the criticism that injustice may occur to schools with lower socio-economic backgrounds)

Value adding is described as being  ‘A class of statistical models that estimate the contributions of schools to student progress in stated or prescribed education objectives (e.g. cognitive achievement) measured at at least two points in time (OECD 2008)’. (Comment: It is noteworthy that there must be ‘prescribed educational objectives’. It is doubtful if any Queensland syllabi produced by QSA, notably in Senior secondary schooling meet that clarity requirement)

Jensen contends that:

· Value added is more accurate and has been supported by head teachers in UK and is preferred in other European countries.

· Institutions such as teacher unions and school associations in a number of countries have also supported the introduction of value-added modelling as the greater accuracy creates a fairer system, particularly for schools serving more disadvantaged communities, a fact that is important in view of the perceived inaccuracy and injustice in the current system, notably teacher unions.

The maths and numerical science achievements by Australian students are inadequate; in Queensland they are deplorable. The Education Establishment TEE (Boards of Study, University Education Faculties, Teacher Unions and elements within governmental education Departments) does not accept that fact.  They react poorly to criticism and are reactionary in that they object to anything which threatens the status quo.  Data such as that quoted above is dismissed. Bearing in mind that all assessment at all levels in Queensland is non-numerical it is unsurprising that they do not accept what the TIMSS or other data says. Seemingly they want to continue as they are – apparently unaccountable.

A further problem in Queensland is the grossly inefficient situation in maths and science in Years 11/12. A huge fraction of the time, effectively whole school terms, is spent on ‘Extended Experimental Investigations’ and ‘Extended response Tasks’ or assignments. The students spend much time learning very little about not much.

The thinking and attitudes about measurement and data that led the Queensland Studies Authority’s (QSA) to produce and impose non numerical assessment systems on all schools is the absolute opposite of Kammerlingh Onnes’s, and to the modern ideas propounded by ACER and implied in Jensen's value adding thinking.

What are the causes of the awful state of maths and numerical sciences in Queensland (and elsewhere)?

It is not the type of school because the problems are across all school types. Also the Longitudinal Survey of Australian Youth LSAYR 22 (2001) showed that individual schools have a far greater influence on ENTER (OP) than school type. The biggest determinants are Year 9 numeracy and Year 9 literacy in that order.

It is not physical conditions.  In the seventies our Queensland SHS had no lights or fans in the classrooms and class sizes were much larger than nowadays.  But look at the results we produced. That high standard was across all school types - State or religious foundations.

The causes of trouble are:

·The pitiful knowledge levels of many teachers. That must be due to reprehensible incompetence within university Education Faculties.

·Extreme syllabus weakening, failure to ‘set clear and high expectations of what students should achieve’ and a decline in subject emphasis were and remain the problem. That is the product of the QSA’s subject syllabi and fanciful assessment structures.

Only Parliament can institute the drastic changes needed to syllabi, assessment systems, teacher training and school attitudes because the Queensland Studies Authority and Education Faculties think everything is fine and most certainly will not, can not make the sorts of changes required.

So, what should the new Queensland Government and Opposition do both now in the campaign and after the election?

Four things are worth consideration and action:

· Accept the ACER recommendation that all aspiring Primary teachers must be able to demonstrate a reasonable level of knowledge in Maths, Science and English. That must be by a formal test set externally (not by QSA) and supervised in a manner not less rigorous than for the Core Skills Test.  Suggested minimal achievement should be at NAPLAN year 9/10 standard and 85% pass level.

· Accept and put into action as soon as possible, certainly this year, Jensen’s recommendation that ‘The current measures of school performance published in ‘My school’ website should be replaced with value added measures of school performance, given their greater accuracy and fairness to schools serving poorer communities’. That could be done with or without Commonwealth involvement.

· Insert, forthwith, in the Queensland Studies Authority Act 2002 a Regulation that stipulates that all subject syllabi must ‘set clear and high expectations of what students are expected to achieve’. Furthermore all assessments systems must be clear and understandable to students, parents and parliamentarians, they must ensure that no group of students is systematically unfairly disadvantaged.

· Form a permanent standing committee of Parliament for School Education. The brief should, inter alia,examine subject syllabi and assessment systems.

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About the Author

John Ridd taught and lectured in maths and physics in UK, Nigeria and Queensland. He co-authored a series of maths textbooks and after retirement worked for and was awarded a PhD, the topic being 'participation in rigorous maths and science.'

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