Education

Examining Educational Failure

Not long ago I was asked to take a relief lesson with Year 9 students and prepare them for their no-calculator NAPLAN numeracy test the next day. To test their mental arithmetic, I asked, “What are seven sixes?” I looked encouragingly from one blank face to another until a girl at the back triumphantly called out, “Forty-two!” This performance was immediately unmasked by a boy at the front: “Aw Sir! She just looked up at the times tables on the back wall.”

When I returned to secondary schools after an absence of thirty years I felt like Rip Van Winkle, except instead of sleeping through the American Revolution, there had been an education revolution. Questions to colleagues brought little enlightenment, but they were not inclined to defend it. Since that first shocking exposure, I have made a living relief teaching and with short-term contracts.

This essay appears in the latest Quadrant.
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Trying to understand what had changed I found guidance from two philosophers; Douglas Gasking’s Examinations and the Aims of Education, first published by Melbourne University Press in 1945, and William Stanley Jevons’s ironically titled “Cram”, published in 1877 in the journal Mind. Gasking set himself against a rising tide of education theory that held exams to be a perversion of the proper course of education. For Jevons, preparation for exams was central to education: “All life is a long series of competitive examinations. The barrister before the jury; the preacher in his pulpit; the merchant on the Exchange flags; the member in the House.” I cite these texts to make a point. Both are unknown in the literature of education. Google Scholar lists only ten incidental references to Gasking’s book, and only one writer cites Jevons’s paper. Their neglect contrasts starkly with the industry of evidence-based theory that has brought Australian education to its present parlous condition. John Hattie’s Visible Learning, for example, offers a synthesis of over 800 meta-analyses of student achievement and has accumulated more than 7000 citations.

While the retreat from exams is a distinctive marker of modernisation, a more fundamental change has gone unremarked—the loss of separation between teachers and examiners and the control of education by educationalists. Year Book Australia 2000 identified the abolition of external exams as the key educational change in the 1960s and 1970s and showed “a newfound trust by authorities in the professionalism of secondary school teachers”. In New South Wales, the Wyndham Report (1957) acknowledged the need to meet the standards demanded by universities but suggested that this should not be at the expense of “a sound general education for all adolescents, not only for the ‘average’ adolescent, but also for the adolescent of talent and for the adolescent who is poorly endowed”. In Western Australia, the key recommendation of the Dettman Report (1969) was that “Because of their fallibility and the restraints which they place on curricula and teaching methods, external examinations should be discontinued and replaced by internal school assessments.”

Educationalists had long complained about exams. In 1939 the South Australian Director of Education, Charles Fenner, argued that the upper secondary curriculum was “too closely directed towards the preparation of students for university courses, and, therefore, insufficiently concerned with setting down broad general secondary courses of study that will be an end in themselves”. John Godfrey, reviewing intermediate exams in New South Wales in the 1930s and 1940s, suggested reforms to school assessment across Australia required “breaking the power of the universities and their professors over the examination system of the secondary school” and allowing schools and teachers to take responsibility for the assessment of “new subjects to cater for the non-academic students”.

In 2020, a group headed by John Polesel reviewing fifty years of reforms to the senior certificates that replaced external exams was still concerned “regarding the appropriateness of a curriculum and assessment regime designed originally to meet the needs of universities for selection of candidates”. Modernisation has not gone far enough. Curricula and assessment still failed to “adequately [report] the achievements of students not intending to go to university” and did not “engage the range of learners now required or wanting to stay on until the final years of schooling”.

The possibility is never raised that universities were an appropriate restraint on education departments and provided a beneficial “separation of powers”, with examiners the equivalent of an independent judiciary. The system served the university’s interest in finding future students but the curriculum also exemplified the disinterested pursuit of knowledge.

The abolition of external exams in the 1960s and 1970s brought an end to gains in equity and meritocratic principle that had characterised Australian education in the post-war decades. The system encouraged students to do their best and reliably identified their relative abilities. This should not have been grounds for complaint any more than in organised sport, yet it was abolished because it was thought to impose unconscionable burdens on students.

In 1939, John La Nauze, an economics lecturer at the University of Adelaide, sought to quantify the “inequality in the opportunity to acquire education beyond the minimum school leaving age”. The vast majority of the 50,000 boys in South Australian schools at the time had very limited prospects of going to university. Although most graduates in Arts at the University of Adelaide were from state schools, most were at university only because they were already teachers, exempt from fees, and studying part-time. Between 1927 and 1937 students from private, non-Catholic schools made up most honours graduates: twenty-four out of twenty-nine in arts, ninety-three out of one hundred and thirty-five in medicine, and ninety out of one hundred and thirty-seven in law, even though these schools catered for only 5 per cent of boys. He wrote: “War brings equality of opportunity in one field [therefore] it becomes if anything more important to see how far it exists in others.”

Despite limited funding, those schooled in the 1950s and 1960s had the advantage of post-war meritocratic aspirations. Although at first few state school students were financially able to take up university places, by the 1960s those doing well were encouraged to apply for scholarships. It was understood that students would repay their debt to society through their professional careers. The spirit of the times can be seen in Prime Minister Menzies’s speech introducing Commonwealth Secondary Scholarships in 1964 to support 10,000 students in the final two years of secondary education: “Many children of ability will be encouraged to stay on at school … to their own benefit and that of the nation.” As Raewyn Connell has noted, university education came to be seen as a “citizen right”. The Whitlam government abolished university fees in 1974, although by the mid-1980s the participation rate made free tertiary education unsustainable. In 1989 the Hawke government reintroduced fees and university education was again a private benefit paid for by the student. As Connell put it, “The changing ratio in Australian universities between income from the federal budget and income from fees is a stark measure of the commodification of higher education access.”

School education also moved to market principles. Today Australia has one of the largest private school sectors in the world—approximately 35 per cent of all students, and 42 per cent of Year 12 students, are educated in private schools. Parents unable to afford the fees may move house to place their children in “good” government schools, which are drawn into wasteful competition with each other. Thirty years ago a sociologist, Phillip Brown, described this trend as a “parentocracy”: “a system whereby the education a child receives must conform to the wealth and wishes of parents rather than the abilities and efforts of pupils”. In this analysis, policies that provide parents with opportunities for choice shift the responsibility for educational outcomes onto parents.

The modernisation of Australian education started with The Future of Education: A Plan for Australia published by the Australian Council for Educational Research (ACER) in 1943 in which the authors looked ahead to a post-war world. Their most remarkable proposal was that private schooling should end: “It is strongly felt that the democratic ideal requires a single rather than a multiple system based on differences in income level, and the religious ideal requires a single rather than a multiple system based on religious affiliation.” This would be fostered by “the avoidance of specific financial assistance to non-State schools”. The political will for this never developed, although, in the immediate post-war years, there was little growth in the private education sector. In South Australia, for example, between 1954 and 1968 the population aged thirteen to eighteen more than doubled, and the average length of schooling increased, producing an almost threefold increase in students, yet, as Professor Karmel noted in his 1971 report, government schools “accommodated almost 90 per cent of the total increase in numbers of pupils entering secondary grades”.

Other changes proposed represented the consensus that directed education policy in subsequent decades: raising the age of compulsory education, eliminating public exams, and progress from primary to secondary school “based on age only and not on educational achievement”. Each state was only slightly different, so South Australia can serve as an example. Transition to secondary school required an externally examined Qualifying Certificate but after 1944 the Progress Certificate was school-assessed. Apart from the ACER plan, there was independent discussion of unsatisfactory rates of grade promotion, creating the problem of the “over-aged child”. In 1943, in a survey of forty-six South Australian schools, the rate of grade promotion was 92 per cent on average through the final four primary years. Repeating a year was not effective in dealing with learning difficulties, although age promotion would be no remedy either. Before 1944, around 90 per cent of Year 7 got the Qualifying Certificate but by 1951 98 per cent of students got the Progress Certificate. As the Inspector of Schools observed, “only the ‘hopelessly incapable’ were … denied entry to high schools”. Rising standards at each level justified some restrictions on grade promotion, but teachers could invoke that possibility to motivate students. That standards might slip without that motivation did not inhibit the move to progression “on age only”.

Without the filter of the Qualifying Certificate, secondary schools set more demanding standards for progress beyond Year 8. As Karmel noted: “The highest level of retardation in government schools occurs at grade VIII as a consequence of more pupils than usual being required to repeat their first year of secondary education—with promotion between grades IX and X almost automatic.” The Year 10 Intermediate exam had been the terminal objective for most students and determined whether they could, or should, progress to the Leaving exam in Year 11, and Leaving Honours in Year 12. In South Australia fail rates ranged above 30 per cent in almost every subject even when the cohort was culled by those standards. Subjects not examined by the Public Examinations Board (PEB)—Music, Drawing, Woodwork, Home Science—were hardly less demanding. In 1964 their average fail rate was 26 per cent. In 1962, 12,988 candidates sat Intermediate exams, and only 5920 “qualified for the Certificate”. In 1963, 9885 candidates took subjects at Leaving level, but only 3742 qualified. In 1964, 2732 took Leaving Honours subjects. Of these, 2236 passed in “one or more subjects” while 18 per cent didn’t pass a single subject.

An equivalent selective pressure prevailed at university. The 1957 the Committee on Australian Universities’ Murray Report found that: “Of every hundred students who entered six universities in 1951 only sixty-one passed the first-year examination, only thirty-five graduated in the minimum time, and only fifty-eight have graduated or are expected to graduate at all.” The report did not demand higher standards in matriculation; it argued that “the demand for graduates is so great, that … universities should … accept all those qualified to enter”. Lower fail rates in British universities were explained by a significantly higher proportion of people being admitted to university in Australia. Uniquely in South Australia, the Year 11 Leaving exam was the basis of university scholarships. About a third of students entered university without Year 12 Leaving Honours, but did very poorly in the first year. A study found that 49 per cent of 162 science students without Leaving Honours failed every subject in the first-year exams but only 6 per cent of the 306 students with Leaving Honours.

Until the late 1960s the University of Adelaide dominated the PEB, and effectively determined the school curriculum. The 1978 inquiry into Year 12 exams in South Australia describes the university’s matriculation requirements as unsatisfactory because of “the narrowness of the range of subjects examined and of methods of assessing”; the “preparation of its syllabuses” which were said “not to conform to modern methods of curriculum design”; and the scaling and grading methods which “give undue weight to mathematics and sciences”. By this time non-matriculation subjects counted towards a non-matriculation certificate. That gave grounds to recommend that “a single authority should assess and certify as wide a range of Year 12 activities as possible”. The authority of the university over secondary education was largely lost.

Schools streamed students so that teachers could address classes of comparable ability ranked from A to D based on tests conducted in the first week of school. Progress to the next level each year and mobility between streams depended on performance in assessments. Fear of being held back motivated students to improve. Streaming was justified by the “doctrine of double effect”; the need for efficiency in state-funded schools made the policy necessary; the motivating effect was beneficial but incidental.

In a modern system, teachers motivate students by making lessons interesting and enjoyable. This is not always easy. Rote learning of the multiplication table is unpopular with children. Adolescents do not spontaneously enjoy learning to solve simultaneous equations, factorise quadratic expressions, or set out a formal proof in geometry. Under the old system, science and maths were compulsory because they were important to the needs of the nation, and the only alternatives were no less demanding arts or trade-oriented subjects at the technical high schools. In classes with externally imposed requirements, all students could be motivated to work, and authentic interest could flourish in those with ability.

Students lacking academic ability either worked, became apprentices, or undertook vocational education. Students who stay on now choose subjects they enjoy since they entail no consequential commitment. Vocational subjects involve little more than a pretence of doing work. The very students with limited capacity for academic abstraction are expected to study practical disciplines abstracted from the real world: child studies without children; tourism without tourists; food and hospitality without customers.

As long as universities retained control of the Public Examinations Board, teachers may have rankled at the syllabus and standards it set. In 1945 the PEB rejected the Education Department’s request “for accreditation and internal assessment of Intermediate Certificate syllabuses prepared by individual schools” and “opposed to any scheme which would take the student’s work throughout the year into account in awarding examination certificates”. In 1973, when external exams were being dismantled, the editor of Public Examinations: The changing scene wrote:

Many teachers believe that they can make assessments of student ability and forecast their likely success in further studies as reliably as the usual examination and that for those not aspiring to enter tertiary studies immediately after secondary school there are better courses to be developed, and more catholic assessments to be made of student performance and interest, than can possibly be part of a public examination system.

Teachers may not have realised how different their roles would be without external exams. A system that constrained their ambitions as educators supported their effectiveness as teachers, in ways they failed to appreciate: “The light dove, parting the air in her easy flight and feeling its resistance, might come to imagine that flight would be easier still in empty space.” The priority of preparing students for exams protected teachers from the political objectives education departments might impose, and students and parents regarded teachers as allies. Teachers today likely lament a 1960s-and-today cartoon in which a parent, a student and a teacher confer over an assignment with a fail grade. In the 1960s, the teacher and parent glare at the embarrassed student; today the parent and student glare at the embarrassed teacher.

Cherry Collins and Lyn Yates characterise the designers of South Australia’s curriculum as having “embarked on a generation-long campaign to find something other than academic knowledge around which to build a common curriculum” and repeatedly attempting “to set in place a new central knowledge task for the secondary school, to find a form of knowledge that would be powerful for young people in a changing world but which would be available to all, and do-able by all, rather than, as they saw it, excluding and elitist”. Education was to become “an enterprise that starts from the child, not from the ‘needs’ of the nation or community, nor from a view of schools as the transmitters of important knowledge across generations”.

The proliferation of new subjects created problems, as a submission to the Gilding Report (1988) observed: “the sheer number now available presents both central authorities and teachers and schools with unnecessary difficulties … [because] schools must choose before they allow students to choose”. The number of subjects available at any time was difficult to assess. For example, a 1992 report listed fifty-six publicly examined Year 12 subjects, fifty-eight school-assessed Year 12 subjects, and ninety-nine school-assessed half-year subjects. Yet despite the claim that the prerogative of choice lay first with schools, time has shown that collective student choice undercut the plans of authorities. Success for All (2006), reported “a pattern in which young people from high socioeconomic backgrounds are concentrated in a limited number of well-established and university-accredited subjects such as Chemistry, Physics, Biology, English Studies, [and] Mathematical Studies”. The consequence of student choice was clear. If only a few students wanted to study Chemistry, a class was unsustainable. In 1992, of 115 government schools, ninety-five offered Chemistry, ninety-two Physics, 101 English Studies and eighty-two Mathematics 2. Two decades later, with 125 government secondary schools, only sixty-two offered Chemistry, sixty Physics, forty-four English Studies and twenty-seven Specialist Mathematics. Despite the implications for the socio-economically disadvantaged, Success for All claimed that “curriculum and assessment must be flexible, responsive to local circumstances, and personalised enough to allow for the learning interests and needs of individual students and groups of students to be identified and met”.

The limited range of subjects examined by the PEB up to the 1960s meant most were available to students in any school. Schools built for baby boomers were equipped with labs to accommodate Year 12 Chemistry, but the flight from STEM subjects has made maintenance uneconomic. The subjects students take instead of STEM are generally justified by their vocational orientation but enrolments are not constrained by career opportunities. In 2014 there were seven times as many students studying Health and Physical Education as the “double maths” that a STEM career requires, and Year 12 enrolments showed only 10 per cent of students studying Physics, 12 per cent Chemistry, 5 per cent Specialist Maths and 7 per cent Modern History. In 1964, 52 per cent of Year 12 students studied Physics, 50 per cent Chemistry, 60 per cent Maths I, 50 per cent Maths II and 23 per cent Modern History.

PEB certificates for Years 10, 11 and 12 simply listed subjects with letter grades, a transparent record of a student’s attainments. In 1966, a technical change introduced a system for aggregating Year 12 exam marks to give an overall score based on the student’s rank in each subject. Initially, letter grades were converted to scores eliminating “failure” from the assessment vocabulary. The 25 per cent of students who earned no score for a subject effectively failed, but at a more lenient rate than the 30 per cent or more failed by PEB examiners.

The aggregation of marks made apparent the need for cross-subject scaling because subjects were not equally difficult. Foreign-language teachers saw the new system as “rapidly and surely killing” their subjects because they were “taught only to superior students in the A and B streams … [hence] it is much harder for a good student to get a 1 or 2 than it is to get the same mark in History”. In 1969 the PEB secretary noted that a system should be “deliberately designed to increase scores in ‘hard’ subjects and decrease scores in ‘easy’ subjects, so that no one student may distort his appearance of overall ‘goodness’ by chance or deliberate choice of ‘easy’ disciplines—the so-called ‘soft options’.” Any effort failed to save foreign languages. In 1964 there were 1131 Year 11 students studying Latin and 1489 studying French, in a cohort of 10,613. In 2014, only one student in South Australia studied Latin in Year 12, and ninety studied French. Choice put downward pressure on academic subjects because they competed with subjects introduced for those “not aspiring to enter tertiary studies”. Ensuring their viability put academic subjects under a “Gresham’s Law”—bad money drives out good. Just as currencies were debased when valuable metal could be shaved off the edge of coins before they were spent at face value, a subject’s contribution to certification was fixed, whereas the demands it put on students was a variable that administrators adjusted in response to declining patronage.

The abolition of the Intermediate exam in 1969 was seen as progressive. The Karmel report noted: “It is to be expected that retention rates between grades X and XI will rise rapidly [because] the external Intermediate examination checked the progress of weaker pupils in the past.” In deciding “whether the upper limit of compulsion [at fifteen years] should be raised”, Karmel suggested that “increasing retention rates made such a move unnecessary … [and] no useful purpose would be served by obliging pupils to stay unwillingly at school”. Moving the matriculation exams to Year 12 made it possible to eliminate the Year 11 public exam in 1974. The most significant move was the 1973 recommendation of a committee of the Examinations Board that:

starting in 1975, a mark derived from the school’s assessment constitute 25 per cent of the total mark in a matriculation subject, the remaining 75 per cent being derived from the examination mark … [and] the policy of the Board be to increase progressively the weight attached to the schools’ assessments of the next few years to 50 per cent.

The 50 per cent weighting of school assessment was retained up to 2011 when it was increased to the 70 per cent level of today. Even so, students avoid subjects that require an exam, notably Chemistry, Physics, Biology, English Studies and Maths. In the non-examination subjects the 30 per cent of the assessment described as “external” involves moderation as a check on teacher grading of students’ work.

With these changes, the pass rate and the distribution of grades became a matter of departmental policy. In 2014, only 6 per cent of Year 12 students failed, and 22 per cent were awarded an A-plus, A, or A-minus. In 1964, the Leaving Honours examiners failed 34 per cent of candidates and awarded credit grades to 7 per cent. Although the changing pass rate might be seen as runaway grade inflation, it is no measure of decline or improvement. For all the differences between the 1960s and today, graduating students are as much “sorted out” by their SACE results when converted to the Australia-wide ATAR rank, as students in the 1960s were “sorted out” by their Year 12 PEB exams. Whether education standards are equivalent is a separate issue and the best indicator may be international comparisons.

The performance of Australian students in the OECD’s Program for International Student Assessment relative to other countries has markedly declined. In their analysis of Australia’s PISA results from 2000 to 2015, one group of researchers called Australia’s steady decline an “unsolved mystery”. Not only are the declines large but they are greatest for the economically disadvantaged: “Whatever is happening in Australian society and its education system, it seems to be having the largest negative academic effect on lower social class youth.” In South Australia, the decline is consistent with the flight from academic studies, especially STEM. In the 1960s about half of all students in senior years studied STEM subjects, today it is about one in ten. Although PISA tests are performed by fifteen-year-olds who have not yet opted out of STEM subjects, most expect to, and they study in schools where teachers with STEM qualifications have been reduced.

Attitudes to exams are apparent in controversies about NAPLAN. In 2012, a Whitlam Institute study sought to determine “whether the regime of high stakes testing throughout the school years is in the best interest of students”. The authors acknowledged that NAPLAN results “are not used to determine grade promotion for any student”, but insisted on characterising the test as “high stakes” anyway, referring to “concerns regarding the negative impact of high stakes testing on students’ well-being [that] date back at least to the early 1990s”. The evidence of harm they cite is made implausible by their failure to reference children’s experiences when examinations did determine grade promotion, and much else. 

The Norwegian social philosopher Jon Elster discusses Hans Christian Andersen’s tale of the farmer who goes to market to trade a horse and comes home with a sack of rotten apples: “The farmer’s road to ruin is paved with stepwise improvements. Each time the farmer believes himself to be better off by the exchange, but the net result of all the exchanges is disastrous.” Authorities view the elimination of streaming, grade retention and external exams, and increasing the school leaving age from fourteen to seventeen, as stepwise improvements, but what are the benefits? In 1944, the Adelaide Exercises in Arithmetic asked commencing Year 7 students to: “Find one-seventeenth of 10 days 19 hours 43 minutes 54 seconds … Divide 765,487 by 326 … Reduce 737,058 square inches to square yards.” In 2016, students taking the Year 9 NAPLAN test were asked: “A shop sells balloons in bags of five. For a party, 20 balloons are needed. How many bags of balloons are needed?”; for a parallelogram with sides marked 110cm and 90cm they are to find the perimeter; and for “a tablecloth of 3 square metres” they must find “the area of the tablecloth in square centimetres”. The thirty-two questions in the NAPLAN test do not range much above these examples in difficulty.

Comparisons between other subjects in today’s SACE and their counterparts in PEB exams show equally troubling differences. In the 1960s Year 12 Physics students could be questioned on anything arising from Martin and Connor’s Basic Physics, a three-volume 1500-page textbook. Today, Physics students study a ninety-page SASTA Physics Study Guide that gives worked examples of questions that will comprise their exam, guaranteeing pass grades for all but the hopelessly incapable.

The abolition of external exams ended an ethos that held students accountable for progress in their studies. The British educational philosopher R.S. Peters, writing in 1966, expressed scepticism about the exam system, sympathising with the teacher who “has to use his expertise in order to get children through [exams] rather than in the cause of education”. He notes the constant complaint of teachers that “the examination system prevents them from doing what they regard as educationally desirable” and concurs that “more direct vocational training is suitable for certain types of children”, to provide “a concrete incentive around which education can be developed”. For Peters, “an examination-geared curriculum is neither educational in itself nor does it provide an appropriate core for educational activities”. The curriculum reform so confidently imagined in the 1960s is less credible after half a century of effort.

Under the old regime, the teacher’s responsibility was to expound a curriculum to students who were duty bound to learn it. In a child-centred system, every deficiency in student performance is not only a reflection of the teacher’s competence, but evidence of a lack of equity in the system. The complexity of the teacher’s role is illustrated in John Hattie’s Visible Learning. Education is a co-operative enterprise between student and teacher, with the teacher having a role like that of a therapist. In the vast literature Hattie draws upon he finds little to show that “teacher subject matter knowledge” is a significant variable in “effective teaching”. This is clear to academically inclined students. A 2021 Department of Education study found that high-achieving school leavers were not inclined to teach because it falls short in intellectual challenge and pay compared with the careers they chose. In 2019, only 4 per cent of graduating students with an ATAR over 80 chose teaching, a decline of nearly a third compared with 2006. Announcing a review of teacher quality in 2021, the federal Education Minister cited concerns about Australia’s declining PISA outcomes “in both absolute terms and relative to other countries”.

When there was a separation between teachers and examiners, everyone had a clear conception of their roles. The conviction that departmental control could do better led to an administrative structure that requires continual reform.

Lyn Yates and Cherry Collins see curriculum initiatives since 1975 as arising from “vigorous national debate about who should control curriculum, what should be included in subjects and what forms pedagogy should take”. In the 1980s and 1990s curriculum authorities attempted “to develop a common Australian template of ‘Statements and Profiles’”, an attempt that was overtaken by recasting curriculum documents as “Essential Learnings”. The researchers describe the “major reports and overarching frameworks” but not “what happened on the ground in schools”. What happened is anyone’s guess because the “frameworks” required interpretation and the outcomes are obscure because of the teachers’ role in assessment.

The “newfound trust” in teachers did not justify entrusting teachers with the assessment of their students, because they are implicitly submitting a measure of their success in teaching. The departmental moderators who certify the teachers’ assessments act under an equivalent conflict of interest. The teachers, moderators, curriculum writers and departmental examiners play their parts in a structure that has degraded educational standards while bringing educationally irrelevant advantages to the socioeconomically advantaged.

Alan Lee is an educationist who lives in Adelaide

25 thoughts on “Examining Educational Failure

  • Paul W says:

    I would like to know how education was handled before the first university was built here in the 1950s.
    Modern universities certainly can’t be trusted with a curriculum anymore than any other government or ‘public’ organisation.

  • lbloveday says:

    Quote: To test their mental arithmetic, I asked, “What are seven sixes?”
    .
    Try asking school leavers what 20×20 is, which should not be much harder than 2×2, but I’ve found that when I ask “Quickly, what is 20×20”? that hardly anyone gets it right.

    • padraic says:

      Take the nought from the second 20 and add it to the first twenty =200 and multiply by 2 = 400. Back in second year high school in Sydney in the 50s I realised I needed some pocket money during the school holidays and the schoolkid grapevine advised that the local Woolies was looking for temporary staff over the Christmas period. So I presented myself for an interview and was quizzed on my arithmetic e.g if a customer wants to purchase 6 items at 3/11 each how much is that. I struggled a bit – never having had to do such a thing in front of an impatient customer (as the interviewer pretended to be) and failed the test in the designated time so he explained how to do the calculation quickly. Pretend the item is 4/- multiply by 6 to give 24/- then take away the sixpence giving 23/6. QED. Since then I have always used that method and others like the 20×20 one above.

      • Brian Boru says:

        Now padraic a test for you.
        .
        Two ducks in front of a duck, two ducks behind a duck and a duck in the middle. How many ducks?

          • padraic says:

            The point I was making was that it seems that education these days does not want to strain the brain and seems to rely on apps and vibe. The article above sets out a good foundation for a revised curriculum.

            • padraic says:

              At the risk of being irrelevant I remember a Bluey and Curley comic cartoon where they had just plowed a paddock and were leaning over the fence and talking to a schoolboy on his way to school on his horse. The posed him a question -If it takes two men to plough a paddock in 4 days how long would it take 5 men? The kid replies that it can’t be done, so they ask why and he replies that the other two men had already ploughed it. It has a certain ring of logic to that reply and sounds like some of today’s politicians.

            • Brian Boru says:

              Agreed padraic.
              The answer to the duck question is 3 but don’t despair because nobody fails these days.
              .
              The first two ducks are in front of the last. The last two are behind the first and there is a duck in the middle.

              • Brian Boru says:

                I tried to put three duck emojis in a line to illustrate but they didn’t appear in my comment.
                Think of just three ducks in a single line. The first two ducks are in front of the last. The last two are behind the first and there is a duck in the middle.
                .
                And my apologies to you for this trivia.

                • padraic says:

                  No apologies needed, Brian. I always welcome a challenge. Sometimes trivia can be used to great effect to illustrate more serious matters. I was tempted to duck the question, but it reminded me of a question I posed some years back on another excellent Quadrant analysis of modern education. There are three “tooze” in the English language – To, Too, and Two. How do you spell “tooze” ? Tooze is my made up plural because there is no official one. You can say the plural but not spell it – a bit like “climate change” – it happens but you can’t stop it by human effort.

                  • Brian Boru says:

                    Thanks for that word “tooze” padraic. I have never before met with a word creator. I hope there is a lexicologist out there in QOL land monitoring this.

            • Alan Lee says:

              We need to be realistic about the difference in what is required of students today as compared with the uncompromising requirements once set by external examiners. In pre-war years students who were not up to Mathematics could choose the more practically oriented subject, Arithmetic. Here is a typical question from the 1938 Leaving (i.e. year 11) ‘University of Adelaide’ Arithmetic Examination:

              A French warehouseman imports from England printed goods weighing 7¾ lb. per roll of 44 yards, costing 5d. per yard in England. Freight and insurance add 7½% to the cost of the goods, and the customs duty is 25 francs per kilogram. If he wishes to make a profit of 15% on his outlay, what price in francs (to two decimal places) per metre must the warehouseman quote to a merchant (i) who pays cash, (ii) who gives a three month bill, reckoning interest at 4%? [Exchange on London, 178.5 francs = £1; 1 metre = 39.37 inches, 1 kilogram = 2.205 lb.]

              I taught a Business Maths and Statistics subject at TAFE, but I boggled when I first saw this. With careful work, and the advantage of a calculator, I got it out in about an hour. But there were 7 questions of equivalent difficulty in that three-hour examination. The real problem here is to understand what has to be converted to what, and in what order, and to what end.

      • lbloveday says:

        Of the first 20 I asked, only my daughter got it right – and it was not because of her formal schooling.
        .
        The power failed when I was in a mini-mart and I took two identical items each $2 to the checkout and the young woman entered 2 x 2 into a manual calculator and beamed as she told me the cost was $4.

  • Brian Boru says:

    Wunce eye cudent spil injunear bt naw eye arr wun.
    .
    Thanks Alan but it was depressing to read just how we are wasting the Nations gold and potential talent.

  • Homer Sapien says:

    I ordered a $6- coffee at a coffee shop. I gave the girl $21-; she took the money and opened the till, staring at me with a blank face. Tired of waiting for too long I said:” Just give me $15- back.” Her face lightened up; problems solved.

  • David Isaac says:

    I loved the article. Let’s encourage people over fifty to teach. ‘Make them do a qualifying examination rather than a b_____t course. Give them a cane. Ban smart phone use by anyone under twenty-one. No computers for most classes. Teach copperplate handwriting.
    .
    Make mental arithmetic sexy again. Cash only allowed for in-person transactions under fifty dollars. Five per cent tax on all credit card purchases. Ban Afterpay and similar.
    .

  • Elizabeth Beare says:

    I studied under an examination-based system, in the 60’s to the mid-70’s, getting a Commonwealth Scholarship aged 20 by private study entirely on an examination basis. I doubt if I would have had the capacity or background, given my disadvantaged cultural origins out of Mt. Druitt in Sydney’s West at that time, to cope with ‘continuous assessment’. My experience of examinations is that they allowed a student to express both knowledge and the capacity to handle that knowledge in the face of a difficult question pertaining to it. Exams allowed for and encouraged flair, quick intelligence and sometimes even a sense of daring to arise and shine in the face of exigency and stress.
    Exams set you up for real life and its challenges.
    This applied to technical and mathematical exams too, as I was to find in later post-graduate work in a complex technological area, in a Faculty of Medicine where traditionalism and exams reigned in some subjects, while ‘ungraded’ assessments had taken over in others. Ungraded assessments did nothing to reward hard work and high achievement; I felt let down by this and relished exams as the opportunity to really check on how I was doing vs others in the cohort. Where I could improve was also made clear.
    Sometimes exams could be poorly set, or even silly, but they were so for everyone and handling such an exam was also a test of skill and knowledge and capacity to cope with the unexpected.

    • lbloveday says:

      The SA government awarded performance-based “Teaching Scholarships” – £55 in year 11 and £65 in year 12 conditional on going to Teacher College and serving as a teacher for 3(?) years.
      .
      That was good pocket money in 1963, and I grabbed it without much thought. Nearing nitty-gritty time I realised that teaching children was far from what I wanted to do so I stopped going to the Billiard Hall and started saving the money from my after school job at Woolworths. I accumulated £118 and asked my father could he give me a cheque for £120, which he did despite thinking I was choosing the wrong road.
      .

  • lbloveday says:

    Bragging! I conducted the Property Settlement trial myself following the Residency trial in the Family Court, for which I hired and instructed a barrister.
    .
    Hence I was seated at the Bar Table when Her Honour and the hapless Legal Aid lawyer simultaneously reached for calculators. Her Honour smiled at me and said “I presume you don’t need a calculator Mr Loveday”. “No Your Honour”, I replied and gave her the answer to 4 significant figures – as much a consequence of mathematics education way back as my innate ability.

  • lbloveday says:

    I passed all subjects I sat for in the SA Intermediate in 1962, the Leaving in 1963, Leaving Honours in 1964, and first year BAppliedSc in 1965 and am surprised at the quoted failure rates; they do not accord with my memories. Maybe that’s because of whom I associated with, but we weren’t egg-heads – I played in both the Australian Rules and Rugby Union first teams.
    .
    Unfortunately I loaned my School Year Books to the organiser of the 50th anniversary of the school’s opening for their display of memorabilia (the school opened in 1961 with classes in Year 8 and 9; I was an inaugural student) and a low-life (NOT the organiser) pinched them, so I can’t look up how we compared to the rest of the State, although I recall the Headmaster (that was his title back then) telling the first assembly of 1963 that we had the highest Intermediate performance (however that was measured) of any school.
    .
    I do recall large classes – I was in a class of 40 in Leaving Honours “Double Maths” (Mathematics 1 and Mathematics 2 as they were known) and my sister was in a year 8 class of 56 in the same year.
    .
    I did French and Latin in Intermediate and we had to drop one subject for the next year. The French teacher, a French woman, asked the class individually whether they would be continuing with French, but did not ask me. I protested that I was the top boy and 6th overall in French (the girls of course dominated). “But you cannot speak the French” she replied. “With a great deal of difficulty, 2/10” she had said after the Oral Examination. Full marks for the Dictation did not rate with her. Not to worry I was going to choose Latin anyway

  • Rebekah Meredith says:

    22 April, 2024
    While I can see the point of working toward a specific test, and enduring the challenge of it (as pointed out by Mrs. Beare above, I do wonder if the best system for the majority of schooling would be what, from my reading of old British school stories (mostly the Chalet School books by Elinor M. Brent-Dyer), seems to have existed in British boarding schools of the mid-1900s. In my home-school curriculum in the 90s and 2000s, term marks were based on frequent quizzes, tests every three weeks or so, and end-of-term exams. Day-to-day work was required, but not marked.
    In contrast, the older British system, as near as I can tell, was based on the pupil’s DAILY, regular work. If this was the case, it would have meant that EVERYTHING was important–as opposed to a system such as I went through, under which only the information on which one would be tested seemed of real importance. This British system was anything but a cop-out for the pupils; it involved posting a form list at the end of the week of how the form had scored, from top to bottom; pupils were also ranked in each subject. They had end-of-term exams, as well; but all through the term, pupils were graded by their daily work. This would have avoided an enigma such as my dad has mentioned more than once, that his sister worked harder in school and did better than he did, but he always scored better on tests because they made her nervous. It would also encourage constant work, rather than the idea that one can fool about from day to day and simply cram for exams. In addition, it would give each pupil the opportunity to know where he stood from week to week, and encourage good, solid competition. There were always pupils who did not care if they were bottom of the form, but most would want to be at least a little higher.
    Of course, such a system would not be considered in most schools, nowadays, because of its obvious “elitism”–particularly as the system was set us so that when a pupil was READY for the next form, he ADVANCED to the next form–not after having “finished” a year (whether or not he needed to, or whether or not he had learned anything).

    • lbloveday says:

      Going way back to when I was in year 1 – funny how some things are remembered so clearly – a classmate was ADVANCED to year 3, and the teacher carefully informed the rest that we were not dumb, he was just very READY.
      He was in still in year 3 when I and most others got there.

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