SCHOOL EDUCATION: by Dr Kevin DonnellyNews Weekly
'Fuzzy maths' doesn't add up
, December 18, 2004
Dr Kevin Donnelly
, author of Why Our Schools are Failing
, says that, now that the literacy debate is centre-stage, it's time to place the spotlight on the other half of the learning equation: numeracy.Just as many argue that the "whole-language" approach leads to literacy failure, many also argue that the way numeracy as now taught is substandard and flawed.
In the USA, the new approach is called "fuzzy" or real-world maths. John Ainley, a researcher with the Australian Council for Educational Research, characterises the new approach as one that:
" ...emphasises the relationship of mathematics to our culture, student motivation, and active learning. The relevance of mathematics to everyday life has been given greater emphasis ...
"Problem-solving, modelling, and investigative approaches are now being used instead of the earlier emphasis on formal algorithms."
Instead of learning their tables by rote, practising mental arithmetic and mastering such algorithms as long division, students use discovery methods of learning based on guesswork, are told that the process is more important than getting answers "right" or "wrong", and are allowed to use calculators.
Instead of the class learning as a whole, the emphasis is on group-work. Teachers are told that they should "facilitate", not teach. Based on a constructivist view of learning - one where students are supposed to create their own knowledge and understanding - it is also considered wrong to provide ready-made solutions.
Such are the faults in the new approach that, when the national mathematics curriculum (which embodied many of the tenets of real-world maths) was designed during the early 1990s, the curriculum was roundly attacked as seriously flawed and a threat to standards.
Some 200 academics condemned the new approach as "a disaster for the mathematics education of the Australian population" and the Australian Mathematical Sciences Council argued:
"Australia will not be able to compete with the rest of the world if its people are hobbled by half-baked and incompetent approaches to the teaching of mathematics".
Evidence that fuzzy maths has led to falling standards is not difficult to find. Talk to your local greengrocer or butcher and the consensus is that it is rare to find a young person who can mentally add up or subtract to calculate the correct amount of change.Declining standards
For some years, maths academics such as Sydney's Garth Gaudrey have argued that standards of first-year students have declined and, as a result, physics and science courses have been dumbed down. David Blest, a Tasmanian academic, adds:
"There seems to be little doubt that the capabilities of students in mathematics from across a wide number of disciplines are not what they were, say, 20 years ago ... I can assess the capabilities of incoming students and see that I can expect less, much less."
While Australian students do reasonably well in international tests such as TIMSS and TIMSS-R, it is also the case that Australian schools fail to fully extend more able students by including more difficult work earlier in the primary years.
Research also suggests that, unlike successful systems, such as Singapore, Hong Kong and Japan, in Australian schools there is a long trailing edge of under-performing students who are allowed to progress through schools without the foundation knowledge and skills essential for successful learning.
That fuzzy maths has failed and is intellectually flawed has been shown by research, both here and overseas.
First, as Sydney academic John Sweller argues, direct instructional learning is more efficient and effective than leaving students to their own devices.
This is especially the case in mathematics, where it is essential that rote-learning and mental arithmetic be explicitly taught to ensure the basic building-blocks are mastered. E.D. Hirsch, drawing on American studies, states:
"... lack of automaticity places limits on the mind's channel capacity for higher-order problem-solving skills ... Only intelligently directed and repeated practice, leading to fast, automatic recall of math facts, and facility in computation and algebraic manipulation can lead one to effective real-world problem-solving."
Second, instead of students working individually or in groups, it is essential that teachers employ more whole-class teaching. In explaining the success of Japan and Korea in international maths tests, a British report stressed the importance of whole-class teaching:
"Inspection evidence and the experience of the national Numeracy Project point to an association between more successful teaching of numeracy and a higher proportion of whole-class teaching."
Over recent months there has been a good deal of debate about literacy and whether the teaching methods employed in Australian classrooms are as effective as they should be. Equally as important as literacy is the question of numeracy.
Let the debate begin.