Friday, September 12, 2008

Does maths deserve its time

Even Einstein worried that modern schooling had the potential to destroy the joy of learning. What is about maths that makes it worth keeping in our curriculum? Why are so many students 'turned off' mathematics? Are we using maths time wisely?


I am no expert in mathematics. I retain within me negative attitudes towards the subject gained from my schooling that stay with me to this day. There must be countless other adults who have similar feelings about school maths.

For all this the place of mathematics is rarely questioned.

As we enter the 21stC schools ought to be reflecting about the attributes and disposition that they want all students to gain from their school experiences. This surely is what is being asked with the introduction of the 'new' New Zealand Curriculum?

All learning experiences need to be judged as to how they contribute to the overall vision of education that each school is being asked to define for itself to suit the needs and talents of their students.

All too often, however, how time is assigned to various subject areas remains unquestioned. Long after the Industrial Age has past, with its need for an elite of clerical workers, the Victorian 'three Rs' still remain central to learning. For those who failed in those days there were plenty of low skilled jobs available. This situation no longer exits. All students now need to gain success from their schooling.

Future students face an ever changing unpredictable complex world that will require new sets of attitudes - or key competencies as defined in the NZC.

As educationalist Guy CLaxton writes 'learnacy' ( or 'learning power') will be more important than traditional literacy and numeracy.

Looking around schools little has really changed. Literacy and numeracy still rule supreme and little time is left to introduce a range of rich learning experiences needed to provide contexts to develop future 'learning power'.

It seems only an outsider can see that the Emperor has no clothes because those in the system have no inclination to challenge the assumptions about how time is apportioned nor the the 'messages' that such an uneven approach gives to their students.

Mathematics ( leaving literacy aside ) seems to have claimed an unassailable place, as of right, in the daily timetable. But, according to Guy Claxton, 'its warrant is under scrutiny'. As the core purpose of education is being contested, he writes, 'powerful new models of teaching and learning are being proposed, and mathematics is in need of a new rational'.

He provides three challenges about the place of mathematics.

First it is not clear that much of mathematics is as directly useful as it has traditionally claimed to be. Many people, he writes, lead happy and successful lives with only basic maths. Research indicates that many people learn what they need through experience or need ( to play darts in the pub). Other research shows that children with a 'playful exploratory approach' to maths develop confidence in the future to involve themselves in more abstract maths later in life. If students are 'turned off' maths them they withdraw from future maths experiences.It seems many students, when faced up to a maths problem, give themselves a few seconds and then give up.

The message for teachers is to find ways to make maths fun and to teach maths in rich meaningful contexts. Less maths done well may mean deeper lasting understanding; much of what is currently taught is soon forgotten if not used regularly in meaningful situations.

Perhaps doing fewer things well would be a valuable idea as would, integrating maths in other areas of learning and defining what aspects of maths ought to be in place at any level, if positive attitudes are to be retained. If teachers focus on introducing fun exploratory maths then time can be reduced and used for other neglected learning areas such as science ? Seymour Papert , the computer educationalist, believes all maths( and science) should be applied.

A good idea is to make it clear when they are doing 'practice maths' and when they are doing real maths - applying it in real situations so they understand what maths is.

The second point Claxton makes is that their is no evidence to the claim that maths provides valuable generic training of the mind ( an argument once used for Latin). To achieve 'transfer' teachers have to highlight where and why maths is used in other problem solving situations.

The third point made is that there is no reason that maths should retain its central role in the school day. The worldview that sees mathematics as so central to learning is archaic.

Teachers need to be alert to see the maths potential in any learning experience including exploring the maths potential of the natural and man made environment.

The best maths, or any learning, is 'just in time' learning, rather 'than just in case', where the need to learn the maths required to solve a worthwhile task is obvious. During such learning students are able to construct their own meanings making what is learnt 'stick' in their brains available for future use; it seems it is a matter of 'use it or lose it'.

In such a classroom the boundaries between the traditional 'disciplines' becomes increasingly permeable. Mathematics becomes a valuable learning tool to solve problems.

According to Claxton, the the fixation of intelligence with literacy and numeracy has been shattered beyond repair. 'Learnacy', the desire to continue learning, is the real issue.

The important issue is to develop the positive appropriate habits of mind - the key competencies of the NZC. It is such attributes that schools should be focusing on achieving. To achieve such a vision will mean 'disrupting' current ways of assigning time to such areas such as mathematics.

Everybody ought to get a feel for mathematics and have the necessary skills and attitudes to make use of maths as necessary. No one is arguing that maths needs to replaced just redefined to suit the 21stC. Many mathematical topics are themselves ideal means to develop future dispositions as well as being embedded into other learning are problems.

Thankfully there have always been educationalists who have seen mathematics as creative and aesthetic and practical to provide resources and guidance. As well there are many creative teachers who have aways seem maths as both a creative learning area in its own sake and who integrate it creativity in the learning problem that provide the learning 'energy' of their classrooms.

Maths in this sense is creativity in action.

6 comments:

Anonymous said...

At last somebody willing to challenge the basis of traditional education.

Bruce said...

I think it is all about re-inventing the role of maths for the 21stC to allow time for learning competencies and talents to be developed in other important learning areas. The question is what maths is essential at any level and how can maths be integrated with other learning areas to ensure a positive attitude is developed about maths

Blogger In Middle-earth said...

Kia ora Bruce!

I agree with Guy Claxton. Learnacy (how ever new this word is!) is where it's at.

I think we academics tend to get too wound up in what we think is important. What was purported to be important when we were taught was a sign of the times. We tend to carry that across, perhaps anachronistically, in our teaching.

I'll bore you with a wee story.

In 1969 I was in my honours year. I often had lunch at what was called The Refectory. One day I walked into the Refectory and saw my old school pal and university colleague sitting chatting to our past mathematics teacher, Mr Manson.

I collected my comestibles and veered across through the crowd to sit with them.

No sooner had I started conversation when Mr Manson stopped me and said, "The name's Jack."

He went on to describe that he could not have done what I was doing - his "brain was full of wee wheels" at my age. I was perplexed, but I didn't realise that this wonderful and inspiring mathematics teacher had been teaching in a secondary school without a degree qualification - permitted way back in those days.

Jack was finishing his honours degree through a scheme designed to upskill practicing but not yet fully qualified mathematics teachers.

To cut a long story short, Jack graduated with a 1st class honours degree and went off to become a principal of a large secondary school in Scotland.

The message here is that learnacy was where it was at for Jack. He, obviously, never lost it.

I have no doubt that what he acquired through his latter university studies didn't help him with his day-to-day work one iota. He followed it through to meet a requirement of the system.

If Jack's story is anything to go by, he had been prepared for life by the system that educated him - he knew exactly what to do to learn what he needed to get his valuable degree. Clearly he didn't really need the knowledge that his degree study gave him to be a successful teacher.

We need to think carefully about what we are teaching children today. Are we teaching them to meet a requirement? Or are we genuinely preparing them for life.

Ka kite
from Middle-earth

richnz said...
This comment has been removed by the author.
richnz said...

I think it is a great time to challenge the time allocations of mathematics. I think the new curriculum gives us the scope to do this as well...
"None of the strands in the learning areas is optional, but in some learning areas, particular strands may be emphasized at different times or in different years. Schools should have a clear rationale for doing this and should ensure that each strand receives due emphasis over the longer term..

Of course then there is NAG 1.. Giving priority to student achievement in literacy and numeracy, especially in years 1 to 4.

Here we have not yet reduced the time but have broadened the topics emphasizing inquiry and investigations with a mathematical angle. Highly motivating stuff.

Bruce said...

Greetings Middle Earth.

I think we all get caught up defending assumptions we are unaware we have about learning.

I am reading all I can that Guy CLaxton has written - I will share his ideas in future blogs. He really makes sense to me.

I really enjoyed your inspirationl story about your maths teacher.I heard a Victoria University professor of maths (on National Radio), when asked for a solution to the maths problem in schools, say that students need to be taught by teachers who love maths.

Greetings Rich - good to have you back.

I know you are expected to 'cover' all the strands but who would ever know! The important thing is to give students the widest range of experiences to deepen their knowledge and to uncover any innate talents they may have.

As for NAG One it could mean, define what it is kids ought to have in place and ensure it is. This could mean cutting out all the unnecessary things and replacing them with the skills and strategies students need to do independent inquiry in the afternoon. This is what was done prior to the 90s by creative teachers.Primary schools have been taken over by contracted advisers pushing reading and maths 'sects'.

Time to toss out these narrowly focused trained 'experts' and apply common sense rather than their imposed 'best practice'!