Dick Evans continues his consideration of skills required forthe future UK economy
In Part 1 I briefly explored some of the current issues associated with skills gaps and shortages and the failure by this and previous governments to tackle and resolve these long-term problems. In this piece I want to address the problem of innumeracy and low maths skills in the population and possible solutions to the problem. I, along with many other committed and enthusiastic individuals and organisations, have highlighted some of the factors involved in perpetuating low mathematical skills amongst the population e.g. gender issues; the perception that mathematics is intrinsically difficult and the impact of cultural attitudes. Time is not on our side to tackle these longstanding problems and improve our international competitiveness. For this country in terms of these skills, it could already be five past midnight!
A bewildering array of initiatives have been introduced to tackle the problem of innumeracy but sadly many of them were either not properly resourced or were of short duration, and in addition many were not fully evaluated for thorough implementation. Very often these initiatives attracted knowledgeable, committed, enthusiastic and innovative facilitators and teachers but still the low levels of numeracy persisted. The current heavily prescribed curriculum in schools and colleges reduces the degree of freedom that teachers and facilitators can exercise. Teaching to the test and an obsession with league tables (supposedly for the improvement of performance and student achievement) further restrict the use of innovative and creative methods of teaching and the greater potential for improvement in learning. Too often pedagogy is side-lined and narrow teaching practices therefore accentuate the problem.
Fundamental changes are essential if the real world of numeracy, mathematics and mathematical processes are to be made more relevant and available to the learners (Burton). This is not easy as Roberts demonstrated when researching mathematical difficulties among low achievers in aspects of problem solving and investigative activities, even when the teachers tried to make the learning experience fun to reduce the scare factor (Roberts, S. 1984). One generally accepted feature to achieve effective learning is to develop greater degrees of autonomy, independence and responsibility in the learner and to create more friendly learning environments ( see Ofsted 2004). This is easy enough to say but difficult to realise with learners.
As with so many things in life a series of complex balances have to be achieved especially with mixed ability/heterogeneous groups. Teachers need to capitalise on the innate curiosity within people and hence develop enquiry skills that will allow them to want to continue to learn. The teaching of mathematics and numeracy presents additional challenges to both teachers and learners because of the reluctance and at times hostility of learners to these subjects. The perception that the subject is difficult and presents a scary experience for learners adds to the problem.
To tackle problems of engagement teachers need to fully exploit the arsenal of increasingly available learning resources and techniques that are available to recognise and manage the diversity of learners and their experiences e.g. low levels of motivation; bad previous experiences of being taught the subject; the influence of parental and societal attitudes towards the subject. This also means that mathematics/numeracy should be particularly well-resourced in institutions in order to cope more effectively with the challenge. It is important too that teachers experience focused and sustained CPD in using these resources to their best advantage.
Although I continue to have reservations about some aspects of the use of IT, it has massive potential in contributing to teaching and learning provided it is managed and monitored carefully and effectively. China is piloting an internet learning network which is already beginning to have positive results. The system has active online support and is very flexible to recognise individual learner’s ability and motivation. With improved management and more tutor intervention/support greater effectiveness can be achieved when using ICT.
Making it relevant
Relevance is a critical factor in teaching numeracy. Learners must see the relevance of the subject in their general lives and/or relate it to the specific skills needed in their work place. The ability to transfer the basic elements of numerical and mathematical skills to specific work tasks is essential. In order to learn the basic concepts and equally important the ability to transfer that knowledge to real life and work situations the teaching and learning must be as realistic as possible. A number of proven approaches e.g. simulation, realistic working environments (RWEs) or in the actual work place show how effective these techniques can be. The first step is to establish the skill needs of the work place and of general life e.g. the use of the four basic rules, percentages and skills required for financial literacy. Because the profile of employment in this country has shifted, skills specifications need to shift to match new needs. For example there has been a shift towards service and media industries that require specific competences in numeracy.
In laying of the basic foundations of numeracy with the young learner it is also important that the learning experience is enjoyable and not off-putting. However, there has to be a role for rote learning but it is a difficult balance between this and making maths engaging and relevant to the real world. It is like a titration in chemistry gradually working out the right proportions to achieve the correct result. To increase interest the lessons should involve:
* a multitude of techniques,
* a variety of learning resources,
* open-ended examples,
* group discussions,
* field work and practical activities that encourage problem solving and investigation activities.
As Ian Stewart says in his excellent book (Stewart, 1.1995):
mathematics is to nature as Sherlock Holmes is to evidence. Nature offers an opportunity to observe and investigate and hopefully instil the excitement of patterns and numbers that occur all around us’.
Greater use of that approach could begin to dispel the negative cultural element toward numbers and mathematics in general. One to one and small group work with a teacher has proved successful and if set in an encouraging and supportive learning environment can maximise learning. These approaches are equally important for older learners who often feel intimidated when they return to study.
Laws of motion
Teachers under pressure to cover the syllabus might start a topic with definitions and equations without explaining what they actually mean and their contextual relevance. As a result many of the learners do not fully engage with the basics. An example from physics might illustrate what I am attempting to convey.
Newton’s Laws of motion are an important topic and are often introduced by formal definitions and then a number of equations that can mean little to the learner. Instead an effective way of introducing the laws is to explain what each means. The first law describes how forces can be identified, the second law how forces can be measured and the third describes how forces behave. Each aspect can be started with demonstrations, open-ended discussions and practical work. Various objects can be observed accelerating under gravity, decelerating under friction and moving in curves under the force of magnetism. When one has explained the meaning of each of the laws the teacher can then begin formally defining the laws and introducing the associated equations. I realise there are some fundamental differences in teaching mathematical and scientific concepts but the example above attempts to illustrate how a topic can be taught in a more effective way. Learners may learn to mechanically recite the laws by rote and but may not grasp what they mean in real situations, for example:
* why the moon orbits as it does around the earth
* the dynamics of falling objects like parachutes,
* the shape of distant galaxies
Surely one of the aims of teaching is to allow people to transfer basic knowledge often couched in mathematical symbols into real life phenomena?
Role of the teacher
Ultimately the solutions lie with both the teacher and the learner. The teacher must be encouraging, friendly and inspiring using a wide range of teaching and learning methods that are available and affordable. To do this they must receive support and adequate resources, e.g. opportunities for CPD and financial, physical resources and most certainly more freedom to deliver the subject and sufficient time to rise to the challenges.
Teaching through the contexts which relate to people’s work is critical. Learners must be able to see the relevance of the numerical skills they have learnt. Lack of context, as Frankenstein (Frankenstein, M. 2008) showed, can trivialise and oversimplify the issues. I appreciate many of the points I have mentioned have been identified and discussed before but the debates must continue if this country is to address and resolve these very important issues.
Dick Evans is a regular contributor to Numeracy Briefing For a look at how these issues might relate to a general awareness and understanding of science see Dick’s website technicaleducationmatters.org
- Burton, L. 1995: Women and mathematics; is there an intersection?
- IOW/ME Newsletter, V0L7 No2, June 1995 Buxton, L. 1981, Do You Panic About Mathematics?’ Heinemann Educational, 1981.
- Roberts, S. 1984: ‘The Study of Some Female Secondary School Underachievers in Mathematics’, MA thesis, The New University of Ulster 1984.
- Ofsted 2004: Mathematics in the Secondary School, Ofsted 2004.
- Stewart, 1.1995:’Nature’s Numbers’. Phoenix. 1995. ISBN 1 85799 6488.
- Frankenstein, M. 2008: ‘Real real-life mathematics’ Numeracy Bulletin. Issues 13 and 14. 2008.