FENTO’s guidelines (2004) on teachers’ knowledge related to minimum core numeracy also has an expectation that teachers will be able to further develop elements of ‘process’ knowledge, which includes decision making in terms of seeking advice from area specialists, addressing the needs of learners with specific difficulties impacting their learning and
interpreting information gleaned from assessment practices (FENTO (b) 2004) all of which are generic teaching skills, and the underlying expectation is that these skills are to be applied with learners who exhibit difficulties or deficits in essential or basic skills. All trainee teachers within the post compulsory sector should have a raised level of awareness provided by the minimum core, including seemingly simple elements, for example the level of language skills required to complete functional numerical exercises should not be overlooked (FENTO (b) 2004).
Trainee teachers are not a breed apart from other human beings. These individuals will suffer proportionately within the population from the same anxieties and struggle with the same difficulties in numeracy as any other adult learner13. Trainee teachers in the post-compulsory sector are required to evidence their skills at level 2 in numeracy14 which is significantly below the requirements of those training to teach in the compulsory (schools) education sector15 who must evidence their skills in addition to having mathematics GCSE C grade or above
mathematics on entry to their teacher education course. Although the disparity appears to rest on the completion of a professional skills test, the attitude with which regulations are enforced makes the difference more acute with limited urgency or reliance on completion in the post- compulsory sector.
2.8 Comparisons between numeracy and mathematics
Concerned with the ideological and political functions of education within the restricted school environment, Apple (1990) pointed to the ideological function of education being circular and self-fulfilling or self-justifying, in terms of removing conflict. Pointing to the way science is taught as an example of a set of technical knowledge, divorced from true application. From this
13
Adult learners are those learners over the age of nineteen years. 14
Evidencing of skills at level 2 is required for completion of QTLS status from the IFL, and is required within the first year on completion of initial teacher training.
15
Although level 2 functional mathematics is seen as an equivalent level of qualification, it does not contain the more abstract elements of GCSE at A*-C grade.
52
standpoint it would be possible to see that the overlaps in the requirements at different levels for numeracy teaching and learning simply justify the need for the teaching of the subject. Apple (1990) expressed the currently popular viewpoint that a ‘normative’ and ‘legitimised’ curriculum adversely affects the development of creativity for instance. It is likely that Apple is able to argue from the position of someone who has an appropriately well-developed set of numeracy skills and therefore has the ability and the tools to develop creativity.Creativity and the development of ‘free thinking’ are reliant in many instances on cognition and self-expression which requires the ability to manipulate abstract concepts. Without numeracy individuals are unlikely to develop realistic levels of cognition that would allow them to be creative, expressive or free thinking, basic numeracy being the most important tool to develop cognition through the manipulation of abstraction. Tammet (2009) and Newby (2005) both provide support for this proposition by stating that people actually need these numerical, reasoning and communication skills to function effectively, especially in the twenty first century environment.
The effect on teachers of the implementation of the older national strategies (for example the national numeracy strategy prior to its re-assessment in 2014) on teachers at primary level for literacy and numeracy was examined by Earl et al (2003) who found that the self-belief of teachers improved as they were empowered, believing their own learning had: ‘been positively affected’. Teachers who have attained a functional level of essential literacy, language,
numeracy and ICT skills themselves (level 2 and above) are more likely to be able to foster and support the essential and transferable skills development required by their learners.
An increased use of ‘whole class teaching’ was also noted by studies such as those of Earl et al, these observations point to a greater depth being employed by teachers at primary level to interact and ‘reach’ pupils taking into account different levels of ability. A strong shift towards learner centred pedagogy (Chappell et al 2003) is implied by the methods expounded within the national strategy, which may also account in part for the observations of Earl et al, as teachers employ and become more confident with an ever expanding range of methods.
The national numeracy strategy has attempted to support teachers to start off the first
53
non-threatening experience for the pupils, which they will then carry with them through the education system into adult life, possibly impacting positively on the learner histories of future mathematics students. Measures to place the student at the centre of the learning process may be beneficial to improve student perceptions of their ability and interest in mathematics and numeracy. So as teachers become more confident, pupil’s performance and attainment correspondingly may improve.In 2004, the Tomlinson Report stated the need for adequately trained teachers for the subject area of numeracy for adults, but also emphasised that more professional recognition was required for them. This ‘professionalism’ was expected to be apparent through the training system, demanding a level 4 subject specialist qualification.16 The qualification, does not hold parity with higher mathematical qualifications of other types, for example a degree or higher diploma, and the view of numeracy teachers as being ‘less’ qualified as their mathematics teaching counterparts has been dominant (Cameron 2003). As yet, there is no degree in England specialising in the subject ‘numeracy’ relating to adult or more advanced learning (although this is available at Master’s degree level) extending this perceived discrepancy for the foreseeable future.
The experiences of trainees in the compulsory sectors can be used as a comparison measure with the experiences of those in the post-compulsory sector, to an extent since the subject matter is similar. There is a strong emphasis on numerical calculation within the professional skills test which only forms half of the numeracy minimum core, making very direct comparison more difficult, since a true comparison of value would require a direct like with like approach. No examination of social factors relating to numeracy skills acquisition is required for the
compulsory sector.
Lessons learned in comparison of the compulsory and post-compulsory sectors, could be positive since the reported improvement in teacher confidence when supported at primary level in implementation of the national numeracy strategy and the learning of skills through a ‘hands on’ approach could be mirrored in numeracy within teacher training, for both the secondary and
16 The level 4 qualification has progressed to be a level 5 diploma in mathematics (numeracy) teaching diploma
qualification and is provided as stand-alone continuing professional development or through integrated generic and subject specific teacher education for the post-compulsory sector.
54
further sectors. This would positively impact on teachers and students but may negatively impact on perceptions.Numeracy is undervalued as a subject, whilst mathematics as a subject is given a high status that also negatively impacts on the learners’ perception. Public opinion and feelings about mathematics and numeracy as subjects and the real influence on society of these subjects do not correspond (Maasz 2005).
Learning elements in an area which requires abstract thought from the outset is more difficult than learning in an area resting on elements which are more concrete. Learning what numbers ‘are’ is a complex process. Counting out items relates to the numerical symbol for the number of items. Two buttons becomes the number ‘2’, the numerical symbol ‘2’ refers to the amount. Without strong guidance to the contrary, the number ‘2’ will easily and naturally be associated with buttons themselves as items and not the amount, as is a common mistake referred to in the primary level national numeracy strategy.
Mathematics (especially at any ‘higher’ level) is associated with occupations that require lengthy study and cognitive development, for example doctors, chemists, engineers and anything related to scientific occupations requires a higher level of mathematics qualification or
knowledge base. Evidence for the perception of difficulty in this subject is provided by the fact that mathematics provision has declined at a higher level (Level 3 or ‘A’ Level) regardless of the expansion in lower level courses for mathematics and numeracy (French 2002).
Higher mathematics has become an unpopular study choice. In 2015 this decline is reported as having halted and started to reverse with Gov.uk (2015) reporting a rise in the number of traditionally unpopular subjects, including mathematics being taken as choice subjects for A- level by students in the UK. If the trend continues this may signify a change in public perception or simply a change in data analysis methods to highlight positive data trends and discount negative ones.