Hidrograma adimensional SCS

This official NCCA narrative sets out a particular critique of the state of mathematics education in Ireland that firmly places the existing curriculum in the modern maths tradition of the 1960s. Through the syllabus revisions that have taken place since then, the authors contend, the ‘modern’ emphasis in the curriculum has been ‘diluted’ and ‘a more eclectic philosophy has taken its place’ (NCCA 2005b, 11). What form this dilution took or what the ‘eclectic philosophy’ is, is not specified. The lack of a root-and-branch revision in mathematics education, the authors contend, may be the reason why ‘more recent trends in mathematics education did not permeate discussions in Ireland’ (NCCA 2005b, 11). The trends may not have permeated ‘official’ education policy discussions and there may not have been any ‘genuinely radical critique of the aims of mathematics education in the junior cycle or of the style of content, pedagogy and assessment that is appropriate for the cohort served by the programme’ (NCCA 2005b, 11), but the influence of recent trends in mathematics education had permeated recent curricular developments.

One such trend the Realistic Maths Education (RME) philosophy and practice are very much in evidence in the revised Primary School Curriculum9_{. The NCCA review itself tells us that, ‘the}

revised Primary School Curriculum is more in line with the RME philosophy and, in particular, with the problem-solving approaches to mathematics education’ (NCCA 2005b, 6). This philosophy together with the changed approach to teaching and learning advocated by the Junior Certificate syllabus revisions implemented in 2000, we are told:

may eventually permeate second level education ‘from the bottom up’ as students transferring to post-primary schools have had longer experience of such approaches at primary school and teaching and learning in mathematics at junior cycle adopt the changed approach advocated by the syllabus revisions implemented in 2000. (NCCA 2005b, 6)

Thus, although ‘post-primary mathematics syllabuses in Ireland do not currently make reference to the modelling or RME approaches’ (NCCA 2005b, 6) the philosophy has indeed infiltrated recent syllabus changes and as already indicated, it is anticipated that it will eventually permeate the post-primary system ‘from the bottom up’. It appears therefore, as

though at least one of the directions of any syllabus remodelling that might result from this NCCA review process, had already been defined.

Apparently the Review’s brief discussion of trends such as problem-solving, modelling and Realistic Mathematics Education (RME) is the ‘official’ introduction into the debate of some of the ‘more recent trends in mathematics education’ (NCCA 2005b, 11). The ‘some’ is significant. The authors of the report do not refer to the ‘conflict-ridden’ academic debate on whether mathematics should be taught as a closed deductive system as opposed to ‘realistic’ mathematics (Dolin 2007, 101). There is no discussion of the more diverse range of perspectives on the teaching of mathematics such as constructivist and competency-based approaches which have been developed by mathematics educators (Lyons et al. 2003, 4) and Critical Maths Education is not mentioned. RME, however, is the mathematical approach on which the OECD/PISA mathematical literacy is based (Shiel et al. 2001b, 8) and success at PISA is an important consideration for the authors of the Review. PISA will be examined in greater detail in Chapter 5.

The PISA assessment was dominant in educational and economic discourse at that time and success in PISA was associated with a country’s attractiveness for inward economic investment. The givenness of PISA means that the priorities of the PISA assessment are not interrogated by the authors and PISA results (among those of other international assessments) are accepted as ‘evidence’ of perceived problems in secondary schools. This, in spite of the fact that PISA does not examine the content of the school curriculum (OECD 1999a, 9) and unfamiliar question formats are present in the assessment; ‘the situating of mathematics problems in a context (e.g. embedded in a real-life setting) was recognised as unfamiliar for the majority of items at all three syllabus levels’ (NCCA 2005b, 15) at Junior Certificate level. Neither are the standards of students at upper secondary level in ‘PISA successful’ countries examined. The authors say that concerns exist in many countries about the standard of mathematics among students leaving second level education (NCCA 2005b, 3), and in particular the standards of those entering third level. Whether these concerns exist in countries which prioritise ‘PISA standards’ and

mathematical literacy as the basis of their curriculum, is not adverted to. PISA, it must be

remembered, is an assessment of fifteen year-olds, who are completing their lower secondary level compulsory education. Consider Finland, a country which has been very successful in the PISA assessments: in 1985, problem-solving was introduced to the Finnish curriculum in

response to an increasing interest in problem-solving around the world at the time, and since 1990 ‘everyday life mathematics’ and related problems are taught. There appears to be a direct causal link between recent curriculum changes and the PISA performance. A syllabus review was introduced in 2004 at Grade 7, Grade 8 in 2005 and Grade 9 in 2006 (Paasonen 2004, 19), and it is this latter cohort which took part in Finland’s triumphant 2006 assessment. However, Finnish academics have been cautious in their welcome for the PISA results; the success has been described as a ‘pyrrhic victory’ (Tarvainen and Kivela 2005, n.p.) and in the view of many ‘the mathematical knowledge of new students has declined dramatically’ (Solmu 2005, n.p.) The argument put forward is that the PISA study gives valuable information about the skills needed in life to solve simple problems, but that these skills are not enough in a world where a mathematical basis is needed in technical and scientific areas (Solmu 2005, n.p.). Thus, concerns arise about the standards of mathematics among students entering third level in Finland and it remains an open question whether adherence to PISA values will have any positive effect on university intake standards. The opposite may well be the case, if evidence from Finland is shown to hold elsewhere. The question then arises, who, if not the universities, are the likely beneficiaries of the swing to PISA values. Despite Ireland’s precipitate move in the direction of PISA-friendly curriculum and pedagogy, there is no evidence that we are likely to solve the problems that pertain here according to the acknowledged narrative. The move is a leap into the twilight, if not the dark. It is the contention of this thesis that other agents wait in the wings to take advantage of the move. The PISA-swing may well solve problems other than those acknowledged or understood in the public discussion, in particular, the problem of human capital.