The Hidden and Salient Messages of the Curriculum: The Verb Analysis of the Curriculum Texts of Mathematics
Author(s):
Harry Silfverberg (presenting / submitting)
Conference:
ECER 2013
Format:
Paper

Session Information

24 SES 04, Mathematics Curriculum & Student Experiences

Paper Session

Time:
2013-09-11
09:00-10:30
Room:
D-405
Chair:
Harry Silfverberg

Contribution

The study examines at to what extent the Finnish mathematics curriculum texts reflect and promote the concurrent paradigm shifts in mathematics education. In this study, we examine the curriculum texts of upper secondary mathematics through two different ‘lenses’ focusing on these changes. The first lens describes the paradigm shift in mathematics teaching where the central feature is the “social turn in mathematics education” e.g. turning of the individual, cognitive (constructivism) point of view to the social (constructivism) point of view. The second lens corresponds to the change in formulating the objectives of the mathematics teaching by learning outcomes instead of instructional/process objectives.

 

There are reasons why we can expect that some attempts to promote the social turn in mathematics education and the learning outcome –formulation of the objectives will be found from the subject the curriculum texts. Firstly, the still holding National Core Curricula published in 2003 by the Finnish National Board of Education is at least at the general level explicitly committed to the social-constructivist conception of learning. Its conception of learning is based “The National Core Curriculum is based on a conception of learning which states that “… learning is a result of a student’s active and focused actions aimed to process and interpret received information in interaction with other students, teachers and the environment and on the basis of his or her existing knowledge structures.” (Anonym 2003, 14) Secondly, in the European Union, the Bologna process spelt out a number of “action lines” where it is emphasized that learning outcomes should express what learners are expected to achieve and how they are expected to demonstrate that achievement (Kennedy et al. 2006). In mathematics the tradition has been to describe the objectives mainly as content based format “the student gets acquainted with …/learns… ”. Actually that is quite close to learning outcome -based formulation of objectives.

 

Contrary to the above said there are as well reasons to suspect that in the part of the curriculum where the subject specific objectives are stated, similar trends or paradigm shifts would not be detectable. The learning of mathematics is often seen as an individual effort and the meaning of the social activities have been diminished. In addition to that often the writers of the national curriculum texts are par excellence the experts of the mathematics subject and not as well familiarized with the theories of learning and the international trends of mathematical education which may cause the issue that role of the produced text is more focused on regulating what content and skills should be learnt than how the learning will happen.

 

For instance, Kennedy et al. (2006) has noted that the outcome-based approach has some behavioristic and ‘neo-magerian’ features. From this perspective the shift to social-constructivist approach in mathematics education and the ‘neo-magerian’ demand to use observable learning outcomes can be seen at least partly contradictory and may be challenging to match together in the writing process of the curriculum texts. 

Method

In this study, the existence and strength of the possible promotion of the paradigm shifts mentioned above are technically examined by looking the differences in the selection of verbs characterizing the learning objectives of mathematics in the two consecutive National Core Curricula for Finnish general upper secondary schools. As in Finland each upper secondary school offer two optional syllabuses of mathematics, short and long syllabus, in the years 1994 and 2003 four different mathematics curricula were published. From each of these curriculum texts, all verbs found in the objectives were first interpreted to express either individual, cognitive or social-constructivist objectives (lens 1) and secondly either instructional/process objectives or learning outcomes (lens 2). Totally 459 verbs consisting of 233 main verbs and 226 auxiliary verbs were analyzed. The changes which have taken place in the choice of verbs from the year 1994 to 2003 both in short and long mathematics courses were then described by comparing the cross-tabulations (Lens 1 x Lens 2) determined by the paradigm changes examined. The slightly simpler version of the method used in this study was pre-tested in the author's earlier study (Silfverberg 2010).

Expected Outcomes

By this two-dimensional verb analysis, we tried to answer at to what extent the subject specific mathematics curriculum texts explicitly promote the above described two concurrent paradigm shifts. The verb analysis of the curriculum texts showed that the first examined paradigm shift “social turn in mathematics education” cannot be detected from the linguistic surface level of the subject specific curriculum texts. In this respect, the examined curriculum texts are quite traditional and do not seem to promote any notable changes in the culture of mathematics teaching and learning which is not in a line with the main message of the national framework curricula. The second question about how curriculum texts reflect the shift from teaching/process objectives to the observable learning outcomes is more complex. It seems that in mathematics the objectives have traditionally been written in the format quite close to learning outcome -format and therefore it is natural that there have not yet happened big changes in this area. The next reform of the national framework curricula, which have already begun, will surely explicitly highlight the problem of how the formulation of the objectives of mathematics education should be made by using observable learning outcomes.

References

Anonym 2003 National Core Curriculum for Upper Secondary Schools 2003. Regulation 33/011/2003. Helsinki: Finnish National Board of Education. www.oph.fi/download/47678_core_curricula_upper_secondary_education.pdf Kennedy D., Hyland A. & Ryan, N. 2006. Writing and Using Learning Outcomes: a Practical Guide. In E. Froment, J. Kohler, L. Purser, L. Wilson, H. Davies & G. Schurings EUA The Bologna Handbook. Berlin: Raabe, C 3.4-1. Silfverberg, H. 2010. Opetussuunnitelmatekstien verbianalyysi - lukion matematiikan oppimäärät opetussuunnitelman perusteissa 1994 ja 2004 [in Finnish]. In E. Ropo, H. Silfverberg & T. Soini (eds.) Toisensa kohtaavat ainedidaktiikat. Department of Teacher Education, Tampere University, Report A31, 369-382.

Author Information

Harry Silfverberg (presenting / submitting)
University of Turku
Department of Teacher Education
Turku

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