Didactical Modeling, Vol. 7, pp. 1-20
ON THE
TRANSFERABILITY OF MATHEMATICAL KNOWLEDGE AND SKILLS IN THE CONTEXT OF THE
INTERNATIONAL ASSESSMENT PROGRAMS FOR MATHEMATICAL ACHIEVEMENTS
Borislav Lazarov
Institute of Mathematics and Informatics, Bulgarian Academy of Sciences
lazarov@math.bas.bg
Abstract
The study presents the author’s viewpoint on the possibility
to evaluate adequately the students’ knowledge and skills in mathematics via
the PISA and TIMSS assessment procedures. A comparative study of the constructs
key-competences, mathematical literacy and numeracy, adopted by the Bulgarian
legislation, OECD and the International Association for the Evaluation of
Educational Achievement, respectively, is done. Two examples illustrates the
conceptual differences between the math style that takes place in the Bulgarian
secondary school and the one adopted by PISA&TIMSS. An ontological distance
is designed to evaluate these differences in a quantative way.
Keywords: assessment of math
knowledge-skills-attitude, transferability of math knowledgeskills-attitude,
synthetic competence
REFERENCES
[1] Bankov, K. The Mathematics Education is in Deep Crisis. Didactical Modeling, vol. 5, 1-8. [in Bulgarian]
[2] Bloom,
Benjamin S.
Taxonomy of
Educational Objectives. Allyn and Bacon, Boston, MA.
[3] European
Commission.
Recommendation of
the European Parliament and of the Council of 18 December 2006, on key
competences for lifelong learning. Official Journal
of the European Union, (2006/962/EC) L 394.
[4] Ganchev, I. and Kuchinov,Y.
Organization and Methodic of the Math Lesson. Modul, Sofia, 1996.
[5] Grønmo,
L., Lindquist, M., Arora, A. and Mullis, I.
TIMSS 2015 Mathematics Framework. International Association for the Evaluation of
Educational Achievement. TIMSS & PIRLS International Study Center, Lynch
School of Education, Boston College.
[6] Lave,
J.
Cognition in
practice: Mind, mathematics, and culture in everyday life.
Cambridge, UK: Cambridge University Press.
[7] Lazarov,
B.
Three Problem Areas
of the Educational Environment. Didactical Modeling, vol. 2, 1-5.
[8] Lazarov,
B.
Application of some
cybernetic models in building individual educational trajectory.
Information Models and Analyses. Vol. 2, No 1, 90-99.
[9] Lazarov,
B.
Decontextualization.
Mathematics and Education in Mathematics. Proceedings of the Forty
Third Spring Conference of the Union of Bulgarian Mathematicians, Borovetz,
April 2–6, 2014, 67-76 [in Bulgarian]
[10] Milev,
A., Nikolov, B. and Bratkov, Y.
Dictionary
of foreign words in Bulgarian language. Nauka i
izkustvo, Sofia. [in Bulgarian]
[11] Ministry
of Education and Science.
Regulation
No 5 of 30.11.2015 for the general education. Darzhaven Vestnik, I.
95 of 08.12.2015. [in Bulgarian]
[12] Ministry
of Education and Science.
Regulation
No 11 of 01.09.2016 for the assessment of the outcomes of the education.
Darzhaven Vestnik, I. 74 of 20.09.2016. [in Bulgarian]
[13] Organisation
for Economic Co-operation and Development.
Pisa 2021 Mathematics Framework (First Draft).
45th meeting of the PISA Governing Board, 23-25 April 2018, Stockholm, Sweden.
[14] Schoenfeld, A. Toward a theory of teaching-in-context. Issues in Education, Vol. 4, No 1, 1-94.