Page 413 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts
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MATHEMATICS IN EDUCATION (MS-19)
Cross-Curricular Integration of Knowledge in Mathematics at the
Primary School Level
Marina Volk, marina.volk@pef.upr.si
Univerza na Primorskem, Pedagoška fakulteta, Slovenia
Cross-curricular integration is one of the key concepts of modern orientations of education
development because students who are involved in elementary school education have to gain
competencies that go beyond the traditional boundaries between subjects so that they will be
able to participate in the society of knowledge. It is important in the transfer of knowledge that
educational institutions are also aware of the extracurricular circumstances in which students
work and take these circumstances into account when teaching. Students are motivated by the
opportunity to use the gained knowledge to solve more complex problems and create new solu-
tions. In recent years, most European countries have renewed mathematics curricula (including
Slovenia in 2011) by giving more emphasis to mathematical competencies, knowledge, and
skills, as well as cross-curricular connections, because mathematical skills are more and more
perceived as a basis for learning other school subjects. Connecting mathematics with other dis-
ciplines and solving authentic problems give mathematical learning real meaning because stu-
dents feel the importance of building and upgrading mathematical concepts. At the same time,
we introduce students to research and problem solving from everyday life. In this paper, we
present and substantiate the cross-curricular approach to teaching mathematics which provides
thinking at higher cognitive levels – the use, analysis, and generalization – while the subject
approach builds and deepens the knowledge of each subject. Based on an educational exper-
iment in which we introduced cross-curricular integration of mathematics with other school
subjects, we ascertained that the students of the experimental group achieved better results at
higher taxonomic levels in comparison to the students of the control group. We can conclude
that cross-curricular integration in the taxonomic sense is a synthesis of knowledge of different
disciplines which is reflected in a new level of integration of knowledge and understanding.
Peano- and Hilbert curve
Jan Zeman, janzeman@email.cz
University of West Bohemia, Czech Republic
In this presentation, we give a historical survey on Hilbert’s interpretation of the space-filling
Peano-curve which Hilbert presented at the GDNÄ session in Bremen in 1890. Since Hilbert
was systematically working in the field of number theory in that period, we try to explain the
reason for his sudden interest and immediate reaction to Peano’s surprising result from the same
year which proved the possibility of a continuous surjective mapping of a line to a square. We
argue that by means of his address, Hilbert was willingly trying to express his positive view on
Cantor’s set theory, an affinity which was also present by selecting the continuum hypothesis as
the first problem on his list of the mathematical problems for the 20th century and which lead
his thinking also long afterwards in the 1920s while working on his so-called Hilbert’s program
in logic. We present also Hilbert’s correspondence with H. Minkowski on this topic.
References
[1] Minkowski, H., Briefe an David Hilbert. Editors L. Rüdenberg, H. Zassenhaus. Berlin,
Springer 1973.
411
Cross-Curricular Integration of Knowledge in Mathematics at the
Primary School Level
Marina Volk, marina.volk@pef.upr.si
Univerza na Primorskem, Pedagoška fakulteta, Slovenia
Cross-curricular integration is one of the key concepts of modern orientations of education
development because students who are involved in elementary school education have to gain
competencies that go beyond the traditional boundaries between subjects so that they will be
able to participate in the society of knowledge. It is important in the transfer of knowledge that
educational institutions are also aware of the extracurricular circumstances in which students
work and take these circumstances into account when teaching. Students are motivated by the
opportunity to use the gained knowledge to solve more complex problems and create new solu-
tions. In recent years, most European countries have renewed mathematics curricula (including
Slovenia in 2011) by giving more emphasis to mathematical competencies, knowledge, and
skills, as well as cross-curricular connections, because mathematical skills are more and more
perceived as a basis for learning other school subjects. Connecting mathematics with other dis-
ciplines and solving authentic problems give mathematical learning real meaning because stu-
dents feel the importance of building and upgrading mathematical concepts. At the same time,
we introduce students to research and problem solving from everyday life. In this paper, we
present and substantiate the cross-curricular approach to teaching mathematics which provides
thinking at higher cognitive levels – the use, analysis, and generalization – while the subject
approach builds and deepens the knowledge of each subject. Based on an educational exper-
iment in which we introduced cross-curricular integration of mathematics with other school
subjects, we ascertained that the students of the experimental group achieved better results at
higher taxonomic levels in comparison to the students of the control group. We can conclude
that cross-curricular integration in the taxonomic sense is a synthesis of knowledge of different
disciplines which is reflected in a new level of integration of knowledge and understanding.
Peano- and Hilbert curve
Jan Zeman, janzeman@email.cz
University of West Bohemia, Czech Republic
In this presentation, we give a historical survey on Hilbert’s interpretation of the space-filling
Peano-curve which Hilbert presented at the GDNÄ session in Bremen in 1890. Since Hilbert
was systematically working in the field of number theory in that period, we try to explain the
reason for his sudden interest and immediate reaction to Peano’s surprising result from the same
year which proved the possibility of a continuous surjective mapping of a line to a square. We
argue that by means of his address, Hilbert was willingly trying to express his positive view on
Cantor’s set theory, an affinity which was also present by selecting the continuum hypothesis as
the first problem on his list of the mathematical problems for the 20th century and which lead
his thinking also long afterwards in the 1920s while working on his so-called Hilbert’s program
in logic. We present also Hilbert’s correspondence with H. Minkowski on this topic.
References
[1] Minkowski, H., Briefe an David Hilbert. Editors L. Rüdenberg, H. Zassenhaus. Berlin,
Springer 1973.
411
