Page 408 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts
P. 408
MATHEMATICS IN EDUCATION (MS-19)
References
[1] Kadijevich, D. M. (2019a). Interactive displays: Use of interactive charts and dashboards
in education. In Tatnall A. (Ed.), Encyclopedia of education and information technologies.
Cham, Switzerland: Springer.
[2] Kadijevich, D. M. (2019b). Cultivating computational thinking through data practice. In
Passey, D., Bottino, R., Lewin, C., & Sanchez, E. (Eds.), Empowering learners for life in
the digital age (pp. 24–33). Cham, Switzerland: Springer.
[3] Stephens, M., & Kadijevich, D. M. (2019). Computational/algorithmic thinking. In Lerman
S. (Ed.), Encyclopedia of mathematics education. Dordrecht, the Netherlands: Springer.
Making a rhombic 1080-hedron
Andreja Klancˇar, andreja.klancar@pef.upr.si
University of Primorska, Faculty of Education, Slovenia
Coauthor: Izidor Hafner
Paper models of polyhedra are attractive but difficult to make. That is why in schools we
prefer to make polyhedra from plastic parts (Polydron, Zometool). We are interested in golden
rhombic solids. There are only five convex golden polyhedra: prolate and oblate rhombohedron,
rhombic triacontahedron (Kepler, 1611), rhombic icosahedron (Fedorov, 1885), and Bilinski
dodecahedron (1960). Our project is to make a polyhedron that has 1080 golden rhombuses as
faces and has the symmetry of an icosahedron. Such a polyhedron has 2160 edges and 1062
vertices. So we need 2160 sticks and 1062 Zometool balls. Theoretically, we could describe the
fabrication by starting with Kepler’s triacontahedron. Each rhombus is divided into 36 smaller
ones. We then do an inversion on the vertices of valence 3 until no two adjacent rhombuses are
in same plane. The orthogonal projection of such polyhedron along an axes of fivefold rotation
form a Penrose tiling.
How sixth graders’ represent some mathematics concepts with drawings
Alenka Lipovec, alenka.lipovec@um.si
University of Maribor, Slovenia
Visual representations enable teachers and researchers to interpret the meanings of mathemat-
ical concepts, relations and processes; therefore, they play an important role in mathematics
education. In the present study, we analysed the students’ understanding of various mathemati-
cal concepts using drawings. Numerical expressions 17 − 9 , 3 · (4 + 5) , 3 of 15 and 23 were
5
provided to sixth grade elementary students (N = 1595). Students were asked to draw one pic-
ture for each numerical expression that describes it. We were interested in whether pictures
adequately represent the concept underlying the expression. The data were analysed with a
combination of qualitative and quantitative methods. The results show that the participants rep-
resented the concepts quite adequately. Expectedly, less abstract concepts were depicted more
adequately. In the qualitative content analysis, two themes emerged. Those themes illustrate
two ways of mathematical understanding (instrumental and relational) and two types of math-
ematical knowledge (procedural and conceptual). Procedurally oriented images predominated;
406
References
[1] Kadijevich, D. M. (2019a). Interactive displays: Use of interactive charts and dashboards
in education. In Tatnall A. (Ed.), Encyclopedia of education and information technologies.
Cham, Switzerland: Springer.
[2] Kadijevich, D. M. (2019b). Cultivating computational thinking through data practice. In
Passey, D., Bottino, R., Lewin, C., & Sanchez, E. (Eds.), Empowering learners for life in
the digital age (pp. 24–33). Cham, Switzerland: Springer.
[3] Stephens, M., & Kadijevich, D. M. (2019). Computational/algorithmic thinking. In Lerman
S. (Ed.), Encyclopedia of mathematics education. Dordrecht, the Netherlands: Springer.
Making a rhombic 1080-hedron
Andreja Klancˇar, andreja.klancar@pef.upr.si
University of Primorska, Faculty of Education, Slovenia
Coauthor: Izidor Hafner
Paper models of polyhedra are attractive but difficult to make. That is why in schools we
prefer to make polyhedra from plastic parts (Polydron, Zometool). We are interested in golden
rhombic solids. There are only five convex golden polyhedra: prolate and oblate rhombohedron,
rhombic triacontahedron (Kepler, 1611), rhombic icosahedron (Fedorov, 1885), and Bilinski
dodecahedron (1960). Our project is to make a polyhedron that has 1080 golden rhombuses as
faces and has the symmetry of an icosahedron. Such a polyhedron has 2160 edges and 1062
vertices. So we need 2160 sticks and 1062 Zometool balls. Theoretically, we could describe the
fabrication by starting with Kepler’s triacontahedron. Each rhombus is divided into 36 smaller
ones. We then do an inversion on the vertices of valence 3 until no two adjacent rhombuses are
in same plane. The orthogonal projection of such polyhedron along an axes of fivefold rotation
form a Penrose tiling.
How sixth graders’ represent some mathematics concepts with drawings
Alenka Lipovec, alenka.lipovec@um.si
University of Maribor, Slovenia
Visual representations enable teachers and researchers to interpret the meanings of mathemat-
ical concepts, relations and processes; therefore, they play an important role in mathematics
education. In the present study, we analysed the students’ understanding of various mathemati-
cal concepts using drawings. Numerical expressions 17 − 9 , 3 · (4 + 5) , 3 of 15 and 23 were
5
provided to sixth grade elementary students (N = 1595). Students were asked to draw one pic-
ture for each numerical expression that describes it. We were interested in whether pictures
adequately represent the concept underlying the expression. The data were analysed with a
combination of qualitative and quantitative methods. The results show that the participants rep-
resented the concepts quite adequately. Expectedly, less abstract concepts were depicted more
adequately. In the qualitative content analysis, two themes emerged. Those themes illustrate
two ways of mathematical understanding (instrumental and relational) and two types of math-
ematical knowledge (procedural and conceptual). Procedurally oriented images predominated;
406
