Volume XXIV , issue 1 ( 2021 )back
Conics constructions by pins and string: tangential and physical properties1$-$11
Pietro Milici and Massimo Salvi
Machines4Math, Italy
nd Ministero dell'Instruzione, dell'Universit\`a e della Ricerca, Italy


We introduce conic sections' construction by pins and string, without rigid linear components. In addition to well-known methods (as gardener's ellipse), we analyze some recent constructions based on tangent properties and, as an original contribution, extend these constructions to all kinds of conics. In this setting, the physical analysis of the string's tension permits us to smoothly analyze these constructions since the first years of high school. \par From a didactical perspective, we think that such ideas can be fruitfully adopted in laboratory activities to deepen the tangential properties of conics by a rich interaction between mathematics and physics. Furthermore, the simplicity of the required materials allows the introduction of these manipulative activities in distance learning.

Creative Commons License

Keywords: Conics; pin-and-string constructions; tangent properties; string tension.

MSC Subject Classification: 97D40, 97G40, 97U60

MathEduc Subject Classification: D40, G40, U60

Probability and statistics---teaching driven by representation12$-$35
Jasmina V. Milinković and Ivica Radovanović
University of Belgrade, Teachers Training Faculty, Belgrade, Serbia
University of Belgrade, Teachers Training Faculty, Belgrade, Serbia


The newest reform of the educational system in Serbia brings forward the introduction of elements of probability and statistics in the elementary school curriculum. The paper explores possibilities for finding an optimal approach for developing basic probability and statistics concepts. Our research aimed to document the effects of alternative teaching methods of instructions based on the representational teaching approach, anchored to problems' representation (enactive, iconic, or symbolic). On a sample of 392 pupils, ages 11 to 14, three variants of the experimental program were compared using a nonparametric statistical procedure. The findings indicate that the iconic representational approach had better effects with younger pupils while the symbolic representational approach was the most effective representational method for higher grades of elementary school. A major implication of the study is that the representational teaching approach can be adjusted to the grade of pupils.

Creative Commons License

Keywords: Representation; probabilistic reasoning; statistics reasoning; teaching method; elementary school.

MSC Subject Classification: 97K60, 97K70

MathEduc Subject Classification: C73, K73

Aslanbek H. Naziev
Ryazan State University, Ryazan Institute of Education Development, State Social-Humanitarian University (t. Kolomna, Moscow Region), Russia


The article proposes a method for finding the center and radius of the sphere circumscribed about a pyramid. The method is based on reducing the problem to finding the circumcenter and circumradius for a specially constructed triangle. The construction of this triangle is the same for all inscribed pyramids. For the calculation of radius minimal information about the pyramid is used---its height, the circumradius of its base and the distance from the circumcenter of the base to pyramid's height.

Creative Commons License

Keywords: Stereometry; problem solving; polyhedra; round figures; combination of figures.

MSC Subject Classification: 97D50, 97G40

MathEduc Subject Classification: D54, D44