| Conics constructions by pins and string: tangential and physical properties | 1$-$11 |
Abstract
We introduce conic sections' construction by pins and string, without rigid linear components. In addition to well-known methods (as gardener's ellipse), we analyze some recent constructions based on tangent properties and, as an original contribution, extend these constructions to all kinds of conics. In this setting, the physical analysis of the string's tension permits us to smoothly analyze these constructions since the first years of high school. \par From a didactical perspective, we think that such ideas can be fruitfully adopted in laboratory activities to deepen the tangential properties of conics by a rich interaction between mathematics and physics. Furthermore, the simplicity of the required materials allows the introduction of these manipulative activities in distance learning.
Keywords: Conics; pin-and-string constructions; tangent properties; string tension.
MSC Subject Classification: 97D40, 97G40, 97U60
MathEduc Subject Classification: D40, G40, U60
| Probability and statistics---teaching driven by representation | 12$-$35 |
Abstract
The newest reform of the educational system in Serbia brings forward the introduction of elements of probability and statistics in the elementary school curriculum. The paper explores possibilities for finding an optimal approach for developing basic probability and statistics concepts. Our research aimed to document the effects of alternative teaching methods of instructions based on the representational teaching approach, anchored to problems' representation (enactive, iconic, or symbolic). On a sample of 392 pupils, ages 11 to 14, three variants of the experimental program were compared using a nonparametric statistical procedure. The findings indicate that the ‘iconic’ representational approach had better effects with younger pupils while the symbolic representational approach was the most effective representational method for higher grades of elementary school. A major implication of the study is that the representational teaching approach can be adjusted to the grade of pupils.
Keywords: Representation; probabilistic reasoning; statistics reasoning; teaching method; elementary school.
MSC Subject Classification: 97K60, 97K70
MathEduc Subject Classification: C73, K73
| METOD OTYSKANIYA CENTRA I RADIUSA SFERY, OPISANNOJ OKOLO PIRAMIDY | 36$-$53 |
Abstract
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.
Keywords: Stereometry; problem solving; polyhedra; round figures; combination of figures.
MSC Subject Classification: 97D50, 97G40
MathEduc Subject Classification: D54, D44