Volume XIX , issue 1 ( 2016 ) | back |

An empirical study in the notion of area: a Socratic educational experience anchored in van Hiele's model | 1$-$23 |

**Abstract**

In this article, our goal is to design a suitable strategy to be implemented on High School students in order to prepare them for the formal study of approximate and exact integration via a Socratic semi-structured interview. Our dialog will be closely dependent on the use of a computer generated tool (applet) to encourage students' participation, provide them with numerical and visual data and allow the linking of the processes of discovery, understanding and conceptualization in the frame of an educational model. What follows contains a description of the interview which is also our instrument for pointing out and detecting the levels postulated by van Hiele's educational model.

**Keywords:** Area; approximation; error; limits; van Hiele's model.

**MSC Subject Classification:** 97I50, 97U50

**MathEduc Subject Classification:** I54, U54

On a calculus textbook problem | 24$-$31 |

**Abstract**

We consider generalizations of a well known elementary problem. A wire of the fixed length is cut into two pieces, one piece is bent into a circle and the second one into a square. What dimensions of the circle and the square will minimize their total area?

**Keywords:** optimization problems; isoperimetric problem.

**MSC Subject Classification:** 97I40, 97I60

**MathEduc Subject Classification:** I45, I65

Geometry and mathematical symbolism of the 16th century viewed through a construction problem | 32$-$40 |

**Abstract**

This paper represents a construction problem from {ıt Problematum geometricorum IV} written by Simon Stevin from Bridge in 1583. The problem is used for illustrating the geometry practice and mathematical language in the 16th century. The large impact of Euclid and Archimedes can be noted. In one part of the construction, Stevin expressed the need for using numbers for greater clarity. Hence, the link with the work of Descartes and the further geometry development is pointed out.

**Keywords:** 16th century mathematics; mathematical symbolism; Simon Stevin; construction problems

**MSC Subject Classification:** 97A30

**MathEduc Subject Classification:** A35

Does the problem complexity impact students' achievements in a computer aided mathematics instruction? | 41$-$55 |

**Abstract**

The paper deals with two aspects of a computer-based analytic geometry instruction: students' achievements, and achievement decay rates. A new mathematics learning environment---a dynamic and interactive one---is being built with introduction of computers and GeoGebra in the classroom. The subject material was introduced to the students mostly through GeoGebra dynamic worksheets. Students of the experimental and the control groups went through three tests within an eight-month period. The tests were different in terms of technology used by the experimental group and the two aspects we took into consideration. In the first two tests we observed students' achievements in different learning environments. The experimental group students showed a lower performance when solving problems in a non-computer environment than they did in a computer-based environment. However, we identified types of problems that are easier to solve in a computer-based environment, and others that do not necessary require computer usage to be quickly solved. This helped us formulate better strategies while choosing types of problems and appropriate ways and technologies to solve them. Parts of the third test helped us estimate achievement decay rates for both groups. Results indicate very close achievement decay rates for both, experimental and control groups.

**Keywords:** GeoGebra; dynamic worksheets; analytic geometry; students' achievement decay.

**MSC Subject Classification:** 97U50

**MathEduc Subject Classification:** U54