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• The theory of functional equations in high school education

  345-360

  Dorottya Bessenyei

  Views:

  147

  In this paper, we are going to discuss some possible applications of the theory of functional equations in high school education. We would like to line up some problems, the solution of which by functional equations are mostly not new results – they have also been treated in [1] and [2] –, although their demonstrations in high school can show a new way in teaching of talented students. The area of the rectangle, the calculating method of compound interest, binomial coefficients, Euler's formula, the scalar product and the vector product of vectors – we are looking for the reasons behind the well-known formulas. Finally, we are going to give a functional equation in connection with mean values. It can be understood easily, but its solution is beyond the high school curriculum, so we advise this part only to the most talented students.

• Sequenced problems for functional equations

  179-192

  Zsolt Ádám

  Károly Lajkó

  Gyula Maksa

  Fruzsina Mészáros

  Views:

  82

  There are many possible methods to solve equations of the form H(f(x + y), f(x − y), f(x), f(y), x, y) = 0 (x, y 2 R), where H is a known function and f is the unknown function to be determined. Here we will create a sequence of problems for equations of type (1) (see on the next page). These sequenced problems are appropriate for the fostering of talented students on different level of mathematical education.

• A KöMaL problem in a new view

  191-201

  Pál Péter Dályay

  Views:

  46

  The object of this paper is finding the general solution f : R^3 → R of the system of functional equations (1) valid for all x, y, z, t ϵ R. First f is expressed by a function of one variable which satisfies a system of two functional equations.This system is resolved by using an algebraic reformulation of the problem in terms of orbits and transversals. Finally the general solution of (1) is obtained.

• Solving word problems - a crucial step in lower secondary school education

  47-68

  Zsolt Fülöp

  Views:

  240

  Algebra is considered one of the most important parts of Mathematics teaching and learning, because it lays the foundations of abstract thinking as well as reasoning abilities among the lower secondary school pupils who have just transited from the world of numbers and computations to the area of equalities, signs, symbols and letters. The present article focuses on the fact that how the transition from arithmetic to algebra can be made more smooth. We have concentrated our experiments towards the approach of algebraic reasoning and its utilities in filling the gap between arithmetic and beginning algebra in lower secondary school education.We also underline the importance of another approach in overcoming the challenges in the transition from arithmetic to algebra, to enhance and make algebraic learning more effective, with special considerations to word problem-solving processes. In our opinion, we have to go through three phases in the introducing of algebra in Grade 7 Mathematics education: Regula Falsi method (based only on numerical calculations); functional approach to algebra (which combines the numerical computation with letter-symbolic manipulation); and writing equations to word problems. The conclusions of the present article would be helpful to Mathematics teachers for applying themselves to develop the pupils’ interest in word problem-solving processes during algebra teaching classroom activities.

  Subject Classification: 97B10, 97C30, 97C50, 97D10, 97D40

• Erratum to the paper "The theory of functional equations in high school education" Teaching Mathematics and Computer Science 10/2 (2012), 345-360

  145

  Dorottya Bessenyei

  Views:

  88

  A correction is necessary in subsection 2.5. although this does not affect the truth of the main formula.