The use of multiple representation for math education

The Math lessons for students have always been difficult. This may be caused by thinking capabilities of students or the lack of general method for teaching Math. In this study we develop a kind of algebraic approach to some basic arithmetical operations using base functions. First of all we define the base functions. Using these base functions we will develop a class of Computable Functions in terms of given base functions. We will see that it is possible to derive new knowledge from the old ones.


Introduction
This study is originally developed in order to study some mathematical aspects of effectively computable functions.This formalism has provided a strong foundations for the family of functionally expressed functions (Myers, 1988;Tepedeldiren, Ozkan & Unal, 2011).We define these functions recursively.In our opinion it is important to build a strong bridge between recursive function theory and these functionally expressed forms.We use a method alike Alonzo Church's; a kind of a way of effectively computable functions.In this study we mainly use conditionals forms given by John McCarthy (1967).Finally we present a formalism for describing functions which are computable in terms of given base functions (in this study functionals) (Tepedeldiren, 1996).

Methodology
Now we are ready to construct the class of computable functions in terms of given base functions.In order to do this we must define the main elements of this class and how to evaluate the conditional forms.Finally we construct the class as we desired.In this class of functions (mainly made up of basic aritmetical operations) the reader can see many of the aspects of these functions in a unique formula.

The design of integer functions using conditional forms
We develop a class of recursively definable functions on the set of non-negative integers.The notation I={0,1,2,…} is the set of non-negative integers.Using successor and equality functions , we develop a class of functions C{F}.
Definition 1 : For n∈I we define the successor function as succ(n)=n+1 and show it as n + Definition 2 : For n1,n2∈I we define the equality function as equ(n1,n2)=( n1= n2→T , T→F) We call both functions as base functions.We are ready to construct other functions using them.Firstly we define the predecessor function which find the one less than the given n∈I.
Definition 3 : Let I + ={1,2,…} and n∈I + .We define the predecessor of n as Definition 4 : Let m,n∈I.We define the basic arithmetic operations given below: The result is 5. What you see in this example is easy to understand.All of the properties of the summation are seen in this formula.

Conclusion
In this study, we have tried to explain how to construct a family of Computable Functions in terms of given Base Functions.These explanations and definitions are perfect to understand a compact formula and its properties.You see all of the properties of certain arithmetic operations in one formula and you can easily understand them.You can also easily construct new formulae from the old ones.These functions will be functionals since they use functions as their domains.It is a kind of a new algebraic method to have functionals using appropriate functions.