# Interactive teaching of mathematics in younger grades of primary school

Interactive teaching is a modern teaching system that strives to overcome the passivity of students and the absence of interaction in traditional teaching.

The concept of interactive teaching implies a model according to which a certain topic or task is mastered through interaction between the participants of the lesson and through the process of interactive learning in a group. It is often defined as “interpersonal cooperative relationship of students” in class whose purpose is to transfer the action from the teacher to the students.

Interaction as the basis of interactive teaching represents “the mutual action” of people who adopt attitudes toward each other and mutually determine their own behavior. The basic characteristics of interaction are: mutual action of persons, taking positions and determining behavior.  Working in a group as the basis of interactive teaching provides the opportunity for students to become active in class and become active performers of the class, between whom there is quality cooperation.

Students remember the multiplication table gradually, using it in calculations. To check the accuracy of what has been memorized, if one factor is less than or equal to five, students count the numbers multiply by adding equal sums. If both factors are greater than five then they can use the rule that we will prove and explain.  Assume that m and n are natural numbers less than 5.  The numbers whose products form the lower right part of the multiplication table have then form 10-m and 10-n, and both belong to the set {6, 7, 8, 9}.

By multiplying the given numbers we get:

(10 – m) · (10 – n) = 10 · 10 – m · 10 – n · 10 + m · n =

= (10 – m – n) · 10 + m · n =

= [10 – (m + n)] · 10 + m · n.

To apply the obtained expression, when calculating the product of the specified numbers, we will first describe the role of the numbers m and n. The number m determines how much the first set is factor less than 10, and the number n the same for the second factor.  The product is equal to the sum in which the first addition contains at least two tens because

​10 – (m + n) ≥ 2,  ​and the second one at most ten because, ​  m · n ≤ 16 (4 · 4 =16).​

The described way of determining the product can be determined by using the fingers on

with joined hands, palms towards you. In this position, the thumbs are the last fingers and they always bend.

The total number of bent fingers on the left hand is equal to the number described m, and on the right n. Outstretched fingers represent tens, i.e. the first addition, and the second addition is the product of bent fingers. The multiplication procedure described in this way can be called finger multiplication. In this way, checking the correctness of the right part is accelerated multiplication tables, which students have the hardest time remembering.

Examples:

The most important advantage in the interactive processing of teaching units, according to the described structure,makes a significantly greater engagement of students’ thinking activities on the basis of which it is carried out conclusion.

At the same time, inductive reasoning is used to a significantly lesser extent, mainly for confirming, expanding and unifying processed content. Although empirical research refers only to a sample from the population of students in younger grades, it can be assumed that by working according to our methodology, students would achieve even better results.  The use of computers, which we did not include in the work of the experimental group, would have a positive effect on the achievement of students in interactive mathematics learning.