EDITORIAL 33 



who were a homogeneous group socially in each school, were divided 

 into two groups A and B, an equal number in each group, alike 

 in ability and similar in age. These groups A and B were taught 

 the definitions. Group A was taught deductively. The definition 

 was written out on the board, such as a triangle is a figure with 

 three sides and three angles. With this were drawn several 

 triangles to illustrate the definition. Pupils were asked to learn 

 this definition in the customary memoriten way, and similarly the 

 others. 



Group B was taught inductively. Thus in learning to define 

 the diameter of a circle "Pointing to all diameters drawn, the teach- 

 er says: 'What can we say about all these?' The answer lines' 

 will be received. He can then ask the question: 'What is the 

 diameter of a circle?' He will be answered, if he choose his ques- 

 tioneewell: 'A diameter of a circle is a line.' He draws a curved 

 line on the blackboard but not within one of the circles, and asks 

 'Is that a diameter of a circle?' He is answered 'No, because it is 

 not on a straight line.' He draws a straight line, still outside the 

 circle, and asks: 'Is that right?' The answer comes: 'No, 

 because it's not in a circle.' 'What is a diameter of a circle?' 

 If he chooses a child's answer, — as he should, from among the 

 least proficient of the class, he will be answered: 'A diameter of a 

 circle is a straight line inside a circle.' He accepts the answer 

 and draws a straight line in a circle which neither passes through 

 the center nor touches the circumference or either extremity. 

 He again asks: 'Is that right?' " And so on until the correct 

 definition has been developed. Repetition of it is avoided. 



When the instruction of the two groups has thus been accom- 

 plished the pupils were asked first: To immediately write defini- 

 tions in response to the questions, what is a square? A triangle, 

 etc. Second: A week later — to write these same definitions. 

 Third: A month later — to do likewise. Finally, some new 

 geometrical shapes were drawn upon the board, rhpmbuses, 

 trapeziums, rhomboids, etc., and these same pupils were asked 

 to make definitions for themselves and write them out. In other 

 words they were to do new work similar to that on which they 

 had been drilled. 



"The main problems were two in number. In the first place, an 

 attempt was made to discover which of the two methods (inductive 

 or deductive) gave the better results when the children were tested 



