PSYCHOLOGY 

 L. self-tAught arithmetic from the age of 



FIVE TO SEVEN AND A HALF 



Sophie Ravitch Altshiller Court 

 Norman, Oklahoma 



(Abstracted) 



This paper is an attempt to describe and to discuss the processes 

 in the worksliop of a child's mind in the realm of arithmetical 

 thought. 



The arithmetical equipment of the boy A. at the age of five 

 years and one month, is given in "Numbers, Space and Time in 

 the First Five Years of a Child's Life," by Sophie R. A. Court 

 (Pedagogical Seminary, March, 1920). 



Two weeks later he suddenly began to count by fives, without 

 any provocation from the outside and without knowing, just what 

 he was doing. He was fascinated by the rhythm and counted in a 

 sing-s®ng up to twenty. A few hours later he discovered, by an in- 

 tuitive process, that it was by fives that he was counting, and 

 verified this discovery empirically by counting on his fingers. For 

 several weeks he enjoyed counting by fives, gradually increasing 

 his scale, until three weeks later he counted well till two hundred, 

 and at the age of five years, nine months, could count by fives and 

 twos correctly and rapidly ad infinitum, as it seemed — having 

 learned the counting by twos in the same spontaneous way. 



He also often counted by tens, and enjoyed the "joke" of saying 

 after ninety, "tenty," "eleventy," "twelfty." 



He was less interested in computation, yet often did little addi- 

 tions — within ten or fifteen — mentally, on his blocks, on the type- 

 writer, and, later, from the age of five and a half, in writing. 



Hearing that odd and even numbers of houses are on the dif- 

 ferent sides of the street, he became interested in recognizing, which 

 numbers are odd and which are even. 



All the time under consideration, as before, he was greatly 

 interested in measuring and used every opportunity to take linear 

 measurements, to find out capacity of utensils, to weigh different 

 objects, to measure depth of water in bathtub or basin, etc. Also 

 compared fractions on a measuring cup, and taught himself, 1-3, 

 1-8. 1-10. 



He liked to tell time, and at five vears two and a half months 



