The Summary of Dolk and Fosnot’s book with the Title of Young Mathematician at Work 1 ch. 3
The students in preschool have already known about number and counting. However, they haven’t fully known yet about the quantity/amount. Although preschool students have already known about numbers and counting, they still have a problem in understanding the amount/quantity. It is caused by the fact that students have not yet construct idea about counting in their mind. Some students are able to understand the magnitude of each group of objects and to compare two, three and four objects in which one group is bigger than the other without counting since they use magnitude. Some students seem to understand about one-to-one correspondence but they don’t know that each number they have mentioned represent the amount of objects correspond with. It is imperative that the students know about cardinality so that they can understand the meaning of number. It is stated also that students sometimes doing subitizing namely seeing small amount as group. However, students will find difficulty when they face large amount of objects. Since they don’t know the meaning of amount, they will have a problem in adding and subtracting objects. Teacher can overcome this problem by asking students to count so that the students are able to see the meaning of number in which the idea of cardinality comes up. When students have done it well, they ease to know hierarchical inclusion, understanding that whole numbers grow by once each time and therefore that numbers nest inside each other : six is inside seven (by removing one). When students understand about hierarchical inclusion, they will know the concept of compensation, for example 6 + 1 = 7 as well as 5 + 2 = 7, while one is removed from six, it means it has been added by 2 to get the same amount.