Two Types of Division

Question: I've been studying p. 39, Teacher Note, and I'm somewhat confused. I thought that the two kinds of division were partitive and measurement division. It was my understanding that partitioning and sharing were the same. I have used two college math methods books to explore the issue. They are Learning Mathematics in Elementary and Middle Schools by Cathcart and Elementary and Middle School Math by Van de Walle. Any insight you can shed on this would be greatly appreciated.

Answer: Thank you for pointing out the confusion about the division terms in the Teacher Note. The Note is confusing because partitioning sounds a lot like partitive which it isn't. For example, consider 24 divided by 3.

How many for each of 3 people is sharing/partitive.
How many groups of 3 is measurement/grouping.

Tom Carpenter et. al. define these this way, in Children's Mathematics: Cognitively Guided Instruction:

Partitive Division [sharing equally or dealing out]: Gene has 4 tomato plants. There are the same number of tomatoes on each plant. Altogether, there are 20 tomatoes. How many tomatoes are there on each tomato plant?

Measurement Division [making groups of a certain size]: Gene has some tomato plants. There are 6 tomatoes on each plant. Altogether there are 24 tomatoes. How many tomato plants does Gene have?

Cornelia Tierney, TERC
November 2002

This information was reprinted with permission of CESAME, Northeastern Univ., and the Educational Alliance, Brown University.