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MFP1501 ASSIGNMENT 2SEMESTER 2 - 2022
UNIQUE NUMBER: 188011
DUE DATE: 29 JULY 2022
, Question 1
Determine five developmental stages of multiplicative thinking.
a. One-to-one Counting:
Children who count in a one-to-one manner are in this phase. They understand technically
what they have to do to answer the “how many question”.
b. Additive Composition:
When children understand that the count is a permanent indicator of quantity they are in
this phase. They know that a collection can be rearranged or counted in a different ways
and the quantity will not change. They know that given two collections, one with four and
one with nine, they do not have to go back and count them all; they can simply count on
from the four or the nine. Using shortcuts makes sense to them.
c. Many-to-one Counting:
When children understand that groups can be counted and that they can keep track of two
things at once — the number of groups and the total of the number in each group — they
are in this phase. They can hold two numbers in their head at once and double count.
Children now know that they can represent one group and count repetitions of that same
group.
d. Multiplicative Relations:
When children come to know that multiplicative situations involve three aspects: groups of
equal size (a multiplicand), numbers of groups (the multiplier), and a total amount (the
product), and can coordinate the grouping structure in both multiplication and division
problems prior to carrying out the count, they are in this phase. Children know which
number tells them how many in a group and which number tells them how to operate on
that group.
e. Operating on Operators:
When children can operate on variables in algebraic situations and operate on operations
they are in this phase. It would mean that they could multiply the multiplier in the way
described by Schmidt and Weiser (1995) in the multiplication problem type they call the
structure of composition of operators.
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