Mapping Pupil’s Learning Progression Using Hand Manipulatives and Touch Screen Applications: Implications to Post-COVID-19 New Normal

Table 1

Checklist on learning progression in the operations of fractions based on the Pirie–Kieren theory Approach.

Level [17]	Description [24]	Learning Progression Expectations about Fractions
1	PWS 1	The child knows moving hand and touch screen manipulatives but does not count aloud the concept of fractions to match with the objects.
Doing
2	PWS 2	The child says numbers as a part of the whole but does with exact correspondence of the uttered concepts of fractions and the manipulatives.
Image-making
3	MSUF 1	For at least five objects in hand and touch screen manipulatives, the child says the exact values and matches each spoken fraction with the objects.
Image having
4	MSUF 2	The child has developed an understanding of the addition and subtraction of similar fractions using the hand and touch screen manipulatives.
Property noticing
5	MSPF 1	The child has understood the multiplication and division of similar fractions using the hand and touch screen manipulatives.
Formalizing
6	MSPF 2	The child has developed an understanding of the addition and subtraction of dissimilar fractions using hand and touch screen manipulatives.
Observing
7	GMSF 1	The child has developed an understanding of multiplication and division of dissimilar fractions using the hand and touch screen manipulatives.
Structuring
8	GMSF 2	The child can explain the operations of fractions and provide more examples using the hand and touch screen manipulatives.
Inventing