Kelompok II1.Chika Rahayu2.Dekriati Ate3.Meta Silvia Gunawan4.Nursa Fatri Nopriati5.Sri Widya Permatasari

Fraction, an integrated perspective

1. Concept aquisition and N distractors

Bagaimana membagi 3 batang coklat untuk 4 orang anak sehingga masing-masing anak akan mendapat bagian yang sama!

Ide Clara

Ide Clara

Clara encountered certain difficulties during this early stage of the learning process. She preferred to stick to notations such as or

In the case where eight children were each to receive Clara Suggested giving them all one and then having them all return

?

When asked whether someone receiving

Clara tried to reconstructing the distribution story of the other fraction which is similar with the example before.12+15

Clara first said theat there were 7 people sharing, an answer which can also be regardeda as N distractor error.

𝟏𝟐+

𝟏𝟓

𝟏𝟐+

𝟏𝟓

𝟏𝟐+

𝟏𝟓𝟏𝟐+

𝟏𝟓𝟏𝟐+

𝟏𝟓

𝟑𝟏𝟐𝟑𝟏𝟐

𝟕

5 5

10

710+0=

12+15

Fraction, an integrated perspective

2. Progression in schematising

After 3 weeks, Clara applied another type of abbreviation

58

𝟐𝟏𝟐4 4

4 8 16

20

32

3 6 12

15

24

In Schematisations with the ratio table. Clara constructed table of 4S : 3C

S 18 36 54

C 8 16 24

Comparing

S 14 28 42

56

C 6 12 18

24

Fraction, an integrated perspective

3. Flexible use of models

13

4 13 4 134 13

• Figure 6

15

5 5 5

Figure 7

Figure 8

4. Ability to build of formal problems

=

1

Indicator 5: the pupil’s own constructions and productions

on the symbolic level

By a monograph we mean a series of fractional number sentences fitting to a single distribution in which the fair sharing takes place in different ways.

After 3 ½ months

Two months later

4 months later

+ Up to after

+

The characteristic of Clara’s test were :

• A relatively large number of assignments for practising the main LOT operations

• Translation assignments into LOT language• A few application assignments, with the view on

the definitions of a LOT numbers.• A few assignments for construction and free

production

6 months later

Clara’s process of fraction construction

Concept acquisition and N-distractors

Progression in schematising

Flexible use of models,

application of schemes and

diagrams

The pupil’s own constructions

and productions on the symbolic

level

Ability to build images of

formal problems

LOT test

This may have helped to increase her self-

confidence and her achievement