Teaching Multiplication of Fractions with Natural Number

Summary on:
Shanty, N.O., Hartono, Y., Putri, R.I.I, de Haan, D. 2011. Design research on mathematics education: Investigating the progress of Indonesian fifth grade students’ learning on multiplication of fractions with natural number. Indonesian Mathematical Society Journal on Mathematics Education (IndoMS. J.M.E), 2.2, 147-162.

The difficulties of students in learning fractions, according to researches, is caused by two main factors. The first one due to teaching method which emphasizes only on technical procedures. As the consequence, the students see the algorithm as meaningless series of steps. Hence, they often forget the steps or might change the procedures with the incorrect ones. The problem is also called ‘algorithmatically based mistakes’. Another factor is the concept of the fraction itself which is NOT consistent with counting principles as it is in natural numbers.

In order to deal with the problems, remodeling mathematics by developing sequence of activities which are RME based seems to be appropriate. Here, we might design learning activities by combining 5 activity-levels in learning fraction (proposed by Streefland) with the 5 tenets of RME. In addition, the 4-level emergent modelling (by Gravemeijer) was also being concerned.

A design, covering the aforementioned needs, has been implemented by Shanty toward the 5th Grade students of SDN 179 Palembang. Here, the following, describes the activity she conducted and its effects to the students.

1. Producing Fractions
The activity employed contextual problems in order to stimulate students’ informal knowledge of partitioning, as meant to be a situational activity. The problem given was about ‘locating flags and water posts on the running route’ and delivered in form of story related to the celebration of Independence Day. In the story, two people were preparing running competition from PIM (Palembang Indah Mall) (A) to Palembang District Office (B). On the way from A to B, 8 flags and 6 water posts were installed, each of them with equal distance among its kinds. The students were, then, asked to locate and label the positions of the 8 flags and the 6 water posts in the provided running map.

The running route from PIM (A) to District Office (B)
Picture is available on https://www.google.co.id/maps

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Learning Decimals


Pramudiani, P., Zulkardi, Hartono, Y. & Ameron, B.V. (2011). A concrete situation for learning decimals. Indonesian Mathematical Society Journal on Mathematics Education, Vol. 2, No. 2, July, (2011), 215-230.

It was found that decimals is an essential part of mathematics whose concepts need to be learned meaningfully in order to prevent students from misconception. The fact, however, showed that Indonesian textbooks could not provide such condition and neither do the learning and teaching activities which finally led the students to the lack of understanding and misconception toward the concept. RME underlying the design of context (in this case precise measurement) and activities seemed to be an appropriate solution regarding this problem. Therefore, the study was conducted, that is, to study how measurement activities promote students’ notion of decimals.

The research was conducted in three main steps, namely, preliminary design (to produce a conjectured local instruction theory containing learning goals, planned activities, and learning process), teaching experiment (involving 26 students from class 5A SDN 21 Palembang in 6 lesson hours, prior to this, 73 students were involved in the pre-assessment and pilot experiment was given to 7 of them each from high, average, and low level students), and retrospective analysis (analyzing data collected and comparing the hypothetical learning trajectory with the students’ actual learning).

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Addition and Subtraction up to 100 Using Empty Number Lines

Reflection on Paper:
Design Research on Addition and Subtraction Up to 100
Using Mental Arithmetic Strategies on an Empty Number Line
At the 2nd Grade of SDN Percontohan Komplek IKIP Jakarta
(Puspita Sari, Dede de Haan, Zulkardi, 2008)

Innumeracy problems experienced by many students nowadays might be caused by inappropriate approach in teaching algorithm in primary schools which seems to be premature and less contextual according to some experts. In order to deal with the problems, realistic approach involving mental arithmetic strategies is suggested in advance, that is, emphasising more on number values rather than number digits.

In case of teaching addition and subtraction to 2nd grade students, an empty number line – number line with no numbers on it – seems to fit the need since it could encourage students’ informal counting strategy to develop. The use of context as demanded in RME is highly required to stimulate a meaningful learning toward the students. For the research, the context applied was celebrating the 63rd Indonesian Independence Day, due to the current d-situation.

The Use of Empty Number Lines in Learning Implementation
1. Empty number line as a model of
In this part, the number line was introduced using a string of beads which was coloured alternately every ten beads, the length of which would be measured by students using a paper strip. This would smoothly redirect the students to think of empty number lines.number lines as model of

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