Design Research on Computational Estimationfor Grade Five Primary School Students in Indonesia.
By: Al Jupri
In this research we try to investigate student’s strategies in solving computational estimation problems and based on the investigation we try to hypothesize students’ learning trajectory in the computational estimation and implement it into a classroom teaching-learning setting.
Many mathematics educators suggested that estimation is more commonly used than exact computation in daily life. Another example of the importance of computational ability for students is that student will be able to check reasonableness of computational results, for example calculation using calculators. In Indonesian mathematics curriculum, estimation is introduced in the grade four primary school students as a little subtopic of whole numbers and it is extended in the grade five.
According to Traftron (1986), most students are uncomfortable with estimation. Students are not sure why they need to do estimation, there are not sure when solving estimation problem directly using estimation strategies. Students view estimation as invalid mathematics.
There are several specific research questions: What strategies do students use when solving estimation question? What are students’ difficulties when solving estimation problem? What are kinds of problem that invite students to be more using estimation strategies instead of using exact calculation?
2. Computational Estimation
There are several definitions of computational estimation, but here we present two of them. First, computational estimation is the process of simplifying an arithmetic problem using some set of rules or procedures to produce an approximate but satisfactory answer through mental calculation. And second, computational estimation is nothing more than quickly and reasonably developing an idea about the quantity of something without actually counting it.
3. Realistic Mathematics Education and Learning Computational Estimation.
The term “realistic” means that the problem situations should be ‘experientially real’ for students. This means that the problem situations could be problems that can be encountered either in daily life or in abstract mathematical problems as long as the problems are meaningful for students. In the learning activity, based on RME, students should be allowed and encouraged their own strategies and ideas, and they should learn mathematics based on their authority.
Regarding to the learning of computational estimation, this raises a question: how to support the students’ learning process on computational estimation meaningfully to reach learning goals?
There are five tenets of RME, according to Treffers, namely as follows:
a. phenomenological exploration
b. using models and symbols for progressive mathematization
c. using students own contributions and productions.
4. Design Research
The method which is used in this research is called design research. Design research is a type of research methods with its core of research is formed by classroom teaching experiments that underpin them.
Design research encompasses three phases, namely as follows:
a. Developing a preliminary design
in this phase, the result is a formulation of what is called a conjectured local instruction theory, that is made of three components: learning goals for students; planed instructional activities and the tools that will be used; and conjectured learning process.
b. Teaching Experiment
In this phase, instructional activities are tried, revised, and designed on a daily basis during the experiment.
c. Retrospective Analysis
In this phase, all data during experiment are analyzed and the HLT is compared with students’ actual learning.
5. Preliminary Research on Computational Estimation
The purpose of this preliminary research was to investigate students’ estimation strategies in solving estimation problems in non teaching-learning setting. To be more specific this research question is specified into three specific research questions: (1) What strategies do students use when solving estimation problem? (2) What are kinds of problems that invite students to be more using estimation strategies instead of using exact calculation? (3) What are students’ difficulties when solving estimation problems?.
We mainly discuss results’ of the preliminary research on computational estimation.
In this procedure the researcher had prepared sets of computational estimation problems and its possible strategies that might be used by students in solving the problems.
b. Students’ Works-the Results
The results of this preliminary research consist of students’ paper works and interview data. This shows that actually student(s), if guided, can find all possible solutions of the problem.
c. Discussion of Students’ Results
The discussion of the results of this preliminary research is based on the research questions that where stated at the beginning of this section.
1. What strategies do students use when solving estimation problem?
We can classify students’ strategies in solving computational estimation problems into two, namely using estimation strategies (rounding and front-end strategy) and using exact calculation strategy.
2. What are kinds of problems that invite students to be more using estimation strategies instead of using exact calculation?
Three types of questions according to Van den Heuvel-Panhuizen and other problems which require comparing are powerful enough in inviting students to solve the problems using estimation strategies. However, not all students could be invited to use estimation strategies with such problems because of several factors: students are used to in using exact calculation, students are not sure if they do not solve the problems using exact calculation strategy first.
3. What are students’ difficulties when solving estimation problems?
(1) Students found difficulties in expressing their thinking in written text when solving estimation problems although actually they are able to solve when asked orally; (2) they frequently made calculation errors using that calculation strategy; (3) many of students found difficulties in solving estimation problems with incomplete data.
6. Hypothetical Learning Trajectory (HLT)
a. Learning Goals
1. to get students use estimation strategies in solving estimation problems instead of using exact calculation (in learning-teaching classroom setting)
2. to investigate students’ estimation strategies in solving estimation problems (in learning-teaching classroom setting)
b. Learning Activities and Students’ Learning Process
In the first phase, students can solve estimation problems in the area of addition (or subtractions) and simple multiplication or division. In the second phase, most of students realize the utility of estimation strategies. In the last phase, students are hoped to be able to solve estimation problems with incomplete data.