The Students Decision Making in Solving Discount Problem

This research is reviewing students’ process of decision making intuitively, analytically, and interactively. The research done by using discount problem which specially created to explore student’s intuition, analytically, and interactively. In solving discount problems, researcher exploring student’s decision in determining their attitude which concern in the used of intuitively, analytically, and interactively. Result of this research showing that the student’s decision making in solving discount problem begin with their intuitively, then interactively and continued with analytically; afterward return to intuition, interaction and end up with analytical. Those three components (intuitively, interactively and analytically) repeated occur until obtaining result which is desire. Keyword: making decision, intuitive interactive, analytical thinking and mathematic problem


Introduction
Research subject about decision making has becoming a phenomenon in some research (Cokely & Kelly, 2009;Ketterlin, Geller, & Yvanoff, 2009;Wang & Ruhe, 2007).Result of the study giving enough information about student's cognitive process in a domain needed to create instructional correction, the cognitive process of decision making can be applied into many other systems which based on decision, while the used of intuition is one way of approaching decision making in managerial field.
Decision making is involving someone cognitive process (Wang & Ruhe, 2007).Decision making is a process that chooses a preferred option or a course of actions from among a set of alternatives on the basis of given criteria or strategies (Wang, Wang, S. Patel, & P. Patel, 2004;Wilson & Keil, 2001).According P. Facione and N. Facione (2007) that the decision can be regarded as an outcome or output of mental or cognitive processes that led to the selection of a course of action among several alternatives available.So that, in exploring someone's decision making will be needed a theory as guidance.Based on the above opinion, the researchers concluded that the decision is an alternative course of action of a series of actions or strategies that the students in making decisions by using intuitively, analytically or interactively at about discounts that are designed to explore the intuitively, interactively or analytically.
One of the theories of a cognitive process is "Dual process Theory (DPT)".The DPT is a Theory of a cognitive processing which contains of two systems; those are system 1 and system 2. System 1 assumed has a quick otonomy process to produce default respond, system 2 interfered by specific order in a higher reasoning or analytical process (Evans, 2013).The popularity of dual process theory is increasing, along with the increasing of criticism from many researchers.They were showing a lot of critic to this theory account.Such as unclear definition of it, lack of coherence and consistency in purposing cluster to the system's attribute with those two accounts.Therefore, this DPT phenomenon gets a lot of attention from several researchers (Evan, 2013;Gigerenzer, 2011;Keren & Schul, 2009;Osman, 2004).
First observation result, there are students with cognitive condition which is not totally included to system 1 (intuitive) and it is also not totally included to system 2 (analytical).This showed from their interview and works done by the researchers to subject.From mathematic problems which given by researchers, subject showing indication of a characteristic based on interaction.In solving mathematic problem subject doing simplification of processing and using large number of data in order to understand it; interactively process and a quick exploration in knowledge; information which giving less advantages will be discarded.
In line with observation result of high school students it has been diagnosed.Diagnose is an integral part of the studies decision making.It is also become a bridge to identify students who are probably at a risk of failure.Diagnose giving valuable information about cognition of the students in a domain which targeted.Students as a domain will directed to decision making process of discount problem, able giving detail and precise information about their thoughts.This information needed to give the students a chance to have an appropriate education which concern in mathematic study.This research examine probability of a student in taking conclusion of solving mathematic problem which given.The studies were based on working analysis of a test result and interview.Specifically, the analysis doing based on a dual process theory, therefore the student's cognition condition which claimed by previous researchers that the student's cognition condition only in system 1 or system 2, or the cognition of student in system 2 as an improvement from system 1 (Hogarth, 2005;Keren, & Schul, 2009) answered.Next on, it becomes important for there are phenomenon which need further exploration to answer many critics appear about the Dual Process Theory.
This research goal is to exploring decision making of a student through intuition and analytical strategy to the problems given.How are the students making decision by using intuitive, analytic, or interactive to the problems which created to explore those three components?Researcher needs instruments which enable her to explore main goal.Instrument builds from theories of Decision Making, Dual Process Theory and also Interactive Metaphor Theory, from Computer Processing Information Theory.These theories enable the researcher to differentiate characteristic of intuitively, characteristic of interactively and characteristic of analytically.Furthermore, researcher will need theoretically point of view to identifying students from many different side of making decision based on intuitively, interactively and analytically to solve discount problem.

Dual Process Theory and Decision Making
Daniel Kahneman interpret style of process which been saying intuition and analysis.Intuition (or system 1), is closely like associate analysis defined as an automatic and quick, it used to have a strong emotional bonding in the analysis process.Kahneman said that analysis type based on a formed habit and it is difficult to change or manipulate.Analytic (or system 2) is slower and more stable and always based on consciousness and consideration (Kahneman, 2003).
Afterward, for the past few years there are some researchers who specialized themselves to exploring ideas that there is fundamental dualism in human thoughts.Since, 1970the Dual Process Theory has been developed by the researchers in many aspects human's psychology, which included deductive analysis, decision making, and social judgment.These theories comes in different kind of forms, but each of it agree in purposing two different kind of processing mechanism to task given, which employing different procedures and able resulting something different, and sometimes having opposite result.Usually one of the process mark as something fast, easy, automatic, unconsciousness, inflexible, very contextual, and light of memory's working.While the other mark as something slow, effortful, controlled, consciousness, flexible, de-contextualized, and demanded memory's working.This theory claimed that a center of human cognition consist of two multi-purpose analysis system, which usually called as system 1 and system 2. The first operation system having fast process characteristic (fast, easy, automatic, unconsciousness, etc.) while other operation system which slower than the first (slow, effortful, controlled, consciousness, etc.) (Stanovich, 2004).
System 1, Barg (1994) was doing re-conceptualized ideas to an automatic process called as "automatic" which consist of four components, such as: consciousness, intentionality, efficiency, and controllability.A mental process labeled as "automatic" for people never realized the process of it, they cannot even realized existence of a stimulus (subliminal), how the stimulus categorized or interpret (stereotype of unconsciousness activation or constructive characteristic) or stimulus effect which occur in someone's action or decision (misattribution).Another way of a mental process to be labeled as automatic is by being unintentional.Intentionality, refer to consciousness or "start up" from a process.The mental process will automatically bias and will begin with self-unconsciousness or unwilling to begin.The third component from automaticity is the efficiency.Efficiency refers to number of cognitive resources which needed to process.The automatic process is efficient for it needs several sources.The fourth component is ability to control.It refers to someone consciousness ability to stop a process.Process which automatically uncontrolled, means that the process will be precede until it finish and a person will not able to stop it.Barg (1994) conceptualized automation as a component view (every consciousness consist of combination, will, efficiency, and control) which contradictive with history concept of automaticity as all-or-without dichotomy.
System 2 is the last and specific evolution for human.This is also known as explicit system, system based on rules, rational system, or analytic system.A person who categorized in system 2 will be thinking consecutive and slow.This is a general-domain, which been processing in the main working memory.Because of it, the person has limited capacity and slower than system 1 which correlated with general intelligence.This is also known as rational system for its reasoning based on logical standard (Evans, 2003;Tsuji, 2009).Therefore, several characteristic which related with system 2 are base on rules, analytic, controlled, demand cognitive capacity, and slow.
Decision theory widely applied in various subject, such as cognitive informatics, computer study, management study, economic, sociology, psychology, politics and statistic.Several decision strategies have proposed from different point and domain application such as maximum utility and Bayesian method.But there are deficiencies in the model of fundamental decision, mathematic decision, and strict cognitive process for the decision making.The decision in a real world assumed as repeated application from important cognitive process.Research result showing that all category of a decision strategy accordance with Ruhe (2007).

Subject and Design
The study was conducted in SMAN 3 Jombang City.Subjects consisted of 40 students in grade 3 with details of 11 men and 29 women.Each subject was given about the discount problem.Purpose of the test is to recognize condition of their thinking condition (intuitively, interactively, and analyticly).Then it was choosing subject to be interviewed with thinking condition.Subject A (Intuitively is wrong, but analyticly is right), and subject B (Intuitively is right while the analyticly is also right) with the consideration that the type of the subject has the potential to meet the desired conditions of the research process.Another method is by designing qualitative research and it will be able to explore decision making by the students.Data collected with method of "think aloud" (van Someren, Barnard, & Sandberg, 1994) which been doing by asking the subject of research repeating working on the test as before and asking them to tell how the process of their decision making done in the same time.By using this method, cognitive process of decision making related with the discount problem which can be recorded and analyzed.

Material
Problem discounts designed to determine intuitively, analyticly and interactively students.Problem is adapted from NCTM (2008) and has been tested legibility, adapted to the high school mathematics curriculum, as well as in consultation with high school mathematics teacher.The problem is as follows: "If the store 1 gives a discount of 50% and then discount 30%, stores 2 gives discount 70%, which of the two stores that offer the cheapest price?"

Procedure
Here is the procedure of research conducted to obtain data intuitively, analyticly and interactively, the order in which participants perform three decision making process.Before every assignment be given decision making, each student was told that they would solve the problem of discount.1) Discount problems is given to all students and then all the students were asked to respond intuitively to write the answers on the paper provided (Glockner, & Betsch, 2008).This is a step to obtain data on student intuitively right/wrong; 2) Researchers collect all the students to correct answers.This is a step to determine the data intuitively students'; 3) Restore the jobs of paper to each student and researcher asks each student do the analysis about the discount given to the use of reason (Betsch, 2007).This is a step to determine the data analyticly students; 4) Researchers collect back student work to determine student analyticly right/wrong.Data obtained from this step is saturated with the condition to think intuitively wrong but analytically right and completely intuitive and analytic right; 5) Researchers chose the subject to think aloud done, the chosen subject based upon consideration of communication skills as well as advice from a teacher.This step occurs from the interaction between students and researchers and obtained data on students' decision making process; 6) Data analysis and conclusions based on the results of think aloud.

Findings and Discussion
Of the 40 students were given matter, the results are as follows: www.ccsenIn the earlier decision making was doing with intuitive.In the next decision making process, it was doing by involving three systems which supporting each other, those system are: system 1 (intuitive), system 2 (analytical thinking) and 3 rd system (interactive).We are positively sure that decision making process of the students with intuitive, analytical thinking and interactive will giving more contribution in the next research and to the school, it will also improving teachers sensitivity and awareness of their student's thinking process.

Figure 3 .
Figure 3. Scheme of student's decision making