The Effectiveness of the Problem Solving Strategy and the Scientific Approach to Students’ Mathematical Capabilities in High Order Thinking Skills

The purpose of this study was to find out more effective teaching among problem solving strategy with a scientific approach to students’ mathematical abilities in high order thinking skills. This quasi experimental study used non-equivalent pretest-posttest control group design. The experimental group was students who were taught with problem solving strategy, and the control group was students who were taught with the scientific approach. The number of participants for the experimental group, n = 138, and for the control group, n = 139 from the 10th grade of public and private high schools in Medan-Indonesia. Based on the hypothesis testing of the study, the results showed that learning through problem solving strategy was more effective than the scientific approach to students’ mathematical abilities in communication, creativity, problem solving, and mathematical reasoning.


INTRODUCTION
Problem solving is still an important issue in school mathematics education.This has been stated by teachers who have joined the national council of teachers of mathematics (NCTM) since the 1980s, and advocated problem solving must be the focus of school mathematics (Sobel & Maletsky, 1988).Problem solving has been one of the general goals overall in the finish curriculum (Pehkonen, 2007).The problem solving is the important part of the mathematics curriculum, because students can use the skills they already have to apply to solving the problem (Posmentier & Krulik, 2009).Solving math problems as an important aspect, and becoming a necessity in a mathematics curriculum throughout the world (Liljedah, Trigo & Malaspina, 2016).Problem solving plays an important role in mathematics education so that students can practice and integrate the concepts, theorems and skills that have been learned (Hudojo, 2005), students get good, diligent, high desire, and confident ways of thinking (Turmudi, 2008), and improve students' mathematical abilities (NCTM, 2010).Another opinion states that problem solving as the heart in learning mathematics, and all creative mathematical activities require problem solving actions (Pinta, Tayruakham & Nuangchalerm, 2009;Yazgan, 2015), can improve students' imagination (Wibowo, et al., 2017), to develop student creativity (Suastika, 2017), and can support students' understanding skills (Mulyadi, 2017).
Problem solving in school mathematics education in Indonesia has actually begun to be adapted in the mathematics curriculum in 2006.However, learning begins with problems, starting in the 2013 mathematics curriculum, and implementation is emphasized through a scientific approach with the aim that students have the attitudes, knowledge and skills elaborated for each education unit (Permendikbud (54), 2013).The expected learning outcomes for aspects of knowledge and skills refer to the PISA standard, namely high order thinking skills (HOTS) (Effendy, 2018).The importance of high order thinking skills in mathematics education is so that students can master mathematics well (Amalia, 2013).There is a significant relationship between high order thinking skills and student learning outcomes in every aspect (Abdullah, et al, 2017;Jailani, Sugiman & Apino, 2017;Tanujaya, Mumu & Margono, 2017;Widodo & Kadarwati, 2013).

PROBLEM SOLVING STRATEGY
Several stages of problem solving methods, Polya (1973) state four stages, namely (1) understand the problem, (2) devise a plan, (3) carry out the plan, and (4) look back.The indicators, namely (1) identify the elements that are known, asked, and the required elements are needed; (2) formulating mathematical problems or compiling mathematical models; (3) applying strategies to solve problems or mathematical models; (4) explain or interpret the results according to the original problem; (5) use mathematics meaningfully (NCTM, 1989).
In mathematics learning, using problem solving strategies has an impact on students' abilities and skills.The results of the study show that the problem solving approach affects the ability and academic achievement of students (Ali, Hukamdad, Akhter & Khan, 2010;Perveen, 2010;Sriasih, Syahruddin & Japa, 2014), makes it easier for students to solve difficult problems (Oztruk & Guven, 2016), and contributes to student achievement and knowledge development (Hodiyanto, 2017;Sappaile & Djam'an, 2017;Diaz, Felmer, Randolph & Gonzalez, 2017).The level of achievement of students taught by problem solving methods is different from conventional teaching methods (Behlol, Akbar & Sehrish, 2018;Hu, Xing & Tu, 2018).

SCIENTIFIC APPROACH
The implementation of scientific approaches in mathematics education includes observing, questioning, experimenting, associating, and communicating.The indicators, namely (1) observing include reading, listening, listening, and seeing, (2) questioning, including asking questions, answering questions, discussing information that has not been understood, clarifying additional information, (3) experimenting, including trying, demonstrating, imitating, reading other sources, collecting data from sources, and modifying, (4) associating, including processing information that has been collected, analyzed, connecting phenomena related to the discovery of a form, and concluding, and (5) communicating, including compiling reports about process, results, and conclusions (Permendikbud (81A), 2013;Hosman, 2014).

HIGH ORDER THINKING SKILL
In mathematics learning, high order thinking skills (HOTS) include several abilities, including communication, creativity, problem solving and mathematical reasoning (Brookhart, 2010;Madu, 2017;Setiawan, 2014;Tambunan, 2018;Wardhani, 2015).The importance of HOTS in learning mathematics is so that students have good abilities.Mathematical communication is an important condition for communicating various ideas into mathematical language (Baroody, 1993).Mathematical communication is needed in mathematics education, because it is the basis of mathematical solutions (Greenes, 1996), and mathematics as a means of communication of science (Armianti, 2009;Dan, 2013).Mathematical creativity is a person's activity to produce new things (Munandar, 1999;Solso, 1995), and a person's ability to choose mathematical solutions (Sriraman, 2011).The aspects of mathematical creativity include flexibility, fluency, novelty, sensitivity, originality, elaboration (Evans, 1991;Munandar, 2012;Silver, 1997).
Problems in mathematics are story problems that are not clear certain rules that can be used to solve (Baroody, 1993;Hudoyo, 2005;James, 1976;Tambunan, 1999).Solving important problems in mathematics education, because problem solving is an effort to solve a problem to achieve a goal that cannot be achieved directly (Polya, 1973), a skill that involves the process of analysis, reasoning, prediction, evaluation and reflection (Anderson, 2009), and as a guide to solving a problem (Wena, 2011).Mathematics is a knowledge of logical reasoning (Soedjadi, 2000), and mathematics is formed as a result of reasoning (Rusffendi, 2006).Mathematical reasoning is a thought process to draw conclusions based on inductive and deductive (Sumantri, 2009).Reasoning is thought that produces a statement and reaches a conclusion on a problem solving (Lithner, 2008).The importance of reasoning in learning mathematics, because it can improve student learning outcomes (Setiadi, 2012).

Research Questions
1. Whether the problem solving strategy is more effective than the scientific approach to students' abilities in mathematical communication 2. Whether the problem solving strategy is more effective than the scientific approach to students' abilities in mathematical creativity 3. Whether the problem solving strategy is more effective than the scientific approach to students' abilities in problem solving 4. Whether the problem solving strategy is more effective than the scientific approach to students' abilities in mathematical reasoning

Purpose of the Study
The purpose of this study is to describe the effectiveness of problem solving strategy with the scientific approach on students' abilities in HOTS, namely communication, creativity, problem solving, and mathematical reasoning.

METHOD
This study uses quasi experiments, because in education it is not possible to do pure experimental research (Johnson & Christenson, 2014).The experimental design used non-equivalent pretest-posttest control group design, the two treatment groups were given pretest, treatment, and posttest (Gay, 1987;Sugiyono, 2010).The experimental group is students taught by two partner teachers with problem-solving strategies (Polya, 1973), and the control group is students taught by two partner teachers with a scientific approach (Permendikbud (81A), 2013).The schematic representation of the research design is illustrated in Table 1.
The participants in this study were 10 th grade students from public and private high schools in Medan-Indonesia, academic year 2018-2019 The number of participants in the experimental group, n = 138, and the control group, n = 139.Participants are in four classes, namely two classes from public schools and two private school classes taken by random sampling techniques (Arikunto, 2010;Sugiyono, 2011).
The research instrument used essay test which included communication, creativity, problem solving, and mathematical reasoning in system of linear equations material in the 10 th grade of high school.To guarantee the validity of the test instrument, it is validated by expert judgment techniques, and the reliability test used Cronbach's alpha formula, that is α (Allen & Yenn, 1979), As a result of the reliability test using statistical package for the social science (SPSS) version 21, Cronbach's Alpha values for mathematical communication, creativity, problem solving, and mathematical reasoning were 0.989, 0.992, 0.990, and 0.969 respectively.
, ̅ is the average, SS is the sum of squares, n is the sample size.Test criteria, if t ≥  (0.025; 1 + 2 −2) , then the null hypothesis is rejected (Steven, 2002).

RESULT
Analysis of research data using SPSS version 21, the results are summarized in the Tables 2-4.Table 2 shows that for all mathematical skills, the average score of the experimental group is greater than the control group.Table 3 shows that for both groups, the pretest and posttest values were significantly linear.Table 4 shows the results of the t test obtained from inter-group comparison testing of mathematical skills, and is used to answer the research hypothesis.

Hypothesis I: Problem solving strategies are more effective than scientific approaches to students' abilities in mathematical communication
The results of the t test show that the value of t = 8.50, Sig.< 0.025, the null hypothesis was rejected, and therefore, problem solving strategies are more effective than scientific approaches to students' abilities in mathematical communication.
Hypothesis II: Problem solving strategies are more effective than scientific approaches to students' abilities in mathematical creativity The results of the t test show that the value of t = 11.743,Sig.<0.025, the null hypothesis was rejected, and therefore, problem solving strategies are more effective than the scientific approach to students' abilities in mathematical creativity.The results of the t test show that the value of t = 11.447,Sig.< 0.025, the null hypothesis was rejected, and therefore, problem solving strategies are more effective than the scientific approach to students' abilities in solving mathematical problems.
Hypothesis IV: Problem solving strategies are more effective than the scientific approach to students' abilities in mathematical reasoning.
The results of the t test show that the value of t = 11.754,Sig.<0.025, the null hypothesis was rejected, and therefore, problem solving strategies are more effective than the scientific approach to students' abilities in mathematical reasoning.

DISCUSSION
The results of this study indicate that problem solving strategies are more effective than the scientific approach to students' abilities in mathematical communication.These results are consistent with the results of a study by Lee (2017), that the problem solving strategy is better than other approaches.Solving problems with the Polya procedure is more effective than other approaches for building students' mathematical communication skills (Abdullah, Tarmizi & Abu, 2010).Increasing students' mathematical communication skills through problem-based learning is better than conventional learning (Sari & Rahadi, 2014).Problem solving strategies are more effective against students' mathematical creativity.This is consistent with the results of research that show that through problem solving can improve students' mathematical creativity skills (Ersoy & Baser, 2014), students' mathematical creativity is better taught by problem solving methods than conventional approaches (Fadillah, 2016;Katminingsih & Widodo, 2015), and there is a very strong influence on problem solving strategies for students' mathematical creativity (Tambunan, 2018).
Problem solving strategies are more effective than scientific approaches to students' ability to solve mathematical problems.These results are in accordance with the results of research that show that problem solving strategies with heuristics are effective against students' abilities in problem solving (Tambunan, 1999).The problem solving method by Polya (1973) can improve students' ability to solve problems (Cheng, She & Huang, 2018;Komariyah, 2011;Selvianti, Ramdani & Jusniar, 2013;Zulyadaini, 2017).It is also more effective against students' abilities in mathematical reasoning.This is consistent with the results of research that show that problem solving approaches contribute to critical, analytical, and reasoning skills (Cheng, She & Huang, 2018;Goh, 2014;Lee & Chen, 2015).Higher student reasoning abilities taught by problem solving models compared to conventional models (Muin, Hanifah & Dwidian, 2018).

CONCLUSION
Many strategies can be used for problem solving in mathematics education.It has been tested, the effectiveness of problem solving strategy, and the scientific approach on students' mathematical abilities in HOTS.The results of this study concluded that problem solving strategies were more effective than scientific approaches to students' abilities in communication, creativity, problem solving, and mathematical reasoning.Therefore, so that students' mathematical abilities are better in HOTS, then problem solving strategy are better used compared to scientific approaches.

Disclosure statement
No potential conflict of interest was reported by the authors.

Table 1 .
Research design Hypothesis testing of this study using the t test from the Bonferroni test, that is  =

Table 4 .
Summary of t test Problem solving strategies are more effective than scientific approaches to students' abilities in solving mathematical problems.