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Mathematical Strategic Thinking Ability Using Quantum Learning Based on Creative Problem Solving in Terms of High School Students Gender

Mathematical strategic thinking ability is one of the strategic thinking aptitude which is needed to confront the challenge in this globalization era. It is because the strategic thinking is useful for problem solving and decision making. The object of this research is the impact quality of Quantum Learning Based on Creative Problem Solving (QBCPS) for the escalation of Mathematical Strategic Thinking Ability (MSTA). This research focused on the gender differences (Boy and Girls) between the students who are received QBCPS with those who got the direct learning. The method of this research is quasi experiment with the population is all of High School students in Bogor City. The research sample is the first year students in one of Bogor City High School with total of 140 students from four class. The result study showed that MSTA on boy and girl students didn’t have any significant difference, whether the QBCPS learning or the other one. But, there is a discrepancy in the increasing of every MSTA learning of boy and girl students for both learning treatment. And also, there is a distinction of significant increasing in MSTA between the boy students with QBCPS learning and the other one, as well as girl students. The MSTA’s enhancement of boy and girl students with QBCPS learning is higher than those with direct learning. This uplift didn’t influenced by diverse gender, but only affected by the learning model treatment.


Introduction
Mathematical strategic thinking ability is one of skill which is needed to confront the challenge in this globalization era, because strategic thinking ability is advantageous in problem solving and decision making [1]. The poor ability of mathematical strategic thinking can affect the student competency in problem solving. When the student solving the problem, the brain is thinking. In mathematics, problem solving is the main focus of learning process [2]. This ability is one of the thinking ability needed in challange from globalization era because benefit of strategical thinking is problem solving and decision making, also thinking to the future [1].
Weak strategic thinking skills have an impact on students ability to solve problems. When students do mathematical problem solving, then there is activity of thinking inside the brain. Though problem solving is a focus in learning mathematics [2]. When students solve mathematical problems using problem solving skills, at the same time, they will make decisions, think critically, and think creatively  [3]. Strategic thinking, according to Henry Mintzberg, is a process of synthesizing problems by utilizing intuition and creativity [1]. Strategic thinking involves the synthesis of information to identify problems, connections, and rules (patterns) that encourage intuitive, innovative and creative thinking. [4] views strategic thinking as a process of synthesis, creative and divergent. A similar opinion was expressed by [5] who viewed strategic thinking as a combination of thinking synthesis, divergent, creative, intuitive, and innovative. From several views on strategic thinking, it is concluded that mathematical strategic thinking is the combination of analysis and synthesis of mathematical problems which are critical ways of thinking with variations of solutions from creative ways of thinking.
Beaufre views strategic thinking as an abstract and rational thought process in problem solving [6]. This thought process depends on the large capacity of the analysis and synthesis of the problem being carried out. Analysis is needed to collect data that can be used as alternative solutions, while synthesis is needed to choose alternative solutions to get the best solution.
The process of strategic thinking in problem solving begins with compiling problems into simple problems, then analyzed to look for possible problem-solving steps to be taken, then proceed with the process of synthesis by drawing the truth from each step of resolution taken [6]. The indicator of mathematical strategic thinking in this research is being able to design, analyze, and synthesize problems.
Given the importance of mathematical strategic thinking skills in problem solving, it is necessary to design a pleasant and conducive learning atmosphere for mathematics that builds creativity. The active learning model and stimulating students express creative ideas in solving problems, as well as a pleasant and effective learning atmosphere. Effective learning is a learning process that is able to actively involve all students [7]. One learning model that fits this goal is quantum learning based on creative problem solving (QBCPS). The effectiveness of quantum learning based on creative problem solving in improving learning outcomes, students' ability to understand concepts and mathematical problem solving is reflected in the results of [8] and [9] research. This research focuses on gender differences on students, because gender differences are found in diverse classes. Differences between men and women in verbal and mathematical abilities, as well as the way men and women socialize. This gender difference needs to be carried out research to review these differences as a result of nature (environment) or differences in treatment. Diane Halpern's research results concluded that women are superior in language arts, reading comprehension, and written and oral communication, while male students are superior in mathematics and mathematical thinking [10].

Experimental method
The method used in this study is quasi-experimental designs, that is the subjects for the experimental and control classes are not randomly selected, but researchers accept the state of the subject as it is [11; 12]. This is due to the school system which makes it impossible to do random selection of subjects. This research was conducted in real life where the two sample groups could not be identical. This study uses a quasi-experimental designs with pre-test-post-test, non-randomized control group (pre-test-post-test design) which refers to the opinion [11; 12].
The research sample was the first grade students of one of the state high schools in the city of Bogor, totaling 140 people or four classes. Two classes as an experimental group and two more as a control group. The experimental group was given quantum learning based on creative problem solving (QBCPS), while the control group was given direct learning. The study was conducted in the even semester in first grade with Trigonometry subject matter. Each research group was given KBSM posttest. KBSM test instruments used in the pre-test and post-test in this study are the same. The goal is to be more measurable in seeing whether there is an increase in treatment or not.

Result and discussion
The distribution of the research sample in the experimental group (EG) and control group (CG) based on the gender of students (male (M), female (F)) is presented in Table 1 below. Furthermore, the data of 140 students were analyzed to make a conclusion and reported as a result of research.

Results
The first step is to do a descriptive and inferential analysis of students' initial mathematical ability (IMA) data based on gender and overall data (combined) in the experimental group (EG) and control (CG). It aims to determine the average equivalence of IMA of the two research groups. IMA data were obtained from the average value of twice the daily tests of the experimental and control group students in odd semester.
Descriptively the results of IMA data analysis based on gender and overall (combined) students are shown in Table 2 below.  Table 2 shows that the average IMA of the experimental and control group students for each gender is relatively the same, as is the standard deviation. Overall it can be seen that the IMA data of the experimental and control group students also have the same average and standard deviation.
Inferential results of the average IMA equality analysis based on gender and overall (combined) students show that each sample group has a Significance value of more than 0.05. This means that there is no difference in the average IMA between students in the experimental and control groups based on gender and their mix. The details are shown in Table 3 below.  Statistical test results show that there is no significant difference in IMA averages based on gender or overall. If after conducting research there are differences in average equivalence, then it was not caused by students' initial mathematical abilities but it was caused by the provision of learning models.

Analisis Descriptive Analysis of Mathematical Strategic Thinking Ability (MSTA)
Analysis of student MSTA data obtained through pre-test and post-test, then the normalized gain (Ngain) was calculated. This data was analysed descriptively based on the gender factors of students (male, female) and research groups (EG, CG). The results of the MSTA descriptive analysis based on gender and learning groups are presented in Table 4 below.  Table 4 shows that there was an increase in MSTA students in the experimental and control groups, both male and female students and overall students. The increase in the average KBSM descriptively occurred in students who received QBCPS and direct learning with the same relative magnitude for each gender. The increase in the average KBSM for all research groups, both men and women, and their combinations ranged from 0.60 to 0.69 which is in the moderate category [13]. Specifically for the increase in the average MSTA of female students in the experimental group, the amount was 0.71 which was classified as high [13].

Inferential Analysis of Mathematical Strategic Thinking Ability (MSTA)
Data analysis was continued with an inferential test for the improvement of students' MSTA in both learning groups based on a combination of all samples and gender. Statistical tests of the increase in the average MSTA used pre-test and post-test data. Pre-test and post-test data groups which are both normally distributed are Paired-Samples T-Test or One-way Anova, whereas for pre-test and post-test data pair groups that are both not normally distributed using the Wilcoxon Signed-Rank Test Test). The results of the MSTA's increase statistical tests of the two research groups based on gender and overall students are shown in Table 5 below. The statistical test results in Table 5 show that each sample group has an Asymp value. Sig. and Sig. less than 0.05, which is 0.000. This means that there is a significant increase in MSTA for each research group (experimental and control) and for each gender (male and female). Then the difference in the MSTA increase in the two learning groups was conducted and based on gender. MSTA data used is normalized data gain (N-gain). The results of statistical tests of differences in the increase in MSTA based on learning groups are shown in Table 6 below.  Table 6 shows the value of Sig. both learning groups are less than 0.05, which is 0.011. This means that there is a significant difference in the increase in MSTA between groups of students who get QBCPS learning with direct learning. Because the average value of MSTA students who received QBCPS learning was greater than direct learning, it was generally concluded that the increase in students' MSTA who received QBCPS learning was significantly higher than direct learning. The results of statistical tests of differences in the improvement of MSTA based on gender and learning groups are shown in Table 7 below. The test results in table 7 show a Sig value of less than 0.05, so in general it can be concluded that there is a significant difference in the improvement of CBC in terms of gender and learning groups. Furthermore, to find out which groups are different, it is necessary to carry out further Kruskal-Wallis tests. The hypothesis formula tested is as follows. H0: There is no difference in the increase in average MSTA rank in terms of gender and groups of students who get QBCPS and direct learning. H1: There is a difference in the increase in the average rank of MSTA in terms of gender and groups of students who get QBCPS and direct learning. The test criteria are based on the difference in the mean rank of the gender pairs and the learning groups with their critical values. If the mean rank difference is smaller than the critical value, then H0 is accepted. Conversely, if the mean rank difference is greater than the critical value, then H0 is rejected. The recapitulation of MSTA paired test results based on gender and learning groups is presented in Table 8 below.