DEVELOPING MATHEMATICAL CREATIVE THINKING (CT) ABILITY STUDENTS THROUGH THE TREFFINGER LEARNING MODEL (LM)

The low ability of CT is a problem that occurs in class VIII students of SMPN 1 Kendari. One reason is the application of inappropriate LM. Treffinger's LM is learning by inviting students to think creatively in solving problems based on the facts around them to come up with various ideas and choose solutions. The purpose of this study was to develop the mathematical CT skills of junior high school students. Class VIII SMPN 1 Kendari as a population consists of 9 classes. Class VIII3 and VIII6 were determined by random sampling technique as an experimental class of 26 students and a control class of 25 students. The finding in this study is that students' mathematical CT skills taught by the Treffinger LM are better than in the guided discovery model. Treffinger's LM is superior in developing CT skills. In addition, Treffinger's LM excels in developing aspects of fluency, flexibility, and elaboration of mathematical CT skills. In contrast, the guided discovery LM excels only in developing aspects of originality.


INTRODUCTION
Creativity is needed in every aspect of human life (Lian et al., 2018).To be able to compete in the world of work and personal life, students must have problem-solving skills and must be able to think creatively (Suarta et al., 2017).Therefore, CT skills must be developed in mathematics learning activities (Yayuk et al., 2020).Creativity is the result of CT skills (Guilford, 2017), oriented to mathematical activities widely developed in schools, such as solving and proposing problems closely related to creativity, namely flexibility, fluency, originality, and elaboration (Gralewski, 2016).Creativity is a deep problemsolving process regardless of the complexity of classroom learning by providing opportunities for students to solve non-routine, complex, and structured problems (Beghetto, 2018;Lithner, 2017).
CT is lateral, cross-field, and divergent thinking with characteristics of subtlety, fluency, flexibility, elaboration, redefinition, and novelty (Guilford, 2017).CT is a process of constructing ideas based on fluency, flexibility, elaboration, originality (Yaniawati et al., 2020), and sensitivity to scientific, industrial, and life situations with creative design, investigation, and problem development original (Chen & Chen, 2021).CT is an organized thought process that can be learned by paying attention to intuition, sparking imagination, revealing new possibilities, opening amazing perspectives, and generating unexpected ideas.(de Bruin & Harris, 2017).
Mathematical CT is the ability to solve problems and develop logical and deductive thinking (Ndiung et al., 2019) Based on the results of observations by conducting a pre-test on class VIII students of SMPN 1 Kendari it was found that the mathematical CT ability was relatively low.The LM used to develop CT skills at SMP Negeri 1 Kendari is guided discovery.Guided discovery is a learning approach in which the teacher presents examples of a particular topic and guides students to understand the topic (Eggen & Kauchak, 2012;Salam, et al., 2020).The guided discovery model is intentionally designed to increase student activity, and is process-oriented, finding identity, and information needed to achieve learning goals (Salam, Misu, et al., 2020;Yuliani & Suragih, 2015).However, in this study, the Treffinger LM will be applied to develop CT skills.
The Treffinger LM aims to generate creativity, which involves cognitive and affective abilities by demonstrating the interdependence between the two in encouraging students to think.(Huda M, 2016;Nizham et al., 2017 Stage III, working with real problems, namely applying skills in the first two stages by using their abilities so that they are meaningful in life.Stage III learning activities are: (1) the teacher gives problems in everyday life; (2) the teacher guides students to create problems and solve them independently; (3) the teacher guides students to make conclusions.
Based on the description above, the hypotheses that will be tested in this study are (1) CT skills increase after being taught the Treffinger LM, (2) CT skills increase after being taught the guided discovery LM, (3) students' mathematical CT skills which use the Treffinger LM is higher than guided discovery, and (4) the quality of improving students' mathematical CT skills using the Treffinger LM is better than guided discovery.

RESEARCH METHODS
This To determine the quality of students' CT skill improvement in each class, normalized gain (N-gain) is used.Using N-Gain eliminates high-effect factors and guesswork to avoid biased conclusions.(Heckler, 2004).
This study was conducted in three stages: (a) giving a pre-test to both classes, (b) implementing learning for 6 meetings, and (c) giving a post-test.

RESULTS AND DISCUSSION
The first research' result is students' CT math abilities are described in Table 1.The results in Table 2, obtained the value of Sig. for variables O1, O2, O3, and O4 more than 0.05.This shows that the data variables O1, O2, O3, and O4 are normally distributed.The N-gain data for the experimental and control classes were not normally distributed because of the value of Sig.smaller than 0.05.Then, the results of the calculation of the homogeneity of the O3 vs O4 and O1 vs O2 variables are described in The results in Table 3 show that the O3 vs O4 variable is homogeneous as indicated by the value of Sig.=0.581 which is greater than 0.05.Likewise, O1 vs O2 data is homogeneous, with sig.= 0.255 is greater than 0.05.
Hypothesis of this research are students' CT ability increases after being taught with the Treffinger LM (Hypothesis 1) and students' CT ability increases after being taught with the Guided discovery LM (Hypothesis 2).
Hypothesis 1 and hypothesis 2 were tested using paired t-tests.The results of testing using SPSS are obtained in Table 4. Table 4 row O2 vs O1 obtained Sig.= 0.00 less than = 0.05.This shows that hypothesis 1 is accepted, that is, students' CT abilities after being taught with the Treffinger model have increased.Visually, the increase in students' CT skills can be explained in Figure 1.

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The next hypothesis of this research is the mathematical CT ability of students who use the Treffinger LM is higher than the guided discovery (hypothesis 3).Hypothesis 3 was tested using an independent sample t-test.The test results are presented in Tables 5 and  6.Table 5 shows that students' CT skills before being given treatment between the control class and the experimental class have the same variance, which is shown by sig.0.97 is greater than 0.05.The mathematical CT ability of students using the Treffinger (O2) LM is higher than the Guided discovery (O4) LM as indicated by sig.0.03 is less than 0.05.In terms of CT skills, the average achievement of each aspect of CT skills can be seen in Table 7.The results in Table 7 show that the average achievement of aspects of fluency, flexibility, and elaboration in the experimental class is higher than in the control class.While on the aspect of originality, the average value of the experimental class is lower than the control class.
The last hypothesis is The quality of increasing students' mathematical CT skills by using Treffinger's LM is better than Guided Discovery (hypothesis 4).Hypothesis 4 was tested using nonparametric statistics, namely the Mann-Whitney test, taking into account that neither the experimental N-gain data nor the control N-gain data was normally distributed.The test results can be seen in Tables 8 and 9. ISSN 2089-8703 (Print) Volume 12, No. 1, 2023, 23-35 ISSN 2442- .000 The results in table 8a show that the experimental average N-gain is 33.75 higher than the control N-gain average of 17.94.Furthermore, in table 8b the value of Asymp.Sig (2-tailed) = 0.00 less than 0.05.These results indicate that hypothesis 4 is accepted, which means that improving students' CT math skills using the Treffinger LM is better than guided discovery.To clarify the comparison of the improvement of students' CT skills between the experimental class and the control class can be seen in Figure 3. From these categories, the comparison of the increase in CT skills between the experimental class and the control class is presented in Table 9.The results of testing hypothesis 1 show an increase in CT skills after being taught with the Treffinger LM.This is because the Treffinger LM is a LM that is specifically designed from basic thinking to more complex thinking, to trigger students' CT skills that involve cognitive and affective abilities (Handayani et al., 2018;Isaksen et al., 2010).In addition, Treffinger's LM leads to the use of critical and CT skills, individually and in groups, to understand challenges and opportunities, create ideas, and develop effective plans to manage change and solve problems (Amanoe & Isnarto, 2021).
The results of testing hypothesis 2 obtained an increase in students' CT skills after being taught with the guided discovery LM.Guided discovery is student-centered learning so that they have the freedom to try, use intuition, and obtain information through group discussions, find solutions, and solve problems based on their activities and observations so that students' ability to analyze increases.(Arya Wulandari et al., 2018;Khasanah et al., 2018).
The finding of hypothesis 3 is that students' mathematical CT skills using the Treffinger LM are superior to guided discovery.In terms of CT skills, Treffinger's LM excels in indicators of fluency, flexibility, and elaboration.While the guide discovery LM only excels in the originality aspect.The results of the independent t-test showed that the CT ability of students who used the Treffinger LM (O2) was higher than that of guided discovery learning (O4).This is due to the dominant characteristics of Treffinger's LM, which integrates students' cognitive and affective dimensions, finding the direction of completion to be taken in solving problems, by giving students freedom as they wish (Nurzulifa, 2021).Treffinger's learning is better in improving students' mathematical CT skills (Triwibowo et al., 2017).While the guided discovery model, students are not given the freedom to solve problems as they wish.In the guided discovery LM, the teacher provides examples of certain topics and guides students to understand the topic to encourage student involvement and motivation, help gain in-depth understanding and explanation of topics, and train students to find concepts with teacher guidance so that there are no misconceptions (Darmawan & Suparman, 2019).The guided discovery model demands being an expert in asking questions and guiding students' thinking (Putri, 2020).
The finding of hypothesis 4 is that the quality of improving mathematical CT skills of students using the Treffinger LM is better than guided discovery.This finding is indicated by the results of testing using Mann-Whitney obtained the Asymp value.(Isaksen et al., 2010) In addition, the Treffinger LM in its implementation seeks to combine cognitive and affective dimensions, thus enabling students to get ideas in solving problems to produce CT that can be used in solving various mathematical problems they face (Huda, 2013;Nizham et al., 2017;Rahmadhani & Ahmad, 2022;Salam & Misu, 2018).
The development of mathematical CT skills in this study involved 4 aspects, namely fluency, flexibility, originality, and elaboration.From these 4 aspects, the experimental class is better at developing aspects of fluency, flexibility, and elaboration than the control class.While the control class is better at developing aspects of originality than the experimental class.This means that the Treffinger LM is superior to the guided discovery LM in developing aspects of mathematical CT skills.This advantage is obtained because in its implementation the Treffinger LM provides opportunities for students to understand various concepts, increase student activity in learning activities, develop students' thinking skills, develop students' abilities in presenting data, analyzing data, creating ideas, and trying various problem-solving, students implement their new ideas or ideas in dealing with every problem (Maharani & Indrawati, 2018).Meanwhile, according to Silver (1997), problem-solving and problemposing can improve CT skills through aspects of fluency, flexibility, originality, and elaboration.
The advantages of the Treffinger LM in developing the aspects of fluency, flexibility, and elaboration that were developed are that the Treffinger LM is better in terms of: (1) developing the ability to generate or generate several ideas quickly, answers and questions quickly and accurately completes relationships, build analogies ; (2) develop the ability to use a variety of different solutions and different answers in a problem solving; (3) develop the ability to detail, develop and generate ideas, solve problems with procedures carried out, logistics, explain, and reasons.While the guided discovery LM only excels in developing aspects of originality, and developing aspects of fluency.The initiation that the guided discovery LM is better in developing the ability to generate original, new, and unique ideas, and answers, ideas; and also good at developing the ability to generate or generate several ideas quickly, answers, and questions quickly and accurately, complete relationships and construct analogies.

CONCLUSION AND SUGGESTION
Based on the discussion above, it can be said: (1) The students' mathematical CT ability can be

Figure 1 .
Figure 1.Students' CT ability after applying the Treffinger model.

Figure 3 .
Figure 3.Comparison of the improvement of students' CT skills between the experimental class and the control class.
O1 is Pre-test of experiment class students, O3 is Pre-test of control class students, O2 is Post-test of experiment class student, and O4 is post-test of control class student (Sugiyono, 2017).
DOI: https://doi.org/10.24127/ajpm.v12i1.543226| test used was the Shapiro-Wilk test, and the data homogeneity test using the Levene test, t-test, and Mann-Whitney test were used to test the hypothesis.

Table 3 .
The results of the calculation of the homogeneity of variance

Table 4 .
Paired sample test

Table 4 row
O4 vs O3 shows the value of Sig.= 0.00 less than 005, then hypothesis 2 is accepted which means CT mathematical skills can be improved through the guided discovery model.Visually, the improvement of students' CT skills after being taught guided discovery can be seen in Figure2.
Figure 2. Graph of increasing students' CT skills after learning with guided discovery models.