Microsoft Word - Yosep_9981-27488-1-ED.docx Vol. 2 (2) (2020) 100-108 IJOLAE | p-ISSN 2655-920x, e-ISSN 2656-2804 100 The Effects of Problem Posing Learning Model on Students’ Learning Achievement and Motivation The Effects of Problem Posing Learning Model on Students’ Learning Achievement and Motivation Agatha Puri Christidamayani1, Yosep Dwi Kristanto2 1,2 Faculty of Teacher Training and Education, Universitas Sanata Dharma, Indonesia DOI: 10.23917/ijolae.v2i2.9981 Received: January 20th, 2020. Revised: January 30th, 2020. Accepted: February 6th, 2020 Available Online: February 8th, 2020. Published Regularly: July 1st, 2020 Abstract Posing high-quality problems is a critical skill to be possessed by students in learning mathematics. However, it is still limited in literature in answering whether problem posing learning model effective in improving students’ learning achievement and motivation. Therefore, the present study aims to investigate the effect of problem posing learning model in the topics of cube and cuboid on students’ learning achievement and moti- vation. This study employs quasi experimental design with 20 students in experimental group and 24 students in control group. The study found that the problem posing learning model has insignificant effect on the stu- dents’ learning achievement but has a positive and significant effect of the learning model on the students’ learning motivation. Further analysis showed that the learning model also has a significant and positive effect on every aspect of students learning motivation, namely students’ interests, enthusiasm, diligence, collabora- tion, and self-control. Keywords: quasi experimental design, problem posing, learning achievement, learning model, learning motivation Corresponding Author: Yosep Dwi Kristanto, Faculty of Teacher Training and Education, Universitas Sanata Dharma, Indonesia Email: yosepdwikristanto@usd.ac.id 1. Introduction Posing high-quality problems is critical skill to be possessed by students in learning mathematics. Engaging students in formulat- ing problems is considered as an effective ef- fort to improve students learning (Cai & Jiang, 2017). Furthermore, formulating prob- lems is an important step in scientific investi- gation. As Einstein stated, “the formulation of a problem is often more essential than its so- lution” (Einstein & Infeld, 1938). Moreover, Socrates has shared a learning method in which the students actively engage in posing problems critically (Singer, Ellerton, & Cai, 2013). Recognizing the importance of the ability to pose problems for students, recently researchers give an emphasize that students need to have more active role in their learning by means of posing problems during the prob- lem posing activities (Kalmpourtzis, 2019; Putra, Herman, & Sumarmo, 2020; Ye, Chang, & Lai, 2019). Various definitions of problem posing are found in the literature. Based on widely cited definition by Silver (1994), problem posing includes the process of new problems genera- tion and process of re-formulating existing problem. In more detail, Hobri (2008) define problem posing as (a) simple formulation of questions or re-formulation of existing prob- lems with some changes so that they are sim- pler and can be mastered; (b) formulation of questions relating to the conditions of the Indonesian Journal on Learning and Advanced Education http://journals.ums.ac.id/index.php/ijolae IJOLAE | p-ISSN 2655-920x, e-ISSN 2656-2804 Vol. 2 (2) (2020) 100-108 101 The Effects of Problem Posing Learning Model on Students’ Learning Achievement and Motivation questions that have been solved to find alter- native solutions; (c) formulation of the prob- lem from the information or situation availa- ble, whether done before, when, or after solv- ing the problem. Other definitions of problem posing have appeared in Cai and Hwang (2019). Problem posing learning model provides benefits for students. Upu (2003) explained that problems posing is one approach that can increase active student involvement in the mathematics learning process. Proposing a problem can be useful in bringing together a number of learning goals, both in group and individual learning setting. Furthermore, Cai, Hwang, Jiang, & Silber (2015) posit that problem-posing activities can improve stu- dents’ learning achievement, reasoning and communication skills, and capture their moti- vation. To sum up, literature give an insight that the problem posing learning model has a po- tential in improving students’ learning achievement and motivation, even though it still limited. Therefore, the research questions of the present study are as follows: (1) Does problem-posing learning model have an effect on the students’ learning achievement? (2) Does problem-posing learning model have an effect on the students’ learning motivation? In problem posing setting, students need to generate new problems or re-formulate the existing problems. To this end, students re- quire to reflect on their prior knowledge and understanding and connect them by using problem posing activities (Moses, Bjork, & Goldenberg, 1990). This cognitively demand- ing process results in a deeper understanding on mathematical concepts. Therefore, our first hypothesis is: Hypothesis 1: Problem-posing learning model have a positive effect on the stu- dents’ learning achievement. Problem posing learning model facili- tates students to have an active role in the learning process. This active involvement in their own learning will make the students more confidence and have positive attitudes (Guvercin, Cilavdaroglu, & Savas, 2014), and in turn, their motivation levels increase. Hence, our second hypothesis is: Hypothesis 2: Problem-posing learning model have a positive effect on the stu- dents’ learning motivation. 2. Method a. Research Design The present study employed pre-test post-test control group design, which is one type of quasi-experimental designs, in inves- tigating the effects of the independent varia- ble (i.e. with and without problem-posing model) on dependent variables (i.e. students’ learning achievement and motivation). With this research design, the causal relationship between independent and dependent variables can be determined since the data are observed under the control of researcher. This study consisted of three meetings in mathematics lesson in the topic of cube and cuboid. b. Subjects The subjects in the present study were 44 eight-grade students of St. Vincentius Pangudi Luhur Middle School, Yogyakarta. They were randomly assigned to the experi- mental and control group. As a result, the ex- perimental group included 20 students whereas the control group consisted 24 stu- dents. c. Data Collection Tools In determining the effects of problem posing learning model on students’ learning achievement and motivation, first, we ensured the implementation of problem posing model in the experimental group and vice versa in the control group by using observation sheets. Vol. 2 (2) (2020) 100-108 IJOLAE | p-ISSN 2655-920x, e-ISSN 2656-2804 102 The Effects of Problem Posing Learning Model on Students’ Learning Achievement and Motivation The observation sheets were developed based on the lesson plans for each group. The lesson plans in problem posing (experimental) group have five key phases, namely informing learn- ing goals, groups formation, presenting prob- lems, posing problems, and solving the prob- lems. The observation on learning implemen- tation was conducted by 2 independent observers. The learning achievement test was used to measure the students’ learning achievement (see, Christidamayani, 2019). This test which consisted five items at the levels of knowledge, understanding, and application was validated by two experts. The revision was made based on the comments from the experts. In measuring students’ learning motiva- tion, the learning motivation questionnaire was developed. The questionnaire consisted five aspects, namely students’ interest, enthu- siasm, diligence in reviewing materials, iden- tity, as well as collaboration and self-control. These aspects were adopted from Brown (as cited by Imron, 1996). The questionnaire has been validated by two experts and revised based on their comments. The Cronbach’s Al- pha reliability coefficient of the questionnaire was 0.881. d. Data Analysis The data of the learning implementation were presented as proportion for each learn- ing phase. The data of students’ learning achievement and motivation were tested by the Kolmogorov-Smirnov test in determining their normality. The statistical analyses con- ducted in this study were independent sample t-test and Mann-Whitney U test. The data analyses were conducted through SPSS Sta- tistics 23 and Minitab 19. The normality test by the Kolmogorov- Smirnov test on students’ learning achieve- ment pre-test, students’ motivation pre- and post-questionnaire showed that the data were normally distributed. However, the same test was conducted on students’ learning achieve- ment post-test and resulted that the data did not normally distributed. The normality test also has been con- ducted on five aspects of students’ learning motivation before and after the implementa- tion. These resulted that all scores were nor- mally distributed except aspect 1 before the implementation for both experimental and control groups, aspect 2 before and after for experimental groups, and aspect 3 after the implementation for experimental group. 3. Result and Discussion The results of data analyses on learning implementation, students’ learning achieve- ment and motivation are described in the fol- lowing subsections. a. Results Regarding the Learning Im- plementation Results of learning implementation in both experimental and control groups are showed in Table 1. Based on the Table 1, it is found that the learning implementation pro- portion for each phase is no less than 83%. These results are prerequisites for the further analysis on students’ learning achievement and motivation. Since the proportion of the learning implementation is high, the next analyses can be conducted. Table 1. Proportion of Learning Implementation in Each Phase Proportion of Learning Implementation Opening Core Closure Control Group Meeting I 100% 94% 83% Meeting II 100% 100% 100% IJOLAE | p-ISSN 2655-920x, e-ISSN 2656-2804 Vol. 2 (2) (2020) 100-108 103 The Effects of Problem Posing Learning Model on Students’ Learning Achievement and Motivation Proportion of Learning Implementation Opening Core Closure Meeting III 100% 100% 100% Experimental Group Meeting I 100% 83% 88% Meeting II 100% 100% 100% Meeting III 93% 100% 100% b. Results on Students’ Learning Achievement Results of two-tailed independent sample t-test (equal variances not assumed) on stu- dents’ learning achievement pre-test scores were given in the Table 2. According to Table 2, there were no significant difference between students’ learning achievement pre-tests scores in ex- perimental and control group. Therefore, it comes to conclusion that the students’ learn- ing achievement in experimental and control groups were equal at the beginning of the pre- sent study. Table 2. Results of t-Test on Students’ Learning Achievement Pre-test Scores Group/Test N M SD t p Experimental Group Pre-test 20 54.20 14.48 0.674 0.504 Control Group Pre-test 24 57.42 17.17 Table 3 showed the results of one-tailed Mann-Whitney U test on students’ achieve- ment post-tests scores. Based on the Table 3, it can be said that students’ learning achieve- ment in experimental group is not signifi- cantly higher than in control group. Therefore, although the problem posing learning model seems to have a positive effect on the student learning achievement, but the effect is not significant. This result does not support hypothesis 1. Table 3. Results of Mann-Whitney U Test on Students’ Learning Achievement Post-test Scores Group/Test N M SD U p Experimental Group Pre-test 20 84.10 11.65 531.00 0.420 Control Group Pre-test 24 79.96 17.78 c. Results of Students’ Learning Motiva- tion The two-tailed independent samples t- test of students’ learning motivation scale be- fore the implementation and the one-tailed in- dependent samples t-test of the corresponding scale after the implementation were given in the Table 4. Based on Table 4, there were no significant difference between the students’ learning motivation in experimental and con- trol groups before the implementation. There- fore, the students came with equal motivation at the beginning of the study. Furthermore, it can be concluded from Table 4 that students’ learning motivation in experimental group was significantly higher than the students in control group after the implementation. Therefore, the problem posing model has a significant positive effect on students’ learn- ing motivation. This result support hypothesis 2. Vol. 2 (2) (2020) 100-108 IJOLAE | p-ISSN 2655-920x, e-ISSN 2656-2804 104 The Effects of Problem Posing Learning Model on Students’ Learning Achievement and Motivation Table 4. Results of t-Test on Students’ Learning Motivation Before and After the Implementation Group/Test N M SD t p Before the Implementation Experimental Group 20 83.25 19.90 1.427 0.162a Control Group 24 91.33 17.16 After the Implementation Experimental Group 20 104.40 13.53 2.980 0.003b Control Group 24 89.25 20.02 To explore the effect of problem posing model on students’ learning motivation in more detail, Table 5 shows the results of two- tailed t-test and Mann-Whitney U test on stu- dents’ learning motivation scale before the implementation. Table 5. Results of t-Test and Mann-Whitney U Test for Each Aspect of Students’ Learning Motivation Before the Implementation Aspect/Group M SD t U p Aspect 1 Experimental Group 18.70 4.46 0.586 0.561 Control Group 17.96 3.82 Aspect 2 Experimental Group 15.85 3.91 632.50 0.030 Control Group 19.08 5.09 Aspect 3 Experimental Group 14.55 5.63 –1.027 0.311 Control Group 16.21 4.95 Aspect 4 Experimental Group 14.40 6.18 –1.211 0.233 Control Group 16.54 5.40 Aspect 5 Experimental Group 19.75 3.78 –1.609 0.116 Control Group 21.54 3.55 According to the Table 5, there were no significant difference between students’ learning motivation scale before the imple- mentation in experimental and control groups for aspect 1, 3, 4, and 5. However, there were significant difference for aspect 2. Therefore, students had equal interest, diligence, identity, collaboration, and self- control at the beginning of the study, but with different enthusiasm. Table 6 gives the results of one-tailed in- dependent samples t-test and Mann-Whitney U test of students’ learning motivation scale after the implementation for aspect 1, 3, 4, and 5. Based on the Table 6, it can be concluded that the students’ motivation on aspect 1, 3, 4, and 5 in experimental group were signifi- cantly higher than the students’ in control group. Thus, the problem posing model has a significant and positive effect on students’ in- terest, diligence, identity, collaboration, and self-control. IJOLAE | p-ISSN 2655-920x, e-ISSN 2656-2804 Vol. 2 (2) (2020) 100-108 105 The Effects of Problem Posing Learning Model on Students’ Learning Achievement and Motivation Table 6. Results of t-Test and Mann-Whitney U Test for Each Aspect of Students’ Learning Motivation After the Implementation Aspect/Group M SD t U p Aspect 1 Experimental Group 20.60 2.70 435.50 0.007 Control Group 18.29 3.86 Aspect 2 Experimental Group 20.00 3.81 459.50 0.029 Control Group 17.08 5.57 Aspect 3 Experimental Group 19.55 4.29 445.50 0.013 Control Group 15.67 5.51 Aspect 4 Experimental Group 20.10 4.27 2.217 0.016 Control Group 17.42 4.27 Aspect 5 Experimental Group 24.15 2.54 2.518 0.009 Control Group 20.79 5.91 Further analysis conducted on aspect 2 of students’ motivation. By utilizing one tailed Mann-Whitney U test on before-implementa- tion scale, it was resulted U = 632.5 and p = 0.015. Therefore, the students’ enthusiasm before the implementation in control group were significantly higher than students’ in ex- perimental group. The one-tailed Mann-Whit- ney U test was also conducted on the corre- sponding after-implementation scale, result- ing in U = 459.5 and p = 0.029. Thus, the stu- dents’ enthusiasm in experimental group were significantly higher than students’ in control group after the implementation. The illustra- tion of these results is showed in Figure 1. Figure 1 shows a cross-over pattern. That is, students’ enthusiasm in experimental group starting out significantly lower than the control group and ending up above them. This is the evidence that the problem posing learn- ing approach effective in improving students’ enthusiasm. Figure 1. Means Graph of Students’ Enthusiasm Vol. 2 (2) (2020) 100-108 IJOLAE | p-ISSN 2655-920x, e-ISSN 2656-2804 106 The Effects of Problem Posing Learning Model on Students’ Learning Achievement and Motivation In the present study we investigate the ef- fects of problem posing learning model on students’ learning achievement and motiva- tion. The results indicate that the problem posing learning model does not have any sta- tistically significant positive effect on stu- dents’ learning achievement, but it does on students’ motivation. The students in problem posing group had higher motivation score than their non-problem posing peers. One possible explanation on why the problem posing in the present study does not have significant positive effect on students’ achievement is the lack of students’ experi- ence on problem posing learning model. It is also one of main challenges in implementing problem posing learning model (Hsiao, Hung, Lan, & Jeng, 2013). Furthermore, Yu, Liu, and Chan (2005) added that the posing prob- lems were difficult task for the low-achiever students. With regard to these challenges, support is needed for students in problem pos- ing learning environment. Our finding on the positive effect of prob- lem posing on students’ motivation is in line with other studies (Irvine, 2017). On top of the problem posing’s positive effect on stu- dents’ motivation, it also has a same effect on all aspects of motivation, namely interest, en- thusiasm, diligence, identity, collaboration, and self-control. Based on this finding and the importance of motivation on students’ learn- ing (Linnen-brink, 2007; Tella, 2007; Wi- jayanti, 2019), the problem posing learning model is a promising strategy to facilitate stu- dents’ learning. Finally, the present study findings give an insight for teachers or instructors in imple- menting problem posing learning model. The teachers who interested in implementing problem posing learning model should pay at- tention to learning components that affect its effectiveness. As mentioned before, support should be provided to the students, especially for inexperienced and low-achiever students. Teachers also may structure the problem pos- ing learning model with innovative teaching strategies and technologies, e.g. worked ex- ample (Hsiao, Hung, Lan, & Jeng, 2013), worksheet scaffold (Choo, Rotgans, Yew, & Schmidt, 2011), game-based problem-solving (Chang, Wu, Weng, & Sung, 2012), “what if not?” strategy (Brown & Walter, 1983; Lavy & Bershadsky, 2003), and Desmos mathemat- ically rich activities (Kristanto, 2019). 4. Conclusion The present study gives a contribution in term of the problem posing’s effect on stu- dents’ learning. The evidence of its positive effect on students’ motivation in learning mathematics gives insight for mathematics teachers and educators in improving the effec- tiveness of mathematics teaching and learn- ing. This study also shows the need for sup- port for inexperienced and low-achiever stu- dents in the implementation of problem posing learning model. 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