IJOLAE | p-ISSN 2655-920x, e-ISSN 2656-2804 Vol. (1) (1) (2019) 37-47 37 Fostering Germane Load Through… Fostering Germane Load Through Self-explanation Prompting in Calculus Instruction Cecep Anwar Hadi Firdos Santosa1, Sufyani Prabawanto2, Indiana Marethi3 1,3Faculty of Education, University of Sultan Ageng Tirtayasa, Indonesia 2Mathematical Education and Natural Science Indonesia University of Education, Indonesia DOI: 10.23917/ijolae.v1i1.7421 Accepted: Januari 02th, 2019. Approved: March 09th, 2019. Published: March 11th, 2019 Abstract The purpose of this research was to investigate the effect of self-explanation prompting to students’ germane load while studying mathematics in the multivariable calculus course. This research employed a quasi- experimental method with matching-only posttest-only control group design. The subject of the research consists of 72 first-year mathematics education undergraduate students. The results indicated that there was no significant difference in students’ germane load between students who implemented worked-example with self-explanation prompting and students who implemented worked-example without self-explanation prompting. However, it was revealed that the students' germane load was categorized high in both classes. It indicates that the worked-example method could foster students' germane load. Nonetheless, these results cannot be evidence that self-explanation prompting is capable to foster students' germane load. However, there is an association between germane load and learning objectives. When students achieve the learning objectives, then its learning method is able to foster the germane load. To assess the learning objectives, the posttest was arranged. The results stated that students who implemented the worked-example method with self-explanation prompting had better test scores than students who implemented the worked-example method without self-explanation prompting. This result was sufficient to provide evidence that the use of worked-example with self-explanation prompting could foster students’ germane load students in the multi- variable calculus course. Keywords: Germane load, Worked-example, Self-explanation prompting Corresponding Author: Cecep Anwar, Faculty of Education, Universitas Sultan Ageng Tirtayasa., Indonesia e-mail : cecepanwar@untirta.ac.id 1. Introduction Multivariable calculus is one of the compulsory subjects that must be completed by mathematics education department stu- dents. The basics for studying calculus have been studied by them at secondary school. However, there are fundamental differences between mathematics in secondary schools and university. Mathematics in university is more formal, rigor, and deductive compared to mathematics at secondary school. (Moore, 1994; Tall, 2008). In addition, to succeed in this course, students must grasp several prerequisite concepts, including the concepts of function (Kashefi, Ismail, & Yusof, 2010), algebra, analytical geometry, and trigonometry (Stewart, 2012). Therefore, calculus courses (including multivariable calculus) are often considered as the difficult subject for students (Job & Schneider, 2014; Martínez-Planell, Gonza- lez, DiCristina, & Acevedo, 2012; Moru, Indonesian Journal on Learning and Advanced Education http://journals.ums.ac.id/index.php/ijolae mailto:cecepanwar@untirta.ac.id Vol. (1) (1) (2019) 37-47 IJOLAE | p-ISSN 2655-920x, e-ISSN 2656-2804 38 Fostering Germane Load Through… 2009; Nursyahidah & Albab, 2017; Orton, 1983; Santosa, 2013). In general, there are at least three sources of learning difficulties in mathematics (Debue & Leemput, 2014; Khateeb, 2008; Sweller, 2008), that comes from mathematics itself, the way the materi- al of mathematics is delivered, and cognitive difficulties in forming the schema when dealt with new information. The first difficulty occurs because of many elements or mathematical material that interact with each other or which must be processed simultaneously in students' cognitive, both the prerequisite material and the new material being studied. The source of this difficulty is practically unavoidable because it adheres to mathematics as a com- plex discipline. Thus, the source of this dif- ficulty is known as intrinsic difficulty (Leahy & Sweller, 2008; Sweller, 2010). Furthermore, the second source of diffi- culty relates to the method or method used to learn calculus. The selection of the ap- propriate teaching method influences suc- cess in learning. Since humans have limita- tions while processing information (Badde- ley, 1992, 2003, 2010, 2012). Old research by (Miller, 1956) and (Peterson & Peterson, 1959) states that humans are only able to store 7 ± 2 information in one process and can only preserve about 30 seconds. Thus, the second type of difficulty is called extrin- sic difficulty (Mattys, Barden, & Samuel, 2014; Paas & Kester, 2006). Contrasting the previous two difficulties, the third difficulty is related to the formation of a knowledge scheme. At that time, stu- dents invested a mental effort that was used to create knowledge schemes and solve the relevant problems. Certainly, the greater the mental effort that is organized, the more possible someone is to be able to solve prob- lems and form new knowledge in his mind. This type of difficulty is called germane dif- ficulty or relevant difficulty (Debue & Leemput, 2014). These three sources of difficulty cause cognitive load (Sweller, 2011; Sweller & Sweller, 2006). Cognitive load is related to one's mental effort when processing infor- mation. High cognitive load without being followed by the formation of a knowledge scheme causes cognitive inefficiency. In this condition, the mental effort is too high com- pared to the achievement. Of course, this condition is an undesirable condition and must be avoided in the learning process. Furthermore, of the three characteristics of the cognitive load, intrinsic cognitive load is a cognitive load that is difficult or even cannot be intervened through learning methods. Conversely, extrinsic cognitive load is a source of cognitive load that can be intervened by an appropriate learning meth- od. Through the use of these learning meth- ods, it is expected that extrinsic cognitive load can be reduced. In contrast to the two types of cognitive load previously, the rele- vant cognitive load (germane) must be fos- tered (Debue & Leemput, 2014), consider- ing the mental effort that is deployed for this cognitive load is closely related to the suc- cess of establishing schemes of knowledge and success in solving problems. The learning method which is empirical- ly to have the ability to reduce extrinsic cognitive load is worked-example method (Bokosmaty, Sweller, & Kalyuga, 2015; Booth, Lange, Koedinger, & Newton, 2013; Hu, Ginns, & Bobis, 2015; Renkl, 2017; Retnowati, Ayres, & Sweller, 2010; Rourke & Sweller, 2009; Salden, Koedinger, Renkl, Aleven, & McLaren, 2010; Santosa, Suryadi, Prabawanto, & Syamsuri, in press.; Van Gog, Kester, & Paas, 2011; Yanuarto, 2016). Worked-example is “a step-by-step demonstration of how to perform a task or solve a problem” (Clark et al., 2011, p. 190). By studying the worked-example, knowledge schemes will be more easily and rapidly obtained by students. IJOLAE | p-ISSN 2655-920x, e-ISSN 2656-2804 Vol. (1) (1) (2019) 37-47 39 Fostering Germane Load Through… Besides that, the important thing to no- tice is the relevant cognitive load (germane). Previous studies state that the use of the worked-example is able to reduce extrinsic cognitive load, but it is not guaranteed that this method can also foster relevant cogni- tive loads. In principle, the learning process using worked-example is considered to help students understand the concepts that have been taught by encouraging them to do self- explanation. Self-explanation can be inter- preted as a process of generating explana- tions on oneself as an attempt to understand the concepts that are being studied, associat- ing with prior knowledge, and refining men- tal models (Rittle-Johnson, Loehr, & Durkin, 2017). At present, almost all calculus textbooks seem to have implemented the worked- example method. For example, books writ- ten by (Purcell, Varberg, & Rigdon, 2007) and (Stewart, 2012) have even been trans- lated into Indonesian. However, students still face difficulties in understanding worked-example presented. Therefore, an appropriate method is needed to help students do self-explanation. One of these methods is to provide self- explanation prompting. Several studies have shown the success of this method, including research by (Rau, Aleven, & Rummel, 2015) on algebra course, (Hodds, Alcock, & Inglis, 2014) to improve mathematical proofing abilities and other related studies (Berthold, Röder, Knörzer, Kessler, & Renkl, 2011; Hefter et al., 2015; Rittle- Johnson et al., 2017; Roelle, Hiller, Berthold, & Rumann, 2017). Although there has been a lot of research related to self-explanation prompting along with the use of worked-example, few of them focused on germane cognitive load. Thus, this study was conducted to reveal the role of self-explanation prompting on the germane cognitive load in multivariable cal- culus instruction. 2. Method Participants Seventy-two first-year undergraduate students in one of a state university in Ban- ten Province Indonesia took part in this re- search. All of the students enrolled multivar- iable calculus subject. The experimental class consists of thirty-nine, while the con- trol class was thirty-seven students. Instruments The instruments used in this study were tests and non-test instruments. The test in- struments provided were in the form of three problems relating to multivariable calculus which had been tested for validity and relia- bility. The validity of these items was 0.71, 0.45, and 0.73, respectively, with a reliabil- ity coefficient was 0.61. Thus, this instru- ment meets the criteria to use in research. Meanwhile, non-test instruments were used to measure the students' germane cog- nitive load when solving mathematical prob- lems. This instrument is a rating scale with nine response scales, one states a low mental effort and nine states a high mental effort. The germane load score category is shown in Table 1. This rating scale is asked after students work on test questions. This in- strument has been tested for reliability by Santosa, Suryadi, and Prabawanto (2016) with reliability coefficient (Cronbach Alpha) was 0.82 (highly categorized). Teaching Material After students learn about the con- cepts/principles of the subject to be studied, students are presented with worked-example and problems related to the concepts learned. However, the worked-example in experi- mental class is combined with self- explanation prompting. Vol. (1) (1) (2019) 37-47 IJOLAE | p-ISSN 2655-920x, e-ISSN 2656-2804 40 Fostering Germane Load Through… Table 1. Germane Load Score Categorization Range Skor Germane Load Category 1-3 Low 4-6 Moderate 7-9 High Experimental Design This research is an experimental re- search, specifically quasi-experimental and the research design is the matching-only posttest-only control group design. The re- search design diagram is as follows (Fraenkel, Wallen, & Hyun, 2012): Treatment group M X O Control group M C O The M in this design means that the subjects in each group have been matched (on certain variables) but not randomly assigned to the groups. The experimental class obtained learning using the worked-example method with self- explanation prompting. This means that each step of worked-example presented is completed by prompting to help students do self-explanation. Prompting used refers to research by (Hausmann, Nokes, VanLehn, & Gershman, 2009), which contains questions to stimulate them to think (e.g. what are you applying on this step?). While in the control class, students are given a work-example without being provided with self-explanation prompting. Experimental Procedure After the experimental and control groups are determined, the first step of the research is to test the prior mathematical abilities be- tween the two classes and categorize stu- dents' initial mathematical abilities. Then each class obtained the predetermined learn- ing, worked-example method for the control class and worked-example with self- explanation prompting for the experimental class. The end of the study was carried out posttest along with testing the mental effort that the students invested when completing the posttest. This experimental procedure was suggested by Paas and Gog (2006). Data Analysis The data obtained were scores of stu- dents' mental effort and posttest scores on learning outcomes. Mental effort scores are categorized as ordinal data while posttest scores are categorized as interval data. The data from the research results will be ana- lyzed descriptively followed by inferential analysis. Especially for mental effort data, which categorized as ordinal data, the data analysis is similar to data analysis for posttest data (parametric analysis). This is in accordance with the opinion of (Norman, 2010) which states that ordinal data can be processed us- ing parametric statistics, especially if the response scale is more than five (Jamieson, 2004). 3. Result and Discuss Students’ Prior Mathematical Ability Table 2 shows that descriptively, the mean and median prior mathematical abili- ties of the control group students are higher than the experimental group with the differ- ence is 1.02 and 2.50 respectively. Whereas based on the size of the data distribution, the control group standard deviation is slightly lower than the experimental group and the experimental group range has the opposite value. From this description it can be seen that there is no high difference between the prior mathematical abilities of the control group and the experiment. This condition is validated by statistical test results using the difference between two independent tests. Table 3 shows that there is no significant difference in the mean score of students' prior mathematical abilities be- tween the control and experimental groups at α = 5%. By obtaining this condition, Paas and Gog (2006) state that the results of this study will give a strong prediction about the effect IJOLAE | p-ISSN 2655-920x, e-ISSN 2656-2804 Vol. (1) (1) (2019) 37-47 41 Fostering Germane Load Through… of learning using self-explanation prompting to students’ germane load. This condition is validated by statistical test results using the difference between two independent tests. Table 3 shows that there is no significant difference in the mean score of students' prior mathematical abilities between the control and experimental groups at α = 5% By obtaining this condition, Paas and Gog (2006) state that the results of this study will give a strong prediction about the effect of learning using self-explanation prompting to students’ germane load. Table 2. Description of Student's Prior Mathematical Ability Score between Control and Ex- periment Groups Statistics Control Experiment Mean 63.67 62.67 Median 62.50 60.00 Std. Deviation 8.31 9.26 Range 42.50 41.30 Table 3. Test of the Difference between Means Score in Students' Prior Mathematical Ability Statistics Score df 74 t Stat 0.50562 P(T<=t) two-tail 0.614626 t Critical two-tail 1.992543 Table 4. Description of Students’ Germane Load Score between Control and Experiment Groups Problem Stat Control Experiment 1 Mean 7.84 8.03 Median 8.00 8.00 Std. Dev. 1.38 1.29 Range 4.00 5.00 2 Mean 8.32 8.33 Median 9.00 9.00 Std. Dev. 1.11 1.20 Range 5.00 5.00 3 Mean 8.03 8.33 Median 9.00 9.00 Std. Dev. 1.44 1.20 Range 6.00 5.00 Students’ Germane Load There are three problems provided to students. Each problem is provided with questions about the mental effort that is in- vested by them when solving the problems. Table 4 shows the results of mental effort measurements that reflect the students' ger- mane cognitive load. For the first problem, descriptively the mean score of germane cognitive load between the control and ex- Vol. (1) (1) (2019) 37-47 IJOLAE | p-ISSN 2655-920x, e-ISSN 2656-2804 42 Fostering Germane Load Through… periment group were categorized high, which is 7.84 for the control and 8.03 for the exper- imental group. While based on the measure of dispersion, the standard deviation of the control group is slightly higher than the ex- perimental group, but vice versa for the range. This result is similar to the students' germane load for the second and third prob- lems. Descriptively, it can be seen that the average score for the control and experiment groups fall into the high category (Table 4). In addition, for standard deviation and range measures, there is a slight difference between the control and the experiment groups (Table 4). Descriptive statistics results in Table 4 validated by inferential statistics in Table 5. Based on the table, there is no significant difference in students' germane load between control and experiment groups at α = 5%. Thus, the results indicate that there is no dif- ference between the worked-example method with self-explanation prompting and worked- example without self-explanation prompting on the students' germane load. The important thing, these results show that both methods could foster students’ germane load and maintain it in the high category. This is in accordance with the research conducted by (Van Loon-Hillen, Van Gog, & Brand-Gruwel, 2012), which states that learning that emphases on the use of worked- example will optimize students’ germane cognitive load. Table 5. Test of the Difference between Means Score in Germane Load Statistics BKG 1 BKG 2 BKG 3 t -.613 -.034 -.971 df 74 74 74 Sig. (2-tailed) .542 .973 .334 Mean Difference -.18780 -.00901 -.28067 Std. Error Difference .30651 .26514 .28892 Students’ Performance Previously it was discussed that there was no dif- ference between the worked-learning method with self-explanation prompting and worked-example without self-explanation prompting to students' germane cognitive load. However (Kalyuga, 2011) states that germane load is closely related to the learning objectives achievement. For that rea- son, to reveal whether a learning method has an influence on students’ germane load or not, we need to explore students’ learning objective achievement. To find out whether the learning objec- tives of multivariable calculus course are achieved or not, we have to arrange tests which the tests indicator derived from the learning objectives. Those tests are repre- sented in the posttest. There are three prob- lems that had prepared. Table 6 shows the description of stu- dents’ posttest score between control and experiment group. Based on the table, the results show that for the first problem, the average and median values of the experi- mental group are higher than the control group. The condition is similar for second and third problem, the students’ cognitive load mean score who implement worked- example learning with self-explanation prompting is higher than students who im- plement worked-example without self- explanation prompting. The results of the descriptive analysis were validated by inferencing analysis in Table 7. Based on the table, for the first problem, the mean score of posttest achievement of the expe imental group was higher than the control group with a p-value = 0,000 at . Furthermore, for the sec- ond problem, the mean score of students' posttest achievement of the experimental group was higher than the control group with IJOLAE | p-ISSN 2655-920x, e-ISSN 2656-2804 Vol. (1) (1) (2019) 37-47 43 Fostering Germane Load Through… a p-value = 0.0005 at . Finally, for the third problem, the mean score of stu- dents' posttest achievement of the experi- mental group is higher than the control group with a p-value = 0,000 at . Thus, it can be interpreted that the students' learning objective achievement in the experimental group is better than the control group. It means that the use of self-explanation prompting on the worked-example method is able to foster students' germane load. Table 6. Description of Students’ Posttest Score between Control and Experiment Groups Problem Statistics Control Experiment 1 Mean 10.27 13.54 Median 8.00 10.00 Std. Deviation 3.20 3.85 Range 12.00 8.00 2 Mean 6.35 7.13 Median 6.00 8.00 Std. Deviation 0.95 1.00 Range 4.00 2.00 3 Mean 3.78 4.77 Median 4.00 4.00 Std. Deviation 0.79 0.99 Range 4.00 2.00 Table 7. Test of Difference between Mean Score of Students’ Posttest in Multivariable Calculus Statistics Masalah 1 Masalah 2 Masalah 3 t -4.030 -3.466 -4.830 df 72.774 73.999 71.925 Sig. (1-tailed) .000 .0005 .000 Mean Difference -3.26819 -.77685 -.98545 Std. Error Difference .81093 .22412 .20404 4. Conclusion Research showed that there was no dif- ference in students' germane load who im- plement the worked-example method with self-explanation prompting and students who implement worked-example methods without self-explanation prompting. How- ever, it was revealed that the students’ ger- mane load in the two research groups in the high category. This indicates that learning using the worked-example method is able to foster students’ germane load. However, these results have not yet shown evidence that self-explanation prompting is capable of fostering students’ germane load. Mean- while, Kalyuga (2011) states that there is an association between germane load and learning objectives. When students achieve learning objec- tives, then the learning method is able to foster students' germane load. To assess the learning objectives, the posttest was ar- ranged to be in accordance with the indica- tors of learning objectives. The results stated that students who im- plement the worked-example method with self-explanation prompting had better test scores than students who implement the worked-example method without self- explanation prompting. 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