| Algebra is widely regarded as the gatekeeper to all high school mathematics(Brawner,2012).Unfortunately,teaching and learning algebra in many countries,including Indonesia,is a struggle due to several of difficulties.Egodawatte(2011)pointed out the problems as: lack of understanding of the meaning of variables,making sense of the relationship between word problems and algebraic expressions,and incorrectly processing the elements in algebraic equations.Jupri,Drijvers,& van den Heuvel-Panhuizen(2014)observed the same phenomenon in Indonesia and specifically mentioned that the difficulties were caused by the gap between arithmetic and algebraic lessons.In the recent TIMSS results in 2007 and2011 in the 8th-grade algebra domain,Indonesian students reported low scores:the average Indonesian score in the algebra domain was 405 and 392,far below the international average of 500 and 500(Gonzales et al.,2008).On the other hand,Habibi(2018)observed the various problems that occur in algebraic learning,such as the tendency to be lazy in thinking in algebraic situations,pessimism,lack of determination in learning,and weak regulations made by students.It can be assumed,apart from the "content" issue,there were other things that occurred in parallel with this problem,namely those related to intrinsic motivation or self-determination.Even the decline of determination in learning mathematics can be found earlier,which is when the process of arithmetic transition and algebra began to occur.These problems are closely related to the students’ low self-determination.Therefore,an approach which can maintain and develop the determination as well as stimulate students’ self-regulating in learning mathematics should be a special concern.Realizing the urgency of problems related to algebraic learning,including those concerning self-determination,an appropriate learning model is needed that can help students to force themselves to think algebraically.Besides that,a stimulus is also needed that can foster an attitude of self-determination simultaneously in order to support students’ passion for algebraic thinking.This study compares the improvement and achievement of algebraic thinking ability and self-determination of students who receive learning using the MultiRepresentation Generative Learning(MRGL)model with students who receive conventional learning.The Algebraic thinking and self-determination are the key variable or final goals to be achieved in this research.While The MultiRepresentation Generative Learning(MRGL)model is defined as means to achieve the desired goals.This research aimed to determine the students’ algebraic thinking and selfdetermination in the mathematics learning process and the effect of the MultiRepresentation Generative Learning(MRGL)model on students’ algebraic thinking ability and self-determination.A quasi-experimental design with pre-test and post-test control groups was used in this study,which included 125 junior high school students from three schools chosen based on school accreditation,distance from the capital city,and establishment year.The students were divided into two groups(a control group in which the students were taught using a conventional teaching method;and an experimental group which was taught using MRGL Model).The students’ Initial Mathematical Ability(IMA)and school ranking(SR)were used as the consideration in dividing the group.In addition,each group consisted of students with high,medium,and low levels of IMA and SR;it was aimed to see if the MRGL model gives a different effect on each level of Initial Mathematical Ability and School ranking.After completing the treatments,the students were given questionnaires to measure each indicator of their algebraic thinking and self-determination.The questionnaire results were then analyzed and presented descriptively.Furthermore,the data were processed using statistical analysis to see the self-determination differences between the experimental and the control group.To determine the effect of MRGL model on the students’ algebraic thinking and self-determination,the difference mean scores in each group(experimental-control)were analyzed and categorized into several indicators.The steps in analyzing the difference score were:(1)normality test of both groups using Shapiro Wilk;(2)if the data is normally distributed,then it is followed by homogeneity test by using Levene test;(3)If the data shows a homogeneous distribution,then the parametric test will be applied using the independent t-test,to see the mean difference between experimental and control groups;(4)if the assumption of normality is not met at step 2,then nonparametric analysis by using Mann Whitney U test would be used to see the mean difference between experimental and control group;(5)The difference in improvement in students’ algebraic thinking and self-determination is measured using N-Gain Analysis;and(6)the Adjusted Rank Transform Test use to determine the effect of the interaction between MRGL model with students’ algebraic thinking and self-determination.The results showed that students who received instruction using the MRGL model achieved and improved their algebraic thinking ability and selfdetermination more than students who received instruction using a conventional approach,both in terms of their Initial Mathematical Ability(IMA)and School Ranking(SR).Furthermore,this research shows that no interaction exists between the MRGL model and IMA when it comes to developing algebraic thinking ability and no interaction between the MRGL model and SR when it comes to increasing algebraic thinking ability.Self-determination is the same way.In conclusion,the results of this research indicate that MRGL model is effective in developing students’ algebraic thinking and self-determination,and appropriate to be applied in mathematics,especially in topic relating to algebraic thinking,and this is also for any students’ level of IMA(low,medium,and high)and School Ranking(low,medium,and high). |
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