ENHANCING STUDENTS’ MATHEMATICAL LOGICAL THINKING ABILITY AND SELF-REGULATED LEARNING THROUGH PROBLEM-BASED LEARNING

International Journal of Education, Vol. 8 No. 1 December 2014 ENHANCING STUDENTS’ MATHEMATICAL LOGICAL THINKING ABILITY AND SELF-REGULATED LEARNING THROUGH PROBLEM-BASED LEARNING Euis E. Rohaeti E-mail: STKIP Siliwangi, Bandung Budiyanto, A.M E-mail: SMAN Tegalsari Karawang, Utari Sumarmo E-mail: STKIP Siliwangi, Bandung Abstract This study was intented to investigate the development of students’ mathematical logical thinking ability and self-regulated learningthroughProblem-based Learning (PBL). This study was a part of a master thesis and a sub-studyof a Postgraduate Research Grant from DGHE in 2013. This study was a pre-testpost-testquasi-experimental control group design involving 93 eleventh-gradestudents of a senior high school in Karawang which were chosen puposively.The instrumentsof this study were an essay test on mathematicallogical thinking, a self-regulated learning scale, and a scale measuring students’ perception on PBL. The study revealed that students getting treatment on PBL attained better grades on mathematical logical thinking ability than students taught by conventional teaching, though the grades were at low level. However, there was no difference in gradesof self-regulated learning between students in the two groups though thegrades were fairly good. Also, there was no correlation between mathematical logical thinking ability and self-regulated learning with students’ positive opinions toward PBL. Keyword: mathematical logical thinking, self-regulated learning, Problem-Based Learning, perception toward PBL. Introduction Basically, mathematical logical thinking ability as acomponent of mathematics learning outcomes should be developed by high school students. The reason is that mathematical logical thinking ability is included in the vision and the goals of mathematics teaching (BNSP, 2006, NCTM, 2000). As for the vision of mathematics,it includes develop mathematical thinking abilities which are logical, systematic, critical, accurate, and creative.In addition, othergoals of mathematics teaching areto generate a reasonbased on mathematical patterns andfeatures, to draw generalization, as well as to proveand to clarify mathematical 54 statements which illustrate the essence of logical thinking in teaching mathematics. Some experts defined the term oflogical thinking differently. Capie and Tobin (as cited in Sumarmo, 1987) assessed logical thinking ability thorugh the Test of Logical Thinking (TOLT) whichcovered five components, namely controlling variable, proportional reasoning, probabilistic reasoning, correlational reasoning, and combinatorial reasoning. Other researchers definelogical thinking as to conclude using reasoning consistently (Albrecht, as cited in Aminah, 2011); to think causally (Strydom, as cited in Aminah, 2011); to think based on certain Euis E. Rohaeti, Budiyanto, & Utari Sumarmo, Enhancing Students’ Mathematical Logical Thinking Ability pattern or rules of inference (Minderovic, Suryasumantri, Sponias, as cited in Aminah, 2011); and to thinkinvolving induction, deduction, analysis, and synthesisactivities (Iove your eyes, as cited in Aminah, 2011). From these definitions, Sumarmo, Hidayat, Zulkarnaen, Hamidah, & Sariningsih, (2012) summarized a ctivities related to logical thinking ability, such as conclud or estimate relevant proportionon probability, correlation, combinatorial computation, and on similarity or analogy; and to generalize, prove, analyze, and synthesis some cases. Glasersfeld (as cited in Suparno, 1997), Nickson (as cited in Hudojo, 2002), and Polya (1973) state teacher’s role plays an important role in improving students’ thinking abilty; teacher not only delivers information but also acts as a student, understands their way of thinking,assists them to build their knowledge,and improves their thinking ability.Essentially, these roles are in line with contructivism philosophy in which the learning process involves students’ active learning,connecting information to the prior knowledge for building a more complex and meaningful schemata, and emphasis on investigating and inventing. One of teaching learning models on the basis of constructivism philosophy is problem-based learningor PBL (Barrows &Kelson; Ibrahim &Nur; Stephen and Gallagher as cited in Ratnaningsih, 2004). Problem-based learning (PBL) starts the learning activities by presenting a contextual problem relevant to the learned material. Furthermore, Ibrahim and Nur (as cited in Ratnaningsih, 2004) listed five stepsin conducting PBL; they are engaging students to the problem, managing them to learn, guiding them to explore it individually or in groups, helpingthem improve and present their work, and helping them analyze and assess theprocess of problem solving. In approachs to teaching and learning, there are some variables that may affect students’ mathematics achievement, particularly on attaining good grades; one of the variables is self-regulated learning (SRL).Several researchers (Butler, 2002; Corno & Randi, 1999; Hargis, Paris & Winograd, 1998; Schunk &Zimmerman, 1998; Wongsri, Cantwell, & Archer, 2002, as cited in Sumarmo, 2006) defined SRL in different ways but principally they proposed three similar characteristics of SRL, namelyplanning a goal, selectinga strategy, and monitoring cognitive and affective processes while answering an academic task. Some studies reported that PBLis better on developing various mathematical abilitiesofsenior and junior high school studentsthan conventional teaching, such as Juandi (2008), Herman (2006), Permana (2004), and Ratnaningsih (2004). Those studies reported that students obtained fairly good grades on various mathematical abilities. Nevertheles, some of other studies employing various teaching approaches reported that senior high school students obtained low to average grades on mathematical logical thinking ability (Maya, 2005; Setiawati, 2014; Sumarmo, 1987; Sumarmo, Hidayat, Zulkarnaen, Hamidah, & Sariningsih, 2012). These studies found out that mathematical logical thinking problems were relatively difficult tasks for most of students. Furthermore, Qohar (2010) reported that implementing reciprocal teaching made students obtained good grades on self-regulated learning. Based on the a forementioned background, the research questions of this study are as following: 1. Are students’ grades of mathematical logical thinking ability and their N-Gaintaught by PBL higher than the grades of those who are taught by conventional teaching method? 2. Are students’gradeson self-regulated learningtaught by PBL higher than the grades of students who are taught by conventional teaching method? 3. Is there any correlation between mathematical logical thinking ability and self-regulated learning? 4. What are students’ perceptions toward PBL? 55 International Journal of Education, Vol. 8 No. 1 December 2014 Theoritical Review Mathematical Logical Thinking and Selfregulated Learning Capie and Tobin (Sum (...truncated)