Metaphorical Thinking of Students in Solving Algebraic Problems based on Their Cognitive Styles

One of thinking concepts which connects real life to mathematics is called metaphorical thinking. Metaphor and modelling are two closely related concepts. Besides, each individual performs different cognitive styles, such as field independent (FI) and field dependent (FD) cognitive styles. This factor possibly leads to different metaphorical thinking in solving algebraic problems. The participants of this qualitative research consist of two students at grade 7 of one of junior high school in Banda Aceh, Indonesia, with FI and FD as their cognitive styles. Based on the findings, it is found that: 1) Metaphorical thinking of the student with FI cognitive style in solving the algebraic problem in the stage of understanding the problem, devising a plan, carrying out the plan, and looking back is considered to achieve the target for each criteria of CREATE; 2) Metaphorical thinking of the student with FD cognitive style in solving the problem in the all four stages but could not reveal all criteria mentioned in CREATE. This happens as the student is unable to find the appropriate metaphor to the algebraic problem. Therefore, the student does not need to explain the suitability of the metaphor to the algebraic problem.

Student’s Anticipation Profile at Rigor Level in Determining Papaya Tree Root Dimensions

Students with a rigor level of geometric thinking can analytically solve problems, yet the ability may not be readily observable. Thus, an example of how students solve problems merits explorations. Inspired by student’s problem solving, this study aimed to examine the student’s anticipatory profile in determining Papaya tree roots' dimensions. This qualitative research utilized tests and interview. Two tests were carried out: van Hiele geometric level grouping test for selecting the research participants and the report-based test for the actual project. Seventeen students took the van Hiele test, and one of them, who achieved the rigor level, was selected for the interview. Data obtained from the interview were then analyzed qualitatively. The study showed that students with a rigor level of geometric thinking anticipated analytically. The subject was able to explain a geometric problem systematically, starting from analyzing problems, clarifying detailss, to presenting arguments clearly and precisely. The findings in this study generate useful information for teachers who train their students to analyze a geometric problem correctly and adequately.

Analysis of Students' Mathematical Creative Thinking Ability in Module-assisted Online Learning in terms of Self-efficacy

The research aims to describe the underlying cause of students' low Creative Thinking Ability (CTA), and examine the effectiveness of online learning assisted by module in improving CTA in terms of self-efficacy. The research applied a mixed-method. The subjects were 8-grade students. The qualitative research subjects were selected purposively, generating two students for each category of low, medium, and high self-efficacy. While quantitative research used cluster sampling to classify experimental and control classes. The independent variable of the study was self-efficacy, and the dependent variable was CTA. Data collection was conducted by observation, interviews, documents, questionnaire, and test. Data was analyzed using descriptive analysis, statistical regression tests, and t-test. The results showed that the underlying cause of low CTA was in students' low and medium self-efficacy. Students with low and moderate self-efficacy highly depended on teacher help. For students with high self-efficacy, the CTA worked well. The results also revealed that the average CTA in the experimental class reached the minimum criteria of mastery learning; the average CTA of the experimental class was better than the CTA of the control class; and the effect of positive self-efficacy on CTA was 38.50% in the experimental category, showing that this learning was effective.

Increasing Mathematical Critical Thinking Skills Using Advocacy Learning with Mathematical Problem Solving

The ability to think critically is one of the abilities students must possess. Students’ critical thinking skills have not been encouraging. There is a need for learning that can improve this ability, one of which is advocacy learning. The study aims to increase students’ critical thinking skills with open-ended mathematical problems in advocacy mathematics learning. This study is a nonequivalent control group design with a pre-test post-test control group. Sampling using cluster random sampling, randomization was carried out in classes at Junior High School 4 Bandung by taking two classes. Data analysis used Mann-Whitney, one-way ANOVA, and Tukey. The results showed that students treated with an advocacy approach by giving open-ended questions had better mathematical critical thinking skills than those who received conventional learning. Also, students with high prior knowledge had better critical thinking skills compared to the other two groups. This research implies that the advocacy can be used as an alternative to learning mathematics for students with high prior knowledge.

Improving Teachers’ Self-Efficacy through Training: An Impact for the Freedom of Students’ Mathematical Thinking

Teacher self-efficacy is an important component of teacher competence. At present, efforts to improve teacher competencies have not been carried out simultaneously for teacher activities in the classroom (open class) and outside the classroom (training). This quasi-experimental study aimed to examine the effectiveness of soft skills training and the practice of lesson study on improving mathematics teacher self-efficacy and describe the impact of teacher self-efficacy on the freedom of students' mathematical thinking. The study involved three mathematics teachers and 90 students from three different junior high school regions in Bandar Lampung, Indonesia (city center, semi-urban, and suburban). Data was collected through questionnaire, observation, and interview. The data were then analyzed descriptively. The effectiveness of soft skills training and the practice of lesson study on improving mathematics teachers’ self-efficacy was examined using Wilcoxon Test. The results showed the differences in the average teachers’ self-efficacy before and after participating in soft skills training and the practice of lesson study (with an increase of 0.82/high). The increase in teachers’ self-efficacy also positively affected the freedom of students’ mathematical thinking.

An Analysis of Errors on Mathematical Symbol as a Metaphor in Linear Programming

Symbol sense is crucial in the understanding of mathematical problems comprising various symbols. The misuses of symbols happen due to misinterpretation, which is considered the constraint to learn algebra more comprehensively, including in linear programming. The term ‘metaphor’ is defined as a means to carry over symbol sense, and is used to improve mathematical understanding. This present research was aimed at analyzing errors on mathematical symbol as a metaphor in linear programming. This research was conducted by means of descriptive qualitative design, with a test and interview as the instruments. The test was made essay, and its results were analyzed qualitatively. The test, further, was administered to five eleventh graders selected according to highest rates of errors committed. This research has shown that the students committed a number of errors in some cases, such as representing symbols as variables, representing numbers, and interpreting symbols as relational operators. In addition, errors which the students committed in constructing mathematical models covered defining the final value, representing numbers, applying inequality system, and interpreting symbols as operation counts. This present research has provided some ways for symbol sense, and thus the errors on mathematical symbol as a metaphor could be lessened. Next, this research can be further followed up by reviewing the effectiveness of remedial instruction according to the committed errors on mathematical symbols.

Students' Critical Thinking Process in Solving Jumping Task According to Gregorc's Thinking Style

Indonesian students are lacking in critical thinking skills, however, studies analyzing critical thinking processes and their relation to thinking styles are limited. This study aimed to describe students’ critical thinking processes in solving jumping task problems according to Gregorc's thinking style. The subjects of this present qualitative research were eight Year 7 students. The instruments included a thinking style questionnaire, tests, and interview guidelines. The results showed that concrete sequential subjects tended to write the completion stages sequentially and analyzed them well. Abstract sequential subjects were inclined to solve the problems based on the known concepts without completing the work. Concrete random subjects tended to write information in their own way without completing their work. Meanwhile, abstract random subjects were inclined to write incomplete information and did not complete their work. Generally, based on the IDEALS model, the two sequential subjects were similar in the identity, define, and enumerate steps, while the two random subjects only had similarities in the identity step. This study results imply that jumping tasks can be used as an alternative in developing students’ critical thinking skills.

Hypothetical Learning Trajectory (HLT) For Fraction of Blind Students Using Braille Media Fraction Block

. Learning fractions is one of difficult topics for students with visual impairments. The aim of this design research is to describe the design process of Hypothetical Learning Trajectory for the addition of fractions using Fraction Block Braille. This research is divided into 3 stages, the preparation for the experiment, the design experiment, and the retrospective analysis. Data collection techniques in this research are walkthrough, observation, interview, and test. This research resulted in a Hypothetical Learning Trajectory design for the addition of fractions contains the following activities: Dividing unit blocks into equal parts, Comparing the sizes of different fraction blocks to get the same size fractions, Comparing the combined sizes of several blocks, Combining several fractions, Determining the fractional block that is the same size as the summed fraction block. The five activities were carried out quite well in the 2-cycle experimental activity. After the implementation of the experimental activities, the students' answers to the practice questions showed that the research subject could understand the material presented.

Students’Metacognitive Abilityin Mathematical Problem-Solvingthrough the Problem-based Learning Model

Students lack metacognitive ability despite its vital role in mathematical problem-solving. The problem-based Learning (PBL) model is one of the learning models to improve metacognitive ability in problem-solving. This study aimed to analyze the students'metacognitive ability in mathematical problem solving through PBL and examine its improvement. This present study applied the explanatory sequential mixed-method design. The population was the Year 11 students from one of the senior high schools in South Aceh Regency, Indonesia. Data collection was conducted using three instruments: pre-test, post-test, and interview guidelines. The pre-test and post-test data were analyzed using the t-test, while students' metacognitive ability was analyzed qualitatively. The results showed that students' metacognitive ability in mathematical problem solving through the PBL model was increased. Furthermore, students' metacognitive abilitywas at the semi-reflective use, the strategic use, the aware use levels for high-ability, medium-ability, and low-ability groups.

Perkembangan Rasa Ingin Tahu Mahasiswa melalui Pengintegrasian Nilai Islami dalam Pembelajaran Matematika

Islamic values are the basis of reference in efforts to improve students' character and attitudes. The low value of students’ character is a scourge of today's problems. This study aims to determine the development of students' curiosity through the integration of Islamic values in mathematics learning. This research is a qualitative exploratory. Data were collected by using interviews and observations. The instruments used were observation sheets and interview guidelines to determine the development of curiosity. The subjects were three students at the Mathematics Education Department, FTIK IAIN Langsa. The results showed that two subjects have developed four indicators of curiosity: namely always asking questions, not accepting something learning as boring, showing listening, speaking, reading and writing skills and showing pleasure in learning. Meanwhile, there is one subject but there is one subject that does not develop curiosity on indicators showing listening, speaking, reading and writing skills. The results of study support theories stating that the integration of learning mathematics and Islamic values has a positive impact on students’ character. Therefore, this research can be considered for the Faculty of Education to further develop learning that integrating science and Islamic values in curriculum development as an effort to develop student character.