Activist Learners’ Creative Thinking Processes in Posing and Solving Geometry Problem

<p style="text-align: justify;">This study aimed to describe the creative thinking process of students with active learning styles in proposing and solving problems on geometry material. The research instruments were Honey and Mumford's Learning Style Questionnaire (LSQ), problem-solving and submission test sheets, and interview guidelines. The LSQ questionnaire was distributed to students majoring in mathematics education at a university in Malang, Indonesia, with a total of 200 students. Students who have an active learning style and meet the specified criteria will be selected as research subjects. Based on research on creative thinking processes in proposing and solving problems in students with active learning styles, it was found that there were differences in behaviour between subject 1 and subject 2 at each stage of creative thinking. However, based on the researcher's observations of the behaviour of the two subjects at each stage of their thinking, there are similarities in behaviour, namely, they tend to be in a hurry to do something, prefer trial and error, and get ideas based on daily experience.</p>

An ethnomethodological analysis of students’ understanding of the concept of trigonometry in a high-stakes examination in South Africa

[English]: In South Africa, National Senior Certificate (NSC) mathematics examination is a capping external examination taken at the culmination of twelve years of schooling. The purpose of this study was to investigate and analyze the responses of examinees in the examinations in the concept of trigonometry. While the study mainly used an ethnomethodological approach, a documentary analytical approach was also adopted. Documentary analysis was necessitated by the private nature of the NSC examination, as we only had access to the written work of the examinees. The major findings were: (1) that the strategies and tactics used by examinees are highly driven by the context of the high-stakes examination; (2) that examinees’ ways of working exhibit the general structure of the practice that is commonly found in mathematical discourse practices. Further studies are required to deepen the understanding of the thinking processes of examinees by conducting focus group interviews, where the examinees are afforded opportunities to explain their workings in school-based assessments. [Bahasa]: Di Afrika Selatan, ujian matematika National Senior Certificate (NSC) adalah ujian tambahan yang diambil pada akhir dari dua belas tahun sekolah. Penelitian ini bertujuan untuk melakukan investigasi dan analisis tanggapan siswa peserta ujian matematika NSC terkait konsep trigonometri. Selain pendekatan etnometodologi yang secara umum dipakai dalam penelitian ini, pendekatan analitis dokumenter yang juga diadopsi terkait karakteristik ujian NSC, dalam hal inipeneliti hanya memiliki akses pada jawaban tertulis peserta ujian. Temuan utama penelitian adalah: (1) bahwa strategi dan taktik yang digunakan oleh peserta ujian sangat didorong oleh konteks ujian berisiko tinggi; (2) bahwa cara kerja peserta ujian menunjukkan struktur umum praktik yang biasa ditemukan dalam praktis diskursus matematika. Penelitian lebih lanjut diperlukan untuk memperdalam pemahaman tentang proses berpikir peserta ujian dengan melakukan wawancara kelompok terfokus, dimana peserta ujian diberikan kesempatan untuk menjelaskan cara kerja mereka dalam penilaian berbasis sekolah.

Unsaid Thoughts: Thinking in the absence of (some) verbal logical connectives

Combining two thoughts into a compound mental representation is a central feature of our verbal and non-verbal logical abilities. We here approach this issue by focusing on the contingency that while natural languages typically verbalise only two of the sixteen connectives from formal logic to express compound thoughts —"and" and "or"— the remainder appear to be entertainable as non-verbal, conceptual representations and this suggests a way to probe how linguistic and non-linguistic thinking processes relate. In a visual world experiment aimed at tracking both comprehension-related and reasoning-related aspects of the capacity to represent compound thoughts, we found that participants are capable of learning and interpreting a made-up word for logic’s NAND operator, indicating that unlexicalised logical connectives are nonetheless conceptually available.

Mindsponge culture: the culture of progress

The Mindsponge culture can be defined as a set of thinking processes, beliefs, and behaviors that is result- or target-driven. It is an entrepreneurship culture that urges me to overcome hardship with a transparent mind about my target. Adopting this culture is a tough process, but its fruitful results are worth the cost. Especially in the next decades, humanities have to acquire two crucial targets for sustainable development: curbing climate change and reducing biodiversity loss. To accomplish these targets, shifting the eco-deficit mindset to the eco-surplus mindset at the individual level and building eco-surplus culture at the organization level (e.g., business sectors) are required. Obtaining the Mindsponge culture can help us progress and actualize these objectives through creative performance.

Mindsponge culture: the culture of progress

The Mindsponge culture can be defined as a set of thinking processes, beliefs, and behaviors that is result- or target-driven. It is an entrepreneurship culture that urges me to overcome hardship with a transparent mind about my target. Adopting this culture is a tough process, but its fruitful results are worth the cost. Especially in the next decades, humanities have to acquire two crucial targets for sustainable development: curbing climate change and reducing biodiversity loss. To accomplish these targets, shifting the eco-deficit mindset to the eco-surplus mindset at the individual level and building eco-surplus culture at the organization level (e.g., business sectors) are required. Obtaining the Mindsponge culture can help us progress and actualize these objectives through creative performance.

Imagination in the Creative Self-Expression of Students in Secondary School Literature Classes

The paper’s aim is to make topical the role of imagination in thinking processes and learning cognition and in the creative self-expression of students in secondary school Literature classes. The paper summarizes theoretical pedagogical and psychological findings about imagination in cognitive activity and links them with the author’s practical experience in the work of a secondary school Literature teacher. The research issue is how to stimulate imagination in secondary school students’ cognitive activity during literature classes, thereby promoting their creative self-expression and self-experience. This issue is topical when contemplating the formation of a creative personality and a skilled, creative reader. The role of imagination is regarded from three viewpoints: the relation of imagination to the development of thinking; the role of imagination in creative self-expression and self-experience of students; creative exercises in secondary school literature classes as imagination stimulators. In the learning process related to artistic cognition, connection between scientific and artistically directed cognitive activity is relevant because the development of a free and creative personality requires linking of critical thinking, imagination and emotional attitudes, which in turn forms creative self-experience of students, the ability to use knowledge, skills and attitudes acquired in the learning process of diverse life situations. Creative problem tasks in Literature classes are one of the pedagogical means to encourage students to look for connections between different science fields, topics, facts, events, objects, phenomena, images and draw independent take-aways and conclusions, as well as encourage students to express themselves creatively. The research methods: literature analysis, content analysis, self-experience analysis, survey.

The Spatial Thinking Process of the Field-Independent Students based on Action-Process-Object-Schema Theory

<p style="text-align: justify;">Spatial thinking has roles to facilitate learners to remember, understand, reason, and communicate objects and the connections among objects that are represented in space. This research aims to analyze the spatial thinking process of students in constructing new knowledge seen from the field-independent cognitive style learners based on Action-Process-Object-Schema (APOS) theory. APOS theory is used to explore spatial thinking processes which consist of mental structures of action, process, object, and schema. This research is qualitative research with an exploratory method. It provided the students' opportunity to solve problems alternately until the method found the most appropriate subjects for the research objectives. The subjects were 2 students of Mathematics Education in the fourth semester of Universitas Muria Kudus Indonesia. The data collection techniques were started by distributing the validated and reliable spatial thinking questions, the cognitive style question, and the interview. The applied data analysis consisted of data reduction, presentation, and conclusion. The findings showed (1) spatial thinking process of holistic-external representation typed learners were indicated by the representative thinking element, abstract-illustrative figure expression to communicate and complete the tasks correctly, (2) spatial thinking process of the holistic-internal representation typed learners were indicated by the representative means, having ideas, connecting with the previous knowledge in the forms of symbols and numbers, and finding the final results correctly although incomplete.</p>

Analysis of Intuitive and Analytics Thinking Processes in Middle School Students in Solving National Mathematics Exam

So far, the teacher's thought process in solving a math problem has rarely been paid attention to by the teacher. The thinking process of students in solving math problems includes intuitive and analytical thinking processes. The aim of this research is to explore the intuitive and analytical thinking process of junior high school students in solving UN questions. The research method used is qualitative research that is exploratory in nature by selecting subjects who have high abilities in mathematics. Data collection in the form of descriptions of students' intuitive and analytical thinking processes was carried out through interviews. The results obtained in this study are a description of the process that students go through in mental when students solve math problems in the form of questions National Examination. The results of the study can be concluded that students in solving mathematics problems in the National Examination prioritize the process of intuitive thinking, where students can spontaneously and directly pour out ideas for solving the problems given. In addition, in the further process, students also use analytical methods. Analytical thinking processes are carried out by students by detailing the answers based on the information in the questions.