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Qualitative research for education: An introduction to theories and methods

미국의 “전국 수학 교사 협의회”(National Council of Teachers of Mathematics, NCTM)는 1989년부터 〈학교 수학의 교육과정과 평가 규준〉(1989), 〈수학 가르침(교수)의 전문성 규준〉(1991), 〈학교 수학의 평가(시험) 규준〉(NCTM, 1995), 〈학교 수학의 원리와 규준〉(2000)을 출판하여 미국의 수학 교육 의 전망(목표, 나아갈 길)과 규준(실행 지침)을 제시하였다. 수학 교사들로 구성된 미국의 NCTM은 학생, 학부모, 학교 행정가 등 많은 사람들과 힘을 합하여 모든 학생들에게 수준 높은 수학 교육을 받을 수 있는 여건(환경, 기회)을 조성하는 데 구심점의 역할을 하였다. 한편 많은 관련 단체들은 여러 배경과 능력을 가진 학생들이 전문성을 지닌 교사(특수 교사를 일컫는 밀이 아니다. 수학 교과를 이해하고 수학의 전문성과 특수성을 가르칠 수 있는 일반 교사를 일컫는 말이다.)로부터 미래를 대비해 평등하고, 진취적이며, 지원이 잘 이루어지고, 공학 도구(IT)가 잘 갖춰진 환경에서 중요한 수학적 아이디어를 이해하면서 학습할 수 있는 수학 교실(미국에서는 우리나라처럼 수학 교사가 수학 시간에 학생의 방(교실: Homeroom)에 찾아가지 않고 학생들이 선생의 방(수학 교실: Classroom)을 찾아온다. 전형적인 수학 교실의 사진은 2쪽에 나와 있다.)을 만들기 위해 함께 힘썼다. NCTM에서 출간한 여러 규준들은 우리나라의 제6차와 제7차 교육과정에도 큰 영향을 미쳤다. 이 글에서는 NCTM(2000)에서 제시한 학습 원리를 간단히 살펴본 다음 이를 중심으로 현재 미국 수학 교육의 교수ㆍ학습 이론의 동향을 살펴본다.

미국 NCTM의 Principles and Standards for School Mathematics에 나타난 수학과 교수,학습의 이론

A difficulty that faced me many years ago, on first coming into contact with occupational therapy as a student, was that of wondering how would it be possible to produce an art form for my Instructor if the cupboard were bare — or if not bare suffering from all too many empty shelves! A similar problem faced me on beginning clinical practice with a group of patients — some of whom had creative talent — but others of whom had obviously little such talent, and yet my basic role was to inspire and encourage them to become creative. This problem has remained with me a long time, but over the years I have found that I could force myself towards a certain amount of creativity although this remained a difficulty with some students and some patients. So it was with interest that I heard of educational attempts that had been made over the years to foster and stimulate creativity, and was eventually introduced to the book APPLIED IMAGINATION by Alex Osborn' and to the work that has developed at the State University of New York at Buffalo. Dr. Osborn pursued creativity for more than 20 years and was the author of several books. Finally, in the early summer of 1967 I was able to attend one of the annual Creative Problem Solving Institutes held at Millard Fillmore College, Buffalo, the purpose of the five-day Institutes being to train participants in a teaching method of creative problem solving, the Institutes having been well described as involvement for five days, twenty-four hours a day. This short article is an account of what was accomplished on that course by the participants, and it will also attempt to describe something of the nature and nurture of creative behaviour. Before proceeding to describe the problem solving process, it might be as well to first establish the hypothesis that creativity as such is often lacking not only in our daily routines, but alas, is increasingly lacking and unappreciated in our basic education, for our continued rising standard of living makes us so often purchase services and facilities and with them opportunities for creativity, that but a few years ago we were happy to provide ourselves. Similarly, we have become passive in our educational processes, all too frequently passively accepting the premise that we have not been endowed with, for example, the ability to spell, whereas in truth hard work has invariably enabled anyone to spell the words he must have to

Creative problem solving.

This study aimed to describe the instructional design to improve the Higher Order Thinking Skills (HOTS) of students in learning mathematics. This research is design research involving teachers and students of class X MIPA 1 MAN Yigyakarta III, Special Region of Yogyakarta, Indonesia. Data collected through focus group discussions and tests. Data analyzed by quantitative descriptive. The results showed that the instructional design developed is effective to improving students' HOTS in learning mathematics. Instructional design developed generally include three main components: (1) involve students in the activities non-routine problem solving; (2) facilitating students to develop the ability to analyze and evaluate (critical thinking) and the ability to create (creative thinking); and (3) encourage students to construct their own knowledge.

https://iopscience.iop.org/article/10.1088/1742-6596/812/1/012100/pdf

Developing Instructional Design to Improve Mathematical Higher Order Thinking Skills of Students

Higher Order Thinking Skills (HOTS) is a skill demanded in 21st century. HOTS is trained in mathematics learning which one of its execution uses teaching materials such as textbook. This article aims to describe the urgency of HOTS content analysis in mathematics textbook. The results of literature review show that HOTS is one of the main goals in education and become one of the top five variables that can improve student achievement. HOTS can be developed but cannot be automated and requires practice. Textbook is one of the learning media that can be used in training HOTS because the textbook is the main learning media for teachers and students. Teacher's decisions in selecting teaching materials and strategies are also directly influenced by textbook used by teachers. Some studies even mentioned that there is a strong relationship between textbook used with student achievement. Thus, it can be said that the more HOTS content in a textbook, the greater the probability of HOTS to be trained and taught to the students. Therefore, a mathematical textbook analysis is needed to find out how the HOTS content in textbook is used by teachers and students.

https://iopscience.iop.org/article/10.1088/1742-6596/1097/1/012147/pdf

Urgency of Higher Order Thinking Skills (HOTS) Content Analysis in Mathematics Textbook

International surveys, such as TIMSS and PISA, frequently put Indonesia in the low ranks. It is an indication that the higher-order thinking skills (HOTS) of students in Indonesia are still low. This research aims to analyze students’ difficulties in solving problems that measure HOTS. This is a case study research with a qualitative approach. Participants studied were 93 high school students in grade XI. Data were collected using test instruments that measure HOTS, which was developed based on the standard contents of high school mathematics. The difficulties were analyzed descriptively by observing students’ errors in answering HOTS test items. Students’ errors were classified based on Newman’s Error Procedure (NEP). The result shows that around 8.33% of the students had difficulties in comprehension, 15.59% in transformation, 32.53% in process skills, and 1.34 % in encoding. Keywords: HOTS problem in mathematics, students’ difficulties, case study, Newman’s error procedure.

/pdf/the-difficulties-of-high-school-students-in-solving-higher-1gks1s05fv.pdf

The difficulties of high school students in solving higher-order thinking skills problems

/pdf/teachers-knowledge-about-higher-order-thinking-skills-and-3tkpd496mz.pdf

Teachers' knowledge about higher-order thinking skills and its learning strategy

The study was to describe the implementation of Problem-Based Learning (PBL) toward the improvement of students’ Higher Order Thinking Skill (HOTS) and characters and to describe the obstacles that had been encountered within the implementation. The study was a mixed research that made use of concurrent mixed method design. The population in the study was the students from eight junior high schools that had been selected from six provinces in Indonesia namely the Yogyakarta Special Region, Bengkulu, South Borneo, West Nusa Tenggara, Southeast Sulawesi and Papua. There were 648 students who had been selected randomly from these schools. The researchers conducted the PBL process within the experimental classes and the expository learning process within the eight control classes. The data gathering process was conducted through the test, the self-assessment and the open questionnaire. The quantitative data analysis was conducted inferentially using multivariate and univariate analysis, while the qualitative data analysis was conducted descriptively. The results of the study showed that: (1) the implementation of PBL had been more effective in comparison to the expository one in terms improving the students’ HOTS; (2) the implementation of PBL had not been more effective in comparison to the expository one in terms of improving the students’ characters; and (3) in overall the obstacles that had been encountered within the implementation of PBL process were related to the teachers’ unpreparedness, the time allocation, the unequal students’ input, the students’ learning habits and the difficult assessment.

/pdf/implementing-the-problem-based-learning-in-order-to-improve-p6h0wd0bzu.pdf

Implementing the problem-based learning in order to improve the students’ HOTS and characters

Recently character education has been holding an important role for improving the human resources quality This study aims to describe the strategy, the implementation and the results of character education in senior and vocational high schools in four provinces within the Java Island, Indonesia The study was a phenomenology-type qualitative research The data collection utilized a questionnaire and in-depth interviews The participants in the study were 108 senior and vocational high school teachers from four provinces in Indonesia namely Yogyakarta Special Region, Central Java, West Java and Banten, Indonesia The data analysis was conducted by implementing the Creswell’s steps The results of the study showed that the strategy that the schools might implement in character education would be providing the character building facilities and designing good programs of character development The schools implemented character education by providing role models, intervention, consistent habituation, and reinforcement The results of the implementation yielded good results for the students’ character development The obstacles that the schools had within character education were the students’ heterogeneity, the society’s paradigm which considered that the focus of the schools should be the cognitive development and limited facilities

https://dergipark.org.tr/en/download/article-file/661109

Ezi Apino

Papers

Developing Instructional Design to Improve Mathematical Higher Order Thinking Skills of Students

The difficulties of high school students in solving higher-order thinking skills problems

Teachers' knowledge about higher-order thinking skills and its learning strategy

Implementing the problem-based learning in order to improve the students’ HOTS and characters

Strategy and Implementation of Character Education in Senior High Schools and Vocational High Schools