Search results for: mathematical knowledge for teaching

Authors: Murray Olowa

Abstract:

This article examines the studies investigating the Mathematical Knowledge for Teaching (MKT) of secondary preservice teachers in Papua New Guinea based on probabilities. This research was conducted due to the continuous issues faced in the country in both primary and secondary education, like changes in curriculum, emphasis on mathematics and science education, and a decline in mathematics performance. Moreover, the mathematics curriculum doesn’t capture Pedagogical Content Knowledge (PCK) or Subject Matter Knowledge (SMK). The two main domains that have been identified are SMK and PCK, which have been further sub-divided into Common Content Knowledge (CCK), Specialised Content Knowledge (SCK) and Horizon Content Knowledge (HCK), and Knowledge of Content and Students (KCS), Knowledge of Content and Teaching (KCT) and Knowledge of Content and Curriculum (KCC), respectively. The data collected from 15-_year-_ ones and 15-_year-_fours conducted at St Peter Chanel Secondary Teachers College revealed that there is no significant difference in subject matter knowledge between year one and year four since the P-value of 0.22>0.05. However, it was revealed that year fours have higher pedagogical content knowledge than year one since P-value was 0.007<0.05. Finally, the research has proven that year fours have higher MKT than year one. This difference occurred due to final year preservice teachers’ hard work and engagement in mathematics curriculum and teaching practice.

Keywords: mathematical knowledge for teaching, subject matter knowledge, pedagogical content knowledge, Papua New Guinea, preservice teachers, probability

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Authors: Gilbert Makanda, Roelf Sypkens

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A mathematical model for knowledge acquisition in teaching and learning is proposed. In this study we adopt the mathematical model that is normally used for disease modelling into teaching and learning. We derive mathematical conditions which facilitate knowledge acquisition. This study compares the effects of dropping out of the course at early stages with later stages of learning. The study also investigates effect of individual interaction and learning from other sources to facilitate learning. The study fits actual data to a general mathematical model using Matlab ODE45 and lsqnonlin to obtain a unique mathematical model that can be used to predict knowledge acquisition. The data used in this study was obtained from the tutorial test results for mathematics 2 students from the Central University of Technology, Free State, South Africa in the department of Mathematical and Physical Sciences. The study confirms already known results that increasing dropout rates and forgetting taught concepts reduce the population of knowledgeable students. Increasing teaching contacts and access to other learning materials facilitate knowledge acquisition. The effect of increasing dropout rates is more enhanced in the later stages of learning than earlier stages. The study opens up a new direction in further investigations in teaching and learning using differential equations.

Keywords: differential equations, knowledge acquisition, least squares nonlinear, dynamical systems

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Authors: Zafer F. Alshehri

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This paper investigated mathematics teachers' knowledge of the effective teaching strategies at the Southern Region of Saudi Arabia. Specifically, it aimed to identify a list of the effective strategies of teaching mathematics; the extent of mathematics teachers' knowledge of these strategies; and the differences (if any) of mathematics teachers' knowledge of these strategies regarding scientific degree, teaching experience, and educational sage. To achieve that, the researcher used the descriptive approach for preparing a list of effective mathematics teaching strategies and developing a questionnaire of a sample of (240) mathematics teachers. As a result, there were differences in teachers' knowledge of the effective teaching strategies, which ranked as a low, and the highest knowledge was in favor of higher degrees. In addition, there were a few recommendations and suggestions for developing mathematics teachers' knowledge of effective teaching strategies, such as involving in workshops of mathematics teaching strategies, integrating technology into mathematics teaching, and using research findings in the instruction process.

Keywords: mathematics teaching knowledge, mathematics teachers, effective mathematics teaching strategies

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Authors: Gilbert Makanda

Abstract:

The problem of the teaching of mathematics is studied using differential equations. A mathematical model for knowledge acquisition in mathematics is developed. In this study we adopt the mathematical model that is normally used for disease modelling in the teaching of mathematics. It is assumed that teaching is 'infecting' students with knowledge thereby spreading this knowledge to the students. It is also assumed that students who gain this knowledge spread it to other students making disease model appropriate to adopt for this problem. The results of this study show that increasing recruitment rates, learning contact with teachers and learning materials improves the number of knowledgeable students. High dropout rates and forgetting taught concepts also negatively affect the number of knowledgeable students. The developed model is then solved using Matlab ODE45 and \verb"lsqnonlin" to estimate parameters for the actual data.

Keywords: differential equations, knowledge acquisition, least squares, dynamical systems

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Authors: Odette Umugiraneza, Etienne Nzaramyimana

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Confidence and beliefs are the main contributors to the improvement of teachers’ mathematical knowledge. The objective of this study was to investigate teachers’ confidence and beliefs towards technology use in teaching mathematics subjects in the Musanze District. The data were collected using closed and open questions. These were distributed to 118 secondary school senior 1 to 6 mathematics teachers in Musanze district. The findings revealed that the teachers’ confidence about the use of technology in teaching mathematics needs improvement. Apart from confidence, almost a third of the teachers convoyed negative beliefs that technology plays great importance in promoting the understanding of mathematics. Teachers as knowledge transmitters are required to join various professional courses towards technology integration in the teaching of mathematics, to improve the effectiveness of teaching and learning.

Keywords: knowledge, technology, teachers’ confidence, beliefs, barriers of technology use

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Authors: R. M. Kashim

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The study investigates the conceptual and procedural knowledge of rational number in primary school teachers, specifically, the primary school teachers level of conceptual knowledge about rational number and the primary school teachers level of procedural knowledge about rational numbers. The study was carried out in Bauchi metropolis in Bauchi state of Nigeria. A Conceptual and Procedural Knowledge Test was used as the instrument for data collection, 54 mathematics teachers in Bauchi primary schools were involved in the study. The collections were analyzed using mean and standard deviation. The findings revealed that the primary school mathematics teachers in Bauchi metropolis posses a low level of conceptual knowledge of rational number and also possess a high level of Procedural knowledge of rational number. It is therefore recommended that to be effective, teachers teaching mathematics most posses a deep understanding of both conceptual and procedural knowledge. That way the most knowledgeable teachers in mathematics deliver highly effective rational number instructions. Teachers should not ignore the mathematical concept aspect of rational number teaching. This is because only the procedural aspect of Rational number is highlighted during instructions; this often leads to rote - learning of procedures without understanding the meanings. It is necessary for teachers to learn rational numbers teaching method that focus on both conceptual knowledge and procedural knowledge teaching.

Keywords: conceptual knowledge, primary school teachers, procedural knowledge, rational numbers

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Authors: Gholam Reza Parvizi, Ali Reza Kargar, Amir Arani

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In the present days, learning and teaching researchers have emphasized the role which teachers, tutors, and trainers’ constraint knowledge treat in resizing and trimming what they perform in educational atmosphere. Regarding English language as subject to teaching, although the prominence of instructor’s knowledge about grammar has also been stressed, but the lack of empirical insights into the relationship between teacher’ self-monitoring and self-response of grammar knowledge have been observed. With particular attention to the grammar this article indicates and discusses information obtained self- feedback and conversing teachers of a kind who backwash the issue. The result of the study indicates that enabling teachers to progress and maintain a logical and realistic awareness of their knowledge about grammar have to be prominent goal for teachers’ education and development programs.

Keywords: grammar knowledge, self-monitoring, self-response, teaching grammar, language teaching program

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Authors: Vojo George Fasinu, Nadaraj Govender, Predeep Kumar

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An Antenna, which remains the hub of technological development in Africa had been found to be a course that is been taught and designed in an abstract manner in some universities. One of the reasons attached to this is that the appropriate approach of teaching antenna design is not yet understood by many engineering academics in some universities in South Africa. Also, another problem reported is the main difficulty encountered when interpreting and applying some of the mathematical concepts learned into their practical antenna design course. As a result of this, some engineering experts classified antenna as a mysterious technology that could not be described by anybody using mathematical concepts. In view of this, this paper takes it as its point of departure in explaining what an antenna is all about with a strong emphasis on its mathematical modelling. It also argues that the place of modelling mathematical concepts into the teaching of engineering design cannot be overemphasized. Therefore, it explains the mathematical concepts adopted during the teaching of an antenna design course, the Strategies of modelling those mathematics concepts, the behavior of antennas, and their mathematics usage were equally discussed. More so, the paper also sheds more light on mathematical modelling in South Africa context, and also comparative analysis of mathematics concepts taught in mathematics class and mathematics concepts taught in engineering courses. This paper focuses on engineering academics teaching selected topics in electronic engineering (Antenna design), with special attention on the mathematical concepts they teach and how they teach them when teaching the course. A qualitative approach was adopted as a means of collecting data in order to report the naturalistic views of the engineering academics teaching Antenna design. The findings of the study confirmed that some mathematical concepts are being modeled into the teaching of an antenna design with the adoption of some teaching approaches. Furthermore, the paper reports a didactical-realistic mathematical model as a conceptual framework used by the researchers in describing how academics teach mathematical concepts during their teaching of antenna design. Finally, the paper concludes with the importance of mathematical modelling to the engineering academics and recommendations for further researchers.

Keywords: modelling, mathematical concepts, engineering, didactical, realistic model

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Authors: Hui Fang Huang Su, Jia Borror

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This study compared two interventions for teaching math to preschool-aged students with autism spectrum disorder (ASD). The first is considered the business as usual (BAU) intervention, which uses the Strategies for Teaching Based on Autism Research (STAR) curriculum and discrete trial teaching as the instructional methodology. The second is the Math is Not Difficult (Project MIND) activity-embedded, naturalistic intervention. These interventions were randomly assigned to four preschool students with ASD classrooms and implemented over three months for Project Mind. We used measurement gained during the same three months for the STAR intervention. In addition, we used A quasi-experimental, pre-test/post-test design to compare the effectiveness of these two interventions in building mathematical knowledge and skills. The pre-post measures include three standardized instruments: the Test of Early Math Ability-3, the Problem Solving and Calculation subtests of the Woodcock-Johnson Test of Achievement IV, and the Bracken Test of Basic Concepts-3 Receptive. The STAR curriculum-based assessment is administered to all Baudhuin students three times per year, and we used the results in this study. We anticipated that implementing these two approaches would improve the mathematical knowledge and skills of children with ASD. Still, it is crucial to see whether a behavioral or naturalistic teaching approach leads to more significant results.

Keywords: early learning, autism, math for pre-schoolers, special education, teaching strategies

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Authors: Shahlan Surat, Saemah Rahman, Saadiah Kummin

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When teachers reflect and evaluate whether their teaching methods actually have an impact on students’ learning, they will adjust their practices accordingly. This inevitably improves their students’ learning and performance. The approach in meta-teaching can invigorate and create a passion for teaching. It thus helps to increase the commitment and love for the teaching profession. This study was conducted to determine the level of metacognitive thinking of teachers in the process of teaching and learning in the classroom. Metacognitive thinking teachers include the use of metacognitive knowledge which consists of different types of knowledge: declarative, procedural and conditional. The ability of the teachers to plan, monitor and evaluate the teaching process can also be determined. This study was conducted on 377 graduate teachers in Klang Valley, Malaysia. The stratified sampling method was selected for the purpose of this study. The metacognitive teaching inventory consisting of 24 items is called InKePMG (Teacher Indicators of Effectiveness Meta-Teaching). The results showed the level of mean is high for two components of metacognitive knowledge; declarative knowledge (mean = 4.16) and conditional (mean = 4.11) whereas, the mean of procedural knowledge is 4.00 (moderately high). Similarly, the level of knowledge in monitoring (mean = 4.11), evaluating (mean = 4.00) which indicate high score and planning (mean = 4.00) are moderately high score among teachers. In conclusion, this study shows that the planning and procedural knowledge is an important element in improving the quality of teachers teaching in the classroom. Thus, the researcher recommended that further studies should focus on training programs for teachers on metacognitive skills and also on developing creative thinking among teachers.

Keywords: metacognitive thinking skills, procedural knowledge, conditional knowledge, meta-teaching and regulation of cognitive

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Authors: Yang Zhuo

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This study explores the integration of MIDI technology as one of the important digital technologies in music teaching, from the perspective of teaching practice, into the process of cultivating students' teaching skills. At the same time, the framework elements of the learning environment for music education students are divided into four aspects: digital technology supported learning space, new knowledge learning, teaching methods, and teaching evaluation. In teaching activities, more attention should be paid to students' subjectivity and interaction between them so as to enhance their emotional experience in teaching practice simulation. In the process of independent exploration and cooperative interaction, problems should be discovered and solved, and basic knowledge of music and teaching methods should be exercised in practice.

Keywords: music education, educational technology, MIDI, teacher training

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Authors: Mihir Halder

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The main aim and objective of the eighteen-month long Diploma in Primary Education (DPED) teacher education training course for in-service primary teachers in Bangladesh is to acquire professional knowledge as well as make them proficient in professional practice. The training, therefore, introduces a variety of theoretical and practical approaches as well as some professional development activities—lesson study being one of them. But, in the field of mathematics teaching, even after implementing the lesson study method, the desired practical teaching skills of the teachers have not been developed. In addition, elementary students also remain quite raw in mathematics. Although there have been various studies to solve the problem, the need for the teachers' views on mathematical ideas has not been taken into consideration. The researcher conducted the research to find out the cause of the discussed problem. In this case, two teams of nine DPED trainee teachers and two instructors conducted two lesson studies in two schools located in the city and town of Khulna Province, Bangladesh. The researcher observed group lesson planning by trainee teachers, followed by a trainee teacher teaching the planned lesson plan to an actual mathematics classroom, and finally, post-teaching reflective discussion in each lesson study. Two DPED instructors acted as mentors in the lesson study. DPED trainee teachers and instructors were asked about mathematical concepts and classroom practices through questionnaires as well as videotaped mathematics classroom teaching. For this study, the DPED mathematics course, curriculum, and assessment activities were analyzed. In addition, the mathematics lesson plans prepared by the trainee teachers for the lesson study and their pre-teaching and post-teaching reflective discussions were analyzed by some analysis categories and rubrics. As a result, it was found that the trainee teachers' views of mathematics are not mature, and therefore, their mathematics teaching practice is not appropriate. Therefore, in order to improve teachers' mathematics teaching, the researcher recommended including some action-oriented aspects in each phase of mathematics lesson study in DPED—for example, emphasizing mathematics concepts of the trainee teachers, preparing appropriate teaching materials, presenting lessons using the problem-solving method, using revised rubrics for assessing mathematics lesson study, etc.

Keywords: mathematics lesson study, knowledge of mathematics, knowledge of teaching mathematics, teachers' views

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Authors: Chinfen Chen

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This paper aims to focus on the challenges and doubts encountered in the implementation of ‘bilingual teaching in some fields of courses’, and propose implementation principles and strategies from the four areas of curriculum design, teaching strategies, teaching language application, and bilingual teaching implementation and operation, as a school The administrative team considers when planning bilingual teaching and also clarifies teachers' doubts about the implementation of bilingual teaching to enhance their willingness and confidence to participate in bilingual teaching.

Keywords: bilingual education policy, language immersion, partial bilingual education, content knowledge and target language acquisition, inquiry-based teaching.

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Authors: Felicitas Pielsticker, Christoph Pielsticker, Ingo Witzke

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Neurological findings provide foundational results for many different disciplines. In this article we want to discuss these with a special focus on mathematics education. The intention is to make neuroscience research useful for the description of cognitive mathematical learning processes. A key issue of mathematics education is that students often behave as if their mathematical knowledge is constructed in isolated compartments with respect to the specific context of the original learning situation; supporting students to link these compartments to form a coherent mathematical society of mind is a fundamental task not only for mathematics teachers. This aspect goes hand in hand with the question if there is such a thing as abstract general mathematical knowledge detached from concrete reality. Educational Neuroscience may give answers to the question why students develop their mathematical knowledge in isolated subjective domains of experience and if it is generally possible to think in abstract terms. To address these questions, we will provide examples from different fields of mathematics education e.g. students’ development and understanding of the general concept of variables or the mathematical notion of universal proofs. We want to discuss these aspects in the reflection of functional studies which elucidate the role of specific brain regions in mathematical learning processes. In doing this the paper addresses concept formation processes of students in the mathematics classroom and how to support them adequately considering the results of (educational) neuroscience.

Keywords: brain regions, concept formation processes in mathematics education, proofs, teaching-learning processes

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Authors: Didiosky Benítez-Erice, Frederik Questier, Dalgys Pérez-Luján

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This paper aims to present two models around the production of students’ experiential knowledge in the teaching-learning process of higher education: the teacher-centered production model and the student-centered production model. From a range of knowledge management and experiential learning theories, the paper elaborates into the nature of students’ experiential knowledge and proposes further adjustments of existing second-generation knowledge management theories taking into account the particularities of higher education. Despite its theoretical nature the paper can be relevant for future studies that stress student-driven improvement and innovation at higher education institutions.

Keywords: experiential knowledge, higher education, knowledge management, teaching-learning process

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Authors: Hari Sharan Pandit

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Mathematics teaching in Nepal has been centralized and guided by the notion of transfer of knowledge and skills from teachers to students. The overemphasis on the ‘algorithm-centric’ approach to mathematics teaching and the focus on ‘role–learning’ as the ultimate way of solving mathematical problems since the early years of schooling have been creating severe problems in school-level mathematics in Nepal. In this context, the author argues that students should learn real-world mathematical problems through various interesting, creative and collaborative, as well as artistic and alternative ways of knowing. The collaboration-incorporated pedagogy is a distinct pedagogical approach that offers a better alternative as an integrated and interdisciplinary approach to learning that encourages students to think more broadly and critically about real-world problems. The paper, as a summarized report of action research designed, developed and implemented by the author, focuses on the needs and usefulness of collaboration-incorporated pedagogy in the Nepali context to make mathematics teaching more meaningful for producing creative and critical citizens. This paper is useful for mathematics teachers, teacher educators and researchers who argue on arts integration in mathematics teaching.

Keywords: peer teaching, metacognitive approach, mitigating, action research

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Authors: Henriette van Rensburg, Betty Adcock

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Concern about the lack of knowledge of quality teaching and teacher retention in rural and remote areas of Australia, has caused academics to improve pre-service teachers’ understanding of this problem. The participants in this study were forty students enrolled in an undergraduate educational course (EDO3341 Teaching in rural and remote communities) at the University of Southern Queensland in Toowoomba in 2012. This study involved an innovative case-based teaching approach in order to broaden their generally under-informed understanding of teaching in a rural and remote area. Three themes have been identified through analysing students’ critical reflections: learning expertise, case-based learning support and authentic learning. The outcomes identified the changes in pre-service teachers’ understanding after they have deepened their knowledge of the realities of teaching in rural and remote areas.

Keywords: rural and remote education, case based teaching, innovative education approach, higher education

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Authors: Hari Sharan Pandit

Abstract:

Mathematics teaching in Nepal has been centralized and guided by the notion of transfer of knowledge and skills from teachers to students. The overemphasis on an algorithm-centric approach of mathematics teaching and the focus on ‘rote–learning’ as the ultimate way of solving mathematical problems since the early years of schooling have been creating severe problems in school-level mathematics in Nepal. In this context, the author argues that students should learn real-world mathematical problems through various interesting, creative and collaborative, as well as artistic and alternative ways of knowing. The collaboration-incorporated pedagogy is an distinct pedagogical approach that offers a better alternative as an integrated and interdisciplinary approach to learning that encourages students to think more broadly and critically about real-world problems. The paper, as a summarized report of action research designed, developed and implemented by the author, focuses on the needs and usefulness of collaboration-incorporated pedagogy in the Nepali context to make mathematics teaching more meaningful for producing creative and critical citizens. This paper is useful for mathematics teachers, teacher educators and researchers who argue on arts integration in mathematics teaching.

Keywords: algorithm-centric, rote-learning, collaboration - incorporated pedagogy, action research

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Authors: Xiao Liulingzi

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It is important for using multi-sensory teaching in music learning. This article aims to provide knowledge in multi-sensory learning and teaching music in primary school. For primary school students, in addition to the training of basic knowledge and skills of music, students' sense of participation and creativity in music class are the key requirements, especially the flexibility and dynamics in music class, so that students can integrate into music and feel the music. The article explains the multi-sensory sense in music learning, the differences between multi-sensory music teaching and traditional music teaching, and music multi-sensory teaching in primary schools in China.

Keywords: multi-sensory, teaching practice, primary music classroom, China

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Authors: Sajjad Ali

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The Quranic pedagogical methods don't imply that the Quran explicitly prescribes teaching methods. Instead, it acknowledges the inherent ways of learning and teaching that align with human nature, offering guidance in this direction. Qur'an briefly describes different angles of acquiring knowledge. Narrative, interrogative, question, analytical, poetic, comparative and critical methods of teaching are briefly described in the Holy Quran. The Muslim Ummah has a firm belief that the Qur'an is a comprehensive book which mentions every dry and wet, but this does not mean that the Qur'an is a manual book. This means that the Qur'an contains symbols and hints about everything. The fact that everything is mentioned in the Qur'an means that the Qur'an only provides guidance, while its interpretation requires contemplation.

Keywords: hadith, knowledge, reality, understanding

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Authors: Abubakar Sa’adatu Mohammed

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This paper reports on a study of problem solving differences between expert and novice Problem solvers for effective physics teaching. Significant differences were found both at the conceptual level and at the level of critical thinking, creative thinking and reasoning. It is suggested for a successful solution of a problem, conceptual knowledge alone may not be sufficient. There is the need of the knowledge of how the conceptual knowledge should be applied (problem solving skills). It is hoped that this research might contribute to efforts of exploring ways for students to acquire a powerful conceptual toolkit based on experts like problem solvers approach for effective teaching delivery.

Keywords: conceptual knowledge, procedural knowledge, critical thinking, creative thinking, reasoning ability

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Authors: Hong Zeng

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In the process of popularization of higher education, it is necessary to innovate teaching methods in order to make the students cultivated suitable for the needs of social development. This paper discusses the limitations and shortcomings of the traditional teaching method of teaching approach to a person's aptitude, personality, and interest and introduces the new teaching method of teaching approach to a person's personality. The teaching approach to a person's personality is a target teaching method that aims to develop students' potential and cultivate professional talents. Therefore, teachers should be professional and can adopt modern teaching methods from the Internet so that students can clearly understand the course and the knowledge structure. Finally, the students using new teaching methods can enhance their motivation to study and quickly acquire professional skills.

Keywords: higher education, personality, target education, student-centered

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Authors: Davoud Ansari Kejal, Meysam Sabour

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For long, there has been a belief that a reader can easily comprehend a text if he is strong enough in vocabulary and grammatical knowledge but there was no account for the ability of understanding different subjects based on readers’ understanding of the surrounding world which is called world background knowledge. This paper attempts to investigate the reading comprehension process applying the schema theory as an influential factor in comprehending texts, in order to prove the important role of background knowledge in reading comprehension. Based on the discussion, some teaching methods are suggested for employing world background knowledge for an elaborated teaching of reading comprehension in an active learning environment in EFL classes.

Keywords: background knowledge, reading comprehension, schema theory, ELT classes

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Authors: Eulalia Torras, Andreu Bellot

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To know whether students’ achievements are the result of online interaction and not just a consequence of individual differences themselves, it seems essential to link the teaching presence and social presence to the types of knowledge built. The research aim is to analyze the social presence in relation to two types of knowledge, declarative and procedural. Qualitative methodology has been used. The analysis of the contents was based on an observation protocol that included community of enquiry indicators and procedural and declarative knowledge indicators. The research has been conducted in three phases that focused on an observational protocol and indicators, results and conclusions. Results show that the teaching-learning processes have been characterized by the patterns of presence and types of knowledge. Results also show the importance of social presence support provided by the teacher and the students, not only in regard to the nature of the instructional support but also concerning how it is presented to the student and the importance that is attributed to it in the teaching-learning process, that is, what it is that assistance is offered on. In this study, we find that the presence based on procedural guidelines and declarative reflection, the management of shared meaning on the basis of the skills and the evidence of these skills entail patterns of learning. Nevertheless, the importance that the teacher attributes to each support aspect has a bearing on the extent to which the students reflect more on the given task.

Keywords: education, online, teaching and learning processes, knowledge

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Authors: Li Shuang

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With rigid teaching procedures and limited academic performance assessment methods, traditional teaching model stands in the way of college English reform in China, which features EAP (English for Academic Purpose) teaching. Flipped-classroom teaching, which has been extensively applied to science subjects teaching, however, covers the shortage of traditional teaching model in EAP teaching, via creatively inverting traditional teaching procedures. Besides, the application of flipped-classroom teaching model in EAP teaching also proves that this new teaching philosophy is not confined to science subjects teaching; it goes perfectly well with liberal-arts subjects teaching. Data analysis, desk research survey, and comparative study are referred to in the essay so as to prove its feasibility and advantages in EAP teaching.

Keywords: EAP, traditional teaching method, flipped-classroom teaching model, teaching model design

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Authors: Elaosi Vhurumuku

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During the past twenty years, there has been an increased interest by science educators in researching and developing teachers’ pedagogical content knowledge for teaching the nature of science (PCKNOS). While there has been this surge in interest in the idea of PCKNOS, there has not been a common understanding among NOS researchers as to how exactly the PCKNOS concept should be construed. In this paper, we analyse and evaluate published accredited journal articles on PCKNOS research. We also draw from our teaching experiences. The major points of foci are the researchers’ presentations of SMKNOS and their centres of attention regarding the elements of PCKNOS. Our content, cluster analysis, and evaluation of the studies on PCKNOS reveal that most researchers have presented SMKNOS in the form of a heuristic or a set of heuristics (targeted NOS ideas) to be mastered by teachers or learners. Furthermore, we found that most of the researchers’ attention has been on developing and recommending teacher pedagogical practices for teaching NOS. From this, we synthesize and propose a subject knowledge content structure and a pedagogical approach that we believe is relevant and appropriate for secondary school and science teacher education if the goal of science education for scientific literacy is to be achieved. The justification of our arguments is rooted in tracing and unpacking the origins and meaning of pedagogical content knowledge (PCK). From our analysis, synthesis, and evaluation, as well as teaching experiences, we distil and construct a meaning for the PCKNOS construct.

Keywords: pedagogical content knowledge, teaching, nature of science, construct, subject matter knowledge

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Authors: Dammar Bahadur Adhikari

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Mathematics teaching begins with human civilization. The rular used to choose mathematician as prime adviser in many tribes and country. Mathematics was powerful tool for understanding economial situation and strength of rular. In ancient Nepal teaching of mathematics starts with informal education provided by religious leaders there after in modern education system seems to follow the world’s educational system. The aim of this paper is to present a brief historical background of the Nepalese mathematicians up to nineteenth century and highlight the transformation in mathematical science in the line with modern world. Secondary data and formal papers and informal publications were studied to explore the present situation of education. The study concluded that there is remarcable change in quality of education and there are sufficient human powers in the mathematical sciences in Nepal.

Keywords: human development, mathematics, Nepal, science, traditional

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Authors: Selahattin Gultekin

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Today, in engineering departments, mathematics courses such as calculus, linear algebra and differential equations are generally taught by mathematicians. Therefore, during mathematicians’ classroom teaching there are few or no applications of the concepts to real world problems at all. Most of the times, students do not know whether the concepts or rules taught in these courses will be used extensively in their majors or not. This situation holds true of for all engineering and science disciplines. The general trend toward these mathematic courses is not good. The real-life application of mathematics will be appreciated by students when mathematical modeling of real-world problems are tackled. So, students do not like abstract mathematics, rather they prefer a solid application of the concepts to our daily life problems. The author highly recommends that mathematical modeling is to be taught starting in high schools all over the world In this paper, some mathematical concepts such as limit, derivative, integral, Taylor Series, differential equations and mean-value-theorem are chosen and their applications with graphical representations to real problems are emphasized.

Keywords: applied mathematics, engineering mathematics, mathematical concepts, mathematical modeling

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Authors: Nigel P. Coutts, Stellina Z. Sim

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Research suggests that the pedagogy we utilize when teaching mathematics contributes to a negative attitude towards the discipline. Worried by this, we have explored teaching mathematics for understanding, fluency, and confidence. We investigated strategies to engage students with the beauty of mathematics, moving them beyond mimicry and memorization. The result is an integrated pedagogy and curriculum arrangement which combines concept-based mathematics with Number Talks, Visible Thinking Routines, and Teaching for Understanding. Our qualitative research shows that students self-report greater self-confidence and heightened engagement with mathematical thinking. Teacher reflections on student learning echo this finding. As a result of this, we advocate for teacher training in the implementation of a concept-based curriculum supplemented with Number Talk strategies.

Keywords: mathematical thinking, teaching for understanding, student confidence, concept-based learning, engagement

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Authors: B. I. Zhumagaliyev, L. Sh. Balgabayeva, G. S. Nabiyeva, B. A. Tulegenova, P. Oralkhan, B. S. Kalenova, S. S. Akhmetov

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The article describes an approach to build competence in research of Bachelor and Master, which is now an important feature of modern specialist in the field of engineering. Provides an example of methodical teaching methods with the research aspect, is including the formulation of the problem, the method of conducting experiments, analysis of the results. Implementation of methods allows the student to better consolidate their knowledge and skills at the same time to get research. Knowledge on the part of the media requires some training in the subject area and teaching methods.

Keywords: professional competence, model of it-specialties, teaching methods, educational technology, decision making

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