Holistic Approach to Teaching Mathematics in Secondary School as a Means of Improving Students’ Comprehension of Study Material

Creating favourable conditions for students’ comprehension of mathematical content is one of the primary problems in teaching mathematics in secondary school. The fact of comprehension includes the ability to build a working situational model and thus becomes an important means of solving mathematical problems. This paper describes a holistic approach to teaching mathematics designed to address the primary challenges of such teaching; specifically, the challenge of students’ comprehension. Essentially, this approach consists of (1) establishing links between the attributes of the notion: the sense, the meaning, and the term; (2) taking into account the components of student’s subjective experience—value-based emotions, contextual, procedural and communicative—during the educational process; (3) linking together different ways to present mathematical information; (4) identifying and leveraging the relationships between real, perceptual and conceptual (scientific) mathematical spaces by applying real-life situational modelling. The article describes approaches to the practical use of these foundational concepts. Identifying how proposed methods and techniques influence understanding of material used in teaching mathematics was the primary goal. The study included an experiment in which 256 secondary school students took part: 142 in the study group and 114 in the control group. All students in these groups had similar levels of achievement in math and studied math under the same curriculum. In the course of the experiment, comprehension of two topics — “Derivative” and “Trigonometric functions”—was evaluated. Control group participants were taught using traditional methods. Students in the study group were taught using the holistic method: under teacher’s guidance, they carried out assignments designed to establish linkages between notion’s characteristics, to convert information from one mode of presentation to another, as well as assignments that required the ability to operate with all modes of presentation. Identification, accounting for and transformation of subjective experience were associated with methods of stimulating the emotional value component of the studied mathematical content (discussions of lesson titles, assignments aimed to create study dominants, performing theme-related physical exercise ...) The use of techniques that forms inter-subject notions based on linkages between, perceptual real and mathematical conceptual spaces proved to be of special interest to the students. Results of the experiment were analysed by presenting students in each of the groups with a final test in each of the studied topics. The test included assignments that required building real situational models. Statistical analysis was used to aggregate test results. Pierson criterion x2 was used to reveal statistics significance of results (pass-fail the modelling test). Significant difference of results was revealed (p < 0.001), which allowed to conclude that students in the study group showed better comprehension of mathematical information than those in the control group. The total number of completed assignments of each student was analysed as well, with average results calculated for each group. Statistical significance of result differences against the quantitative criterion (number of completed assignments) was determined using Student’s t-test, which showed that students in the study group completed significantly more assignments than those in the control group (p = 0.0001). Authors thus come to the conclusion that suggested increase in the level of comprehension of study material took place as a result of applying implemented methods and techniques.

A Case Study on Vocational Teachers’ Perceptions on Their Linguistically and Culturally Responsive Teaching

In Finland the transformation from homogenous culture into multicultural one as a result of heavy immigration has been rapid in the recent decades. As multilingualism and multiculturalism are growing features in our society, teachers in all educational levels need to be competent for encounters with students from diverse cultural backgrounds. Consequently, also the number of multicultural and multilingual vocational school students has increased which has not been taken into consideration in teacher education enough. To bridge this gap between teachers’ competences and the requirements of the contemporary school world, Finnish Ministry of Culture and Education established the DivEd-project. The aim of the project is to prepare all teachers to work in the linguistically and culturally diverse world they live in, to develop and increase culturally sustaining and linguistically responsive pedagogy in Finland, increase awareness among Teacher Educators working with preservice teachers and to increase awareness and provide specific strategies to in-service teachers. The partners in the nationwide project are 6 universities and 2 universities of applied sciences. In this research, the linguistically and culturally sustainable teaching practices developed within the DivEd-project are tested in practice. This research aims to explore vocational teachers’ perceptions of these multilingualism and multilingual educational practices. The participants of this study are vocational teachers in of different fields. The data were collected by individual, face-to-face interviews. The data analysis was conducted through content analysis. The findings indicate that the vocational teachers experience that they lack knowledge on linguistically and culturally responsive pedagogy. Moreover, they regard themselves in some extent incompetent in incorporating multilingually and multiculturally sustainable pedagogy in everyday teaching work. Therefore, they feel they need more training pertaining multicultural and multilingual knowledge, competences and suitable pedagogical methods for teaching students from diverse linguistic and cultural backgrounds.

Educational Path for Pedagogical Skills: A Football School Experience

The current pedagogical culture recognizes an educational scope within the sports practices. It is widely accepted, in the pedagogical culture, that thanks to the acquisition and development of motor skills, it is also possible to exercise abilities that concern the way of facing and managing the difficulties of everyday life. Sport is a peculiar educational environment: the children have the opportunity to discover the possibilities of their body, to correlate with their peers, and to learn how to manage the rules and the relationship with authorities, such as coaches. Educational aspects of the sport concern both non-formal and formal educational environments. Coaches play a critical role in an agonistic sphere: exactly like the competencies developed by the children, coaches have to work on their skills to properly set up the educational scene. Facing these new educational tasks - which are not new per se, but new because they are brought back to awareness - a few questions arise: does the coach have adequate preparation? Is the training of the coach in this specific area appropriate? This contribution aims to explore the issue in depth by focusing on the reality of the Football School. Starting from a possible sense of pedagogical inadequacy detected during a series of meetings with several football clubs in Piedmont (Italy), there have been highlighted some important educational needs within the professional training of sports coaches. It is indeed necessary for the coach to know the processes underlying the educational relationship in order to better understand the centrality of the assessment during the educational intervention and to be able to manage the asymmetry in the coach-athlete relationship. In order to provide a response to these pedagogical needs, a formative plan has been designed to allow both an in-depth study of educational issues and a correct self-evaluation of certain pedagogical skills’ control levels, led by the coach. This plan has been based on particular practices, the Educational Practices of Pre-test (EPP), a specific version of community practices designed for the extracurricular activities. The above-mentioned practices realized through the use of texts meant as pre-tests, promoted a reflection within the group of coaches: they set up real and plausible sports experiences - in particular football, triggering a reflection about the relationship’s object, spaces, and methods. The characteristic aspect of pre-tests is that it is impossible to anticipate the reflection as it is necessarily connected to the personal experience and sensitivity, requiring a strong interest and involvement by participants: situations must be considered by the coaches as possible settings in which they could be found on the field.

An Epidemiological Study on an Outbreak of Gastroenteritis Linked to Dinner Served at a Senior High School in Accra

Background: An outbreak of gastroenteritis occurred in December 2019 after students of a Senior High School in Accra were served with kenkey and fish during their dinner. An investigation was conducted to characterize the affected people, the source of contamination, the etiologic food and agent. Methods: An epidemiological study was conducted with cases selected from the student population who were ill. Controls were selected from among students who also ate from the school canteen during dinner but were not ill. Food history of each case and control was taken to assess their exposure status. Epi Info 7 was used to analyze the data obtained from the outbreak. Attack rates and odds ratios were calculated to determine the risk of foodborne infection for each of the foods consumed by the population. The source of contamination of the foods was ascertained by conducting an environmental risk assessment at the school. Results: Data were obtained from 126 students, out of which 57 (45.2%) were cases and 69 (54.8%) were controls. The cases presented with symptoms such as diarrhea (85.96%), abdominal cramps (66.67%), vomiting (50.88%), headache (21.05%), fever (17.86%) and nausea (3.51%). The peak incubation period was 18 hours with a minimum and maximum incubation periods of 6 and 50 hours respectively. From the incubation period, duration of illness and the symptoms, non-typhoidal salmonellosis was suspected. Multivariate analysis indicated that the illness was associated with the consumption of the fried fish served, however this was statistically insignificant (AOR 3.1.00, P = 0.159). No stool, blood or food samples were available for organism isolation and confirmation of suspected etiologic agent. The environmental risk assessment indicated poor hand washing practices on the part of both the food handlers and students. Conclusion: The outbreak could probably be due to the consumption of the fried fish that might have been contaminated with Salmonella sp. as a result of poor hand washing practices in the school.

Blended Learning through Google Classroom

This paper discusses that good learning involves all academic groups in the school. Blended learning is learning outside the classroom. Google Classroom is a free service learning app for schools, non-profit organizations and anyone with a personal Google account. Facilities accessed through computers and mobile phones are very useful for school teachers and students. Blended learning classrooms using both traditional and technology-based methods for teaching have become the norm for many educators. Using Google Classroom gives students access to online learning. Even if the teacher is not in the classroom, the teacher can provide learning. This is the supervision of the form of the teacher when the student is outside the school.

School and Teacher Level Predictors for Students’ Information Literacy in Chinese Rural and Urban Education

This study aimed to investigate the level of secondary school students’ information literacy in China and examine the contribution of school and teacher level factors on students’ information literacy between rural and urban schools. A total of 598 schools, 56415 students and 18286 teachers participated in this study. The findings of this study were as follows: (1) the overall of secondary schools students’ information literacy only reached an average level and urban school students’ information literacy were significantly higher than that of rural school students; (2) In rural schools, teachers’ ICT collaboration was a positive predictor for students’ information literacy, while teachers’ ICT use for learning was identified as a negative predictor of students’ information literacy; (3) In urban schools, ICT management, ICT operation and teachers’ ICT self-efficacy were found to be significantly associated with students’ information literacy. Based on the findings, suggestions for improving students’ information literacy between rural and urban schools were discussed.

Quebec Elementary Pre-service Teachers’ Conceptual Representations about Heat and Temperature

This article identifies the conceptual representations of 128 students enrolled in elementary pre-service teachers’ education in the Province of Quebec, Canada (ages 19-24). To construct their conceptual representations relatively to notions of heat and temperature, we use a qualitative research approach. For that, we distributed them a questionnaire including four questions. The result demonstrates that these students tend to view the temperature as a measure of the hotness of an object or person. They also related the sensation of cold (or warm) to the difference in temperature, and for their majority, the physical change of the matter does not require a constant temperature. These representations are inaccurate relatively to the scientific views, and we will see that they are relevant to the design of teaching strategies based on conceptual conflict.

Motivational Orientation of the Methodical System of Teaching Mathematics in Secondary Schools

The article analyses the composition and structure of the motivationally oriented methodological system of teaching mathematics (purpose, content, methods, forms, and means of teaching), viewed through the prism of the student as the subject of the learning process. Particular attention is paid to the problem of methods of teaching mathematics, which are represented in the form of an ordered triad of attributes corresponding to the selected characteristics. A systematic analysis of possible options and their methodological interpretation enriched existing ideas about known methods and technologies of training, and significantly expanded their nomenclature by including previously unstudied combinations of characteristics. In addition, examples outlined in this article illustrate the possibilities of enhancing the motivational capacity of a particular method or technology in the real learning practice of teaching mathematics through more free goal-setting and varying the conditions of the problem situations. The authors recommend the implementation of different strategies according to their characteristics in teaching and learning mathematics in secondary schools.

Developing Proof Demonstration Skills in Teaching Mathematics in the Secondary School

The article describes the theoretical concept of teaching secondary school students proof demonstration skills in mathematics. It describes in detail different levels of mastery of the concept of proof-which correspond to Piaget’s idea of there being three distinct and progressively more complex stages in the development of human reflection. Lessons for each level contain a specific combination of the visual-figurative components and deductive reasoning. It is vital at the transition point between levels to carefully and rigorously recalibrate teaching to reflect the development of more complex reflective understanding. This can apply even within the same age range, since students will develop at different speeds and to different potential. The authors argue that this requires an aware and adaptive approach to lessons to reflect this complexity and variation. The authors also contend that effective teaching which enables students to properly understand the implementation of proof arguments must develop specific competences. These are: understanding of the importance of completeness and generality in making a valid argument; being task focused; having an internalised locus of control and being flexible in approach and evaluation. These criteria must be correlated with the systematic application of corresponding methodologies which are best likely to achieve success. The particular pedagogical decisions which are made to deliver this objective are illustrated by concrete examples from the existing secondary school mathematics courses. The proposed theoretical concept formed the basis of the development of methodological materials which have been tested in 47 secondary schools.

Pupils´ Questions at School Attendance Beginning and Teachers´ Teaching Strategy

Pupils´ inquisitiveness at the beginning of their school attendance is reflected by characteristics of the questions they ask. Clearly most of the classroom communication sequences are initiated by the teacher. But the teaching process also includes questions initiated by pupils in the need to satisfy their need for knowledge. The purpose of our research is to present the results of our pre-research strategy of occurrence of pupil-initiated questions in math lessons at the lower elementary school level, and to reveal the extent to which they are influenced by the teacher´s teaching strategy. We used the research methods of direct and indirect observations of fifth year classes in primary school. We focused on questions asked by the pupils in their math lessons. Our research sample for the pre-research observation method was a collection of video recordings available online. We used them for analysing the nature of pupils´ questions identified there. On the basis of the analysis, we hereby present the results concerning the nature of pupils´ questions asked in math lessons on the lower elementary school level. The interpretation of the collected results will be the starting point for the selection of research strategies in the next research stages concerning pupils’ questions in the future.

A Conversation about Inclusive Education: Revelations from Namibian Primary School Teachers

Inclusive education stems from a philosophy and vision, which argues that all children should learn together at school. It is not only about treating all pupils in the same way. It is also about allowing all children to attend school without any restrictions. Ten primary school teachers in a circuit in Namibia volunteered to participate in face-to-face interviews about inclusive education. The teachers responded to three questions about their (i) understanding of inclusive education; (ii) whether inclusive education was implemented in primary schools; and (iii) whether they were able to work with learners with special needs. Findings indicated that teachers understood what inclusive education entailed; felt that inclusive education was not implemented in their primary schools, and they were unable to work with learners with special needs in their classrooms. Further, the teachers identified training and resources as important components of inclusive education. It is recommended that education authorities should perhaps verify the findings reported here as well as ensure that the concerns raised by the teachers are addressed.

Causes and Implications of Obesity in Urban School Going Children

Obesity is an abnormal physical condition where an increased and undesirable fat accumulates in the human body. Obesity is an international phenomenon. In the present study, 12 schools were randomly selected from each district considering the areas i.e. Elite Private Schools in the private sector, Government schools in urban areas and Government schools in rural areas. Interviews were conducted with male students studying in grade 5 to grade 9 in each school. The sample size was 600 students; 300 from Faisalabad district and 300 from Rawalpindi district in Pakistan. A well-structured and pre-tested questionnaire was used for data collection. The calibrated scales were used to attain the heights and weights of the respondents. Obesity of school-going children depends on family types, family size, family history, junk food consumption, mother’s education, weekly time spent in walking, and sports facility at school levels. Academic performance, physical health and psychological health of school going children are affected with obesity. Concrete steps and policies could minimize the incidence of obesity in children in Pakistan.

Urban and Rural Children’s Knowledge on Biodiversity in Bizkaia: Tree Identification Skills and Animal and Plant Listing

Biodiversity provides humans with a great range of ecosystemic services; it is therefore an indispensable resource and a legacy to coming generations. However, in the last decades, the increasing exploitation of the Planet has caused a great loss of biodiversity and its acquaintance has decreased remarkably; especially in urbanized areas, due to the decreasing attachment of humans to nature. Yet, the Primary Education curriculum primes the identification of flora and fauna to guarantee the knowledge of children on their surroundings, so that they care for the environment as well as for themselves. In order to produce effective didactic material that meets the needs of both teachers and pupils, it is fundamental to diagnose the current situation. In the present work, the knowledge on biodiversity of 3rd cycle Primary Education students in Biscay (n=98) and its relation to the size of the town/city of their school is discussed. Two tests have been used with such aim: one for tree identification and the other one so that the students enumerated the species of trees and animals they knew. Results reveal that knowledge of students on tree identification is scarce regardless the size of the city/town and of their school. On the other hand, animal species are better known than tree species.

Tolerance and Perspective towards Disability: A Mixed Methods Study

Society has a lot of diversities according to sex, age, religion, abilities or disabilities, education, etc. According to differences, everybody needs to be tolerated and equally included in society. In order to provide quality inclusion, society needs to tolerate differences. This study relates to the differences in disability. To examine tolerance towards disability and inclusion, this study was conducted with students attending regular elementary and high school. The main goal was to examine their attitudes towards their classmates and elderly people with disabilities. The study begins with the hypothesis that the environment has a highly developed tolerance towards people with disabilities, regardless of age. The sample was divided according to tasks and methodology analysis. Students attending regular elementary school were asked to make drawings of their classmates with disabilities. The drawings were analyzed using quantitative methodology according to the colors children used and the position of character on the paper. Students attending high school and members of general population were asked to complete a questionnaire designed for this study during a workshop held on the International Day for Tolerance. Responses were analyzed using qualitative methodology. The hypothesis was confirmed.

The Effect of Cross-Curriculum of L1 and L2 on Elementary School Students’ Linguistic Proficiency: To Sympathize with Others

This paper reports on a project to integrate Japanese (as a first language) and English (as a second language) education. This study focuses on the mutual effects of the two languages on the linguistic proficiency of elementary school students. The research team consisted of elementary school teachers and researchers at a university. The participants of the experiment were students between 3rd and 6th grades at an elementary school. The research process consisted of seven steps: 1) specifying linguistic proficiency; 2) developing the cross-curriculum of L1 and L2; 3) forming can-do statements; 4) creating a self-evaluation questionnaire; 5) executing the self-evaluation questionnaire at the beginning of the school year; 6) instructing L1 and L2 based on the curriculum; and 7) executing the self-evaluation questionnaire at the beginning of the next school year. In Step 1, the members of the research team brainstormed ways to specify elementary school students’ linguistic proficiency that can be observed in various scenes. It was revealed that the teachers evaluate their students’ linguistic proficiency on the basis of the students’ utterances, but also informed by their non-verbal communication abilities. This led to the idea that competency for understanding others’ minds through the use of physical movement or bodily senses in communication in L1 – to sympathize with others – can be transferred to that same competency in communication in L2. Based on the specification of linguistic proficiency that L1 and L2 have in common, a cross-curriculum of L1 and L2 was developed in Step 2. In Step 3, can-do statements based on the curriculum were also formed, building off of the action-oriented approach from the Common European Framework of Reference for Languages (CEFR) used in Europe. A self-evaluation questionnaire consisting of the main can-do statements was given to the students between 3rd grade and 6th grade at the beginning of the school year (Step 4 and Step 5), and all teachers gave L1 and L2 instruction based on the curriculum to the students for one year (Step 6). The same questionnaire was given to the students at the beginning of the next school year (Step 7). The results of statistical analysis proved the enhancement of the students’ linguistic proficiency. This verified the validity of developing the cross-curriculum of L1 and L2 and adapting it in elementary school. It was concluded that elementary school students do not distinguish between L1 and L2, and that they just try to understand others’ minds through physical movement or senses in any language.

Teachers Leadership Dimension in History Learning

The Ministry of Education Malaysia dynamically and drastically made the subject of History mandatory to be in force in 2013. This is in recognition of the nation's heritage and treasures in maintaining true facts and information for future generations of the State. History reveals the civilization of a nation and the fact of national cultural heritage. Civilization needs to be preserved as a legacy of sovereign heritage. Today's generation is the catalyst for future heirs who will support the principle and direction of the country. In line with the National Education Philosophy that aims to shape the potential development of individuals holistically and uniquely in order to produce a balanced and harmonious student in terms of intellectual, spiritual, emotional and physical. Hence, understanding the importance of studying the history subject as a pillar of identity and the history of nationhood is to be a priority in the pursuit of knowledge and empowering the spirit of statehood that is nurtured through continuous learning at school. Judging from the aspect of teacher leadership role in integrating history in a combined way based on Teacher Education Philosophy. It empowers the teaching profession towards the teacher to support noble character. It also supports progressive and scientific views. Teachers are willing to uphold the State's aspirations and celebrate the country's cultural heritage. They guarantee individual development and maintain a united, democratic, progressive and disciplined society. Teacher's role as a change and leadership agent in education begins in the classroom through formal or informal educational processes. This situation is expanded in schools, communities and countries. The focus of this paper is on the role of teacher leadership influencing the effectiveness of teaching and learning history in the classroom environment. Leadership guides to teachers' perceptions on the role of teacher leadership, teaching leadership, and the teacher leadership role and effective teacher leadership role. Discussions give emphasis on aspects of factors affecting the classroom environment, forming the classroom agenda, effective classroom implementation methods, suitable climate for historical learning and teacher challenges in implicating the effectiveness of teaching and learning processes.

Students Perceptions on the Relevance of High School Mathematics in University Education in South Africa

In this study we investigated the relevance of high school mathematics in university education. The paper particularly focused on whether the concepts taught in high school are enough for engineering courses at diploma level. The study identified particular concepts that are required in engineering courses whether they were adequately covered in high school. A questionnaire was used to investigate whether relevant topics were covered in high school. The respondents were 228 first year students at the Central University of Technology in the Faculty of Engineering and Information Technology. The study indicates that there are some topics such as integration, complex numbers and matrices that are not done at high schools and are required in engineering courses at university. It is further observed that some students did not cover the topics that are in the current syllabus. Female students enter the university less prepared than their male counterparts. More than 30% of the respondents in this study felt that high school mathematics was not useful for them to be able to do engineering courses.

A Design-Based Approach to Developing a Mobile Learning System

This paper presents technologically innovative and scalable mobile learning solution within the SCOLLAm project (“Opening up education through Seamless and COLLAborative mobile learning on tablet computers”). The main research method applied during the development of the SCOLLAm mobile learning system is design-based research. It assumes iterative refinement of the system guided by collaboration between researches and practitioners. Following the identification of requirements, a multiplatform mobile learning system SCOLLAm [in]Form was developed. Several experiments were designed and conducted in the first and second grade of elementary school. SCOLLAm [in]Form system was used to design learning activities for math classes during which students practice calculation. System refinements were based on experience and interaction data gathered during class observations. In addition to implemented improvements, the data were used to outline possible improvements and deficiencies of the system that should be addressed in the next phase of the SCOLLAm [in]Form development.

Practical Problems as Tools for the Development of Secondary School Students’ Motivation to Learn Mathematics

This article discusses plausible reasoning use for solution to practical problems. Such reasoning is the major driver of motivation and implementation of mathematical, scientific and educational research activity. A general, practical problem solving algorithm is presented which includes an analysis of specific problem content to build, solve and interpret the underlying mathematical model. The author explores the role of practical problems such as the stimulation of students' interest, the development of their world outlook and their orientation in the modern world at the different stages of learning mathematics in secondary school. Particular attention is paid to the characteristics of those problems which were systematized and presented in the conclusions.

Inner and Outer School Contextual Factors Associated with Poor Performance of Grade 12 Students: A Case Study of an Underperforming High School in Mpumalanga, South Africa

Often a Grade 12 certificate is perceived as a passport to tertiary education and the minimum requirement to enter the world of work. In spite of its importance, many students do not make this milestone in South Africa. It is important to find out why so many students still fail in spite of transformation in the education system in the post-apartheid era. Given the complexity of education and its context, this study adopted a case study design to examine one historically underperforming high school in Bushbuckridge, Mpumalanga Province, South Africa in 2013. The aim was to gain a understanding of the inner and outer school contextual factors associated with the high failure rate among Grade 12 students.  Government documents and reports were consulted to identify factors in the district and the village surrounding the school and a student survey was conducted to identify school, home and student factors. The randomly-sampled half of the population of Grade 12 students (53) participated in the survey and quantitative data are analyzed using descriptive statistical methods. The findings showed that a host of factors is at play. The school is located in a village within a municipality which has been one of the poorest three municipalities in South Africa and the lowest Grade 12 pass rate in the Mpumalanga province.   Moreover, over half of the families of the students are single parents, 43% are unemployed and the majority has a low level of education. In addition, most families (83%) do not have basic study materials such as a dictionary, books, tables, and chairs. A significant number of students (70%) are over-aged (+19 years old); close to half of them (49%) are grade repeaters. The school itself lacks essential resources, namely computers, science laboratories, library, and enough furniture and textbooks. Moreover, teaching and learning are negatively affected by the teachers’ occasional absenteeism, inadequate lesson preparation, and poor communication skills. Overall, the continuous low performance of students in this school mirrors the vicious circle of multiple negative conditions present within and outside of the school. The complexity of factors associated with the underperformance of Grade 12 students in this school calls for a multi-dimensional intervention from government and stakeholders. One important intervention should be the placement of over-aged students and grade-repeaters in suitable educational institutions for the benefit of other students.