Abstract: 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.
Abstract: 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.
Abstract: 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.
Abstract: 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.
Abstract: The aim of this study was to examine the effect of
cooperative learning method on student’s academic achievement and
on the achievement level over a usual method in teaching different
topics of mathematics. The study also examines the perceptions of
students towards cooperative learning. Cooperative learning is the
instructional strategy in which pairs or small groups of students with
different levels of ability work together to accomplish a shared goal.
The aim of this cooperation is for students to maximize their own
and each other learning, with members striving for joint benefit.
The teacher’s role changes from wise on the wise to guide on
the side. Cooperative learning due to its influential aspects is the
most prevalent teaching-learning technique in the modern world.
Therefore the study was conducted in order to examine the effect
of cooperative learning on the academic achievement of grade 9
students in Mathematics in case of Mettu secondary school. Two
sample sections are randomly selected by which one section served
randomly as an experimental and the other as a comparison group.
Data gathering instruments are achievement tests and questionnaires.
A treatment of STAD method of cooperative learning was provided
to the experimental group while the usual method is used in the
comparison group. The experiment lasted for one semester. To
determine the effect of cooperative learning on the student’s academic
achievement, the significance of difference between the scores of
groups at 0.05 levels was tested by applying t test. The effect size
was calculated to see the strength of the treatment. The student’s
perceptions about the method were tested by percentiles of the
questionnaires. During data analysis, each group was divided into
high and low achievers on basis of their previous Mathematics result.
Data analysis revealed that both the experimental and comparison
groups were almost equal in Mathematics at the beginning of the
experiment. The experimental group out scored significantly than
comparison group on posttest. Additionally, the comparison of mean
posttest scores of high achievers indicates significant difference
between the two groups. The same is true for low achiever students
of both groups on posttest. Hence, the result of the study indicates
the effectiveness of the method for Mathematics topics as compared
to usual method of teaching.
Abstract: This paper discusses the potential benefits of an
interactive multimedia information representation in enhancing
students’ critical thinking aligned with history reasoning in learning
history amongst Secondary School students in Malaysia. Two modes
of multimedia information representation were implemented;
chronologic and thematic information representations. A qualitative
study of an unstructured interview was conducted among two history
teachers, one history education lecturer, two i-think experts, and five
students from Form Four secondary school. The interview was to
elicit their opinions on the implementation of thinking maps and
interactive multimedia information representation in history learning.
The key elements of the interactive multimedia (e.g. multiple media,
user control, interactivity and use of timelines and concept maps)
were then considered to improve the learning process. Findings of the
preliminary investigation reveal that the interactive multimedia
information representations have the potential benefits to be
implemented as an instructional resource in enhancing students’
higher order thinking skills (HOTs). This paper concludes by giving
suggestions for future work.
Abstract: The purpose of this study is to identify the teaching method practices of the practical work subject in Vocational Secondary School. This study examined the practice of Vocational Teaching Method in Automotive Practical Work. The quantitative method used the sets of the questionnaire. 283 students and 63 teachers involved from ten VSS involved in this research. Research finding showed in conducting the introduction session teachers prefer used the demonstration method and questioning technique. While in deliver the content of practical task, teachers applied group monitoring and problem solving approach. To conclude the task of automotive practical work, teachers choose re-explain and report writing to make sure students really understand all the process of teaching. VTM-APW also involved the competency-based concept to embed in the model. Derived from factors investigated, research produced the combination of elements in teaching skills and vocational skills which could be used as the best teaching method in automotive practical work for school level. As conclusion this study has concluded that the VTM-APW model is able to apply in teaching to make an improvement with current practices in Vocational Secondary School. Hence, teachers are suggested to use this method to enhance student's knowledge in Automotive and teachers will deliver skills to the current and future workforce relevant with the required competency skilled in workplace.
Abstract: Tanzania secondary schools in rural areas are geographically and socially isolated, hence face a number of problems in getting learning materials resulting in poor performance in National examinations. E-learning as defined to be the use of information and communication technology (ICT) for supporting the educational processes has motivated Tanzania to apply ICT in its education system. There has been effort to improve secondary school education using ICT through several projects. ICT for e-learning to Tanzania rural secondary school is one of the research projects conceived by the University of Dar-es-Salaam through its College of Engineering and Technology. The main objective of the project is to develop a tool to enable ICT support rural secondary school. The project is comprehensive with a number of components, one being development of e-learning management system (e-LMS) for Tanzania secondary schools. This paper presents strategies of developing e-LMS. It shows the importance of integrating action research methodology with the modeling methods as presented by model driven architecture (MDA) and the usefulness of Unified Modeling Language (UML) on the issue of modeling. The benefit of MDA will go along with the development based on software development life cycle (SDLC) process, from analysis and requirement phase through design and implementation stages as employed by object oriented system analysis and design approach. The paper also explains the employment of open source code reuse from open source learning platforms for the context sensitive development of the e-LMS for Tanzania secondary schools.
Abstract: The aim of this study is to discover secondary school students’ perceptions related to information technologies and the connections between concepts in their cognitive structures. A word association test consisting of six concepts related to information technologies is used to collect data from 244 secondary school students. Concept maps that present students’ cognitive structures are drawn with the help of frequency data. Data are analyzed and interpreted according to the connections obtained as a result of the concept maps. It is determined students associate most with these concepts—computer, Internet, and communication of the given concepts, and associate least with these concepts—computer-assisted education and information technologies. These results show the concepts, Internet, communication, and computer, are an important part of students’ cognitive structures. In addition, students mostly answer computer, phone, game, Internet and Facebook as the key concepts. These answers show students regard information technologies as a means for entertainment and free time activity, not as a means for education.