CHAPTER ONE/INTRODUCTION

The interactions between the variables of instructors, students, curriculum, local context, and other aspects in teaching have an impact on what will occur in courses (Stigler and Hilbert, 1998). Rubenstein (2004) endorsed the idea that teaching is a difficult task. The foundational knowledge for teaching mathematics comprises an understanding of mathematics, the relationships between mathematical concepts, student learning, and school culture. Creating a learning community, pushing students to make sense of mathematical concepts, and fostering students’ growing knowledge are all part of the teaching process. Teachers are one of the most significant variables influencing students’ success and the teaching process, according to Rubenstein (2004).

Math instruction that is effective involves instructors and students interacting in ways that provide pupils the best chance to learn as much as possible. There are many different ways that pupils and instructors communicate in a classroom. Some encounters lead to classroom discussions, teacher- and student-initiated inquiries, and student learning. Cooperative group work, peer tutoring, and a variety of other feedback mechanisms, including assignments, tests, and electronic response mechanisms like the personal responses system (PRS) and the personal data assistant (PDA), are examples of instructional strategies that offer some degree of two-way communication in which knowledge about what is taught and what is learned is exchanged between two people. On the other hand, some teaching systems have students just sitting still in classrooms with one-way communication between the instructor and the pupils. on the campuses of several universities and institutions. As an example, the professor serves as the legendary “Sage on the stage,” and the didactic lecture serves as the ideal method of instruction. Although giving a lecture to a large group of students is an effective way for a teacher to convey information, simply giving information to someone does not guarantee that they will learn it. In order to know whether learning is occurring, in addition to the instructional interactions, there must be teacher-student assessment interactions.

When instructors collect data on students’ learning and use it to assist students better comprehend ideas and principles and apply knowledge, rather than merely learning factor, that is when assessment interactions between students and teachers take place. Formative assessment is characterized as the following sort of assessment interaction: In order to increase students’ accomplishment of the planned instructional goals, instructors and students employ a method called formative assessment, which gives feedback during teaching (council of chief school states officers, 2008). It is evident from this definition that formative assessment is a process that may involve tests or various other types of assessments, but it may also involve interactive instructional strategies like classroom discussion, assignments, homework, quizzes, projects, investigations, electronic response systems, or oral questions in order to direct and enhance students’ learning (Angelo and Cross 1993, Fennell, 2006) It might be difficult to create a math classroom with an engaging learning atmosphere where kids are actively studying arithmetic.

Students may feel self-conscious about their understanding of arithmetic concepts and may be reluctant to speak out during class discussions or in response to instructors’ spoken questions. Also, staying focused while navigating the complicated interactions between instructors’ speak, students’ discussion, and the classroom dynamic requires a specific set of abilities. These classroom dynamics are seen as a social endeavor in certain models of “best practices” in mathematics teaching and learning (Cobb and Bauersfield, 1995), where the classroom functions as a learning community where thinking, criticising, arguing, and agreeing are encouraged. When this dynamic is successful, it may lead to the development of a learning environment where students’ learning flourishes and they assume an increasing amount of responsibility for their own learning.

A effective learning environment, according to Motani and Garg (2002), is one in which instructors and students may engage freely, constantly, and without any restraint. In this kind of learning environment, instructors monitor their pupils’ learning to ensure that they are understanding the concepts being taught. The adoption of an immediate feedback system and its execution are crucial to this achievement. When students misinterpret a concept or principle that is crucial to achieving the learning goals, instructors may step in right away thanks to quick feedback. A teacher may need to change their approach to teaching, provide various examples, or often offer alternate explanations. Teachers demonstrate their understanding and appreciation of the fact that earlier attempts to teach the topic or principle were unsuccessful by making these improvements.
According to Guskey (2003), all students learn better when educational changes are made right away with the goal of reaching all students, including less successful ones. Teachers of mathematics have a variety of tools at their disposal to assess how effectively their pupils are absorbing the subject they are being taught.

There are both non-electronic and electronic mechanisms for receiving feedback, according to Motanic and Garg (2002). Class discussions, collaborative group projects, board assignments, seat assignments, and responding to queries that are put forward verbally are examples of non-electronic mechanisms. Although while these interactive tactics are successful, a significant drawback is that at any one moment, only a portion of the class is actively sharing information with the instructors about what they are learning and getting feedback from the teachers. to encourage more students to participate in the interactive activities. It is important to take precautions to ensure that interactive assessment methods used by teachers—such as assignments and exams—are successful in assessing what and how much pupils have learned.

The fact that pupils are not given feedback during education is one reason why caution must be used. Students may have advanced to “learning” new material when they reply to questions on assignments or exams. The cumulative impact of knowledge coupled with no corresponding feedback might put pupils at risk of subpar performance or even failure. If there were misunderstandings of the previous subject that were not quickly corrected when it was delivered. The fact that students often concentrate on doing whatever is required to receive the best score on assessment methodologies employed by students in this curriculum may also be a contributing factor in how little learning occurs.

Also, the authors agree with Tyler’s (2000) observation that math learning should occur via the students’ engaged behavior and the teacher’s compelling instruction.
Lastly, Tyler (2000) said that learning occurs not as a result of what the instructor does but rather as a result of what the students do.

Background

As reported by the World Health Organization, a novel coronavirus (2019-nCoV) was identified as the causative virus of Wuhan pneumonia of unknown etiology by Chinese authorities on 7 January, 2020. The virus was named as severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) by International Committee on Taxonomy of Viruses on 11 February, 2020. This study aimed to develop a mathematical model for calculating the transmissibility of the virus.

Methods

In this study, we developed a Bats-Hosts-Reservoir-People transmission network model for simulating the potential transmission from the infection source (probably be bats) to the human infection. Since the Bats-Hosts-Reservoir network was hard to explore clearly and public concerns were focusing on the transmission from Huanan Seafood Wholesale Market (reservoir) to people, we simplified the model as Reservoir-People (RP) transmission network model. The next generation matrix approach was adopted to calculate the basic reproduction number (R₀) from the RP model to assess the transmissibility of the SARS-CoV-2.

Healthcare impact of COVID-19 epidemic in Nigeria: A stochastic mathematical model

 

Introduction

WHO declared COVID-19 a pandemic on 11 March 2020.1 Worldwide it has exploded to 784,794 cases and caused 37,788 deaths by 30 Mar 2020.2 In India the first case was reported on 30 Jan. By 30 Mar, India had reported 1,251 cases and 32 deaths.3 The spread of any epidemic depends on infectivity of the pathogen and the available susceptible population. For a novel infection, when disease dynamics are still unclear, mathematical modeling estimates the number of cases in worst and best-case scenarios. It can also help estimate the effect of preventive measures adopted against COVID-19.

With Suppressive strategies, the aim is to maintain the effective Reproduction number (R) below 01, to prevent further spread of infection, while in a Mitigation strategy, the aim is to blunt the effect of the epidemic.4 Non-Pharmacological interventions (NPIs) utilized to contain epidemics (Social distancing, closure of schools, universities and offices, avoidance of mass gatherings, community-wide containment etc.) may be applied to the general population, contacts of cases (Contact tracing, Surveillance, quarantine) and the cases themselves (Early Reporting, Isolation).4,5 India appears to be in early stages of the epidemic. It is important to predict how the disease is likely to evolve amongst the population. This will help in estimation of health care requirements and permit a measured allocation of resources.

Considering the differences in the way COVID-19 has spread in different countries, any planning for mounting a fresh response has to be adaptable and situation-specific. When the actual numbers are relatively few, a mathematical simulation approach is best suited towards understanding this epidemic and formulating an appropriate response.

Hence, we decided to create a early stochastic mathematical model of the COVID-19 epidemic in India with the objective of determining it’s magnitude, assessing the impact on health care resources and studying the effect of certain NPIs on the epidemic.

PURCHASE 15K

 

A stochastic mathematical model of COVID-19

EFFECT OF STUDENT PERCEPTION ON TEACHING AND LEARNING MATHEMATICS
CHAPTER ONE

INTRODUCTION

Teaching is a complex system which affects what will happen in classes through the interactions among the factors of teachers, students, curriculum, local setting and others (Stigler and Hilbert, 1998). Rubenstein (2004) supported teaching as a complex endeavor. The knowledge base behind mathematics teaching includes the knowledge of mathematics of connections among mathematical ideas, of student’s learning and school culture. The process of teaching involves creating a learning community, challenging students to make sense of mathematical ideas and supporting students’ developing understanding. Rubenstein (2004) stated that teachers are considered as one of the most important factors playing on role in students’ achievement and teaching process.

Effective mathematics learning is one in which students and teachers interact in ways that allows students to have an opportunity to maximize how much they learn. These are variety of ways in which students and teachers interact in a learning environment. Some interactions result in student learning classroom discussion, teachers and students initiated questions. Cooperative group work, peer tutoring and a host of other feedback system such as assignments, examinations and electronic responses system such as the personal responses system (PRS) and the personal data assistant (PDA) are instructional strategies that provide a measure of two-ways communication in which information about what is taught and what is learned is exchange between two people on the other hand, there are instructional strategies in which students sit passively in classrooms where there is one-way communication from teachers to students. On many colleges and university campuses. For example, the professor operates as the proverbial “Sage on the stage” and the didactic lecture is the model way of teaching. And although the lecture is an efficient method for transmitting information from a teacher to a large group of students, telling information to some one does one does not mean that learning take place in order to determine whether is occurring-infant to ensure that learning is taking place, there must be teacher-student assessment interactions along with the instructional interactions.

Assessment interactions between students and teachers occurs when teachers gather information about students learning and use that information help students better understand concepts and principles and apply knowledge, not just learn factor. This type of assessment interaction referred to as formative assessment is defined as follows: Formative assessment is a process used by teachers and students during instruction that provides feedback to adjust on going teachers and learning to improve students’ achievement of intended instructional outcomes (council of chief school states officers, 2008). It is clear from this definition that formative assessment is a process that may employ tests or various other types of assessments, but it may also employ interactive instructional strategies such as classroom discussion, assignment, homework, quizzes, project, investigations electronics response system or oral question to guide and improve students learning (Angelo and Cross 1993, Fennell, 2006) creating an interactive learning environment inside the mathematics classroom in which students are engaged in mathematic learning can be challenging.

Student may experience discomfort about their own level of mathematics content knowledge and may shy away from participating openly in class discussion or responding to teachers’ oral question. Further, this complex negotiation of teachers talk, students talk and classroom dynamic while remaining on task require certain skills and know how. In some models of “best practices” in mathematics teaching and learning these classroom dynamic are viewed as a social Endeavour (Cobb and Bauersfield, 1995) in which the classroom function as a learning community where thinking, critiquing disagreeing and agreeing are encourage. When this dynamic work well, the result can be the creation of a learning environment in which critical thinking and quantitative reasoning develop, students learning thrives, and students take increasing responsibility for their own learning.

According to Motani and Garg (2002), a successful learning environment is one in which students and teachers interact easily, continuously and without any inhibition. In this type of learning environment, students learning is not left to chances, rather, teachers knows whether their student understand intended concept. The key to this success is the implementation and use of an instantaneous feedback system. Instantaneous feedback enables teachers to intervene immediately when students misunderstand a concept or principle which is important in meeting the learning objectives. A teacher may have to adjust a teaching strategy, provide different example or often alternatives explanations. In making these adjustments, teachers’ shows that they recognize and appreciate that previous attempt at teaching the concept or principle were not effective.

Guskey (2003) stated that making adjustments in teaching instantaneously with the aim of reaching all students, and especially less successful students, leads to improved learning for all students. Mathematics teachers can use several strategies to get and give feedback about how well students are learning materials that is being taught.

Motanic and Garg (2002) observe that there are electronics and non-electronic mechanism for getting feedback. Non electronic mechanism may include class discussions, cooperative group work, board-work, seatwork or answering questions that are posed orally. While these interactive strategies are effectives, a major short coming is that at any particular time, only a subset of the students in the class are actively providing information to the teachers about their learning and receiving feedback from the teachers. In order to engage more student in the interactive activities. Even when teachers employs interactive assessment strategies such as assignment or examinations to determine what and how much students have learned, care must be taken so that these strategies are effective in improving students learning. One reason that care must be taken is because the feedback to students does not occur during the instruction. When students respond to question on an assignments or examination, they may have moved on to “learning” new content. If understanding the old content and if there were misunderstanding of the old content that were not addressed immediately when it was presented, then the cumulative effect of understanding couples with no correlative feedback could put students at risk of under performance or even failure. A second reason is that students generally focus on doing what is necessary to get the highest grade possible on assessment strategies used by students in this content may result in very little learning.

In addition to this, the writers will agree with the view of Tyler (2000) which noted that learning of mathematic should take place through the active behaviour of the students and impressive teaching of the teacher.

Finally, according to Tyler (2000) said it is not what the teacher does, but through what the students does that learning takes place.

1.1 BACKGROUND OF THE STUDY

In general, mathematics has been playing important role in the development of the society both locally and internationally. But this study will lay an emphasis on the perception of teachers in teaching mathematics in schools with 50%-100% students as mathematics learners with their perception in learning mathematics. One could observe that out of thousands of students passing out from the secondary school every year, very few of them (about 0.52%) choose mathematics as a discipline. Even those that choose the subject as a career does so when there is no other alternative. There is shortage of qualified mathematics teachers in some schools, somebody that read Economics, Geography, Biology, and P.H.E etc. are assigned to teach the subject mathematics. This type of arrangement has an advert effect on the performance of students in mathematics and allied subject such as the science and the applied science which are of great importance to the nation, socially, economically and technologically.

More so, the study will encourage the mathematics teachers to keep up with the reform and the development in the educational literature to be skillful enough for realization their role. If this is realized by the teachers, students learning level will be realized. In conclusion, the study will help to improve and overcome some of the problems the secondary schools teaching encountered when teaching mathematics which is likely to improve students’ performance in mathematics.

1.2 STATEMENT OF THE PROBLEM

This study was aimed at examining different facts within the teaching and learning of mathematics in Nigeria secondary schools. This is an area that has been researched however there are certain as facts that research have not attended yet. Overview of many aspects of attitudes towards mathematics including a review of instructional is still unclear how the school environment affects the development of studies attitudes towards mathematics. As a result the researcher believes that it is important to investigate and identify factors influencing students’ attitudes towards mathematics subject. Therefore, the present study was motivated to access whether the perceptions of the senior secondary school students toward mathematics played any role in their attitudes towards mathematics.

The present study was structured to investigate from the point of view of each student the most important school related determinants of likely and disliking mathematics. The particular value of the present study is that it should identify and categories different perceptions and outcome of different students.

1.3 PURPOSE OF THE STUDY

The purpose of this study is to reveal the perceptions of teachers in teaching mathematics with different kind of teaching methods and to assess the perceptions of senior secondary school students towards mathematics i.e. to what extent do students believes the school influence their attitudes towards mathematics i.e. whether they like or dislike mathematics.

Furthermore, it will also determine if there is difference in students’ perception of interaction that occurs between themselves and their teachers across section of their mathematics.

Finally, this present research was to explore the general attitude of the students towards mathematics and to established the factors that influence such as well as determining whether gender differences affects students towards learning mathematics or not.

1.4 RESEARCH QUESTION

The following research questions will be addressed in this study.

How does the teacher’s perception on different teaching methods aids in the teaching of mathematics.
Does the effective use of textbooks and instructional aids influence students’ attitude towards learning mathematics.
Does the learning environment have effect on the students’ attitude towards mathematics?
Does students’ belief has as influence on their attitude towards mathematics.
RESEARCH HYPOTHESIS

H0 – There is no significant difference between the teachers’ perception and the use of varying teaching methods in teaching mathematics.

H1 – There is significant difference between the teachers’ perception and the use of varying teaching methods in teaching mathematics.

H0 – The students belief do not have any influence on their attitude towards mathematics.

H1 – The students’ belief has an influence on their attitude towards mathematics.

SIGNIFICANCE OF THE STUDY

The significance of this study is to identify the factor which influence the attitude of students towards mathematic in the senior secondary school.

Also, the teacher would identify their deficiencies and limitations as regards the teaching and learning of mathematics and make necessary adjustments where necessary.

More so, as mathematics becomes part of daily life, the need for proper teaching and learning has become extremely essential. Because of this increase in need demands have also been placed in school to educate students and make them “ mathematically equipped” Additionally, attitude are not only feeling that help prevent accesses but also place a limit on students learning. If a person does not like mathematics, he/she may feel anxious when expected to utilize this, such a person is unlikely to want to learn and obtain skills or participate in assignment that require `the use of mathematical knowledge, on the other hand, students who exhibit positive attitude towards a subject are more likely to actively engage during and after instruction. When students dislike mathematics, his/her attitude is reflected in action resulting in limited engagement with mathematics. So in a sense the attitude affect subsequent actions. It is acknowledge on the present study that there are many other factors that influence students attitude towards mathematics.

Moreover, the aim of this presents study is to give a deeper understanding of the ways in which factors such as classroom environment, teachers, students attitude, parents, gender difference and students attitudes towards mathematics plays role in how students views mathematics in senior secondary school in Nigeria. It is almost impossible to develop mathematical skill when factor related to students attitude are not identified as a matter of urgency, and feasible strategies and interaction programme organized. Such strategies might help in addressing the problem and hopefully encourage students in adopting meaningful and positive attitude towards mathematics.

Finally, the students would be alerted on both positive and negative effects their attitude, perception towards mathematics at their level will have on their present and future career.

1.7 OBJECTIVES

The objective of this study is to find out the following:

Whether the qualification of mathematics teachers in school makes the teaching of mathematics difficult.
Whether lack of adequate and enough instructional materials in senior secondary school make the teaching of mathematics difficult.
May be lack of provision of library in school and whether the average class sizes of the students in school affect the teaching of mathematic.
To know whether the teachers have or adopt adequate and appropriate teaching methodology in teaching of mathematics in our secondary school.
To know the problem encountered by the teachers of mathematics.
1.8 LIMITATION OF THE STUDY

This study will be limited to the ijebu-ode municipality of Ogun State. It deals specifically with the perception of students and teachers in teaching and learning of mathematics within the municipality. This restriction is necessary in order to carry research in within the relatively short period of time allowed.

1.9 DEFINITION OF TERMS

Mathematics: Mathematics in a strict sense is the abstract science which investigates deductively the conclusion impact in the elementary concept of spatial and numerical relation. It has also be defined as a science size and numbers of which arithmetic algebra, trigonometry and geometry are the branches.

Roux (1994) defined attitude to be a “positive or negative emotional relationship with or predisposition towards an object institutional or person” pointing to get another definition.

Becker and Wiggins (1991) defined attitude as “enduring non-verbal features of social and physical world, and they acquired through experience and exert a directive influence on behaviour “both these definitions reveals that, an attitude can be understand as an emotion that has an influence on the behaviour of human being”.

Factor: Factor is defined as any of the conditions and influences that act in other to bring about result. It is also referred to as generally anything that has some casual influence some effects on a phenomenon.

Teach: To show somebody how to do something so that they will be able to do it themselves or to give lesson in a subject to a class or pupil.

Learn: To gain knowledge or skill by study, experience or being taught or become aware of.

Perception: The ability to see, hear or understand things.

Interact: To act so as to affect each other.

Modeling Economic Output and Economic Growth with respect to Economic Freedom A COMPARATIVE STUDY OF DEVELOPING AND DEVELOPED COUNTRIES

 

Background to thesis

 

The governing dynamics behind the output of an economy (GDP) is subject to constant debate in economics. What makes an economy prosper and why are some countries more prosperous than others? Alongside the debate, extensive theoretical and empirical research has tried to answer this question.

 

The original neoclassical growth model from economists Solow (1956) and Swan (1956) suggest that the GDP of poor countries will – under the right conditions – grow faster than the GDP of rich countries, which is why the starting level of income must be of importance to economic growth. The models did not provide a satisfying explanation for why productivity was lower in poorer countries, but it laid the foundation for empirical research on the subject.

 

Extensions from economists Romer et al. (1992) provided a model that took human capital in account for explaining why productivity was lower in developing countries. Further extensions from Hall & Jones (1999) suggested that social infrastructure also should be included in the model in order to describe the environment in which agents ultimately produce economic output. Within the term social infrastructure there are defining measures such as rule of law, property rights and freedom of contract – all measures of economic freedom.

 

The relationship between economic freedom and economic growth has been examined by researchers with varying results. Notably, De Haan & Sturm (2000), used cross-sectional data from 80 countries over years 1975-1990 and found that there was a significant positive correlation between economic growth and changes in economic freedom – but not between economic growth and the level of economic freedom. Other researchers such as Scully (2002) and Dawson (2002) found a significant positive correlation between the level of economic freedom and economic growth.

 

As mentioned above, most papers have examined the relationship between GDP/capita growth and economic freedom on a cross-country sample, which arguably signifies short- term growth (Hall & Jones, 1995). This paper aims to further expand the knowledge on long-term economic growth by examining the GDP/capita level of 50 countries (of which 25 are developing and 25 developed) in relation to their respective level of economic freedom, using more recent data from year 2000 to 2013 – as well as the short-term growth by studying the GDP/capita growth rate. Furthermore, this paper will examine what impact economic freedom has within the sample groups of developed and developing countries.

REMOTE MONITORING AND MANAGEMENT OF SERVERS FROM MOBILE DEVICES

ABSTRACT

Internet usage has tremendously increased these days. The services that users access across a network and the servers that host these services need to be monitored for availability/protection and efficiency. The need for remote monitoring of servers as well as the services is essential,  since this will notify the user/administrator instantly when something happens to the server, also the user can be anywhere to monitor the server. The development of a remote server monitoring system that permits an administrator to check the status of a server from a mobile phone is the subject of this research. The application was designed using Java technology (Java 2 Micro Edition). Access to the server is provided through an SMS gateway, which is connected to the network through the wired network. The application also enables the administrator to restart a machine, after power outage, which is common in our locality. The system that achieved the aforementioned objectives was developed and tested with the attendant benefits of reducing the time and overhead of server management.