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In the past few decades, Society has made a strong move toward formal education and marked its step toward an improving literacy rate. In the early days, there was no concept of formal learning, people used to teach things to their children for survival purposes. However, when the life of the ancient's started changing with discoveries and inventions, the necessity of a formal education system became vital to hold and maintain the development chain for a developed society. In today's time, formal education and school-based education converted into an integral part of our education system. As the importance grows, the urge for education also hits a new bar.
The necessity of learning mathematics was never an option in the structure of education, knowledge about the basics is always considered a part of curriculum development in primary and early primary. This study aims to analyse the learning in the Curriculum and teaching-learning procedures, Curriculum development and children’s learning requirements Teaching strategies and more on measuring the learning achievement of the student.
The structure of the school-based education system includes the base, students, teachers and the school and most importantly the curriculum development. For a better understanding of economics, environment or political issues every student needs the proper, structural education. As primary and early primary is the base of the education system, it is essential to include all basic knowledge regarding almost everything in those years (Nxumalo, 2019). During this time the ability of a child to absorb new things is at the top, therefore they can understand things more easily and this creates the base for further and more complex education.
The age group that denotes the primary and early primary base, is 3 to 11 almost. During this period their study evolves around subjects like Mathematics, Science, History, Geography, English and languages (if there is any other specific one). However, the growth and knowledge of those subjects depend on the capability of every individual (Slot, 2018). A strong base of primary education indicates a better and brighter future in higher studies, that is the reason behind the Education system emphasises a proper, methodical, planned way of education.
In Education System, the necessity for curriculum development in primary and early primary should be the priority of the Government. As it does not only about students, teachers and the schools, rather it includes the overall development of a society. Curriculum Development helps students to solve the upcoming problems in every kind of condition in future (Dere, 2019). It plays a crucial role to understand and analyse the economic structure of the country. Apart from socio-political aspects, and economical equations, it needs a strong knowledge of mathematics. The stronger the base is, the easier the whole process will be. That is the reason teachers focus on Making maths easy for the students of primary and early primary, through the teaching-learning process (Hasnidar and Elihami, 2019). For the age group of 3-11, teachers follow a basic pattern and several topics cover the whole syllabus. Among 3-11, there are age groups like Early Years, Reception, Year 1, Year 2, Year 3, Year 4 and year 5 and year 6. In every group, there are a few common topics that get covered, For example, the number and place value, Addition and subtraction, multiplication and division, fractions, geometry and shapes, measurement, statistics, ratio and proportions and algebra.
Mathematics is one of the vital parts of the curriculum, including patterns, numbers and shapes that nurture logical development and a methodical mindset among the students. In addition, knowledge attainment is crucial for opening up new doors for employment opportunities.
Figure 1: Student’s performance in Math test
(Source: asset. Publishing.service, 2022)
According to the recent report in context to student performance, only 27% of the students received high standards in math in 2019, thereby indicating the importance of the math curriculum development by keeping in mind the learning requirements of the pupils belonging to age group 3 to 11.
Teaching strategies implemented within the curriculum focus on promoting math learning through songs and fun games. Cognitive learning theory highlights that the learners or the student are the active participants associated with the learning process (Madani, 2019). Active participation of the students provides meaningful experiences to the learners, thereby contributing to overall learning development. Math curriculum for learners belonging to the age group 3 to 11 has been designed in a way where students are provided with the opportunity to explore geometric shapes through modelling clay. Children belonging to the age group 5 to 6 gain confidence while working with numbers and are well informed about 2D and 3D shapes. Since cognitive learning theory emphasizes on relating newly acquired information with the existing one, educators are responsible for creating a safe learning ambience nurturing learner's curiosity. Children are often asked to count objects around the home, using toys for exploring fractions. In context to children aged 9 to 10 years, the curriculum has been designed to encourage children to use operations, for instance, cube, prime, square and interpret timetables and line graphs (Spiteri and Chang Rundgren, 2020). Dice are used as learning aids to facilitate the learning development of the children
Skill development is very necessary during the early education of the students. It further helps the students achieve efficiency within their learning and in their professional fields in the future. Therefore, the selected curriculum has been designed in a way that focuses on the development of the communication, visualization, and problem-solving skills of the students.
Math skills are very important, from calculating space to measuring financial transactions. At the pre-primary and primary levels, the students need to focus on skill development to enhance better learning of the subjects. Curriculum development in the context of mathematical learning among students belonging to age groups 3 to 11 has been designed to contribute toward improved learning outcomes for the students. In order to develop problem-solving skills among the students, the numicon approach has been implemented by the educators to assist children in finding relations between numbers (Caltonet al. 2022). Educators to solve complex mathematical ideas often use colourful numicon shapes. Problem-solving skills enhance the student's own problem-solving ability and then motivate them to apply their own strategies to solve them. Reasoning [R] skill helps the children to think logically and understand the proper concept of mathematics. This skill further helps students to build confidence in the capability to reason and explain their own mathematical thinking. In this curriculum, the students are taught how to develop their reasoning ability in their mathematics. This skill is generally taught to the students who belong to the 4-8 year age group. Practice is the key factor that is prioritized by the educators (Bradbury, 2019). Educators to develop the reasoning abilities of the learners use several funny activities.
Figure 2: Curriculum and skill development
(Source: Petrie et al. 2018)
Visualization [V] is in which the student visualizes all the mathematical concepts and numbers, and it helps them to solve the problem even in an effective way. Number visualization occurs when children mentally represent the numbers and compare those numbers. Teachers give them various visual representations of various numbers through cubes and letters so that they can mentally evaluate these. Mental Mathematics and Estimation are one of the important skills that are taught in this curriculum. Mental mathematics is a combination of connotative strategies that allow the students to enhance a strong number sense and flexible thinking. Thus, it helps to do the calculation more quickly and correctly. This particular skill also enables students to propose strategies and determine answers without pencil and paper. It improves computational fluency, accuracy, efficiency and flexibility within the calculation.
The learning requirement and curriculum development are closely related to the development of the whole educational process of the students. Each student from each age group needs different learning strategies and processes. Teachers generally introduce the basic number system to the students who belong to the 3-4 groups (Petrie et al. 2018). Teachers help them to count and give them homework asking them to write from1 to 20. Furthermore, the students from 4 to 5 years old needed to be taught the basic concepts of addition and subtraction. The teachers generally give them the primary idea about how to do addition and subtraction and also give teeth the talk of solving the addition and subtractions. The students go from 5 to 7 years of children and need to be introduced in the number and place values and to develop their basic calculation counting skills. The teachers show them different numbers in the classroom, blackboard, behind the cars etc., to provide a clear idea about the number system. They also need to know the concept of quarters and halves, the measurement of time, backward and forward counting to 100 and the ideas of dividing and multiplying (Rebele and Pierre, 2019). The teachers give tasks to the students from the books provided by the schools, and from them, they ask the students to do the exercises and practice them regularly.
Furthermore, the teacher writes the number on the blackboard and asks the students to practice with him or her to ensure an effective way of learning. 7 to 8 years old students need to be introduced to the 3, 4, 5 and 6 times table, subtract and add two, three and four-digit numbers. Teachers generally give them the counting from 30 to 100 and the tables of 3 to 6 to be learned. Theory gives various exercises from learning process regularly slice at home and also in the school. Students from 8to 9 years of age needed to be taught with the advanced subtraction and addition problems with a special emphasis on complex continuing. They also need to develop their own problem solving and reasoning at this stage. The teacher gives me multiple three and four-digit addition and subtraction in this stage. The students of this age group learn how to solve multiplication and division, and teachers introduce an easy way of solving them. In the students of 9 to 11, the written calculation method and the practice of mental math are needed in the learning process. The concept of algebra and geometry needs to be developed in this stage. The teachers use various shapes and sizes of vicarious elements like dice and cubes to give them basic ideas about geometry.
The “Indian education system” undertakes a series of chapters that are used for teaching mathematics to the students of 3 to 11 years. Chapters like “knowing numbers”, “whole numbers”, “basic ideas of geometry”, “elementary shapes”, “fractions”, “and decimals” and “integers” are some of the major contents of “Indian education”.
The “Indian education system” is organized by some of the supreme “educational facilities” in India. Among them, the “University Grant Commission (UGC) controls the “college education” in India. Then there is “National Council of Educational Research and Training (NCERT)” that controls the secondary education in the Indian curriculum (Raj et al. 2020). Apart from that, there are other organizations like “Indian Council of Agricultural Research (ICAR)” and “All India Council for Technical Education (AICTE)”, that controls the base of the “Indian education system”.
The “Indian education system” is segmented into four different levels categorized for students of different age and merits. The first level is the “lower primary level” where students from age 6 to 10 are enrolled for their initial education. After that, there is “upper primary” level where students from age 11 to 12 are enrolled. Then there is the “high school” where students from the age of 13 to are enrolled for their education. Finally, there is “higher secondary” where student from the age group of 17 to 18 goes for their secondary education. These four levels can be considered the stages of the “Indian education system”.
The “Indian education system” follows the “10+2 system” for creating the stages of education in India. For the students of the 3 to 11 years age group, the math curriculum is segmented into four different parts. First, the “warm-up section” is initiated where students will spend 10 to 15 minutes. After that, there will be “problem solving stage” where possible problems will be solved (Aithal and Aithal, 2020). Then, there is the “focus lesion” stage of “10-15 minutes where students will understand how to focus on getting lessons. Finally, there will be “small group intervention” which may take up to 20 minutes for completing the maths curriculum successfully.
The teaching process can be implemented in a teaching process that should be needed for every student's further future growth and development. The teaching process is essential in the learning process as it allows the students a great opportunity in the overall learning process. The teaching process and the curricula activities are very important in the overall growth and development of a student. In the learning process, the appropriate curriculum activity is needed for the future development of the students. The teaching process and curriculum activities are closely related to each other. Through the proper application of the teaching process, the students will have the opportunity of learning in an effective way. It can only be possible through an effective way of teaching by which the students can be assured of the innovative and effective way of learning. As opined by Sahika (2018), curriculum development is one of the vital procedures that determine the learning assessment and the teaching strategies implemented by the educators towards meeting the learning requirements of the students.
In this chosen curriculum, the students learn the basic concept of addition, subtraction, division and multiplication within the learning process. They learn how to add, subtract, divide and multiply basic numbers. Effective construction of curriculum development enables students to learn in a more effective way. Math is one of the most important subjects that should be given proper emphasis in a particular matter. Knowing and understanding the measurement and calculation of math is very much important to a student from the very beginning of their learning process (Erstad and Voogt, 2018). In this context, an effective and innovative teaching process is needed to enable the students to solve any kind of mathematical problem within their study.
There are different teaching processes that teachers could implement in teaching mathematics. The chosen curriculum for the ages 3 to 11 are being concentrated. Teachers generally apply various techniques and strategies to learn mathematical problems. In the 3 to 4 age group, the teachers mainly focus on introducing the figures and numbers of the math. The teacher gives the students various numbers and asks them to choose the right number from them. When the student grows, the teachers increase the number system and then implement the place value of the numbers. In this stage, the teachers also teach them the basics concept of addition and subtraction and the easy way to solve them.
The teacher uses numicon activities, which allow the students to do math with the help of videos and sheets in the home. The teacher also introduced the number facts in which they taught the students about how to solve any math problem by using five interesting mathematical games. Addition and subtraction are introduced in later stages of the learning process. They use various tools and number images and also the exercises from the books to solve addition and subtraction problems. According to Nouri et al. (2020), the students who belong to the 9- 11 age group are taught the concept of shape and geometry. The teachers generally use various images of cones, cubes, squares, rectangles and triangles to teach the students about the various shapes within geometry.
The teachers can approach an intuitive approach in which the teacher gives examples to the students and then asks the students to find the rule. It is one of the effective ways of teaching, which is considered very effective in learning. As opined by Sahika (2018), teachers also use the collaborative approach to increase the collaboration among the students in learning methods. Teachers divide the students into small groups, and theory gives them slime specific tasks and asks them to solve questions. This further helps the capability of problem-solving in a collective way. Teachers also use the deductive approach within their learning process. This is the traditional way of learning in which, at the beginning of the class, the various information about the target language and rules are presented before the students and then the teacher proceeds by giving various examples. This particular method can be used in a different way, but it is a very useful method and is mostly preferred by the teachers. This is one of the effective learning methods, and it enables the tag to present the idea at the very beginning and then goes to the further details of the subject matter. Thus particle teaching approach is generally taken when the teachers are willing to teach the mathematical rules. According to Sahikaet al. (2020), over the years, most teachers have preferred the deductive approach as it allows the students to have the proper idea and concept at the very beginning and then proceed by exercising the examples of that particular rule.
All these approaches are generally made by the teachers in order to provide the best kind of learning experience to the students. The teachers use all these methods differently in various ways. According to Sahikaet al. (2020), these teaching strategies are implemented by the teachers in the different age groups based on the needs and demands of the students. The teachers are needed to develop all these things in order to implement effective learning within the learning process. Any of these methods can be implemented in the learning process for the development of the students. All these teaching approaches are essential for the teachers to be implemented successfully and effectively. Ensuring all these theories are in an appropriate manner, the teachers, as well as the students, can have the opportunity to effective learning. If all these methods can be applied in a great way, then it will be the future if the students have greater access to the learning method, they can also properly use all the effective learning processes within their study, and such further help them to build the proper future.
The structure of the evaluation in mathematics is based on the principle of contents, learning, and equity. It also calculates how well the mathematics and its topics reflect on students learning. In the educational system, the age group of 3 to 11, represents the students of primary and early primary and covers all the basic topics of mathematics that are mandatory for further studies. For example, in the early age group for giving the basic knowledge of maths, singing songs and rhythm, talking about numbers, reading together, counting and playing maths games are used (Rad et al. 2022). For the reception group building bricks, talking about time, basic counting, spotting patterns and forming numerals were used the most (Bradbury, 2019). In year 1, working with numbers up to 100, basic ideas of addition, subtraction and equals, simple problems of Multiplication and division, recognising and finding the name half, quarter of objects, shapes and quantity, basics of geometry and measurement. In year 2, with a few complex numbers, additions-subtraction and multiplication, measurements and other chapters from part one it includes the basic statistics.
In year 3 the recognition of 3digit numbers, strategies to solve the additions, and the wider and more complex range of shapes, interpretation and present data in a range of ways. In year 4, working with numbers of 4 digits, addition, subtraction, multiplication and division with 4 digit numbers. For statistics, students will interpret the data in bar charts, pictograms and tables (Delalibera and Ferreira, 2019). In Year 5, it works numbers up to 1,000,000, basic knowledge of geometric properties, it involves problems of decimal measurement, time and money. In the final stage Year 6, works with numbers up to 10,000,000 and it includes addition, subtraction, multiplication, division, ratio and algebra, fractions decimals and percentage, calculating and converting the 3 decimal measurements including miles and kilometres, basics of algebra, interpretation and presentation of the discrete and continuous data range.
The learning process of every single student differs from each other by the individuals’ capability of the learning. In the process of teaching, the most important part for a teacher is to understand different types of learning processes (Jooet al. 2020). For proper education, it is mandatory to follow a proper theory to make students understand, especially in maths. In the early years, reception, years 1 to 3 the basics things that students learn are- characteristics of everyday objects, the basic knowledge of size, weight, capacity, positions, distance and time. Discoveries of 2D and 3D objects and solving problems practically support them in their overall development and understanding of the stakeholders which is a student in this context. According to the Cognitive Learning Theory, students can be influenced by both internal and external elements (Mercer et al. 2019). The basic thought process of the students helps them in learning and creates better learning opportunities.
In the years 4 to 6, from counting steps to will be introduced negative, decimal and as well roman numerals, will learn more about angles and symmetry, graphs, learn mental and written calculation methods and will develop skills to solve more complex problems. According to Constructivism Learning Theory, students create their learnings from their past experiences means they take their own experiences and include them in the learning process (Shapiro and Stolz, 2019). It helps them in creating their reality-based solution, which is personal and individual for every student.
At the primary and early primary levels, it is important to learn and absorb the basics of mathematics because it plays the most vital role in life skills. From solving problems on their own to primary knowledge of measurements and shapes, students learn basic patterns of mathematics between their early class to year 6. Teaching maths to primary and early primary level students need to be done using multiple teaching strategies and learning methods (Arnott and Duncan, 2019). However, if the concept of mathematics is unclear and a lack of learning mathematics, in the beginning, can affect further education.
It is observed that in the early ages if the concept of numbers and place values were left unclear, the student faces problems in solving maths in year 1. For that, if colourful images and interesting theories can be introduced in the beginning stage, students will learn easily.
In year 2, if a student finds the basic understanding of statistics complicated, then it will get more complex with each passing year. For clear knowledge, the step of ‘asking and answering the simple questions about Data’ can be followed (Saxena et al. 2020).
Some students encountered problems in understanding shapes and objects properly. For them, the subject 'geometry and shape' can be tough. Without the basic knowledge and recognition of shapes, it is impossible to move further. For those students, teachers can use structures and original objects to make them understand the shape (Cekaite and Bergnehr, 2018). It will help them to make it easy to calculate, measure the shapes and understand the complex geometry.
Every simple to a complex problem is a representation of addition, subtraction and multiplication and division. In year 3, it all starts with 3 digits numbers, if the student is facing a problem in solving questions with 3 digits, it will affect his further study. For help, the teacher can use objects, or coloured paper notes, with those students can experiment and learn how to solve mathematical problems, practically.
Curriculum meeting children’s learning needs
For a better understanding of any subjects at the primary and pre-primary level, the most important thing is to present the subject as per the student's capability. As every student demands a different kind of technique depending on his or her capacity, it should be planned that way. Subjects like mathematics are completely reality-based, that is the reason it demands real problem-solving methods. It needs to plan to keep in mind all the experiences that students will encounter in the reality. Mathematics helps students in developing logic and cultural and moral values among the students. In the beginning, stage if mathematics does not get proper importance in the curriculum, students will not get enough opportunity for mental exercise and in absence of that, it directly affects the intellectual development of students.
Mathematics provides the most effective way to build a proper mental discipline for a student and encourages logical reasoning. At the primary and pre-primary levels, there are very few processes that teachers follow to make students understand maths easily. The first is, Problem-solving skills, it helps students to strengthen their ability to solve problems on their own. It gradually reflects on their personal life and gives them the confidence of solving further problems. In the Reasoning part, it creates a sense of logic in students, which helps them in figuring out the reasons behind every reality-based problem (McDonald et al. 2018). By the time they learned how to solve mathematical reasoning it enhances their capability of learning. Visualisation is one of the best curricula that can be used among the age group of 3 to 11.
It helps students to sharpen their power of visualisation and it reflects on their daily life, gradually it will enhance their mental ability. This is considered one of the best ways to make students learn new things. Mental Mathematics and Estimation is among the most used curriculum to teach maths. It emphasises making a strong number sense for the students that creates flexibility for the students (Barrable, 2019). It helps students in increasing the power of calculation and provides flexibility. All those curricula create depth in students' minds and give clarity to mathematics. As mathematics is a reality-based subject it needs to be solved by real-life experiences, and in the process of learning students start achieving the ability to imply all methods to real problems and try to solve them.
The curriculum is the most important process to make students understand the basic problem-solving methods of mathematics. With each curriculum students' gets the ability to solve their real-life problems too and that helps them in gathering experiences from real problems that they encountered. Not only mathematics but also every subject that is included in primary and pre-primary levels should be taught with the help of a curriculum (Essa and Burnham, 2019). Learner procedure depends on how good the curriculum is and with the best quality of it students thinking and ability can be developed. In this ever changing world, everything should be changed or modified with each passing time (Moss, 2018). It applies to the Curriculum too, with more advanced thought processes students can get more clarity of knowledge and it is going to help them in their higher education.
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