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Informed approach to curriculum planning in mathematics

Introduction

In the recent era of globalisation, there are increasing numbers of research and developmental activities along with different thesis papers, where mathematics is plying a crucial role. The researchers try to utilise mathematical formulas to resolve the problems and draw final conclusion and thus there is different application of mathematics in different subject matter of interest. Hence, mathematics is important to many researchers along with policy makers and others, who try to develop creative solutions through mathematics (Van der Nest, Long and Engelbrecht, 2018). The study focuses on curriculum planning of mathematics where the teaching professionals are engaged with the subject mathematics for providing the best learning programs to the students. Curriculum planning in mathematics must be organised and developed efficiently after reviewing different aspects of curriculum and the importance of different forms of mathematics. There are several aspects of mathematics which are necessary to be included in the curriculum, so that the learners can maximise their knowledge and skill in the subject matter of interest. This literature review is base of the specific subject mathematics, where the discussion on different mathematical aspects will be helpful for the teachers and curriculum planners to develop good curriculum planning. The rationale of choosing the subject mathematics as well as the aspects of different curriculum planning in mathematics will be evaluated by reviewing different books and published journals.

Rationale of choosing mathematics

Mathematics is a fundamental part of human thoughts and logic as well as it is integral to understand the world. It provides an effective way of building mental disciplines and encourages logical reasoning and mental rigor. Hence, in the educational field and research field, mathematics is playing a crucial role in develop human thoughts and improve the capabilities of the people to perform better. In the school subjects, it is hereby an important part and along with this, in the higher studies, the teaching professionals try to develop good curriculum planning so that the student can get support to improve their skill and knowledge in resolving mathematical problems and other critical issues in research activities. Mathematical literacy is hereby a crucial attribute of the individuals living with more effective lives as constructive, concerned and reflective citizens (Van der Nest, Long and Engelbrecht, 2018). Mathematical literacy is taken to include basic computational skills, quantitative reasoning, spatial ability etc. where the researchers and students are utilising mathematics in daily life and also in critical researches. Mathematical concepts and procedures are used to solve problems in science, engineering, economics and additionally, the understanding of complex numbers is a prerequisite to learn many concepts in electronics. Hence, curriculum planning in the subject of mathematics must be planned accordingly since mathematics provides foundational knowledge and skills for other school subjects, such as sciences, art, economy, etc. Nowadays, the integrated course structures are developed across the world to support the students with mathematics and other core subject area of interest. Hence, mathematics is a key subject which is required to resolve different problems in science, electronics and other field of research (Gueudet, Pepin and Lebaud, 2021). Hence, both quantitative and qualitative description of mathematics is important to develop a good curriculum planning for supporting the students and other researchers in specific research field. The literature review is effective to review different aspects of curriculum planning in organising the courses of mathematics and supporting the students with adequate books and journals to develop their understanding and knowledge in this subject area.

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Aspects of the curriculum planning in mathematics

Mathematics has evolved with science of structure, order and relation as well as counting, measuring and describing the shapes of objects. Mathematics deals with logical reasoning and quantitative calculations. Since the 17th century, it has been an indispensable adjunct to the physical sciences and technology, to the extent that it is considered the underlying language of science (Pepin et al., 2017). There are several branches of mathematics which includes algebra, analysis, arithmetic, combinations, game theory, number theory, optimisation, probability, set theory, statistics and topology as well as trigonometry and geometry. Hence, there are several aspects of curriculum in depending the mathematics courses for supporting the students in learning and improving own knowledge on this subject matter of interest (Trouche et al., 2019). Before designing and planning the curriculum in mathematics, the teaching professionals review the aspects of the curriculum planning by considering different branches of mathematics so that it would be possible to develop good curriculum structure and include different mathematical aspects for guiding the students and enhancing learning and developmental programs. The major braches of mathematics will be evaluated further in order to design good curriculum planning in the subject matter, mathematics.

Algebra

Within the broad field of mathematics, algebra is effective to solve complicated generic algebra expression by manipulating them to come up with the final answer. It involves several rules and complicated formulas that manipulates the equations and derive the ultimate solutions from the problem posed. The quantities within the said equations are unknown to us and therefore not represented via numerical digits, instead, they are represented within the equation via a variable, which could be any character from the English lexicon, ‘a’, ‘x’, ‘b’ or ‘c’, sometimes Greek and Latin lexicons are used as well (Baker and Galanti, 2017). Hereby, Algebra is one of the most important branches of study for mathematics and is applied in various other fields of study where the teaching professionals must include algebra in the mathematics curriculum course to improve knowledge and understanding among the learners and researchers for resolving the solutions in diverse field such as physics, biology, engineering, biotechnology, chemistry, as well as economics and accounting. there are also several examples of utilising algebra in daily life such s tax calculations, developing effective technologies, budgeting as well as developing spatial intelligence, making schedule for activities and astrological calculations (Pepin et al., 2019). Hence, algebraic expressions are necessity for the students to understand this branch of mathematics and develop own knowledge in resolving different mathematical problems.

Arithmetic

Arithmetic is another main branch of mathematics, which is mandatory to be included in developing curriculum planning of the subject mathematics. It involves in dealing with numbers and their applications in calculations etc. Properties such as simple addition, subtraction, multiplication, and division come into play here and there are basic calculations that the students can understand and perform better in future for resolving critical problems. Despite being simple, it is the root reason why the people are now able to solve the most complex of the problems and come up with a solution. Arithmetic also involves more complex concepts of mathematics such as limits, exponents, etc. Hence, for curriculum planning, arithmetic is paying crucial role in developing knowledge of the individuals in simple calculations and it is mandatory in daily lives to stay with effective standard of living (Trouche, Gueudet and Pepin, 2018). It is also essential in future for getting employed and fulfilling the professional career aim of the people.

Number theory

Number theory is a branch of pure mathematics devoted to the study of the natural numbers and the integers. It is the study of the set of positive whole numbers which are usually called the set of natural numbers, where the learners can identify the numbers and resolve the mathematical issues successfully. Number theory is one of the oldest branches of mathematics which is effective for the evolution of computers and internet (Hu et al., 2020). The numbers theory involves establishing a relationship between a set of real numbers, integers, whole numbers and natural numbers. Properties of numbers such as addition, subtraction, multiplication, modulus which further branches out to the associative and dissociative properties are involved in the number theory. It also deals with the concept of encryption, binary and cryptography as well as game theory. Hence, the numbers theory is effective branch of mathematics and the teaching professionals must encoded this in the mathematics coursework to maxims knowledge and efficacy of the students in numbers. Number theory is effective in mathematics for the pupils who are learning mathematics to understand the concepts of the numbers and integers and resolve the mathematical problems successfully. Additionally, in computer science and internet technology, the number theory is applied for exploring creative solution. Hence, the mathematic teaching professionals must include numbers and calculations in the coursework in order to support the pupils.

Geometry

It is also another major branch of mathematic that includes the shapes such as squares, circles, rectangles and triangles but in depth, these are not only just shapes, but also angles, tangents and volumes. It involves the study of angles, shapes, sizes, figures, or any geometrical object in both the dimensions, 2D and 3D, where the 3 dimensional figures are such as cubes, cones, bars, spheres etc. trigonometry is another form of geometry which is also widely utilised and hence, in the primary and secondary education as well as in higher studies of mathematics, inclusion of geometry is mandatory as an important part of mathematics. The teaching professionals try to include different shapes and figures to apply the geometry calculations for exploring final solution. Trigonometry specifically focuses on studying the angles and sides of the triangle in order to determine its distances, lengths, and other properties and these are also applied in daily lives for resolving critical problems. Different properties of geometry and calculations are acknowledged by the pupils where the teaching professionals must consider the geometry in the coursework of mathematics (Pepin, Gueudet and Trouche, 2017).

Statistics and probability

This is another most important ranch of mathematics which is mandatory in the mathematics curriculum planning so that the pupils can get effective coursework with statistical programs and probability. Probability utilizes mathematical concepts to predict events that are likely going to happen and on the other hand, statistical interpretation and analysis re as much as important in mathematics along with other research field and daily life. The researchers and policy maker conduct in-depth research and developmental projects which is based on the statistical analysis. Hence, statistics is mandatory to be included in the curriculum planning, so that the students can understand the concept and apply the formula for data analysis in future. For completing the researches, the statistical analysis is essential where the researchers acknowledge different data collection and data analysis methods for meeting the research objectives. It is applied in various fields of natural and social sciences such as marketing (Trouche et al., 2019). Hereby, the statistical analysis must be known to the students which includes SPSS analysis, mean, median and mode analysis correlation coefficient and regression analysis and apart from that, there is also descriptive statistics, such as tabular representation, using diagrams and charts which are effective for sorting the data and analysing it to draw final conclusion. Hence, statistics and probability must be included in the mathematics curriculum planning, so that the teaching professionals can provide effective resources and guidance to the students to develop their abilities to perform statistical functions for conducting in-depth research and analysis.

Topology

It is another form of mathematics and Topology is applied in calculus, knot theory, Riemann surfaces, etc. it is mainly utilised in defining layouts of network, its structure and shapes physically and logically, hence, for mathematical analysis, topology is widely utilised. There are two types of network topologies which are physical and logical. Physical topology emphasizes the physical layout of the connected devices and nodes, while the logical topology focuses on the pattern of data transfer between network nodes. Calculus is hereby also another coursework which is mandatory under the subject area, where the teaching professionals try to learn the students about continuous changes which are the combination of arithmetic algebra and shapes (Trouche et al., 2019).

The above mentioned branches of mathematics are mandatory to design an effective curriculum planning, where the teaching professionals must include all the areas of mathematics to teach the students about the concepts, mathematical analysis, reasoning including logical and physical as well as arithmetic and geometry. It is hereby a vast subject which is mandatory to be developed efficiently where the teaching professionals focus on the coursework so that they can develop a structured curriculum planning. Vast range of mathematical braches long with the aspects of curriculum planning will provide a scope to the professionals to arrange study materials and support the students with effective mathematics coursework.

Discussion on future curriculum organisation and planning

Curriculum design can be referred as purposeful, deliberate and systematic organisation of curriculum within the coursework, where it is helpful or the students to get a structured course for developing their understanding and knowledge in a specific subject matter of interest. It is the role of the teaching professionals in the educational institutions including schools, special educational system and colleges, to arrange effective curriculum planning on the subject mathematic (McDuffie et al., 2018). Mathematics is itself a complex subject which needs in depth knowledge and expertise to teach the pupils in the institutions, hence, the teaching professionals are skilled and they have the experience in teaching mathematics by arranging good study materials and supporting the students with practical classes and theoretical classes. The major purpose of developing curriculum planning is to support the students with structured coursework on mathematics, which covers basic mathematics and critical problem solving in mathematics, so that the student’s abilities in solving mathematical problems along with conducting different research and thesis papers can be maximised. There are several ways to develop good curriculum planning which includes subject matter design, learner centred design and problem centred design. Generally, in schools and colleges, the teachers and staff members focus on subject centred curriculum planning, in order to design the course structure and provide effective resources for learning and skill enhancement programs (McDuffie et al., 2018). Subject-centred curriculum design revolves around a particular subject matter where it is the core curriculum planning that supports the whole educational system. For the subject mathematics, in school and college coursework, all the braches of mathematics such as mathematical analysis, algebra, number theory, geometry, topology, probability and statistics are mandatory to be included. These branches are effective for the students to get basic idea of mathematics and improve their knowledge in each branch of the mathematics.

In addition to this, learner centred curriculum design is another aspect of organising and planning the curriculum and casework, where I is based on the choice and preferences of the learners in the educational institutions. Learner-centred curriculum design takes each individual's needs, interests, and goals, where it provides a scope to empower learners and allow them to shape their education through choices. The earners are getting involved to choose the coursework and it is mainly useful for the higher studies and the mathematic oriented research and developmental practice. It gives the opportunity to the students to choose assignments, learning experiences or activities and further motivate the learners to access the study materials and coordinate with the teachers for fulfilling their personal and professional career aim (Olivares, Lupiáñez and Segovia, 2021). On the other hand, problem centred curriculum design is also another aspects of curriculum design where the teaching professionals can organise and plan the course working the basis of the problems to come up with the creative solutions. Students are thus exposed to real-life issues, which helps them develop skills that are transferable to the real world. Hence, for the educational research and thesis papers, the teaching professionals arrange professional training and curriculum planning to support the student for developing their knowledge and skill set to perform better (Remillard and Kim, 2017). It is also one type of the student centred approach where the learners can choose the curriculum on the basis of their choice and preferences. Hereby, for the student centred approach, the teaching professionals aim at empowering the students and arrange student counselling session, for acknowledging their requirements and proposing them a good curriculum planning on the specific subject mathematics. Mathematic is a complex subject with different branches and this student centred approach provides a scope to the students to choose differentiated coursework as per their academic and professional career aim.

As per the discussion, it can be stated that, the teaching professionals must focus on the objectives of the curriculum planning and organise the coursework activities and arrange adequate learning resources for the students. In schools and colleges, the different branches of mathematics are mandatory to be included (Hajer and Norén, 2017). Arithmetic and algebra are essential branches that help the students to understand different equations and resolve the mathematic problems. Along with this, the calculus and mathematical analysis as well as topology are also mandatory in the higher studies, to support the students with mathematical problems and social researches, so that they can perform better and conduct in-depth analysis in different field such as marketing, data analysis, economic and finance, accounting and business analysis. on the other hand, probability and statistics as well as geometry are others forms of mathematics which are also essential to include in the coursework to support the students with data analysis process by utilising statistical tools and geometric solutions (Hassan et al., 2019). Continuous communication among the teachers and education authorities along with collaborative decision in organising the curriculum planning on mathematics will be helpful for the teachers to restructure the courses and provide an effective coursework to the students with adequate learning resources and practical works.

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Conclusion

As per the discussion, the informed approach to curriculum design on the specific subject mathematics is mandatory to provide the best coursework to the students. In this regard, identifying the aim of the curriculum planning, exploring teaching methods, content of the books and journals, time table of the courses, educational standard and collaborative decision making practice are effective step to structure the mathematics curriculum planning for supporting and guiding the students with effective classwork, practical session and study materials. The teaching professionals also need to interact with the students and identify their problems in mathematics to restructure the coursework and this student centred approach is beneficial to engage the learners and motivate them to learn more and acquire skill in conducting mathematical research and resolving the mathematical problems.

Reference List

Baker, C.K. and Galanti, T.M., 2017. Integrating STEM in elementary classrooms using model-eliciting activities: responsive professional development for mathematics coaches and teachers. International Journal of STEM Education, 4(1), pp.1-15.

Gueudet, G., Pepin, B. and Lebaud, M.P., 2021. Designing meta-resources for mathematics teachers in the context of curriculum reforms: the case of digital technology use and student autonomy in France. ZDM–Mathematics Education, 53(6), pp.1359-1372.

Hajer, M. and Norén, E., 2017. Teachers’ knowledge about language in mathematics professional development courses: From an intended curriculum to a curriculum in action. EURASIA Journal of Mathematics Science and Technology Education, 13(7b), pp.4087-4114.

Hassan, M.N., Abdullah, A.H., Ismail, N., Suhud, S.N.A. and Hamzah, M.H., 2019. Mathematics Curriculum Framework for Early Childhood Education Based on Science, Technology, Engineering and Mathematics (STEM). International electronic journal of mathematics education, 14(1), pp.15-31.

Hu, S., Torphy, K.T., Evert, K. and Lane, J.L., 2020. From Cloud to Classroom: Mathematics Teachers' Planning and Enactment of Resources Accessed within Virtual Spaces. Teachers College Record, 122(6), p.n6.

McDuffie, A.R., Choppin, J., Drake, C. and Davis, J., 2018. Middle school mathematics teachers’ orientations and noticing of features of mathematics curriculum materials. International Journal of Educational Research, 92, pp.173-187.

Olivares, D., Lupiáñez, J.L. and Segovia, I., 2021. Roles and characteristics of problem solving in the mathematics curriculum: a review. International Journal of Mathematical Education in Science and Technology, 52(7), pp.1079-1096.

Pepin, B., Artigue, M., Gitirana, V., Miyakawa, T., Ruthven, K. and Xu, B., 2019. Mathematics teachers as curriculum designers: an international perspective to develop a deeper understanding of the concept. In The'Resource'Approach to Mathematics Education (pp. 121-143). Springer, Cham.

Pepin, B., Choppin, J., Ruthven, K. and Sinclair, N., 2017. Digital curriculum resources in mathematics education: foundations for change. ZDM, 49(5), pp.645-661.

Pepin, B., Gueudet, G. and Trouche, L., 2017. Refining teacher design capacity: Mathematics teachers’ interactions with digital curriculum resources. ZDM, 49(5), pp.799-812.

Remillard, J. and Kim, O.K., 2017. Knowledge of curriculum embedded mathematics: Exploring a critical domain of teaching. Educational Studies in Mathematics, 96(1), pp.65-81.

Trouche, L., Gitirana, V., Miyakawa, T., Pepin, B. and Wang, C., 2019. Studying mathematics teachers interactions with curriculum materials through different lenses: Towards a deeper understanding of the processes at stake. International Journal of Educational Research, 93, pp.53-67.

Trouche, L., Gitirana, V., Miyakawa, T., Pepin, B. and Wang, C., 2019. Studying mathematics teachers interactions with curriculum materials through different lenses: Towards a deeper understanding of the processes at stake. International Journal of Educational Research, 93, pp.53-67.

Trouche, L., Gueudet, G. and Pepin, B., 2018. Open educational resources: A chance for opening mathematics teachers’ resource systems?. In Research on Mathematics Textbooks and Teachers’ Resources (pp. 3-27). Springer, Cham.

Van der Nest, A., Long, C. and Engelbrecht, J., 2018. The impact of formative assessment activities on the development of teacher agency in mathematics teachers. South African Journal of Education, 38(1), pp.1-10.


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