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An academic curriculum is designed to equip the learners to learn from the skills taught in a way they will be able to apply the taught skill in a real-life situation or in the advancement of a certain concept later in life. The paper’s main focus will be on the various Australian academic levels, a brief description of the **mathematical modelling** concepts taught in the various primary levels, the examples of resources used in the development of mathematics among the students and rationalization of how each of the resources enhances student learning and engagement in the content taught.

The obvious reason to create a future-oriented curriculum provides an opportunity for improved and intensive teaching methods. It is evident that the future’s society will be multifarious and competitive, so as to ensure that the future inhabitants of that society thrive well, the change that will change the future will have to begin from the present times.

The aims of the Australian mathematics curriculum include educating young Australian citizens, enhance their activeness and incorporate mathematical concepts in the ways they predict future events such as financial planning and make personal decisions. Maths learning also enhances and enriches the learning of other subjects and concepts that may include in other learning disciplines. It is also designed to change they way of thinking of citizens. Once the citizens are able to think in a mathematical manner, they are able to come up with accurate future and problem-solving plans that will greatly impact on the development of the nation as a whole. Moreover, math has its own beauty once understood and it is intended that every learner will appreciate the role mathematics plays in improving their ways of thinking.

It is evident to everyone that all curriculums are developed depending on a child's age. This section of the paper tends to look deeper into the mathematical concepts that can be taught in the various levels of the curriculum. Since the Australian curriculum is so vast, the paper will just take an example of one year in each of the curriculum levels which can be divided into Years K-6 which comprises of pupils who are 5-12 years old, years 7-10 which comprises of students between 12-15 years old and years 11-12 which comprises of students between 15-18 years old.

In the early years of the curriculum, this paper will focus on the year 2 class which comprises of students typically aged 8 years old. During this stage, the best concept that would fit this type of students would be the intensive learning of numbers and algebra. By this year, the students are more familiar with numbers and basic ways to apply them in their studies and real life. However, for them to advance further in the understanding of numbers at a later stage in their curriculum, they need to be familiar with algebra.

The reason as to why algebra should be taught at this early stage is because it is known as the ‘gateway subject’. By using the term ‘gateway subject’, this means that without the understanding of algebra, a student is not able to understand future math concepts that will be introduced later in the curriculum. Such math concepts include trigonometry, calculus and geometry. Secondly, algebra provided learners with knowledge and expertise for making daily life decisions and it also sets the trajectory in the rest of the math education of the student. Most of the colleges also recruit new students with a series of exams which Algebra is a part of dominantly. If a student does not pass the algebra based test, they are required to take supplementary classes that will ensure they learn algebra. But so as to avoid such inconviniences, it would be important that algebra is introduced at an early stage in a student’s life. In most of the practical courses at the university, one is also required to have an advanced knowledge algebra.

As for the middle level of the curriculum which comprises of years 7-10 which comprises of students between 12-15 years old. In this section, the paper will focus on the curriculum of students in year 7. During this stage, the students are so much familiar with both numbers and algebra. Hence, their understanding in those sections should enable them to learn and gain the understanding of measurements and geometry.

Geometry includes all the concepts such as area and perimeters, triangles and trogonomety, angles and lines and other shape related problems. Studying geometry enables a student to to develop skills which include problem solving, logic among many others. It improves and individuals way of visualizing shapes when practiced frequently. Geometry is also linked to so many other areas of maths such as when students begin to learn about 2D shapes and their properties, they will need to have relative knowledge in geometry.

Geometry is of major importance when it comes to the career development of students who want to focus in areas such as architechture, interior designing and computer animation. For architects and interior designers, they need to ensure that all angles and measurements are done precisely to ensure that the building is safe to live in. Mistakes made in such areas would be greatly catastrophic. For those dealing with computer animation, will use geometry as they construct animated films.

The upper level of the curriculum comprises of students of years 11-12 who are aged between 15-18 years old. They are the upper most level in the curriculum. Moreover, this would mean that they are well educated and have acquired most of the mathematical skills one would expect them to have. As a result, they should be introduced to more complex mathematical concepts which enable them to become more competent in math. Such a concept would be on Statistics and probability.

Statistics and probability are on of the most important skills one can gain. Do people tend to ask why is this skill of importance? This paragraph will explain the importance of this skill in everyday life. Firstly, we ourselves were a probability before we became who we are. Nobody knew of who he/she was going to give birth to when they were pregnant. During conception, it all depended on the sex cells which were numerous. Moreover, nobody is normally sure about the future, as a result, humans have learnt to work with probability as a means of survival. An example is when you walk on foot in a game park full of predators, the probability of being killed by the predators is high than when one is walking on the streets of a city. Hence, no one would dare to walk alone in a game park because of his/her understanding of probability. As for statistics, it enables one to present data in a more presentable and efficient way and hence can be used in future to determine future events from past experiences.

Generally, we have seen the development of the above described mathematical concepts in the curriculum based on the various levels. In the early stage, the paper focused on the importance of numbers and algebraic expressions in the students’ development in the subject. The paper has described the process in which most especially algebra plays a major role in the mathematical development of a student. The paper described algebra as a ‘gateway subject’ which enables the student to understand further more complex mathematical concepts taught at a higher level. The paper also went on to focus on the middle level curriculum where it discussed the importance of learning geometry and measurements at that particular stage. The main reason was that geometry needed to be learnt at an early stage to enable the student to gain first hand experience in the subject especially those who were to take up careers related in geometry and measurements.

The study also focused on the higher level curriculum which described the importance of learning probability and statistics. The subject is more based on future forecasting, survival and **data analysis** representation. The topic can be described as a ‘wrapper subject’ most especially statistics which involves mathematical data organization and representation.

In today's world, technology has become the back bone of many activities and institutions. As a result of the advancement of technology, it has made things easier for everyone. One of the latest teaching methods is through the use of technology. One of the example technology has impacted the education sector is through the use of multimedia. Multimedia includes pictures and clips. They play a big role in the curriculum as they enable the students to capture a better picture of what they are being taught. An example is when a student is taught about the circulatory system without the use of picture or demonstrations, they are likely not to understand the concept being taught. But when they are taught using pictures and clips of how the circulatory system works, they visualize of how it functions and they are able to understand more of the concept being taught. The same principle would apply in how they understand the mathematical concepts being taught.

This type of method is efficient across all the levels of learning. As for the learners in the lower level, since they have a limited experience on learning new things, they tend to understand further through this kind of method as the images and videos shown to them sticks in their mind and hence they understand what they are being taught. As for the students in the middle and upper levels, this tends to become an effective mode of learning most especially where they are introduced to completely new concepts that they don’t have an understanding of. This can also be used to enable them to to remember of the concepts taught in class. It is also widely used when complex concepts are introduced, ones which they are not familiar with.

Another ICT resource that could be used in the math curriculum development of the students would include the use of e-learning sites. E-learning sites are normally a meeting point of the teachers and students at an individual and corporate level. The teacher is able to post the various learning materials students require such as notes and past papers. The most important value incorporated by the e-learning system is consistency. This is as a student is able to track his or her personal development using the site. The teacher is also able to check on the progress of each and every individual student and also the class as a whole. This ensures that both the teachers and most especially the students become responsible and accountable for their progress.

Thirdly, another resource that can be used in the enhancement of learning would be the invitation of local experts and carrying out of field trips. Invitation of experts in a classroom setting mskes the student’s learning become more interactive and they are able to relate with the reality of the mathematical concepts being taught in class. An expert also poses extra knowledge which the teacher doesn’t have, hence he/she may impart some great understanding and knowledge of the concept hence enhancing the students learning capabilities.

Carrying out of filed trips also enhances the students learning as they are able to visualize and understand the real life applications of the topic that they are being taught. Hence they are able to understand more of what they are taught in class. Carrying out field trips also enhances the learning abilities of the student as it makes learning more fun, unlike the normal classroom setup. When the students become interested in whatsoever they are learning, they gain a better understanding of the concept being taught. Carrying out of field trips applies to all the three levels of the curriculum. However, it is most effective amongst the highest level of the curriculum as they have learnt on the methods used to gather more reliable information during a field trip and ways they can record the data that they have collected.

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