Mathematics as a fundamental science
Discuss about the Determining Specialised Knowledge For Mathematics.
Mathematics is a subject, which has fuelled human progress over countless centuries and still doing. The basic ability to use numbers for counting enabled human being to progress ahead of all the living beings. The mathematical progress has not just limited itself to its subject domain but has also helped the other subjects of not just pure science but also subjects related to the humanities to apply the mathematical equations in their fields of study. The technological progress till date has been possible due to the mathematical and computing abilities of human beings. The usage of mathematics is immense in the daily functioning of human beings. The essay is about my experience of studying mathematics and how to inculcate the interest of mathematics as a preferred subject in young students. The fear of mathematics prevents many people to run away from mathematics without even understanding the subject fully. The mathematical concepts which are fundamental in understanding the subject are essential for the students to comprehend. If the students have conceptual clarity in mathematics, then the subject can be immensely benefitted. The personal experiences of learning mathematics as a young student are shared and how the high school played a pivotal role in making me love the subject. The current trends in high school with some harsh realities as to why mathematics is avoided by many students due to various reasons are also given. The curriculum regarding mathematics in both ACARA and SACE are also mentioned. The future of mathematics is discussed elaborately.
I am a researcher in Mathematics in University of Adelaide. Mathematics being my subject of expertise has had deep and profound impact on my life. It is a truly wonderful subject and is also referred to as the fundamental science which provides the base to all the other sciences dealing with the physical substances of space and time. It deals mainly with numbers and symbols which are operated upon using Mathematical rules and equations. For the common people, the subject appears incomprehensible and difficult to comprehend but with conceptual clarity, Mathematics is one of the most interesting subjects anyone can study. Mathematics mainly emphasizes on reasoning as the universe is made up entirely of matter spread over the space-time quantum so mathematical equations and formulae are used to calculate such complex units. Mathematics can be of two types- Pure Mathematics and Applied Mathematics. Pure mathematics deals with the concepts which are entirely based on the paradigms of Mathematics as a subject. Applied Mathematics on the other hand, deal with the application of mathematics in other fields such as Physics, Chemistry. Mathematics is a subject which develops the intellect as it emphasizes more on the accuracy and reasoning and requires alertness and mental sharpness of the researcher (Huang and Radenovic 2015).
My experience with mathematics education
I was a student of Adelaide High School and my school was the first free high school to be established in South Australia. More than 1500 students are enrolled in this school from Years 8-12. It is a successful and innovative school and is widely reputed high school. The school follows a curriculum which helps in developing the students not just in the academic line but also develops them to become better human beings. While I was at Adelaide High school, I was immensely benefitted by the Pastoral Care Programs which taught me to imbibe skills so as to contribute in a better way to our school as well as our local and global communities. I am grateful to the school for developing in me the fondness for Mathematics as it was because of the conceptual clarity which was mainly due to the efforts of our Mathematics Teacher due to which I am in the position I am at present (Adelaidehs.sa.edu.au, 2018).
It is a big challenge to teach mathematics at the grass-root level especially when the students are in the formative years and have no concepts whatsoever about the subject of Mathematics. I remember when I was just promoted to high school, I was a bit tensed about Mathematics as a subject due to the fear which is instilled in the minds of every person regarding the difficulty of mathematics. The discipline of Mathematics was taught in a very lucid and easy manner by our teacher and it is my good fortune that I was able to clear each and everydoubt on time due to the constant support of my teacher. The curriculum was driven by an all inclusive view-point and the whole class was made a part of the process rather than focusing on one or two potential students who showed promise and had mathematical acumen (Healy,Fernandes and Frant 2013). Now, I realize that this should be the way a subject should be taught as it helps in understanding a subject in a much better way. Everyone has different capabilities and potential; some students grasp the mathematical concepts faster than others but it is important for the teacher to clearly elaborate and define the concepts of mathematics to the students so that they can understand the subject much better and then decide whether or not to pursue further education on that subject (Carrillo et al. 2013). From my own personal experience, I have seen that including all the students into a mathematical research makes one realize that there are multiple ways in which a mathematical task can be completed. Once the teacher made us solve a mathematical equation and it was seen that each of the students completed the task in his/her own unique way and all the processes were correct. This made us learn new mathematical techniques and grasp the subject in a much better way. The current scenario in High Schools is grim as students are seen avoiding mathematics (Taylor and Medina 2013). This is more so in the case of girls than boys. It has been noticed that the teaching of mathematics is done on gendered and class lines. Boys are encouraged to take up mathematics as they perform better. Girls are normally seen not taking up the subjects related to the technical fields (Hausmann 2013).
Challenges in teaching mathematics to young students
The STEM subjects such as science and technology, engineering and mathematics are avoided by the girls due to various reasons. The government as well as international organizations have implemented a lot of policies to encourage more and more women to take up the STEM subjects. Doing this will result in the participation of more women towards nation building as well as reduce the gender gap in education, wages and equality. The common reason of women not taking up STEM subjects is that women are not encouraged to pursue further education fie to the persistence of patriarchal norms in the society, but it is imperative for the High Schools and Universities to inculcate a feeling of equality and self-confidence among the girls from a young age (Gjersoe, 2018). Most of the students selecting mathematics are from rich and high-class families. This should not be the case and the teacher must encourage an all-inclusive teaching of the students. The educational authorities in Australia need to introspect and delve into the matter because in order to realize the potential of the society, all the members need to participate in its growth and development and no group must feel left out (Rothstein 2013).
The importance of teaching mathematics to students of year 8 is of prime importance because this is the age when the impression regarding a subject will stay for the whole life with the student. If I get an opportunity to teach a group of students of year 8 then I will make sure that the students get a proper understanding of the patterns which involve indices and decimals as well as identify the common factors in algebra and arithmetic, understand the linear graphs and importance of statistics and mensuration (Highfieldand Goodwin2013). The emphasis should also be on improving the fluency of the students to accurately calculate equations involving decimals, indices, integers as well as teaching the students how to factorize and simplify basic algebraic expressions. The students of year 8 need to feel that mathematics is not difficult, provided they understand the concepts and have clarity in using mathematical equations. The students need to be appreciated even if they fail while trying because it’s very important to engage the students, to make them competent enough to try new things. Mathematics is all about innovating (Ngurah and Lynch 2015).
The students of year 11 need to be made aware about the immense opportunity of mathematics in the global scenario. The students of year 11 are at the most important juncture of their lives and any decision they take will shape their future, therefore it is important they choose their subjects wisely. If I were a teacher for the students of year 11, then I would focus more on guiding them towards the opportunities of taking mathematics as a subject in their future course of specialization. The clarification of all their mathematical concepts would be of prime importance to me. Also, I would pay more attention to encourage my students to develop an empirical and rational outlook not just towards their subjects but also towards their life as well. The students of year 11 need to be made aware about the different concepts of pure mathematics as well as applied mathematics and encouraged to take up mathematics in their future course as it is a challenging profession but holds immense opportunity for growth and developments. The prospects of taking mathematics are extremely bright as mathematics is a widely sought-after subject and with the development of science and technology, the prospects of mathematics have kept rising higher and higher (Hackling 2014).
Current trends in high school mathematics education
The Australian Curriculum Assessment and Reporting Authority emphasizes on laying the foundation for developing Mathematical skills and knowledge in the students. It aims to develop the numerical capability of the students which are needed in their personal and professional lives and emphasizes on encouraging the students to apply mathematical concepts in their daily lives. ACARA emphasizes more on imparting practical knowledge rather than theory based knowledge. ACARA has explicitly mentioned about the mathematical implementation policy in their website and it was easily available (Acara.edu.au, 2018). The SACE board of South Australia is a professional body of educators which emphasizes on improving the standards of teaching as a profession by providing registration, managing the professional aspects and developing code of ethics for all the educators. Although there are numerous disciplines which are taught at SACE, finding mathematical related documents was not so easy in SACE (Sace.sa.edu.au, 2018).
The future looks immensely bright for the discipline of mathematics as with modernization, the development of the natural sciences the demand for mathematics has always been increasing. The amount of research which is done in Mathematics is a lot more than any other discipline. There is always a great demand for mathematicians in every institutions whether it be for applied mathematics or pure mathematics. Mathematics is the subject which encapsulates the whole of humanity’s progress. Mathematics is driven by logic, reasoning, quantitative analysis and rational judgments. All the other disciplines, including humanities, have some sort of dependence on mathematics for research and empirical analysis. Human progress has been driven by the advancements of science and technology, and scientific innovations were possible because of the mathematical innovations and advancements. The recent progress in space exploration by NASA has made the scope of mathematics open to a whole new level (Skrobot 2015). Every other discipline works in close harmony with mathematical equations. The importance of mathematics is not relevant to the offices, but it is applied in daily life as well. All the bank transactions, the financial deposits, the medical test analysis, the chemical tests and economical as well as statistical calculations are possible mainly due to mathematics. A mathematics degree is held very highly in all over the world and not just in Australia. The constant demand for mathematicians means that a person with a degree in mathematics will never run out of work. There is immense scope to do further research in the subject or if the student wants, he or she can even become professor of the subject and take up teaching as a profession (Grozdev and Dekov 2015). Mathematicians are required by the Government as well to help formulate plans and policies which involve complex calculations and mathematical equations. The status of mathematician in a society is also very high as mathematicians are respected and revered all over the world (Othman et al. 2015).
Encouraging girls to take up STEM subjects
From the above analysis, mathematics is a subject which has always been in high demand. It is imperative that the fundamental concepts of mathematics are cleared for the students from a very young age as anything which is learnt in the formative years of one’s life stays with an individual for a long time. The fear regarding the subject must be removed from the minds of the students by making them feel at ease while doing mathematical equations. Mathematics should also not be segregated on the basis of gender or class and must be taught with an all-inclusive approach. The teacher teaching mathematics must encourage the whole class to be interactive while solving mathematical problems as interaction will result in the removal of doubts which might arise in the minds of the young students. The more the doubts are clarifying the better for the grasping of mathematical knowledge. The students who are in the final years of their high schools must be made aware about the immense opportunities and prospects of taking up mathematics as a professional subject. The scope of research is huge in mathematics. The demand of mathematicians is always high whether it be in the pure mathematics or in the applied mathematics. Mathematics must be treated as an important subject in schools and universities as it helps an individual develop the traits of intellect, accuracy, rationality, logical reasoning.
Reference
Acara.edu.au. 2018. ACARA – Mathematics – Foundation to Year 12. [online] Available at: https://www.acara.edu.au/curriculum/learning-areas-subjects/mathematics [Accessed 1 May 2018].
Adelaidehs.sa.edu.au. 2018. Home – Adelaide High School. [online] Available at: https://www.adelaidehs.sa.edu.au/ [Accessed 1 May 2018].
Carrillo, J., Climent, N., Contreras, L.C. and Muñoz-Catalán, M.D.C., 2013. Determining specialised knowledge for mathematics teaching. In Proceedings of the CERME (Vol. 8, pp. 2985-2994).
Gjersoe, N. 2018. Bridging the gender gap: why do so few girls study Stem subjects?. [online] the Guardian. Available at: https://www.theguardian.com/science/head-quarters/2018/mar/08/bridging-the-gender-gap-why-do-so-few-girls-study-stem-subjects [Accessed 1 May 2018].
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Hackling, M.W., 2014. Challenges and opportunities for Australian science education. Professional Educator, 13(5), pp.4-7.
Hausmann, R., Tyson, L.D., Bekhouche, Y. and Zahidi, S., 2013, March. The global gender gap index 2012. In World Economic Forum.
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Highfield, K. and Goodwin, K., 2013. Apps for mathematics learning: a review of’educational’apps from the iTunes App Store.
Huang, H. and Radenovic, S., 2015. Common fixed point theorems of generalized Lipschitz mappings in cone b-metric spaces over Banach algebras and applications. J. Nonlinear Sci. Appl, 8(5), pp.787-799.
Ngurah, A.A.M.I.G. and Lynch, D.P., 2013. A confirmatory factor analysis of attitudes toward mathematics inventory (ATMI). The Mathematics Educator, 15(1), pp.121-135.
Othman, H.R.H., Suhaimi, Z., Shahrill, M. and Mahadi, M.A., 2015. To pair or not to pair: Investigating the dynamics of teacher-student interactions in different classroom settings. Turkish Online Journal of Educational Technology, pp.675-684.
Rothstein, R., 2013. Why our schools are segregated. Educational Leadership, 70(8), pp.50-55.
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Skrobot, G., 2015. NASA Launching Your Small Satellites.
Taylor, P.C. and Medina, M.N.D., 2013. Educational research paradigms: From positivism to multiparadigmatic. The Journal of Meaning-Centered Education, 1(2), pp.1-13.
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