Kerry and Emily make a persuasive argument that we should learn Mathematics with understanding on how it is applied to our daily lives. They made a compelling augment that most schools present Mathematics as a difficult subject. They further argue that the emphasis of most school curriculum is grades and not pragmatic understanding of Mathematics.
The article is a well-knitted compelling read and with a call for action conclusion for more discussion on in-depth learning and more understanding of Mathematics
I think Mathematics is misunderstood by most people. It is not some big revelation that many people don’t quite ‘get’ fractions or concepts of trigonometry; articles upon articles are written about the poor performances of school students in standardised mathematics tests, and while that is concerning in its own right, perhaps the bigger loss to society is not in the misunderstanding of mathematics syllabi, but actually in the misunderstanding of mathematics as a science. Mathematics is a logical framework that triggers critical thinking, abstract thinking, and creative thinking, and that fosters effective communication. The public image of mathematics paints it out to be some exclusive practice for the gifted, that is done to display intellectual prowess, or to solve some problem that appears in the work of only maybe an engineer or a physicist. Mathematics is not arithmetic. Studying mathematics is not redundant in your life just because you have access to a calculator, and search engines. To reiterate: The importance of studying mathematics does not lie in the ability to restate theorems and ‘do sums’, just as how the importance of studying a language does not lie in the ability to apply grammar rules and identify parts of speech, but say perhaps rather in the interpretive, analytical thinking, and communicative skills that a school student may learn when studying a piece of literature.
Mathematical skills have applications in everyday life. For example, logic is a fundamental aspect of mathematics; mathematical proofs begin with an assumption and end with a conclusion that is reached through logical reasoning. Common sense is just real-life logic! Most decision-making involves the process of predicting which decision shall have the outcome that is most favourable to your needs. In other words, you are predicting the outcomes of decisions through logical deduction. To provide a simple example: If you see that the weather forecast predicts that it is going to rain (you are treating the occurrence of rain as your assumption), then by that assumption you further predict that you will get wet when walking outside, (because you have a ‘rule’ or an ‘axiom’ in our natural world that says that walking in the rain makes you wet) and so you decide to bring an umbrella with you today (because you also know that an umbrella will protect you from getting wet). In making the simple decision to carry an umbrella with you when rain has been predicted, you have unknowingly applied multiple mathematical concepts such as an implication (rainy weather implies getting wet if you walk in the rain), and a proof by axioms, achieved using logical deduction.
What would life be without logic? It would be pure chaos! People would constantly be doing things without any common sense. Problem solving is a fundamental skill of mathematics and is very useful in everyday life. Unfortunately, it is a rather underdeveloped skill. Schools heavily focus on teaching pattern recognition of problems rather than how to actually solve problems in general. Often the reasoning behind the solution is disregarded.
Perhaps if there was a higher focus on developing problem-solving skills in mathematics class at school, we would all benefit from it. Sometimes people who achieved distinctions in mathematics at school fail their introductory mathematics courses at university because the skills are quite different. At university it’s impossible to just memorise what to do when you see something of a specific form, but the skill of how one can use their knowledge to find the answer and make a logical conclusion.
A better understanding of logic and improved problem-solving skills will help one better manage their time and money, a very helpful skill in life. Mathematics is visible all throughout our lives, and although a person does not need to take a maths lesson to know to bring an umbrella out in the rain with them; the development of mathematical skills will allow them to tackle more difficult life problems tactically and effectively. For example, a person who is more mathematically literate, would be less susceptible to falling for seemingly cheap payment plans that amount to far more than an items retail value, or they could better explain their reasoning for making a decision to someone else, as they’d have an enhanced ability to follow logical process in each step of coming to a conclusion. Problem-solving skills are so sought-after and useful, and so it would make sense to take full advantage of the potential that mathematical teaching has to develop such skills among other important skills that are developed through mathematics such as creative thinking and effective communication? Unfortunately, the public persona that mathematics currently has does not associate it with universally relevant and accessible skills beyond maybe basic arithmetic skills which are felt by many to be more and more redundant as basic technology becomes so widely accessible.
You cannot blame people for not seeing the relevance of learning mathematics to their lives, because mathematics is consistently misrepresented in school classrooms and in media. By portraying mathematics as an inescapably difficult subject that only a small minority could possibly enjoy, apply, and succeed in studying, a psychological block is placed on students who consequentially struggle to believe that they could ever understand mathematics. Film characters who take an interest in mathematics are portrayed as ‘nerdy’, and abnormal. When school students aren’t part of the top performers in their school mathematics class, then they conclude that they are not one of these ‘nerds’, and thus they are not suited to do mathematics. When do we ever see stories about students who are passionate about mathematics, but not necessarily ‘good at it’? In reality: studying mathematics is not a binary: You aren’t either great at it or awful at it, and you do not have to explore high-level concepts to gain most of the skills that mathematics can give you. Sure, maybe the ‘nerd’ will go on to be an actuarial scientist or a mathematician, whose career is centered in mathematics, but the everyday student will still be living a life surrounded by mathematics, as has been described previously. School students would be more inclined to consider the importance of mathematics in their lives if they could see that there is actually a place for them in mathematics regardless of their perceived academic abilities.
Schools teach content for students to acquire academic results and ultimately qualifications, not to acquire skills. School students are not exposed to enough real-world examples of the concepts that they study, and so the importance of studying mathematics in their lives appears to be just a means of obtaining grades and achieving qualifications. Grades can be incredibly misrepresentative of a student’s mathematical abilities and understanding. The use of grades as a measure of a student’s mathematical understanding leaves students thinking that just as how good grades imply good mathematical understanding, so too does a good mathematical understanding imply that you achieve good grades, or else your understanding is inherently poor (may the irony of the incorrectly evaluated implication stand as a case study). Grades holding the highest position of importance means that understanding the content is often not attempted if decent grades can be achieved without having to understand the work. For example, students try to recognize and reiterate patterns in the solutions to problems rather than obtaining the solution to the problem by solving it themselves. The students will obtain the marks because of their correct solutions, despite having no understanding of how that solution was reached. In addition to not encouraging proper understanding, the heavy emphasis on grades can also misrepresent the capacity of a student’s mathematical understanding, as perceived by the student. If you are going to equate a grade with a student’s understanding of mathematics, then students are going to consider the maximum grade that they can achieve in mathematics to be representative of their learning-capacity, and in turn, the maximum level of ‘value’ that mathematics can provide to their lives.
Mathematics is an existing subject in school systems that, can be used as a vessel to develop important skills in society. Until schools prioritize understanding over grades, school students will continue to neglect the importance of understanding in learning mathematics. Until school students are cleansed of the belief that they cannot pursue, enjoy, or benefit from studying mathematics unless they are the top performers in their class, then most school students will feel that mathematics is not worth their while. Mathematics is relevant in the lives of everyone – Not just people whose occupations have them writing down calculations on a daily basis. We believe encouraging more discussion surrounding the appearance and relevance of mathematical concepts in real life will also assist in building up students’s investment in pursuing and understanding the subject. It is possible to create a mathematically literate society that thinks more critically and creatively and communicates more effectively.
Kerry Porrill
BSc Mathematical Sciences (Focal Area: Abstract Mathematics), 2nd year
Emily Warwick
BSc Mathematical Sciences (Focal Area: Mathematics), 2nd year
