Algebra: Maths most useful topic for modern life
Of all the mathematics taught at school at GCSE level, a lot can seemingly be disregarded. I am often asked: “What use of trigonometry will I find in the future”, “Where on earth will I need to use the quadratic equation”. They are all valid questions. If you are going to studying a technical vocation, then a fair chunk of what you are shown can be set aside, but having a good understanding of basic mathematics, rapid mental arithmetic and a general knack for problem-solving.
Algebra of all topics covers the problem-solving aspect that most modern roles ask for. The concepts at the foundation of algebra: balancing equations, solving for unknowns, substitution methods, inspection via examining equations, quadratics; these may not have direct application to a shopping list or how to prepare a recipe, but there are techniques embedded in the teaching of algebra that are universally useful.
Abstraction
The technique of abstraction - the ability to remove information from a question to have only the most useful and relevant content to solve a question.
How you go about selecting what is relevant information is a skill of its own. New specification GCSE Exams call for more worded questions in the name of problem-solving. Quite a few students do struggle to digest these denser questions and putting into practice the idea of abstracting away useless information.
Take this question. Irrelevant information that can be removed:
- The manufactures name
- What they are manufacturing (Unless the question is about the context)
- Other information about reasoning and things that add things grammatical structure
Taking those points- highlighted in yellow is actually what is relevant to completing the question.
Abstraction is not a technique in mathematics that is purely restricted to algebra - as is seen with this probability question, however, I find that algebra offers the best and most direct way of teaching. For example, via Simultaneous equations and taking the costs of teas and coffees in different combinations and then reducing it into some simple algebraic expressions. Once this has been mastered, it can be applied in several other situations.
Clear layout and presentation
Solving equations involves an understanding of how to reverse operations and how equations are affected by applying operations. I have found many students take time to adapt to the idea that if you apply the reserve operation, it cancels out. To solve an equation you also have to be happy with the idea of collecting like terms, simplifying fractions and what many key terms and symbols mean.
One thing this all requires (mainly to insure markers can credit work properly) is a clear layout and good presentation of steps. Take the solving of this equation:
There may be some redundant steps such as listing that you are subtracting by 3, yet the general presentation is clear and concise.
The skill of being able to clearly show an idea in a condensed and simple form is - again- not only applicable to algebra, but I believe it is the best form to promote and show this idea at an early age and in a very easy and applicable form.
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