I have taught mathematics to children and adults for over ten years in school, colleges and community centres around Kent. Yet it has been my recent experience as a full-time tutor that has made clear that a firm understanding of the basic techniques of algebra will enhance a students’ understanding of KS3 and GCSE mathematics. The algebraic skills taught at KS3 and GCSE are fundamental to allowing students to progress beyond secondary school mathematics. It is also one of the topics that many students commonly have problems mastering.
Algebra is often introduced too early for many students
Loss of confidence caused by the early ‘failure’ undermines the student’ determination to succeed. Each subsequent failure undermines the student’s confidence to the point where they see any effort expended to succeed as being ‘pointless’. It is important to succeed and nothing succeeds like success.
There is a perception that all algebra is hard
Algebra is not an easy subject, but each new technique is built upon the foundations of earlier ones. We can all succeed in taking the first step even if we cannot be sure how far we will progress.
There is a perception that algebraic skills will not be used after leaving school
It is unlikely many students will use formal algebra on a daily basis after leaving school. But many skills developed in learning it can help solve a wide range of problems in real life. A grasp of the fundamental techniques of algebra will also help a student understand many of the other maths topics, This is necessary if they are going to achieve level 4+ in foundation GCSE papers and vital if they want to progress far in the higher paper.
Knowledge of algebra enhances understanding and reduces the need for memorisation and rote learning
Many school textbooks prepare students to take their foundation GCSE papers, by teaching a wide selection of formulae and algorithms each relating to a specific instance or phenomena, the foundation level student is expected to memorise and use. Being able to use algebraic techniques to manipulate formula is considered a higher level skill. Yet it can be argued that most students who are struggling at GCSE maths find it difficult to memorise formulae. Time spent learning algebra reduces the need for memory and enhances understanding which is helpful to everyone.
A Short Introduction to Algebra
I believe basic algebraic concepts and techniques should be considered a fundamental part of teaching both KS3 and GCSE mathematics. It should not be restricted to only those students who are considered as able to succeed at the higher paper. Algebra holds an important place in my teaching of the GCSE maths curriculum and this is why I am planning to provide short-term tuition aimed at providing students with a strong understanding of basic algebra. Depending on demand these will be presented either as face to face lessons or online. If anyone would like to know more about the tuition of algebra or maths in general, please feel free to contact me using the link below
Does the popular view of maths as being difficult lead to lack of confidence in performing mathematics?
In an insightful article published on 14 October 2017 the blogger ‘Solve My Maths’. He writes about how the popular view of mathematics creates an unrealistic perception of its practitioners that is impossible for anyone to fulfil. He goes on to suggest that it is time to develop a more realistic idea of maths that ‘gives permission’ for anyone who ‘does’ maths to be able to consider themselves a ‘mathematician’ You can read the whole article by clicking the link directly below.
Reading the article by ‘Solve My Maths’ made me wonder if such a change in perception would also improve the confidence of students to ‘do maths’ that so many seem to lack. You can read my response below.
Lack of confidence is not the same as lacking capability
A realistic level of critical awareness of how you can perform a task is a useful talent. It can provide both incentive and a direction to self-improvement. However, taken too far, self-criticism ceases to inspire improvement but actively work against it.
Many students lack confidence in performing mathematics not because they are unskilled or unable to learn but because they underestimate the value of their effort and talent while overestimating that of others. In making this comparison, the student always comes off second best.
Maths isn’t an easy subject, and we have to be realistic how we view it and encourage our students to do likewise. ‘Solve My Maths’ points out in his article – maths is such a vast subject, and nobody can be fully conversant in all it fields. Any attempt by anyone to measure their success against that of others is meaningless and probably counter-productive.
Have you achieved your personal best?
Encourage the student to recognise the value of their skill and not compare it with the skills of others. Not all athletes are capable of world records, but all athletes are capable of personal bests.
One of the problems faced by parents and carers of primary school children when helping them with their maths homework is being able to understand and explain some of the ‘new’ techniques now commonly used to teach multiplication and division in primary maths lessons. These teaching methods generally came into use in 1999 with the introduction of the National Numeracy Strategy. I plan to write about the rationale behind the National Numeracy Strategy and how it fits in with the current national curriculum at another time. Now I would like to post this video in response to a question posed by Lee on Facebook. What is chunking?
What is chunking?
Chunking is an informal method of carrying out division based on repeated subtraction. Watch the video below to see how it works.
I hope you enjoyed this post and feel free to leave comments, make suggestions or ask questions by clicking the link on the side of the page.