Algebra – Why Bother?

Algebra for the many,  not the few

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.

Image of algebraic calculations
Algebra is vital to understanding a wide range of mathematical topics

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

Contact Phil Wastell Freelance Maths Tutor

About Phil Wastell Freelance Maths Tutor

Identity | Solve My Maths

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.

Source: Identity | Solve My Maths

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.

A good pass – who are qualifications actually for?

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Is the high cost of buying textbooks damaging our children’s education?

 

A price worth paying?

On Friday I purchased two textbooks covering the foundation and higher papers of the GCSE Maths 1-9 syllabus.  I would like to say I was shocked by the price cost, but to be honest, I wasn’t.

Maths GCSE 1 to 9 Textbooks
The two books I purchased at Waterstones.

Even with Waterstones running a buy one and buy a second for half-price the combined cost still came to just under thirty quid.  On Amazon, each book cost £21.37 with Prime and £17.38 for a used copy through ‘other sellers’  To be fair,  these are well-written books with beautifully colourful diagrams and illustrations quite capable of supporting the study of any able and well-motivated students on their own.

A fair charge of just taking the ……….?

Unfortunately, the price charged for textbooks means that only the most well-off can easily afford or even justify buying them.  And the same is also true of schools.  Like medicine is to the NHS, books are the lifeblood of our education system.  Are the prices charged by publisher fair, or are they, like the pharmaceutical companies with the NHS, taking advantage of government policy that in seeking to fragment the provision of education to a point where individual institutions are unable to benefit from the economies of scale to influence the price charged to them?   Whatever the reason, the high cost of textbooks harms the education of our children.

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A good pass – who are qualifications actually for?

 

One Bad Apple?

St Olave’s Grammar school in Orpington has reversed its decision to bar students from returning for the second year of their A-level courses if they failed to achieve the schools ‘stringent academic requirements’ at the end of the first year.     The climb down was forced on them through a combination of poor publicity, parent complaints and the accompanying threats of legal action.  Click the link to the Guardian online for more information on this story.

That this kind of thing goes on will surprise nobody who has any experience of the education system.   But we also see the anguish and damage caused to students by the pressure placed on them by education establishments desperate to achieve good grades to the point where they are willing to work against best interests of their students in pursuit of improved league position and positive OFSTED reports.

GCSE result may have kept improving, but do these indicate increasing long-term benefits for student, school or the country as a whole.   Should we look again at what it means to have a good pass?

A good pass?

What should we consider a good pass, or, to put it another way, who is the qualification for and what should the qualification tell them, and us,  about the student?

For employers, as well as,  FE/HE establishments and the student,  the qualification must fairly represent the level of skill attained.  At the same time it should also provide the student with something to aspire to, something that is truly able to demonstrate to them and others, that effort put into the study was worthwhile.   Here, a good pass would be one that reflected the student’s fullest achievement of their potential at that time, while a less than good pass would be a measure of the extent by which the student did not achieve it.  From an employer, FE/HE institution or student’s point of view,  a good pass is one that adequately reflects the current ability and potential of a candidate.  Importantly the student always remains the measure of it.

Testing the school, not the student

But this all changes when national qualifications, such as GCSEs and A-levels, are no longer used just to measure the student but make up a significant part of measuring the school.  At this point what is considered a ‘good pass,’ is no longer related to the ability or potential of the student but the arbitrary decisions of governments, civil servants,  regulating bodies and exam boards.  And because of the power and influence of these institutions, it is their definition of a ‘good pass’ that holds sway and affects the way schools teach and behave,  directly impacting the well being of their students.

Achieving the unachievable

The pressure exerted both psychologically and through increased workload on students to achieve what the government and the schools themselves consider a  ‘good pass’ has never been greater.  But while the number of those attaining ‘good grades’ have on average, continued to rise since the introduction of the league tables, other indicators may suggest something else might be going on.

  • On 6 December 2016, the BBC reported that according to the OECD PISA test, the UK lags behind in global school rankings with maths 27th in the world rankings, its lowest position since 2000 and English in  22nd.  Only science has shown recent improvement up to 15th place its highest position since 2006.     http://www.bbc.co.uk/news/education-38157811.

 

Close up of hand writing
The pressure of gaining a good pass in GCSEs may have led to 9% rise in calls to Child Line concerning stress in the year 2015/16

Time to remove the incentive?

2017 is the first time that final exams have been held testing the new 1-9 syllabus in English and Mathematics.  We are told they are more rigorous than the previous GCSE introduced in 2010.  They will be rolled out across the rest of the curriculum over the coming years.  Perhaps they will be better at measuring the real ability of the students taking them.  But while they continue also to be used as a way of ranking teaching establishments, a role they are not designed for,  many of these institutions will continue to find ways of gaming the system at the expense of their students.  Isn’t it time we removed their incentive to do so?

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