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Things You Need to Know.
How Does Tutoring Differ from Regular

  • The regular teacher has at least four contact periods per week. 
Typically  a tutor would have just one.Apple iPad as a Whiteboard
  • The regular teacher may have better facilities such as whiteboards, overhead projectors, video projectors
I use a portable white board and my iPad gives me access to teaching material on my website.
  • The primary objective of the regular teacher is to present material for the students to learn.  By skilful presentation s/he can make the material easier for the students to assimilate. 
The Tutor deals with a student's comprehension and problem-solving  failures.  The tutor probes the student's core-skills needed to understand the new material, and then presents the material (together with possible core-skills revision) in additional ways which have specific relevance for the student concerned.
  • Regular teachers address some students' learning difficulties and more talented students' frustrations by grouping the students into 'sets' of students with approximately equal aptitude:  Typically there may be four or five sets for a given subject and grade.  For each new item to be taught we may consider three aspects;  the key elements to be understood,  exercises to commit the material to memory and then extension wherein the newly learned skills are applied to existing problems as well as to new and often interesting problems.  Students in the lower sets will receive more emphasis on the key-elements and exerciseUpper set students spend more time in extension with stimulating problems solving.
A tutor will try to understand the reason(s) behind a student's learning difficulties.  The results of previous medical and psychological assessments and treatments are useful here.  It is my opinion that a strong aptitude for a subject such as mathematics is relatively rare:  Most students and people in general can nevertheless perform well in mathematics if they make the necessary effort.  We are not all not all Pavarotti but this does not mean we cannot sing and enjoy singing.   Those of us with only average abilities easily fall prey to anxiety and stress in assessment (test and exam) situations and fail to give of our best.  As a tutor I teach my students to recognise deal with stress.  Providing a procedure for dealing with the "I have no idea" situation in exams has helped many students. 

We are not all possessed of instant and perfect memory recall.  A technique for stimulating memory's own recall mechanism is helpful here.  I started out suggesting the student just pause and study a problem before plunging in to solve it:  This The Lune of Hippocratestechnique  has proven helpful but sitting and thinking about the problem while precious seconds are ticking by can also be stressful, causing students to abandon the pause.  Students prefer a 'method' or formula which they can apply over an 'idea' which they must implement themselves.  As a result I have now given structure to the 'pause' using the respected technique of Critical Thinking which uses appropriate questions to indirectly stimulate memory.

Many of my students, once they have learned to deal with stress and have achieved some success in mathematics, become interested in unusual and challenging problems such as the Lune of Hippocrates
in Grade 8 (show that the area of the Lune is equal to the area of triangle AOB).  

To summarise,   I suspect that tutors do what regular teachers would like to do if only they had time.  Cooperation and consultation between regular teaching staff and tutors can be most productive

Tutors can help to reach the high school education process' goals (outcomes) for students who, for some reason, are not achieving the results their fundamental ability suggests they should.  Nothing, they say, succeeds like success:  Similarly failure often-times breeds discouragement and more failure.  To break the failure-cycle requires intervention.  Tutors can often provide this.

When Does a Student Possibly Require Tutoring?

Grahamstown's  private  secondary schools and the top government (public) secondary schools  do a generally fine job of preparing your daughter or son for tertiary education.  The other schools do their best under difficult circumstances and deserve our assistance if our country is to realise its potential.  However, if you feel that your child is being well schooled and is still not realising their academic potential,  you may require the help of a tutor.  Put in real terms of cold logic, tutoring may help you to maximise the value-received for your School-Fees or Tax-Rands.
The final paragraph of the preceding section speaks of the failure-cycle and the need for intervention.  The intervention may at some stage, take the form of medical diagnosis and treatment and  psychotherapy.  Once underlying problems have been addressed a tutor can guide the student back to a path to success.      

How Much Tutoring is required?

When a tutor is engaged at the start of a term a single hour per week may be sufficient.  The initial week will require two sessions for a new student so that I can undertake a needs-analysis which includes probing the student's core skillsIn the case of engagement at the start of term, core skills are the minimum set of skills acquired (hopefully) in the preceding term which are required to tackle the work in the forthcoming term.

Core Skills:

For example, a student entering Grade 8 is expected to be numerate. In addition to performing binary operations with +, -, x and /  the student is expected to have number sense, operation sense and the ability to perform complex calculations using the 4-functions.  On entering Grade 9 a student is expected to have mastered basic symbolic maths (algebra), geometry and number patterns.

Later Engagement:

It frequently happens that a student does well at school and then suddenly in a new term his/her marks start to drop.  Calculator Used by Many StudentsThere are several possible reasons for this.  Success in sport may lead to extra practice time and a loss of study time. 
Clubs and the debating society may soak up study time.Despite previous success new material to learn and use may find her/his core skills lacking.  For example in the previous term use of calculators may have masked a lack in numeracy.  When calculators have the capability shown at the right this is not surprising :-(  When new material requires that calculators are NOT used things can suddenly go very wrong.  For example a student is asked  to write down the third side of a right-angled triangle when two of the sides are 26 and 10 cm long.  This can be solved using Pythagoras' Theorem and that does require a calculator.  However, the instructions say that no calculator may be used.  Numeracy is required.  Number Sense shows that the sides are 2x13 and 2x5 cm.  The third side must be 2x12 cm  since the triangle is a 5-12-13 Pythagorean Triple with the sides doubled.

Whether the student will require one lesson per week or more will depend upon the results of an initial needs-analysis and the time remaining before the end-of-term exam.

Emergency Engagement:

In most cases I strongly discourage this type of engagement.  A sudden burst of extra lessons close to an exam rarely achieves very much.  There is is insufficient time to make a meaningful assessment of the student since s/he is increasingly stressed.  It is more educationally- and cost- effective to take one or perhaps two lessons per week over a longer period. 

Pre-examination Tutoring:

An increase of lesson-freqency close to the exam after a period of systematic one-per-week lessons can be useful: The extra lessons allow us to spend more time on past examination papers.          
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