Tutoring 11+ Mathematics
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Hi Guest55
Not sure who your last posting was directed at.
Tutors prepare children for 11+ mathematics tests using methods & techniques that have not been taught in the school. This is because a large proportion of 11+ mathematics questions are at Key Stage Level 5.
Children who sit 11+ entrance tests in September-October of year 6 would not have completed the full Mathematics Level 5 syllabus and most children in year 5 would not have covered any of the Level 5 syllabus.
The preparation tests completed in the schools have time constraints placed on them and the direct teaching of any element of 11+ entrance tests is limited by rules laid down by the LEA.
Although NQTs may have seen some multiple choice question within their course, they may not see mathematics 11+ questions either in their mathematics content or in the verbal reasoning content.
(O.T. but related)
Mathematics teachers tend to be one-dimensional, only teaching within their subject areas. As the individual gains higher qualifications within their subject they move further away from the content of lower qualifications and become "experts" in one single subject.
Tutors however need to work in multiple-disciplines. Of the 164 selective schools I am not aware of one that uses mathematics as a sole entrance test.
Tutors, depending on the LEA, need to work in mathematics, english, verbal reasoning and non-verbal reasoning. Even in LEAs where verbal rasoning is the sole examination a tutor will need knowledge of methods & techniques required to answer mathematics, english, problem solving and logic questions.
I don´t think that a one-dimensonal mathematics graduate with a PGCE in Mathematics Education has all the skills to teach each of these disciplnes from within the training they have received. However, they would undoubtedly have the aptitude to learn the additional skill required.
Regards
Mike
Not sure who your last posting was directed at.
Tutors prepare children for 11+ mathematics tests using methods & techniques that have not been taught in the school. This is because a large proportion of 11+ mathematics questions are at Key Stage Level 5.
Children who sit 11+ entrance tests in September-October of year 6 would not have completed the full Mathematics Level 5 syllabus and most children in year 5 would not have covered any of the Level 5 syllabus.
The preparation tests completed in the schools have time constraints placed on them and the direct teaching of any element of 11+ entrance tests is limited by rules laid down by the LEA.
Although NQTs may have seen some multiple choice question within their course, they may not see mathematics 11+ questions either in their mathematics content or in the verbal reasoning content.
(O.T. but related)
Mathematics teachers tend to be one-dimensional, only teaching within their subject areas. As the individual gains higher qualifications within their subject they move further away from the content of lower qualifications and become "experts" in one single subject.
Tutors however need to work in multiple-disciplines. Of the 164 selective schools I am not aware of one that uses mathematics as a sole entrance test.
Tutors, depending on the LEA, need to work in mathematics, english, verbal reasoning and non-verbal reasoning. Even in LEAs where verbal rasoning is the sole examination a tutor will need knowledge of methods & techniques required to answer mathematics, english, problem solving and logic questions.
I don´t think that a one-dimensonal mathematics graduate with a PGCE in Mathematics Education has all the skills to teach each of these disciplnes from within the training they have received. However, they would undoubtedly have the aptitude to learn the additional skill required.
Regards
Mike
Mike Edwards is a co-author of The Tutors product range.
I do not know any one-dimensional Maths graduates! it's not that sort of subject - personally I am also an expert in teaching 'thinking skills' and ... and ...
I have done a lot of tutoring - not just in Maths and I don't charge.
A good Year 5 teacher will teach level 5 - my child got level 5 in the QCA optional tests in Y5.
Let's face you are a business man - your tutoring is a business - yes I earn from teaching but no-one does it for the salary as I could earn far more as an accountant, in insurance or .... as a tutor
I teach because I want to make a difference to the lives of all children - not just those who can afford a tutor - many of the misconceptions I deal with day to day have come from poor tutoring - far more than from poor teaching.
You still have not explained how you know your pedagogical knowledge is appropriate to prepare children for secondary education.
I have done a lot of tutoring - not just in Maths and I don't charge.
A good Year 5 teacher will teach level 5 - my child got level 5 in the QCA optional tests in Y5.
Let's face you are a business man - your tutoring is a business - yes I earn from teaching but no-one does it for the salary as I could earn far more as an accountant, in insurance or .... as a tutor
I teach because I want to make a difference to the lives of all children - not just those who can afford a tutor - many of the misconceptions I deal with day to day have come from poor tutoring - far more than from poor teaching.
You still have not explained how you know your pedagogical knowledge is appropriate to prepare children for secondary education.
Hi Guest55
The question I posed at the beginning was whether it is necessary for a tutor to have a PGCE in Mathematics Education to tutor the mathematics elements of 11+ courses.
A further question would be whether it is necessary for a tutor to have a degree in mathematics to tutor the mathematics elements of 11+ courses.
A further question would be whether a teacher with a degree in mathematics and a PGCE in mathematics has the skills to tutor the verbal reasoning, non-verbal reasoning and english elements of 11+ tests or whether they would need to acquire additional skills.
Of all the secondary school mathematics teachers that I have employed, none of them had the knowledge to tutor any element of the 11+ tests outside their subject area without additional training.
In my experience, where a secondary school mathematics teacher is asked to teach a class outside their subject area they tend to teach mathematics. This is the case with most secondary school teachers who are one-dimensional as far as subject knowledge is concerned. I would not doubt that they are multi-dimensional in other ways.
Whereas, I have tutored; mathematics, english, english literature geography, sociology, psychology, physics, chemistry, human biology, business studies, religious studies and history to GCSE level and psychology, sociology and human biology to "A" level.
Having a General Studies Degree makes me "Generally Studious" and not an expert in any one area.
Regards
Mike
The question I posed at the beginning was whether it is necessary for a tutor to have a PGCE in Mathematics Education to tutor the mathematics elements of 11+ courses.
A further question would be whether it is necessary for a tutor to have a degree in mathematics to tutor the mathematics elements of 11+ courses.
A further question would be whether a teacher with a degree in mathematics and a PGCE in mathematics has the skills to tutor the verbal reasoning, non-verbal reasoning and english elements of 11+ tests or whether they would need to acquire additional skills.
Of all the secondary school mathematics teachers that I have employed, none of them had the knowledge to tutor any element of the 11+ tests outside their subject area without additional training.
In my experience, where a secondary school mathematics teacher is asked to teach a class outside their subject area they tend to teach mathematics. This is the case with most secondary school teachers who are one-dimensional as far as subject knowledge is concerned. I would not doubt that they are multi-dimensional in other ways.
Whereas, I have tutored; mathematics, english, english literature geography, sociology, psychology, physics, chemistry, human biology, business studies, religious studies and history to GCSE level and psychology, sociology and human biology to "A" level.
Having a General Studies Degree makes me "Generally Studious" and not an expert in any one area.
Regards
Mike
Mike Edwards is a co-author of The Tutors product range.
Hi Guest55
Purely Off-Topic, but for the purposes of being polite this is the up-to date version of the qualification I started in 1996.
http://www.cityandguilds.com/cps/rde/xc ... _term=7407
It has similar content to "Pedagogy and Practice: Teaching and Learning in Secondary Schools"
There are generic modules that are transferable to the peadagogical skills required of a tutor.
Mike
Purely Off-Topic, but for the purposes of being polite this is the up-to date version of the qualification I started in 1996.
http://www.cityandguilds.com/cps/rde/xc ... _term=7407
It has similar content to "Pedagogy and Practice: Teaching and Learning in Secondary Schools"
There are generic modules that are transferable to the peadagogical skills required of a tutor.
Mike
Mike Edwards is a co-author of The Tutors product range.
This is a pointless discussion as you always think you are right
Yes - I do think you need a mathematics degree to prepare children for a secondary school mathematics curriculum.
Yes - a graduate mathematician with a PGCE has the necessary skills to coach
You are clearly unlucky with the people you have come across - mathematician are the most flexible learners of all because they have mastered a very wide range of topics.
I think you should be concerned that you frequentlty disagree with the advice practising teachers give - can you be sure your pedagogy [not androgogy] is up-to-date.
Yes - I do think you need a mathematics degree to prepare children for a secondary school mathematics curriculum.
Yes - a graduate mathematician with a PGCE has the necessary skills to coach
You are clearly unlucky with the people you have come across - mathematician are the most flexible learners of all because they have mastered a very wide range of topics.
I think you should be concerned that you frequentlty disagree with the advice practising teachers give - can you be sure your pedagogy [not androgogy] is up-to-date.
Mike,
Not sure If I understood your last post
Are you saying that generally children who are level 5 standard as per the Sats at the time of the 11+ exam are the ones who would be most successful?
Obviously children in year 5 would have not been taught anywhere near this standard at school so this is where the tutors step in.
When I queried with with Bexley Council (kids will be tested in Sep and not Nov in future), Council said that only work covered will be tested.
I don't believe this one bit and I think the Council has a duty to tell parents exactly what levels will be tested and that the schools will not be able to prepare the children for the exams.
Could you enlighten me here.
Thanks
Not sure If I understood your last post
Are you saying that generally children who are level 5 standard as per the Sats at the time of the 11+ exam are the ones who would be most successful?
Obviously children in year 5 would have not been taught anywhere near this standard at school so this is where the tutors step in.
When I queried with with Bexley Council (kids will be tested in Sep and not Nov in future), Council said that only work covered will be tested.
I don't believe this one bit and I think the Council has a duty to tell parents exactly what levels will be tested and that the schools will not be able to prepare the children for the exams.
Could you enlighten me here.
Thanks
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Bexley Mum 2
- Posts: 851
- Joined: Sat Nov 17, 2007 9:55 pm
- Location: Bexley
Tracy - my understanding is that, because children who are more able in maths will work at a higher level than the rest of the class, many will have completed the KS2 syllabus by the end of year 5. My eldest two have said to me that most of year 6 maths was just going over what they'd done in year 5. I also remember my eldest's Y4 teacher saying he was doing Y6 maths and my youngest, who is currently in Y4 is also, according to his teacher, doing Y6 maths.
I also think that in Bexley at least the 11+ has and - will continue from September - to favour those children who are good at maths.
I also think that in Bexley at least the 11+ has and - will continue from September - to favour those children who are good at maths.
BM2 - that's interesting.
From what you are saying, the children pick up a topic in year 4, take it further in year 5 and further still in year 6. So it's not a case of learning something new in year 6, simply those who are able take it to a new level?
Tough luck though if you have bad teachers in years 4 an 5! Our best teachers have been moved to year 6, what a surprise!
From what you are saying, the children pick up a topic in year 4, take it further in year 5 and further still in year 6. So it's not a case of learning something new in year 6, simply those who are able take it to a new level?
Tough luck though if you have bad teachers in years 4 an 5! Our best teachers have been moved to year 6, what a surprise!
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Bexley Mum 2
- Posts: 851
- Joined: Sat Nov 17, 2007 9:55 pm
- Location: Bexley
Yes, our best teachers are in Y6 too - they used to be in Y5 which was much better from the 11+ perspective.
Maths is very much about building on prior knowledge, so if you've had a bad teacher and not grasped some of the 'building blocks' it can cause problems.
It makes sense that key topics are repeated every year and gradually developed. For example you might start with basic fractions in Y3 and repeat the topic every year until you get to more complex fractions in Y6.
I know we've moved away from the National Strategy now, but I've got a copy of the National Numeracy Strategy here and, for example, year 5 and 6 have pretty much the same topic headings: Place value, ordering and rounding; properties of numbers; fractions, decimals, percentages, ratio and proportion etc etc but Year 6 stuff will be more complex than year 5. I think therefore it might be difficult to prove whether or not the 11+ maths paper contains stuff which a child hasn't studied - unless they include algebra, which clearly isn't on the KS2 syllabus (although, unlike Kent, I'm not aware Bexley has included algebra, certainly in the past few years).
In our primary school children are streamed for maths so, for example, the top maths set in Y4 will probably do Y5/Y6 work, the middle set Y4 work and the bottom set more basic stuff. I know some will object to streaming at such a young age, but having helped in class before streaming was introduced, I think it works.
That's all just my impression of course - don't quote me!
Maths is very much about building on prior knowledge, so if you've had a bad teacher and not grasped some of the 'building blocks' it can cause problems.
It makes sense that key topics are repeated every year and gradually developed. For example you might start with basic fractions in Y3 and repeat the topic every year until you get to more complex fractions in Y6.
I know we've moved away from the National Strategy now, but I've got a copy of the National Numeracy Strategy here and, for example, year 5 and 6 have pretty much the same topic headings: Place value, ordering and rounding; properties of numbers; fractions, decimals, percentages, ratio and proportion etc etc but Year 6 stuff will be more complex than year 5. I think therefore it might be difficult to prove whether or not the 11+ maths paper contains stuff which a child hasn't studied - unless they include algebra, which clearly isn't on the KS2 syllabus (although, unlike Kent, I'm not aware Bexley has included algebra, certainly in the past few years).
In our primary school children are streamed for maths so, for example, the top maths set in Y4 will probably do Y5/Y6 work, the middle set Y4 work and the bottom set more basic stuff. I know some will object to streaming at such a young age, but having helped in class before streaming was introduced, I think it works.
That's all just my impression of course - don't quote me!
The Primary national strategy still exists and is the basis for the curriculum in Primary schools:
http://www.standards.dfes.gov.uk/primaryframework/
It is just online now -
http://www.standards.dfes.gov.uk/primaryframework/
It is just online now -
