An alternative Maths curriculum

Alternative staffing models for Maths

Dave Appleby

24th February 2012.

Dotheboys Hall School faces an impending crisis. Of the 5 Maths teachers, two are leaving and no-one can be replaced. They will only have Glenda Gauss, Nicy Newton and Rajendra Ramanujan.

Fortunately thay have three excellent LSAs called Candice Carnelian, Jade Jet and Peter Pearl.

In each half year group there are 120 pupils in 5 setted classes.

Each class has 5 periods per fortnight.

There is one computer room with 25 machines.


Another little problem facing Dotheboys is that sets split. When the pupils arrive at Dotheboys in year 9 they are tested to see how good they are at Maths and this measure is used to group them. Thus pupil 24 is in set 1 and pupil 25 is in set 2. They then experience mostly whole class teaching aimed at more or less the centre of the class. Thus pupil 24 struggles to keep up with pupil 13 whilst pupil 25 coasts along compared to pupil 38. In general this means that pupil 24 progresses faster in Maths than pupil 25; when they are retested the difference between them is greater than it had been. Generally the setting is confirmed.


The pupils who come from Salem House (whose Maths teacher, Mr Creakle, is less than brilliant) tend to be assigned the lower sets. It soon becomes impossible for them to catch up with the pupils who have been taught Maths better at Dr Blimber's Academy.


This has led to some anomalies. Pupil 60, in set 3, has never been much good at Maths but towards the middle of year 10 something clicks and she suddenly makes progress. By the start of year 11 she has clearly demonstrated her potential for Higher Level Maths. Unfortunately she has been taught Foundation Maths until now. There is no mechanism for her to catch up on the Higher Maths she has missed. Despite having the potential to achieve an A she is entered for a paper where the maximum possible is a grade C.

The headteacher, Wackford Squeers, has a cunning plan.

He has heard of the School Of One in New York City. This school personalises the maths curriculum. It aims to maximise differentiation in ‘Math’ by offering a variety of learning opportunities including:

• A Math computer lab

• A Math investigative and collaborative learning lab
• A Math seminar class of no more than 12 pupils
• One to one online Math tuition
• Proper ‘Math’ lessons taught by a real ‘Math’ teacher
• Individual learning Math sessions in which supervised pupils complete worksheets

The clever bit is that School Of One assesses each pupil daily and then assigns them to the appropriate learning opportunity in next day’s timetable. Wackford doubts that Dotheboys Hall is yet quite ready for such Yankee technology. Nevertheless, he is a fan of giving pupils at different levels of Maths different experiences.

He proposes four types of Maths experience:

• A Maths computer lesson which will offer individualised instruction using a variety of computer systems such as MyMaths, Mangahigh, and Successmaker (for the lowest achievers). This will be supervised by an LSA (Candice)
• A Maths collaborative investigation in which 6 teams of 4 pupils will try to solve a Maths challenge. These sessions will by pedagogically founded on the work by Sugatha Mitra. They will be led by an experienced Maths teacher, Glenda.
• Individualised Maths workshops in which pupils will work through problems hand-picked for them supervised and supported by a pair of LSAs (Jade and Peter).
• There will also be ‘trad Maths’ lessons taught by his other experienced Maths teachers, either Nicky or Rajendra.

Mr Squeers has devised possible schemes based on these experiences. He has one scheme for 5 ppf and one for 6ppf.

5ppf model

	Lesson 1	Lesson 2	Lesson 3	Lesson 4	Lesson 5
Set 1	Computer Maths with CC	Investigation Lab with GG	Maths with NN	Maths with NN	Maths with RR
Set 2	Maths with RR	Computer Maths with CC	Investigation Lab with GG	Maths with RR	Individual Maths with JJ & PP
Set 3	Maths with NN	Individual Maths with JJ & PP	Computer Maths with CC	Investigation Lab with GG	Maths with NN
Set 4	Individual Maths with JJ & PP	Maths with RR	Maths with RR	Computer Maths with CC	Investigation Lab with GG
Set 5	Investigation Lab with GG	Maths with NN	Individual Maths with JJ & PP	Individual Maths with JJ & PP	Computer Maths with CC

• Every set sees a qualified Maths teacher at least twice per fortnight.
• Every set has a computer session which means the IT resources are fully used.
• Every set has an Investigation lab.
• Set 1 has 3 trad Maths sessions; sets 2, 3 and 4 have 2 trad maths sessions; set 5 has a single trad Maths session.
• Sets 2, 3 and 4 have a single individualised maths workshop; set 5 has two such sessions.
• Both RR and NN see 80% of the students; GG sees them all.

6ppf model

	Lesson 1	Lesson 2	Lesson 3	Lesson 4	Lesson 5	Lesson 6
Set 1	Computer Math with CC	Investigation Lab with GG	Maths with NN	Maths with NN	Maths with RR	Investigation Lab with GG
Set 2	Maths with RR	Computer Math with CC	Investigation Lab with GG	Maths with RR	Individual Maths with JJ & PP	Maths with RR
Set 3	Individual Maths with JJ & PP	Maths with NN	Computer Math with CC	Investigation Lab with GG	Maths with NN	Computer Math with CC
Set 4	Maths with NN	Individual Maths with JJ & PP	Individual Maths with JJ & PP	Computer Math with CC	Investigation Lab with GG	Maths with NN
Set 5	Investigation Lab with GG	Maths with RR	Maths with RR	Individual Maths with JJ & PP	Computer Math with CC	Individual Maths with JJ & PP

• Every set sees a qualified Maths teacher at least three times per fortnight.
• Every set has a computer session (set 3 has 2) which means the IT resources are fully used.
• Every set has an Investigation lab (set 1 has 2)
• Set 1 has 3 trad Maths sessions; sets 2, 3 and 4 have 2 trad maths sessions; set 5 has a single trad Maths session.
• Sets 2, 3 and 4 have a single individualised maths workshop; set 5 has two such sessions.
• Both RR and NN see 60% of the students; GG sees them all.

This new system means:

• Every pupil learns Maths using a collaborative investigative method.
• Every pupil uses ICT to aid their learning at least once per fortnight.
• Every pupil experiences a mix of learning styles.
• Every pupil has a qualified Maths teacher at least twice per fortnight.
• The balance of learning styles can be better tailored to the pupil’s prior achievement.
• Where pupils are being given extra one-to-one tuition they can be taken from the individualised workshops without disrupting their learning of content (presuming that pupils in set 1 do not need to come out of lessons).
• GG develops special skills in teaching in this investigative style; CC develops special skills in running computer lessons.
• Given that we normally staff 5 sets with 5 qualified teachers and an LSA and given that qualified teachers earn more than LSAs, we will save on staffing costs. Mr Squeers likes that! But more importantly it solves his problem of the shortage of specialist maths teachers.
• This system builds differentiation in. The Investigation Lab, the Computer lesson and the Individual Workshops are all highly differentiated. Set 1 in the 5ppf model experiences 40% of these types of lessons; every other set experiences more. The average pupil will experience 60% highly differentiated lessons.
• This will reduce the tendency of sets to split. The pupil perceived as the best in set 2 might well be assigned more challenging work than the pupil perceived as the worst in set 1.
• Pupils in the lower sets will experience higher amounts of personalised work. It should be possible for pupil 60 to catch up with a significant amount of Higher Level work; certainly sufficient for her to be entered at this Level.