Figure 4.3 Years 5 and 6
Task 4.1 Maths words
For each of the words below, create a sentence with the everyday (non-mathematical) use of the word and then another sentence explaining the mathematical meaning:
• average • sum • difference
• group • error • parallel
• reflex • plus • kite
• variable • mode • simplify/solve
• equals • factor
Mathematical literacy refers to the ability to understand the mathematics that occurs in newspaper articles, magazines, sports, advertisements and many other situations in life.
In terms of developing the pupils’ mathematical literacy, teachers can assist by discussing the following issues as they arise in the syllabus:
• interpreting graphical and tabular representations of data;
• understanding probability in relation to the likelihood of a situation occurring in everyday life such as a lottery win;
• interpreting statistics reported in a newspaper—pie charts, graphs—in the context of sport, economy, our lifestyle, world issues;
• understanding the importance of using a representative sample in statistical reports;
• using ‘basic’ arithmetic skills such as calculate a percentage discount, VAT, work out change, add on a gratuity in a restaurant;
• reading a timetable, converting from a 24-hour to 12-hour clock;
• understanding a bank statement;
• reading a telephone, electricity or gas bill correctly;
• working out exchange rates;
• using ratio and proportion in cooking or building;
• working confidently with fractions or decimals;
• calculating areas or volumes for painting or decorating walls, or making garden ponds;
• communicating mathematically to a variety of audiences.
Coursework and other oral and written pieces in mathematics also allow pupils to engage in communicating their mathematical ideas and findings to an audience within and outside the classroom. Using ICT it is now possible to ‘write’ for any audience—
scientists in NASA, researchers in universities, businesses and industries who may be interested in new ideas but unable to fund a dedicated research staff.
In many cases the most important form of literacy for pupils is being able to understand and interpret the question in the examinations. Like all aspects of education, the area receiving the most attention in the classroom is the one in which measurements can be made—namely, the assessed parts of the course.
National Strategy for Key Stage 3
Research from Keele University revealed that just over 60 per cent of pupils in the early years of secondary education were making ‘reasonable progress’, while the remaining 30 per cent of pupils fell into one of three categories:
1 The disappointed—20–30% of pupils were bored.
2 The disaffected—10–15% of pupils were beginning to truant or behave badly on a regular basis.
3 The disappeared—2–5% of pupils had given up school altogether.
(Barber, 1997) The aim of the Key Stage 3 National Strategy was to address these problems by
‘transforming teaching and learning in a way that will engage and attract pupils across the curriculum’ (DfES, 2001b).
Based on the work of the NNS and NLS, the National Strategy for Key Stage 3 focuses on five strands: English and mathematics plus literacy and numeracy (from 2001 to 2002) followed by science, ICT and the foundation subjects of history, geography, music, art, RE, PE and D&T (from 2002 to 2003). The Strategy emphasises the need for a short, snappy starter activity as part of the whole-class teaching, followed by a teacher-led demonstration of the work to be completed alone or in pairs/small groups. Next, the pupil-centred activity occurs and finally the lesson ends with a whole-class plenary where the learning is reviewed.
The four main principles of the Strategy are:
• expectations—high expectations and challenging targets set by teachers;
• progression—developing the work covered in KS2 into KS3 without re-teaching;
• engagement—use of activities which motivate pupils and require active participation;
• transformation—using professional development and support mechanisms to guide and refine teaching.
(DfES, 2001b)
Task 4.2
By referring to the Qualifying to Teach document (TTA, 2001), map each of these principles to the teaching requirements for ITE. For example, your planning, preparation, assessment, monitoring and recording will assist pupils to progress in their learning.
Training materials to assist teachers in implementing the Key Stage 3 Strategy are available from the DfES for the following themes: Assessment for Learning, Teaching Repertoire, Structuring Learning, and Knowing and Learning. Case Studies of ‘best practice’ in schools and mini-packs containing teaching resources such as videos and CDs are also available for each year group on the DfES website (www.standards.dfes.gov.uk/keystage3).
The Mathematics Framework for Key Stage 3
In the context of maths, the purpose of the National Strategy for Key Stage 3 was to:
• promote continuity across the transition from Key Stage 2 to Key Stage 3;
• ensure pupils working below level 4 received an opportunity to ‘catch-up’;
• provide practical support and guidance to teachers.
(DfES, 2001b) Like the NNS, the Key Stage 3 Framework consists of yearly teaching programmes linked to the National Curriculum programmes of study. These programmes continue and extend the progression and expectations in pupils’ mathematical abilities from primary school. In Year 7, the level 4 work is revised but most of the content is directed at level 5;
in Year 8, level 5 work is consolidated and some work at level 6 begins; Year 9 constitutes a revision of level 5 work and continuation of level 6 activities. For the more able students, level 7 and some level 8 objectives may be addressed.
Within the yearly programmes, key objectives central to the pupils’ progress are highlighted and planning charts exemplify the grouping of mathematical topics throughout the year. Examples of what the pupils should know and be able to do at the end of each academic year are included to illustrate the depth of content and coverage of material. The final section of the Framework contains a checklist of mathematical vocabulary spanning the content for the three years.
A summary of the distinctive features of each area of maths at Key Stage 3 are included in the programme and teachers are encouraged to use a mixture of paper-based, practical and ICT approaches in each topic. A three-part lesson similar to that of the NNS is advocated with the requirement that each lesson contains direct teaching and interaction with the pupils, and activities or exercises that the pupils will complete in class. The development of thinking skills is highlighted in terms of the application of mathematics in novel contexts or investigations.
The plenary
A plenary is multi-functional. It is usually a means of bringing the class together to round off and summarise the main learning points of the lesson (DfES, 2002a). Often it is used to re-focus the pupils on what they have achieved and to look forward to future work. If pupils are offering their own feedback from a learning activity, then it is also the time when teachers can assess learning, identify misconceptions and plan accordingly. Ofsted raised concerns during the Key Stage 3 pilot that ‘teachers tended merely to sum up what happened during the main phase and pupils did not have the opportunity to articulate what they had learned’.
Although the majority of plenaries occur at the end of a lesson, many teachers find it useful to initiate some discussion midway through the lesson to consolidate understanding and move pupils to the next stage of the learning process. Plenaries can range from two minutes during a sequence of related lessons to twenty minutes at the start or end of a topic. Some ideas for suitable pupil involvement in plenaries is offered in the DfES document The Plenary, which is available online from the Standards website (www.standards.dfes.gov.uk/keystage3) (DfES, 2002a).
Low-achieving students in Key Stage 3
For students working at level 3 in mathematics, booster materials are available to assist pupils in ‘catching up’ with the rest of the class. The Springboard 7 materials issued in November 2001 (DfES, 2001c) were designed as a two-term teaching programme to complement and not replicate the teaching materials created for summer numeracy schools. The purpose of the materials was to allow the low-ability pupils to work alongside their peers who had already achieved level 4 at the end of Key Stage 2, but to
‘catch up’ on unlearned skills while consolidating new learning with their classmates.
The National Strategy’s Springboard 7 pack of teaching materials can be obtained from the DfES website.
High-ability Key Stage 3 students
At the opposite end of the spectrum, the high-ability students need to be stretched and challenged in mathematics classes. The Key Stage 3 Strategy advocates that teaching is
‘blended’ to incorporate increased pace (acceleration), depth (extension) and breath (enrichment) within the middle phase of each lesson. Approximately 5–10 per cent of pupils in every school are ‘gifted’ or ‘talented’. ‘Gifted’ students have high levels of attainment in academic subjects, while ‘talented’ students excel in a creative or expressive art or sport. The DfES publication Teaching Gifted and Talented Pupils (2002b) includes a section on Guidance on Teaching Able Mathematicians, with a focus on developing the pupils’ skills in problem-solving, communicating and reasoning. It encourages teachers to establish a classroom ethos that celebrates success for all pupils to reduce the social pressures that result in under achievement in this subgroup of students.
It also counsels the use of challenging questions at an appropriate level of difficulty with extension material of an open-ended nature. The emphasis is on quality and not quantity:
focusing on one challenging question is deemed more worthwhile than responding to 20 routine questions. The DfES Framework for Teaching Mathematics: Years 7, 8 and 9
offers suggestions for extension material for the more able students. Further sources of ideas, support and guidance can be found on the following websites:
http://www.mathsnet.net/ http://www.cut-the-knot.com/
http://www.1000problems.com/ http://www.worldclassarena.org/
http://www.counton.co.uk/ http://www.nrich.maths.org/
The transition from Key Stage 2 to Key Stage 3
The main reason for pupils becoming disengaged and disaffected in the early years of post-primary education is the lack of continuity in the learning process between the two schools. Many secondary schools spend six weeks or almost a full term getting to know the pupils’ level of attainment in mathematics. During this time pupils become bored and frustrated being exposed to the low-level work that they have already mastered at primary school. Before the introduction of the Key Stage 3 Framework, the pupils also found the style of teaching in secondary schools too dry and didactic compared to the interactivity of the NNS lessons.
Although the Common Transfer Form summarises pupils’ attainment in the end of key stage assessments, teachers in post-primary schools often find it difficult to interpret this information in terms of the pupils’ strengths and weaknesses in the various areas of mathematics. As a result, transition units have been introduced to complement the existing information available for each pupil. The transition units are intended to ensure that:
• pupils experience a lesson structure they are familiar with and understand;
• there is a consistency in teaching approach that will help pupils to respond to new people in new surroundings;
• pupils are able to build on their early successes and demonstrate what they know, understand and can do in the context of the work they did in Year 6;
• teachers are better informed about pupils’ strengths and weaknesses and can use the lessons to confirm their assessments and plan teaching programmes that meet the needs of their pupils;
• there is greater continuity and progression and less repetition of work.
(DfES, 2003a) The Year 6 transition unit is completed during the summer term and focuses on the pupils’ problem-solving and mathematical reasoning skills in the context of Number.
This unit is then developed further in the Year 7 transition unit to sustain the same teaching style and also maintain the momentum in the learning process. The key objectives for Key Stage 2 are revised and extended in Year 7 (DfES, 2002d). During this time the teacher can assess the pupils’ abilities and become familiar with the collective areas of strengths and weaknesses within the class. Using this information, future lessons can be planned to address the needs of the students without restricting their progress or losing any of the pupils’ enthusiasm for the subject.
Year-on-year transition units are also available for use within Key Stage 3. The key topics addressed are the links between fractions, decimals and percentages, and thinking
proportionally (DfES, 2003b; 2003c). Further exemplification and details of the transition units can be found on the DfES website.