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Planning for Learning (at Key Stage 4)
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Planning for Learning (at Key Stage 4)
Planning lessons involves an overview of many different aspects
Whether teachers are planning learners’ work for a whole year, for a series of lessons or for a single lesson, they will use what they know and understand about many different things. In addition to knowing what the national curriculum and framework documents require them to teach, following national guidance and taking account of research findings, they will draw on their recollections of past experiences and the wisdom derived from them.
Main Section
Creative and efficient planning for learning mathematics is often a collaborative enterprise. Whether or not teachers develop good planning skills by working with colleagues, in any planning activity they draw on their recollections of past experiences, the understanding they have derived from them, and their knowledge. They will draw on what they know about many things, which must include what the National Curriculum requires them by law to teach. The Mathematics programme of study for key stage 4 and attainment targets, which is an extract from The National Curriculum 2007, can be downloaded here. At the Qualifications and Curriculum Authority (QCA) web site teachers will also find guidance on planning and assessment, notes on how mathematics links to various things, such as 'functional skills', and curriculum case studies.
When planning learning at key stage 4, teachers will also use the renewed Framework for secondary mathematics (2008) which builds on the original Framework for teaching mathematics that was produced in 2001. It is based on the programmes of study for the new secondary curriculum. To enable the National Strategies to keep content updated continually, the Secondary Framework for mathematics can now only be viewed online (http://www.standards.dcsf.gov.uk/secondary/framework/maths/fwsm/); it is not all in a download format as were previous publications. However, 'The Framework for secondary mathematics: overview and learning objectives' can be downloaded here.
Following the 1419 Education and skills White Paper (February 2005), and the Skills White Paper (March 2005), the DfES gave QCA a remit to develop functional skills in English, ICT and mathematics. The resulting 'Standards for functional skills' can also be downloaded from the QCA web site (http://www.qca.org.uk/qca_6066.aspx). The Quality Improvement Agency (QIA), Secondary National Strategies (SNS) and the Learning and Skills Network (LSN) have produced resources to support the delivery of functional skills (http://excellence.qia.org.uk/functionalskills) including 'Teaching and learning functional mathematics'. In planning for key stage 4, teachers may also want to prepare learners for the teaching of financial capability, which is an aspect of QCA's Framework for Work Related Learning (2004). (Since September 2004, Work Related Learning has been a statutory requirement for all Key Stage 4 students.)
Knowledge about research in the teaching and learning of mathematics will inform all successful planning. A good place to start is the British Society for Research into Learning Mathematics (BSRLM) (http://www.bsrlm.org.uk/), which is 'a supportive environment for both new and experienced researchers to develop their ideas'. The BSRLM meets three times a year to present and discuss the latest research in mathematics education, informal brief reports of which can be downloaded (http://www.bsrlm.org.uk/informalproceedings.html). The BSRLM also provides links to sources of research evidence from UK universities and national and international organisations (http://www.bsrlm.org.uk/links.html). There are several BSRLM working groups, including the NCETM/BSRLM working group which is developing a framework for researching CPD in mathematics (internal link).
Teachers usually develop long term, medium term and short term plans. Long term plans show how units or topics or modules fit together over a school year to provide varied opportunities for learners to try to meet learning objectives set for the year. Medium term plans indicate in more detail how learners will encounter ideas in the units for a term or half a term through different kinds of activities. Short term plans are detailed plans for a single lesson or a short series of lessons. They include objectives, descriptions of tasks and activities, resources, assumed prior learning, and misconceptions or obstacles that the teacher may need to address.
When creating long term plans teachers need to consider how mathematical ideas or themes will recur, so that learners can extend and deepen their understanding. (See Mathematical Themes). They also need to be aware of the complex ways in which mathematical ideas are linked, perhaps connecting ideas using concept maps or an online thesaurus, such as the 'Connecting mathematics' web site (http://thesaurus.maths.org/mmkb/view.html?resource=index). For example, algebraic and graphical ideas explored earlier in the year might be encountered again, and extended, in geometrical explorations. (See Spiral Curriculum and Spiral Tasks). When devising a long term plan it is very important that the teachers have audited the content covered against the content they are required to teach to ensure sufficient coverage. It will be necessary to take an overview of the content coverage for Foundation and Higher GCSE; functional skills; financial capability and any other courses that are being planned for. More help on planning for the National Curriculum can be found on the QCA site (http://curriculum.qca.org.uk/key-stages-3-and-4/subjects/mathematics/keystage4/Planning_across_the_key_stage_in_mathematics.aspx)
More able learners may be given the opportuity to take further qualifications in mathematics during key stage 4. (see pathways and options ) These will need to be included in long, medium and short term planning.
Drawing up a medium term plan is an opportunity for teachers to think about how learners can be motivated by varying the kind of activity that they engage in. For example, a unit in which learners use dynamic geometry software to explore constructions and loci, might be followed by a unit about probability in which learners discuss answers to questions stimulated by real data such as airline delay statistics. A unit about graphs in which learners perform experiments and track data using a graphic calculator and find lines of best fit might then follow this. Although in all three units learners may experiment, discuss, conjecture, generalise and reflect, the thinking is generated by learners physically doing different kinds of things: working at computers, using data, graphic calculators and even making things. At key stage 4 medium term planning might also include time for assessment and revision and include notes on where process skills are being demonstrated. The new functional skills exams will be testing mathematics used in context so opportunities need to be there for learners to experience this.
When devising short term plans for a lesson, a good teacher thinks carefully about each part of the lesson. Having decided what the learning objectives for the lesson are (see Lesson Objectives and planning teaching and learning using a lesson objective), the teacher selects or devises activities with the potential to enable learners to meet the objectives (see Selecting Suitable Learning Activities (at key stage 4)). She will usually provide several distinct activities that together form an effective, progressive learning experience (see Learning Trajectory). Although the three-part lesson, consisting of a starter, a main activity and a plenary session, can be effective, it is not necessary to stick rigidly to this form. A teacher may vary the lesson structure; research shows that it is how learners are drawn into the ideas that matter, rather than the shape of the lesson (see Lesson Details and LessonStructures).
When planning a lesson it is important that the teacher 'plays the lesson through' in her mind beforehand, visualising how the learners are likely to be acting at each stage, and what she will be doing and saying to encourage learning. In doing this, the teacher brings to mind her knowledge about effective teaching strategies (see Selecting Teaching Strategies (at key stage 4)), including where it may be helpful to pause (see Pausing). In playing the lesson through in her mind, the teacher also thinks about previous learning on which the lesson will build (see Prior Learning, Starting From Where Learners Are and Curricular Continuity and Progression). The teacher can focus on mathematical language which she may introduce, in the hope that learners will find that language helpful in thinking and talking efficiently about the ideas (see Rate of Learning (Progression)). Imagining the lesson in advance helps the teacher anticipate misconceptions and stumbling blocks. It also reminds the teacher of resources that might be helpful, as well as essential resources (see Selecting and Using Resources for Learning (at key stage 4)). All these considerations are important aspects of planning.
Another part of planning a lesson, or series of lessons, is deciding how the teaching will extend the learners' 'big picture' of what doing mathematics is. In every lesson the teacher can remind the learners of some aspect of what mathematicians do. (See Start with the Big Picture).
Before creating short term plans, possibly when drawing up long term plans, a good teacher will have thought about how the mathematics that the lessons are about is connected to other mathematical ideas. They will know where the topic came from historically, why it is in the curriculum, and in what contexts it is relevant (see Structure of a Topic). However, because even an excellent teacher does not know everything, it is a good idea to have strategies for dealing with learners' unexpected insights (see I thought I knew).
Probes and promptsHave you checked that all the GCSE content is covered in your long term plan?
At the appropriate level?
What plans do you actually use? What is their form?
What plans do you devise, or help to devise?
What aspects of your plans are useful, and what aspects are not so useful?
Do all the members of your department use the same planning format? Does it matter? Taking actionLong term: audit your content coverage
Medium term: audit process skills, types of activity, functional skills (maths in real situations)
Short term: think about a lesson that you will be teaching soon.
Read all the plans that you have that are relevant to that lesson.
'Play the lesson through' in your mind.
If you think other reminders or prompts would help you immediately before or during the lesson, write them in the plan.
After the lesson, look again at your plans and any reminders and prompts that you wrote. What was useful, and what was not? Case studiesA new head of maths is looking at the department planning. At present teachers with KS4 classes are each "doing their own thing" based on the exam board syllabus. There are end of year exams but all other assessments are teacher devised.
The head of maths first sits with the team and decides which GCSE levels the different sets are aiming for. The, starting with the top sets, he splits the content into related topics to be covered over the first five terms of years 10 and 11; allocating a topic to each week or so as needed and including set times for assessment, revision and follow up. He made decisions on which topics could be left as "optional" for middle sets (e.g. sine and cosine rule) and which were compulsory for all. Teams of teachers then took the topics for each half term and wrote medium term plans that included activities to develop process skills and opportunities to practice maths in context where possible. Developing resources and plans as a team gave each teacher more ownership and a coherence to the course. Learners could move more easily between sets and there were higher expectations (and exam results) for each class. Research SourcesJones, K. and Smith, K. (1997), Student Teachers Learning to Plan Mathematics Lessons. Paper presented at the 1997 Annual Conference of the Association of Mathematics Education Teachers (AMET1997). Leicester. 15-17 May 1997.
Perks, P. and Prestage, S. (1994), Planning for Teaching. In B Jaworski and A Watson (eds), Mentoring in Mathematics Teaching. London: Falmer.
Ref: Mason, J. (1993) with Hewitt, D. & Brown, L. Ways of Seeing, in M. Selinger (Ed) Teaching Mathematics, Routledge & Kegan Paul, London.
Oliver Caviglioli & Ian Harris (2001), Mapwise: Accelerated learning through visible thinking, Network Educational Press
Robert Powell (1997), Active Whole-Class Teaching, Robert Powell Publications
Griffin, P. & Gates, P. (1989). Project Mathematics UPDATE: PM753A,B,C,D, Preparing To Teach Angle, Equations, Ratio and Probability, Open University, Milton Keynes.
Mason, J. & Johnston-Wilder, S. (2006 2nd edition). Designing and Using Mathematical Tasks, Open University, Milton Keynes.
Mason, J. (2002). Researching Your own Practice: The Discipline of Noticing. London: RoutledgeFalmer
Perks, P. (2002). Progression in mathematics. In Haggarty, L. (Ed) Aspects of teaching secondary mathematics: perspectives on practice. London: RoutledgeFalmer
Mason, J. & Johnston-Wilder, S. (2004). Fundamental Constructs in Mathematics Education, RoutledgeFalmer, London.
Gardiner, A. 1992, Recurring Themes in School Mathematics: Part 1 direct and inverse operations Mathematics in School, 21(5) p5-7.
Gardiner, A. 1993a, Recurring Themes in School Mathematics: Part 2 Reasons and Reasoning, Mathematics in School, 23(1) p20-21.
Gardiner, A. 1993b, Recurring Themes in School Mathematics: Part 3 generalised arithmetic Mathematics in School, 22(2) p20-21.
Gardiner, A. 1993c, Recurring Themes in School Mathematics, Part 4 infinity, Mathematics in School, 22(4) p19-21.
Categories
Curriculum, Pedagogy
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