POST GRADUATE CERTIFICATE IN EDUCATION SECONDARY PROGRAMME
2014/2015
MATHEMATICS
SUBJECT STUDY HANDBOOK
Mathematics Subject Handbook Contents
2014-2015
Page
Introduction 2
Location of Subject Study sessions 2
Your Subject Study Co-ordinator 2
Key contact details 2
Expectations 3
Module outlines 3
Moodle 3
What Will I Learn? 4–7
Structure and Content
Module 1: The Induction Phase 8–12
Module 2: The Advanced Development Phase 13-15
Assessment
Summative Assessment 16
Details of Assignment 1 17-18
Details of Assignment 3 19-20
Formative Assessment
Summary of components of formative assessment 21
Post-16 research tasks 22–23
Subject knowledge audit 24
Tutorials 24
Summary of subject teaching experience form 25
Lesson Design and Planning 26-27
Lesson plan pro forma 28-30
Weekly lesson planner 31
Who will support me? 32
How will I learn? 32
Advice from former students 33
Evaluation
Subject co-ordinator’s response and action points 34-36
Resources 37-38
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Introduction Your subject study modules will run alongside your Professional Studies programme and are complementary to your School Experience. Subject study sessions for Mathematics take place in M1.15 in Mordington House or occasionally in an ICT room on the Bognor Regis Campus Your Mathematics Subject Study co-ordinator is Jeremy Smith. He will be your Academic Adviser (this role is explained in the Programme Handbook) and your first point of contact if you are experiencing any difficulties during your PGCE. However he leads a team of tutors with whom you may work on the route. The main tutors are listed below, with contact details.
Jeremy Smith Mathematics Co-ordinator [email protected] [email protected] 01243 812069
Roger Beeney Mathematics Tutor [email protected]
Adrian Pinel Mathematics Tutor [email protected]
Peter Hurst Mathematics Tutor [email protected]
Simon Pyle Mathematics Tutor [email protected]
Other useful contacts are:
Julia O’Kelly PGCE Co-ordinator
[email protected] 01243 812160
Melanie Hopkins Programme Administrator
[email protected] 01243 812043
Gail Graffham Librarian [email protected] 01243 812094
SIZ Helpdesk Student ICT queries etc
[email protected] 01243 816222
Melanie Hopkins can be found in the Programme office which is in St Michael’s F2. The office is open between 8.30 am and 5.00 pm every day except Friday, when the office closes at 4.30 pm.
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Expectations You are expected to demonstrate the professional attributes of a teacher in your approach to your subject study. You are expected to:
Attend every session
Participate actively in all sessions and in a sensitive and professional manner which is compliant with the University’s published policies as detailed in the Programme Handbook
Use Moodle regularly for communication and information
Complete all pre and post session tasks as directed
Attend all tutorials arranged with your academic adviser and subject tutor(s)
Be pro-active in addressing the targets set for you in conjunction with your subject tutor / academic adviser
Take responsibility for meeting deadlines, and submitting assignments/ documentation to the correct place e.g. programme office
In the event of any absence please follow the procedures detailed in the Programme handbook. This includes absence from school experience through illness, personal reasons and interviews. Module outlines for your subject study modules can be found in the Programme Handbook. Moodle: Information about your subject study, including this handbook, and session notes will be posted on the university’s Moodle, which can be accessed from the university website. You will also use the Moodle for communication with other student teachers on your subject route.
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COURSE TITLE: Mathematics Subject Study COURSE HOURS: 110 hours, Modules 1 and 2 USUAL DAYS: Wednesday, Thursday and Friday TIMES: 9.30 am-12.30 pm & 1.30-3.00 pm (with tutorials to 3.30) COURSE TUTOR: Jeremy Smith (Subject Co-ordinator)
What Will I Learn? These two Mathematics Subject Study modules together aim to produce reflective, analytical, critical and effective classroom practitioners. This module introduces you to the place and purposes of mathematics within the curriculum, and to the understanding, knowledge and skills necessary to become effective secondary mathematics teachers. It is designed to enable you to relate the standards required for the award of Qualified Teacher Status (QTS) to the teaching of mathematics. The modules draw upon and enhance your prior mathematical experiences, understanding, knowledge, and skills. They aim to develop and extend your understanding of the structure, progression and connections within the secondary mathematics curriculum, your ability to make mathematics relevant and interesting to pupils, and to pose mathematical questions effectively for a variety of professional purposes. They will build upon your prior experience and skills, to equip you with the knowledge and understanding of the specific subject knowledge and skills that will enable you to become an effective teacher of Mathematics. You will:
learn to plan effectively in line with the requirements of the National Curriculum,
develop insights into individual pupils’ learning progression and
become effective communicators in a variety of contexts. This M-Level course will address the new “Teachers’ standards” published by the Department for Education in May 2012. You will be prepared to demonstrate all relevant Professional Skills during your school placements. Learning Outcomes are set out in full in the Module Outlines to be found in your Programme Handbook. NB Tutorials to agree targets for the Subject Knowledge Profile (see Assessment
section of this Handbook) will be included.
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1. Principles
The Mathematics modules will:
recognise you as an individual student and give you the task of creating, reviewing and updating your own action plans, with tutors giving support as and when required
attempt to draw collaboratively upon all existing strengths within the group, so giving you opportunities for practising tutorial skills on each other through peer-teaching
provide, through its sessions, assignments and tasks, opportunities for you to achieve all relevant standards, or to support you in achieving these standards within and through other programme components
be designed to inspire you with enthusiasm for teaching mathematics, that you will take with you in to both school placements, and to act as a launch pad into your NQT year.
provide you with access points to a wide and deep base of research and inspection evidence, and guidance in accessing this
2. Strands
To ensure coherence and support accessibility, the Mathematics modules will contain identifiable strands:
Mathematics Knowledge and Understanding – profound understanding of fundamental mathematics and of the mathematics curriculum
Mathematics Teaching: Planning activities, lessons and units of work, including monitoring and assessment and class management. Planning takes centre stage in the first module to prepare you for the planning demands of School A.
Mathematics Teaching: Understanding key issues including progression, inclusion, differentiation, language vocabulary and questioning, learning styles, differing profiles of intelligence, the differences between procedural and conceptual understanding, relating pedagogy and practice: the effectiveness and appropriateness of different teaching strategies, the importance of communication, reasoning, mathematical thinking, problem solving, and problem posing.
Working Knowledge of Frameworks: Understanding and using the National Curriculum and examination syllabi.
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3. Tasks To help you to meet the standards and achieve in a continuous and sound way, tasks are specified. These tasks are a compulsory part of modules one and three, and although not all will be formally assessed, all should be completed on time, and be available to be inspected by the subject coordinator at any point in the course:
alongside each day of the modules there are often pre-tasks, tasks to be carried out during the day, and follow-up tasks. These will be specified in writing during university based sessions, with copies available via Moodle.
a set of research tasks will be set looking at how A-level maths is taught in schools. These will be completed during your “post 16 observation experience”, either at one of your two placement schools, or at an additional placement organised towards the end of your training year.
Your Audit of Subject Knowledge and Understanding for Mathematics 11-16 is an extremely important document which you will initially complete during Module 1 sessions. You will need to show this to your mentor in both school placements and keep it up to date as the course progresses. In consultation with your subject tutor and subject coordinator you will agree some specific Action Points on which to focus during your first school placement, which will be reviewed in January. Remember that you can use the expertise of School A colleagues to help you to tackle these Action Points
Your Audit of Subject Knowledge and Understanding for Mathematics 16-19 must be completed even if you have chosen not to be assessed as a post 16 teacher. This information is shared with your mentor, and included in your school experience documentation.
For all students who elect to be formally assessed at teaching post 16, an additional research task looking at how mathematics is organised in undergraduate mathematics courses at university will be completed.
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4. Resources A good selection of resources is often the difference between a well-designed teaching plan leading to an effective lesson and a less than successful lesson. Accordingly, resources and their critical selection and adaptation form a recurrent theme throughout.
Your course-base is a resource-rich environment to which tutors will add resource ideas and materials.
The University of Chichester has an excellent learning resources centre for your purposes on the Bognor campus, and through Moodle you have access to a wide and expanding range of electronic resources and internet sites
Mathematics ICT resources – software and hardware – are featured regularly within your modules.
Effective use and evaluation of internet based resources is also a key part the course, and one day in September focuses entirely on this.
Notes:
You will have access to a range of tutor support in a number of complementary ways - initially your tutor for that module session and the Subject Co-ordinator. Your Academic Adviser will normally be your Subject Coordinator. Your School A Subject Tutor will advise you on your files, visit you in School A within the scheduled period, and draft your reference. While in Schools A and B, you will be allocated a Subject Mentor, and the school will have designated a Professional Tutor to advise you and to continue guiding your training.
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Structure and Content
Module 1 : The Induction Phase Room: Mordington 1.15 unless stated Preparation and Follow-up tasks will be set on most days. In groups or pairs, you will make links between each session and Standards S1 – 8, noting these down in the Standards column; a few standards are placed there to give you a start; this activity will help to familiarise you with the Standards in relation to the experience and content of the course. Please note: At the time of writing, I am awaiting confirmation from two guest speakers, who will be running sessions with the group in September and January. Once these sessions have been finalised, the order in which other sessions are delivered may have to change. An up to date schedule will be maintained on Moodle.
WEEK OUTLINE Teachers’ standards
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MONDAY 8 SEPTEMBER 1–2 pm
Introductory meeting. Welcome / Introductions Specific immediate tasks –
finding starters (preparation for Friday’s session)
Data gathering re school placements
Alert re producing personal profile
WEDNESDAY 10 SEPTEMBER
Mathematics in Schools – why is it taught? What aims and purposes does it serve? What describes effective teaching?
Planning a mathematics lesson – our lesson plan blank
What makes a good starter?
Planning starters
Introduction to the first micro task. Complete your Personal Profile by 3.00 p.m. please. An electronic version as a Word File should be e-mailed to [email protected] and [email protected] by 4.00 p.m.
S 4
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1 THURSDAY 11 SEPTEMBER
Introduction to the National Curriculum
Resources and tools for mathematics teaching and learning
Using interactive whiteboards
Illustrative examples of the application and value of software tools in lesson contexts
Initial analysis of ICT strengths and needs – informing action plans
Using ICT in the presentation of mathematics
Time for preparation of starter activities
S 3, 4
1 FRIDAY 12 SEPTEMBER
Completion of Starter Activities
Teaching to a time limit
Planning to engage a class
Micro-teaching – teaching a starter, engaging and sustaining the interest of an audience, learning lessons of ‘classroom presence’
S 4, 7
2 WEDNESDAY 17 SEPTEMBER
“Success and Excellence in mathematics”
A day spent challenging your perceptions of mathematics teaching, presented by two leading teachers from an outstanding local school. (To be confirmed)
S 1, 2
2 THURSDAY 18 SEPTEMBER
Using the internet to find useful resources
Critically evaluating teaching resources
Finding appropriate resources to help lesson planning
Using interactive webpages in mathematics lessons
Using ICT in assessment
S 4, 6
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2 FRIDAY 19 SEPTEMBER
Understanding the transition from KS2 to KS3
Cultural issues in the teaching of mathematics
Teaching mathematics to students for whom English is an additional language
Teaching mathematics to Gifted and Talented pupils
Teaching mathematics to Pupils with Special Educational Needs
The Historical and Cultural context for mathematics taught in schools
[Afternoon] THE CROSS CURRICULAR ROLE OF MATHEMATICS
A joint session with PGCE science students looking at the applications of mathematics in the science curriculum
S 1, 3, 5 S 8
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THURSDAY 25 SEPTEMBER
Using financial contexts for teaching mathematics
Subject knowledge review and action planning
Functional Maths Bridging the gap between GCSE and ‘A’ level
FRIDAY 26 SEPTEMBER
Forms of assessment
Using assessment to inform teaching
Identifying pupil misconceptions
Learning mathematics through problem solving and investigations
Assessing open ended mathematics tasks
Classroom observations
Preparing for school ‘A’
S 3
3
S 5, 6
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4 FRIDAY 3 OCTOBER
Review of experiences from the first three days in school
An introduction to Mathematical research
Critical reading of research papers
Assignment one
Additional work on lesson planning and assessment
S 2, 5 S6
5 FRIDAY 10 OCTOBER
Microteaching – delivering and evaluating a short lesson activity.
Checking of sample lesson plans
Tutorials with designated subject tutors for School A, checking students’ preparedness
S 4, 7
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THURSDAY 31 OCTOBER
Subject Knowledge Enhancement day – addressing any remaining gaps in subject knowledge and examining ways in which topics can be delivered in an inspiring way to pupils. School Experience tutorials: These are to ensure that students are sufficiently well prepared for the next phase in schools. Students’ subject tutors will specifically refer them to this session if their draft lesson plans are less than convincing on the 10th of October.
S 4, 5, 6
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The Oasis Day 1
WEEK UNIVERSITY STANDARDS
10 FRIDAY 14 NOVEMBER
Subject Study Day at the mid-point of Placement A: Review of practice to date Sharing resources and ideas Review effectiveness of strategies [for planning,
teaching, assessing, evaluating and standards evidence gathering]
Progress on assignment one - tutors will check on how far advanced this research is, so that there is sufficient time for students to get this done before the end of the placement.
Preparations for subject tutor visits and joint-observations
Tutors will check the quality of completion of school experience documents and pick up any weaknesses in time for these to be addressed effectively before the end of the placement.
Assignment 2: tutors will check on completion of ethics forms, and how far advanced research is, so that there is sufficient time for students to get this done before the end of the placement.
All
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Module 2 :The Advanced Development Phase
16 5 – 9 JANUARY
Key Stage 2 Experience
17 WEDNESDAY 14 JANUARY
Review of Primary school experience Review of School A The National Curriculum – further inputs New qualifications, and proposed changes to
national assessment; review of impact on teaching in school A.
“The Unseen Child” and its impact for mathematics teachers
Subject knowledge development activities
THURSDAY 15 JANUARY
Using and Evaluating schemes of work. Constructing a sequence of lessons. Briefing on Assignment 3 Engaging pupils interest in mathematics The role of mathematical games Sharing fun learning activities from school A Subject knowledge development activities
FRIDAY 16 JANUARY
(to be confirmed) “Using technology to enhance
pupil learning and make effective use of assessment in mathematics lessons” – a day of practical activities using “TI-inspire” technologies, delivered by experts from Texas Instruments.
S 2, 5 S 4, 6, 8 S 1, 4, 6
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18 THURSDAY 22 JANUARY
“School immersion day”
A day spent in a school in Portsmouth, finding out how schools are working collaboratively together, learning more about the NQT induction year and available support, and hearing advice from a head teacher on what they are looking for at interview in a prospective maths teacher.
FRIDAY 23 JANUARY
Effective assessment; types of assessment; using
assessment to inform your teaching Examples of assessment used in school A Differentiation input Review and evaluation of “Financial maths” directed
task
S 8 S2, 3
19 FRIDAY 30 JANUARY
Review of the first three days of school B Looking at A-level syllabuses Post 16 experience and tasks Subject knowledge audit of post 16 syllabus content Reviewing subject knowledge audit for GCSE Use of language and questioning skills Reflection on research papers and how they can
improve your teaching Subject Knowledge development activities
S 6, 8
15
20
THURSDAY 5 FEBRUARY
Student led day “Sharing of resources and ideas from school experience”
S 1, 4
FRIDAY 6 FEBRUARY
Pre-School Tutorials with designated subject tutors
for School B, checking students’ preparedness
All
The Oasis Day 2
26 FRIDAY 20 MARCH
Subject Study Day at the mid-point of Placement B, before the last ‘synoptic’ nine weeks Review of practice to date Sharing resources and ideas Review effectiveness of strategies [for planning,
teaching, assessing, evaluating and standards evidence gathering]
Progress on assignment three Preparations for subject tutor visits and joint-
observations
All
The Conference – Knowledge Transfer
37 WEDNESDAY 17 JUNE and THURSDAY 18 JUNE
Presenting Assignment 3 to your group Students’ course evaluation
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Assessment
A definition of summative and formative assessment is included in the Programme Handbook.
Summative Assessment What do I have to do? What will my assessor be looking for? The following chart can also be found in the Programme Handbook. Your subject study summative assessment is highlighted to show how it combines with other elements of the PGCE Programme to contribute towards your overall summative assessment:
Subject Study – Module 1
One 4,000 word (or equivalent) assignment graded at least ‘D’ – minimal pass
20 M level credits
Professional Studies – Module 1
Reflective log highlighting the links between professional studies and subject application Satisfactory attendance and active participation in sessions and tasks
School Experience ‘A’
Joint Summative Report from School A on which you are graded as having achieved the Standards at a Minimal level or above
Professional Studies - Module 2
One 4,000 word (or equivalent) assignment graded at least ‘D’ – minimal pass
20 M level credits
Subject Study – Module 2
One 4,000 word (or equivalent) assignment graded at least ‘D’ – minimal pass
20 M level credits
School Experience ‘B’
Joint Summative Report from School B on which you are graded as having achieved the Standards at a Minimal level or above Completion of Standards Tracking Document
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Module One Assignment 1 (4,000 words)
Critically examine the place and purpose of mathematics in the school curriculum, focusing on a current debate on how the subject should be effectively delivered in schools. Within your assignment you should explain how your own approach to teaching will develop “profound understanding” of mathematics by your pupils, as well as allowing them to apply the techniques outlined in the curriculum, and discuss whether any tension exists between these two methodologies. You should also give some insight in to how you can “engage, motivate and inspire” pupils with a life long enjoyment and understanding of the subject. To illustrate this, you should show how your philosophy of teaching has been influenced by wider reading, and make reference to lessons you have taught during your teaching practice. Evaluate your experiences carefully, not forgetting to indicate what progress has been made by pupils, and how you have assessed their understanding. Reflect on how you could improve your professional practice in future. Include clear explicit references to the Teachers’ Standards within the text, to provide evidence that you are making progress towards meeting these standards in your teaching. For Masters level credits to be awarded:
Throughout your assignment, you should engage critically with published research on the teaching of mathematics. This “critical engagement” is an essential characteristic of Masters level writing, and can only be demonstrated by a detailed discussion of your sources, when appropriate comparing and contrasting the findings of different studies and authors. Show that you understand the links between theory and practice by discussing how your reading relates to your own experiences of teaching during your school experience. Refer to lessons that you have taught, making clear the ways in which your engagement with research has informed your planning process.
Specific Assessment Criteria In addition to the general criteria, which can be found in the Programme handbook, you will be expected to demonstrate:
your understanding of the debate in the mathematics education community about why and how mathematics should be taught in schools
that you know the difference between “profound understanding” of a topic and the ability to apply a technique to answer a structured question
that you are able to “motivate and inspire” pupils through your own teaching strategies
Critical engagement with recent and relevant published material from peer reviewed sources
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A clear understanding of the links between educational theory and your own teaching practice
a well structured, reflective and informed position that is argued with balance, lucidity and accuracy;
an appropriate academic writing style; Standard English; Harvard style referencing; originality and flair (see also assignment writing guidelines in Appendix A of the Programme handbook);
explicit references to the ways in which the writing of this assignment has helped you towards meeting the Teachers’ Standards (2012)
NOTE: specific reference to the Standards is required Submission date: Thursday 18 December 2014 by 12.00 noon
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Module Two Assignment 3 (4,000 words equivalence) Briefly evaluate a section from an existing scheme of work. This is likely to be the scheme of work from your school B placement school, but could be from a different school, or from a nationally published source if appropriate. The sequence of lessons should be for teaching a single topic or group of very closely linked topics, and will typically last between three and six hours of teaching time. Critically discuss an alternative way of delivering a sequence of lessons to teach this topic, showing how you can strengthen and enrich the learning of pupils with original ideas of your own. You should show evidence that your choices have been informed by critical engagement with recent published research, including mention of common misconceptions in this topic. You should evaluate your chosen strategies, making clear and explicit references to lessons that you have taught. Lesson plans for these lessons should be included in an appendix, but a chronological description of the lesson sequence is not required. By analysing the results of assessments you have carried out, you should give compelling evidence that pupil learning has been enhanced by your chosen strategies. Include clear explicit references to the Teachers’ Standards, to provide evidence that you are making progress towards meeting these standards in your teaching. The Assignment is based upon the critical review, evaluation and adaptation of a unit of work within a wider scheme of work. The assessment of the assignment will be in two parts:
a paper, in the form of a critical commentary demonstrating conceptual understanding [3000 weq, 75% of assessment]
a presentation, in a conference setting, involving knowledge transfer. [1000 weq, 25% of assessment]. This should be a summary of your written submission, designed to inform and be of interest to an audience of your peers. Your presentation should be no longer than ten minutes, with around five minutes to answer questions.
Specific Assessment Criteria: in addition to the programme’s general assessment criteria, you should demonstrate your:
understanding of the principles of curriculum planning and design, exemplified with a review of a sequence of lessons that you have delivered during your school experience.
ability to engage and motivate a class through imaginative classroom activities and resources
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understanding of how to assess pupils’ understanding of and attitudes towards lessons that you have taught
ability to communicate findings to peers, and to a wider audience within a formal written paper, through writing coherently and concisely, based upon the synthesis of reading and upon evaluating critically and reflecting upon professional practice.
ability to interest and inform an audience of your peers in a conference setting
ability to provoke and sustain discussion To achieve these you will need to: Demonstrate your knowledge and understanding of the teaching of your
chosen aspect of mathematics Make explicit reference within the text to the ways in which your work on this
assignment has helped you to collect evidence towards meeting the Teachers’ Standards
Show informed reading of recent and relevant literature pertaining to your chosen subject
Critically analyse current issues and theories relating to your chosen subject Analyse your own classroom practice and that which you have observed (no
names should be mentioned)
Utilise a clear structure with a fluent developmental argument
Use an appropriate academic writing style; standard English; Harvard style referencing; originality and flair (see also Assignment Writing Guidelines in Appendix A of the Programme Handbook).
Conference dates for presentation: Wed 17 June and Thurs 18 June 2015 Submission date for paper: Monday 15 June 2015 by 4.00 pm
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Formative Assessment All formative assessment is designed to demonstrate your ability to achieve the required level of attainment in your two subject specific assignments and to complete Modules 1 and 2 of School Experience successfully. As such it is predicated upon your agreed individual needs. There are several forms of formative assessment during your subject study modules:
Micro Directed Tasks You will be required to complete a number of subject specific tasks during university based sessions and during school experience, as directed by your subject tutor, in order to address your specific analysed needs. You will be able to be proactive in this respect, where you recognise a need for evidence that cannot readily be provided otherwise. These tasks will include your detailed subject audit, your post 16 tasks, and an analysis of using financial contexts in your teaching.
Subject Knowledge Audit Auditing your subject knowledge, and taking steps to enhance the breadth and depth of your knowledge effectively is a continuing process throughout the PGCE programme. A formal audit of your GCSE knowledge will be carried out at the beginning of the course, while an audit of your post 16 knowledge will be carried out during the subject study days in January 2015.
Tutorials These take place with your subject tutors to review your individual progress.
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Post-16 Experience and Research There follows a list of specific tasks which you need to complete during your post-16 experience. Rationale Regardless of the Key Stages chosen for assessment, during the Programme, each student teacher should gain experience (either direct or by observation) of planning, teaching and assessment at post-16. This is even more important for a teacher of just KS3 and KS4 students, as they need to be able to advise students appropriately on their A-level choices. As evidence that this has taken place, you should complete the following subject-specific directed tasks via observation of Mathematics teaching and discussion with teaching staff as well as an investigation into and critique of resources and approaches to teaching Mathematics at this level. By the end of the Programme, you should have become more familiar with and have reflected on recent developments in the teaching of ‘A’ and ‘A/S’ levels in mathematics and you should have learnt and reflected upon possible approaches that may be used when teaching an ‘A’ level class. Micro Directed Tasks specific to Post-16 Note: Your PDP contains a form on which you list the dates of post 16 experience, lessons you have observed and conversations you have had. In addition you should include the evidence required below where it says “For your file”. This must be submitted electronically during the course, and no later than Friday 29 May, either via Moodle or by e-mail to [email protected] 1. Study the syllabuses and specimen papers of the courses being taught in the
mathematics department. Look closely at the questions and associated marking schemes. Consider what teaching and learning strategies could be employed in order to tackle such questions effectively and discuss these (and other) approaches with staff in the department:
What do the students need to know?
What skills do they need to employ?
For your file: state which exam board your placement school uses. 2. Note ways in which ICT applications are used to consolidate and deepen the
knowledge and skills of students. For your file: write a brief summary of how much ICT is used in the
teaching of A-level mathematics at your post 16 placement institution. Be honest, and if the answer is “very little”, then write this.
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3. Find out which A-level mathematics modules are taught at your post 16 placement institution. Ask why these modules are offered in preference to others. Find out if a choice of module is offered to students, and when and how this choice is made.
For your file: summarise your findings in a brief paragraph. 4. Ask whether any students at your post 16 placement school complete
coursework tasks as part of their A-level mathematics studies. You are not required to complete the coursework yourself, but if you do have the subject knowledge to complete this then you might find this interesting and useful.
For your file: record whether or not coursework is done at your
placement school, and if it is provide a brief description of when and how this is completed.
5. ‘A’ level syllabuses are often selected by departments in the light of three
considerations: personal preference, staff expertise and the resources available. Try to find out why the department has chosen the course that they use. In addition, find out which text books or other support resources are used by the students, and how these are viewed by students and staff.
For your file: record your findings in a brief paragraph.
6. Observe as many A-level mathematics lessons as possible. Make brief notes
on these lessons, including the topics covered, the resources used, and any pupil misconceptions that you identify. The level of detail of these notes will depend on how involved the teacher allows you to become in the lesson.
For your file: record a list of which A-level maths lessons you have
observed, and which topics you have seen taught. This will duplicate information required on the form in your PDP, so it would be acceptable to submit an electronic version of this form.
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Subject Knowledge Audit From your early subject study days onwards, you will start to complete a Subject Knowledge Audit. Your subject tutor will work with you to support your Subject Needs Analysis, which will be discussed and agreed with you, leading to an action plan. On this basis you will build up a Subject Knowledge Profile, which will be monitored by subject mentors during School Placement A and reviewed periodically by subject mentors during School Placement B. You will be expected to be pro-active in addressing any gaps in subject knowledge identified in your action plan. Responses to the 11-16 audit sections are submitted in a Subject Study session in September. Your 16-18 audit will be completed as part of your post-16 evidence. Your completed Subject Knowledge Audit can be used as evidence of meeting the Subject Knowledge requirements of the Standards. Submission date: 11-16 Audits will be completed during the first week of the course and submitted to your subject coordinator on the 26 September. It must be shown to your mentors in both school placements, and will be revisited and updated in January 2015. There may be action points arising which can be addressed prior to the Oasis Day on 20 March 2015.
Tutorials Tutorials with your subject tutor are scheduled before the beginning of each School Experience to check your preparation for school experience and discuss your targets and subject needs. In addition clinics will be available before School A. Following the marking of your assignments, you will receive feedback to help you to consider any areas for development identified. This is designed to help you to improve your level of attainment in the following assignment. Your summary of teaching experience will help you and your subject tutor to ensure that you cover the required range of teaching during your school placement.
Summary of teaching experience In the following table, record the topics that you have actually taught. The amount of space available indicates the level of detail required. You will need to show this table to your subject tutor at various times during the course, and during the subject tutor visits to your placement schools.
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PGCE SECONDARY MATHEMATICS
Summary of Mathematics Teaching Experience for 2014/2015
NAME: ……………………………………………………………….... Assessment Option…………………………………………
Experience of Teaching at KS2
Experience of Teaching at KS3 Experience of Teaching at KS4 Experience of
Teaching at 16+ Experience of
Teaching using ICT
S C H O O L A : ………………………………………………………………. [NAME OF SCHOOL A]
S C H O O L B: ………………………………………………………………. [NAME OF SCHOOL B]
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Planning lessons for Lesson Objectives and Learning Outcomes
Criteria to bear in mind when framing lesson objectives:
Does the objective define a learning outcome?
Does the objective help you to determine whether pupils have learned anything at the end of the lesson?
Do you have ways of checking that you have met your objectives, in other words that the student has learnt that which you intended?
Consideration should be given to the part that the lesson plays in the context of long term progression of learning in terms of skills, concepts, knowledge and understanding it addresses.
Consideration should also be given to learning issues arising from the previous lesson.
Some useful world phrases that will give you the precision that you need in a learning objective:
By the end of the lesson pupils will be able to ….
select … extract … give example of … relate … identify … choose … connect … link … make a link between … explain … illustrate … show the relationship between … explain the relationship between … comment upon … remember … recall … ask questions about … choose questions that … find … design … prioritise … extend … amplify … reorganise …
classify … sort … arrange … justify … justify their thinking concerning … explain their thinking concerning … compare … contrast … define … analyse … join up … organise … reconsider … reflect … support … support a view that … evaluate … create … construct … draw out … challenge … build … structure … represent …
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Avoid words like discuss, complete, fill in, annotate, listen, finish or gather. These are descriptions of procedures, tasks or activities. They are not learning objectives. They are fine for your activities in your lesson plan – but not for your objectives. You might legitimately want pupils to ‘do the exercise’ or ‘fill in the table’ or ‘finish the graph’ or ‘do the experiment’ but these are not learning objectives. Avoid words like become aware of, experience, learn about, empathise with or understand. These are too vague for you to assess whether or not learning has taken place. Also, they don’t help you with defining what pupils are learning. They are perfectly valid aims and experiences, but your job is to specify the learning outcomes that will demonstrate some headway towards such aims and experiences.
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University of Chichester PGCE Secondary MATHEMATICS LESSON PLAN 2014/2015
DATE: GROUP / CLASS:
LOCATION: NUMBER IN CLASS:
LESSON TIME: FROM: TO:
TEACHER: LEARNING SUPPORT ASSISTANT: Yes / No Name:
SEN / IEP: Information:
LESSON FOCUS:
Learning Objectives for pupils: (to include differentiation)
ASSESSMENT : How will you know what progress has been made by pupils?
TEACHING AND
LEARNING
RESOURCES
TEACHERS’ STANDARDS
Health & Safety issues:
Plan checked by class teacher or mentor? Yes No
PRE LESSON UNDERSTANDING:
What will pupils need to know in order to be able to access the lesson? How will I check that they do know this?
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LESSON CONTENT / PROCEDURE AND ORGANISATION
STARTER/ INTRODUCTION
NOTE TIMINGS
MARGIN (for use in post
lesson evaluation)
MAIN PART OF LESSON TO INCLUDE DEVELOPMENT AND DIFFERENTIATION
PLENARY: WHAT have they learned today? HOW can they use it?
HOMEWORK: (If set)
Indicate by when it is to be completed
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POST LESSON EVALUATION, USING ASSESSMENT for LEARNING
Immediately after the lesson, you should annotate your lesson plan, indicating briefly what went well, which parts of the lesson did not go as you expected, and in particular identify any pupil misconceptions that arose. Further notes can be made at the bottom of this page if they will help you in your future lesson planning. In addition, you should briefly consider the following questions: What pupil learning took place? At the end of the lesson… …all pupils can: …most pupils can: …some pupils can: …no pupils can:
Were the lesson objectives met? If not, why not?
How could I have achieved more student progress in this lesson?
What do I need to do next lesson?
Additional notes:
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SECONDARY MATHEMATICS Weekly Lesson Planner
YEAR: UNIT / SOW TITLE: OBJECTIVES:
CLASS / ABILITY RANGE:
REGULAR CLASS TEACHER:
WEEK BEGINNING:
Date and Day Topic Brief description of activities HOMEWORK (if applicable)
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Who Will Support Me? Your Subject Co-ordinator is Jeremy Smith, and he is also your Academic Adviser (see the main Programme Handbook). Jeremy will lead the team who support your progress in your academic studies. The expert team of subject tutors – Roger Beeney, Adrian Pinel, Peter Hurst and Simon Pyle - will also work with you on your school experience. These subject tutors will meet you for tutorials at key points in the Programme, notably:
at the start and end of both teaching blocks.
during Oasis days in November and March.
How will I learn?
Jeremy will introduce theoretical sessions, supported as appropriate by visiting speakers. You will be expected to outwork the ideas addressed through discussions, collaborative planning activities with your peers and the completion of practical tasks. There will be an emphasis during all subject sessions on sharing experience, reflection, critical analysis of practice and evaluation. These sessions will mirror school practice. They will also support your development towards fulfilling Standard 8 in terms of developing professional relationships with colleagues. You will be expected to take responsibility for your own learning and to demonstrate originality and determination in tackling and solving problems. At different points in the course, each student will:
Prepare and present a starter activity
Participate in a videoed micro-teaching exercise
Peer-teach an aspect of mathematics or an ICT application to a fellow student
Present their work on Assignment 3 to the whole group
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Advice from former students At the very end of their course I asked the members of a previous cohort to write down some advice that they wished somebody had given them when they started the course. Here are some of their responses.
Don’t make more work for yourself than you have to. The tasks you will be given have the potential to be endless if you make them so!
Try to get as many lesson observations completed as soon as possible and ensure that you keep copies of them secure.
During induction/observation periods at the school placements, find and collect as many resources as possible, and get the directed tasks done.
Ensure you get to grips with the ICT used in your school early on, especially practice on the interactive whiteboards.
DON’T PANIC! If things look like they are going wrong speak to your tutors. Most problems are not new.
Register for TES connect, and get to know it before going in to school. It is one of the most useful sources of teaching materials I found this year.
Get a watch – the clocks in schools are never the same as the bells, and the pupils keep changing them when you are not looking!
Really familiarise yourself with Moodle. It is not that easy to navigate but contains a wealth of information.
Use the Weekly Lesson Planner
Try to get professional studies tasks finished as soon as possible, as it will get very busy if you leave them until school ‘B’.
Collect the “How to reference” purple booklet from the library to help your assignments.
Do good research for assignment 2 during school A
DIDLESs do not need to take very long to complete. If you write them up quickly by hand immediately after teaching the lesson you can get them done in just a few minutes, and what you write is more useful in the long run
You learn the most from your worst lessons. Remember this when you have a bad one, and don’t beat yourself up when things seem to go wrong.
Make sure you give yourself some time off each week. You will perform better when you are refreshed
Stay in touch with your fellow students and never be afraid to go to them for help or just to let off steam – they are going through the same thing that you are, and will understand when nobody else seems to!
If you don’t understand, ASK!!!
Keep your eyes on the prize. It is a long road and it is hard work, but I promise, now I have finished it really IS worth it.
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Evaluation: The Programme Board
Each subject route is required to select a representative member of the Secondary PGCE Programme Board. The Programme Board meets three times a year and each student representative is offered the opportunity to raise issues on behalf of their subject group.
Evaluation: Student’s responses Details of the evaluation of the Secondary PGCE Programme can be found in the Programme Handbook. As part of this process, each subject study module is evaluated. You will be asked to complete a module evaluation form. Your subject tutors will analyse the responses and identify areas for development. The responses from the 2013/14 cohort were as follows:
STUDENT MODULE EVALUATION
Secondary PGCE 2013–2014 Module Evaluation - Mathematics
Module Title Mathematics Subject Study
Course tutor Jeremy Smith
Eleven course evaluations were completed by students. This was the ten students who completed the course plus one student who intermitted towards the end of their second school placement, but who had completed all of the university sessions and tasks.
1. By the end of this module have you made progress in terms of the following learning outcomes?
Yes No
continue extending their understanding, skills, and knowledge of mathematics, recognising how secondary mathematics is structured into schemes and units of work;
100%
become effective in the planning, informed adaptation, implementation and critical evaluation of schemes of work consistent with the requirements of the National Curriculum and other relevant national strategies and syllabuses;
100%
become autonomous, analytical researchers of the wealth of mathematics education resources available, developing and using critical skills to adapt schemes to enhance pupils’ learning;
100%
appreciate through systematic enquiries that mathematics learning is frequently problematic: recognising current and intractable issues;
100%
through focused research, prepare themselves and plan mathematics lessons effectively, defending their plans; plans will include key questions, teaching points, resources, simplifications and challenges to ensure access, appropriate provision for all pupils, opportunities for formative assessment, and analytical evaluation of their practice;
100%
recognise the place of mental mathematics and catechetics in developing and refining pupils’ methods of solving mathematics problems, and of productive practising in consolidating learning gains.
100%
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2. Were you motivated by the learning and teaching approach?
Yes
100%
No
Comment
There were many interactive and engaging activities
I found the micro teaching task was too long and my attention waned. I would have preferred it if it was shorter.
Great tutor
3 Was all the information you needed to complete this module available through the handbook?
Yes
100%
No
Comment The handbook was very helpful, especially the reference list for assignment three.
For the following 2 sections, please use the 1-4 scale as indicated:
1 very good 2 good 3 satisfactory 4 poor
4. Please evaluate the resources available.
1 2 3 4
Rooms 64% (7)
36% (4)
Learning Resources Centre 73% (8)
27% (3)
Electronic Resources 36% (4)
55% (6)
9% (1)
5. Please evaluate your own contribution to the module
1 2 3 4
Attendance 91% (10)
9% (9)
Preparation for and follow-up to sessions 73% (8)
27% (3)
Active participation in sessions 55% (6)
45% (5)
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6. Did this school experience module contribute to your knowledge and understanding of current DfE National Priorities?
Yes No Comment
SEND 100%
Diversity 100%
Behaviour for learning 100%
Pupil Premium/ Closing the Gap/ Unseen Children
100%
7. What are the strengths of this module?
The course tutor (6 comments)
The coarse tutor (1 comment)!!
The Oasis days (9 comments)
Gave us a broad background introduction for working in schools
Lots of opportunities to share ideas
The focus on developing school experience (3 comments)
University sessions were always engaging, with interesting discussion
Opportunities to reflect on teaching experiences and strategies
The chance to practise teaching skills in “micro teaching” activities at the university (4 comments)
The level of support with every decision I had to make this year
8. Subject Co-ordinator's response and Action Points:
Once again the feedback from students has been overwhelmingly positive, which reflects the cohesive and supportive nature of the group. Several comments from students reveal the key to this – that they have supported each other well throughout the year. While some students identified specific aspects of the programme which they felt had not been as useful as others, such as the micro teaching tasks, other students rated this as a very useful activity. Although few points were raised where the students identified a need for action, I will be prioritising the following next year:
Increased use of Moodle, with more resources available and the opportunity to engage in a forum and submit work online, and the use of “Google docs” to share information while students are in school.
An improvement in the environment in which most subject sessions take place (Mordington room 1.15)
An increase in the amount of time spent on how assessment can be effectively used in the classroom.
As well as to the students who have been such a delight to work with this year, I would like to thank the schools and mentors where students have completed placements. In particular I would like to pay tribute to my team of subject tutors who have contributed so much to the programme this year, and who have supported the students magnificently. Jeremy Smith Subject Coordinator Secondary Mathematics PGCE course.
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Resources
Good selection of resources is often the difference between a well-designed teaching plan leading to an effective lesson or to a less than successful lesson. Accordingly, resources and their critical selection and adaptation form a recurrent theme throughout.
The University of Chichester has an excellent library for your purposes on this campus, and will provide you with access to a wide and expanding range of electronic resources, and, of course, internet sites
Your course-base is a resource-rich environment to which tutors will add resource ideas and materials.
Mathematics ICT resources – software and hardware – are featured regularly within your modules
In addition, the following books are highly recommended: CHAMBERS P & TIMLIN R (2013)
Teaching Mathematics in the Secondary School
Sage
FOSTER C (2013)
The Essential Guide to Secondary Mathematics
Routledge
LEE C, JOHNSTON-WILDER S &WARD-PENNY R (2013)
A Practical Guide to Teaching Mathematics in the Secondary School
Routledge
OLLERTON M (2009) Mathematics teacher’s handbook Continuum international publishing group
SAVAGE J & FAUTLEY M (2010)
Secondary Education Reflective Reader Learning Matters
ELLIS, V [Ed] (2010) Learning and Teaching in Secondary Schools
Learning Matters
HAGGARTY. L [Ed] (2002)
Aspects of Teaching Secondary Mathematics: Perspectives on Practice
Routledge-Falmer
ORTON & FROBISHER (2004)
Insights into Teaching Mathematics Continuum international publishing group
MORGAN WATSON & TICKLY (2004)
Mathematics: Teaching School Subjects 11-19
Routledge-Falmer
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JOHNSTON-WILDER, JOHNSTON-WILDER & PIMM (1999/2005)
Learning to teach mathematics in the secondary school
Routledge
BIRD (2009)
Overcoming difficulties with number SAGE
WATSON, A, & MASON, J (1998)
Questions and Prompts for Mathematical Thinking
ATM
Website http://www.education.gov.uk/schools/teachingandlearning/curriculum/secondary/b00199003/mathematics
The Department of Education’s page that gives access to the national curriculum for maths, including attainment target descriptions
Website:
http://www.aqa.org.uk/exams-administration/exams-guidance/find-past-papers-and-mark-schemes
An index page for a library of old AQA exam papers (or just navigate from www.aqa.org.uk)
Website www.ncetm.org.uk
A resource rich website for teachers of mathematics
Website:
http://www.cimt.plymouth.ac.uk/ An excellent site with a huge amount of useful resources and ideas for maths teachers as well as some good research, and the MEP materials for teaching maths from KS3 to A level
Website:
http://www.tes.co.uk/maths-secondary-teaching-resources/
According to one of my trainees last year, “the most useful source of teaching materials out there”. This is a site for maths teachers to share their best teaching resources. The quality varies, but some is very good indeed
Recommended
