Mathematics Subject Mentor Training

Subject Specific Mentoring in Mathematics 2016/17

WelcomePlease introduce yourself to the group on your

table:

• Name ?

• School ?

• How long have you been a subject mentor ?

• What are you looking forward to this year ?

Objectives1. To establish the role of the subject mentor when

working in partnership with Birmingham City University

2. To discuss subject-specific mentor practice that enables trainees to be coached and assessed effectively against the teachers’ standards

3. To support the development of subject and phase specific mentoring that develops trainee knowledge of high quality subject teaching and the latest subject developments from subject associations.

New National Curriculum

“The national curriculum for mathematics aims to ensure that all pupils:

• become fluent in the fundamentals of mathematics…

• reason mathematically…• can solve problems…”

DfE (2013, p. 2, original emphasis)

Mathematical Fluency

“become fluent in the fundamentals of mathematics, including through varied and frequent practice with increasingly complex problems over time, so that pupils develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately.”

DfE (2013, p. 2, original emphasis)

“the notion that if a child repeats a meaningless statement or process enough times it will become meaningful is as absurd as the notion that if a parrot imitates human speech long enough it will know what it is talking about”

(Holt, 1990, p. 193)

Mathematical Fluency

Mathematical fluency is not a bad thing

“[W]e need to attain fluency in handling a wide range of arithmetical, algebraic, trigonometric, and geometrical procedures, so that each new procedure can eventually be exercised automatically, quickly, and accurately. Once this level of automaticity is achieved, the brain is left free to focus on those more demanding aspects of a problem that require genuine thought”

Gardiner (2012, p. 20, original emphasis)

“I have observed, not only with other people but also with myself … that sources of insight can be clogged by automatisms. One finally masters an activity so perfectly that the question of how and why is not asked any more, cannot be asked any more, and is not even understood any more as a meaningful and relevant question.”

Freudenthal (1983, 469)

But fluency has its dangers…

Fractions

1

6

1

25

3

5

3

20

4

15

5

8

Add up as many of these fractions as you like. You can’t use any of them more than once.

Try to get a total as near to 1 as possible.

Is this a good set of fractions to use for this puzzle? Can you invent a better set?

Edexcel, Mathematics (Linear) – 1380, June 2011, Paper 1, Q11

Edexcel, Mathematics (Linear) – 1380, June 2011, Paper 1, Q26

Edexcel, Mathematics (Linear) – 1380, June 2011, Paper 4, Q3

Edexcel, Mathematics (Linear) – 1380, June 2011, Paper 1, Q11

• How do we prepare learners for questions like this without just giving them questions like this?

Edexcel, Mathematics (Linear) – 1380, June 2011, Paper 1, Q11

• Deconstruct the mathematics:354 × 26

2 3 4 5 6

Edexcel, Mathematics (Linear) – 1380, June 2011, Paper 1, Q11

• Deconstruct the mathematics:354 × 26

2 3 4 5 6

Using one multiplication sign and each of the digits 2, 3, 4, 5 and 6, once each, what is the largest product you can make?

Or the smallest?What other questions can you ask?

Edexcel, Mathematics (Linear) – 1380, June 2011, Paper 1, Q26

• Let’s try it:x2 + 3x – 4x – 12

= x2 – x – 12

Edexcel, Mathematics (Linear) – 1380, June 2011, Paper 1, Q26

• Let’s try it:x2 + 3x – 4x – 12

= x2 – x – 12

What possible integers can go in the box so that this expression factorises?

x2 + x – 12

How many solutions are there? Why?

Edexcel, Mathematics (Linear) – 1380, June 2011, Paper 4, Q3

Start with the answer (15) and find possible questions.

HCF and LCMThe HCF of two numbers is 15.What could the numbers be?How many possible answers are there?Why?

Try this with an LCM of 15 instead.

What about numbers other than 15?What happens if there are more than two numbers?

Foster, C. (2012). HCF and LCM – beyond procedures. Mathematics in School, 41(3), 30–32.

x + 7 2x + 4

4x – 88

Foster, C. (2012). Connected expressions. Mathematics in School, 41(5), 32–33.

The Role of the Subject Specific Mentor

Effective mentoring

• Impacts widely on the school, building the capacity of the school as a whole.

• Focuses on how teachers learn• Supports trainees to reflect on practice,

and how to effectively and analytically observe in the classroom.

• Provides structured school experiences that are carefully planned.

The Role of the Subject Specific Mentor

Characteristics of effective mentors

• Outstanding teachers who are also skilled in deconstructing and explaining their practice

• Teachers who are subject experts aware of latest subject developments

• Teachers who have a secure understanding of the Techers’ Standards and a range of methods for assessing progress against standards to support trainees to go beyond minimum requirements for meeting them

• Role models of all Teachers’ standards including engagement with personal research

The Role of the Subject Specific Mentor

Inspectors evaluate the extent to which trainees benefit from:

• Is provided by experienced and expert mentors.

• Responds to trainees’ specific training needs, including enhancing their subject and curriculum knowledge and phase expertise.

• Improves trainees’ teaching skills.• Models good practice in teaching.• Provides high-quality coaching and mentoring,

and access to relevant subject association guidance to enhance trainees’ professional development.

The Role of Subject Mentor

Impact on Pupil Progress!

Supporting Pupil Progress through effective mentoring

Using large sheets of paper, list actions and activities that a mentor can do to identify evidence of pupil progress in classes that Participants are teaching.

To consider:

Time?

Resources?

Accuracy of evidence?

Supporting Pupil Progress through effective mentoring

Strategies include:

• Link to Teaching standards 2, 5 and 6 in observation feedback.

• Complete book scrutinies/ share outcomes of whole school book trawls.

• Review termly/ end of year data.

• Critically review progress of identified groups of learners

• Set Pupil Progress NQT Action plan target

You can help us by………

1. Participants need to ‘see’ and ‘experience’ excellent maths teaching from within the department

What does this look like in your department?

Please discuss on your table and make a summary

on the flipchart paper.

What Ofsted say about Excellent Mathematics Teachers…….

Building on prior

knowledge

Good modelling

Do not just give answer

Develop curiosity

Consistent approaches

Address misconceptions

Use of active

learning

Adaptable

Mathematicalvocabulary

Planning and differentiation

Ofsted: Effective Maths teaching 2012

Sharing resources

How you can help us……….

2. Participants need to show evidence of high quality marking and feedback – impact on pupil progress.

• Assessment without levels – what do you do?

• Book scrutinies

• Using their journal to reflect on how assessment and marking impact on pupil progress

• RJA2 assignment – focus on marking and feedback

How you can support Subject knowledge development

• Subject Knowledge Action Plans

• Lesson Planning and evaluations (min 3 a week for Teaching File)

• Opportunities for joint planning within the department

• Sharing resources

The Standards Tracker

• A set of descriptors to help participants, tutors and mentors to track their progress against each sub-heading of the standards;

• Used across the PGCE programmes at BCU;• Used to offer formative feedback using a consistent language of

expectation to determine where additional development might be needed, or to identify areas where a participants is already demonstrating strong practice;

• All participants recommended for QTS must meet all of the standards at least at the ‘Establishing’ level;

• The language we use is very important!

The Language of Lesson Observation

• Standards tracker• Emerging–‘beginning to…’, ‘with support…’, ‘recognise the need to…’,

‘developing knowledge…’, ‘initial recognition’, basic awareness...’• Establishing–‘routinely…’, ‘take some responsibility for…’, ‘sufficient

knowledge…’, ‘lessons usually motivate, inspire and enthuse…’, ‘sound understanding…’

• Embedding –‘reliably…’, consistently for most…’, ‘regularly‘…’, ‘well-targeted interventions’ ‘well-developed knowledge’, ‘secure knowledge’, ‘systematically…’

• Enhancing –‘constantly’, ‘very effective…’, ‘actively promote…’, ‘detailed, in-depth knowledge…’, ‘proactive…’, ‘very strong understanding…’, ‘imaginative, creative…’, ‘accurate’, ‘astute’, ‘challenging…’, ‘confident’.

Observing lessons using the R&A

Watch the clip of one of a maths lesson

Use the blank R&A form to:

• Identify strengths linked to the Teaching Standards

• Set Targets for improvement

• https://www.teachingchannel.org/videos/surface-area-lesson

• Discussion

Observation & FeedbackWorking Practices

Choose only 3 standards to focus on

• Use the language on the Standards Tracker to provide feedback on what is observed.

• Comment on the progress within the 3 identified standards

• Refer explicitly to the standard strands (5a, 6b) within the feedback

• Strengths and areas for development are determined in terms progress against the teaching standards

List strengths linked to the 3 focus standard strands

Provide targets that are linked to the 3 focus standards- try not to use the same strand as a strength and developmental area

Review and Analysis form Non Judgemental Observations?

Discuss with a different partner how lessons observations are normally conducted in your school. Are they assessed and if so how are the findings used?

Study the Standards Tracker and the Review and Analysis forms.

To what extent do they differ from the system used in your school?

What makes the exemplar R&A form stand out?

Mathematics subject knowledge issues?

• What sort of issues will you see?

• How will you deal with them?

• Here are a few common situations that we have seen regularly.

Support for Mathematics Subject Knowledge

• In pairs look at the cards.

• For cards A-D are these statements by the teacher OK? If not, what advice or explanation would you give?

• For cards E-H. What is the misconception here? How would you correct this?

Subject Days

Every subject day will contain a range of elements. These will include:

• Subject knowledge and pedagogy

• Sharing good practice and resources

• Microteaching

• Links with research

• Introductions and guidance for assignments

• Visiting speakers

More details in your mentor

pack

Assignments

Assignments

• Subject Pedagogy – Due 24th February

• Professional Studies – Due 21st April.

• Professional Enquiries – 20th/21st June

Summary 1

Subject Mentor

1. Observe Outstanding

teaching

2. Develop Subject

Knowledge

3. Regular Lesson

Observations

4. Effective and regular Feedback

Behaviour

CPD & STEMTermly

Reports

Lesson planning

Post - 16

Numeracy and

Literacy

Practical Maths

NC changes

Summary 2

FEEDBACK

Do not focus JUST on

Behaviour management!

Try to set subject specific

targets

Find evidence of impact on pupil

progress

Link lesson feedback to

subject days at BCU

Discuss subject knowledge action

plan

Link to teaching

standards

High quality feedback

and marking

What we don’t do

• Specific exam syllabuses

• School based assessment and marking policies

• Long term planning

How could you support you participant here?

•Any questions?

• Feedback: Please take a few minutes to complete the online evaluation form.

• https://goo.gl/qVg9Bn