43 Best practice Mathematics Paddy Shevlin ETI

Useful ETI references/documents: •Better Mathematics 2006 •Commentary on post-primary mathematics teaching 2007 •Follow-up to Better Mathematics 2010 •Best Practice Survey 2013... Bett

Best practice

Mathematics

Paddy Shevlin

ETI

To start us thinking! A question (and an answer)

• What is the difference between numeracy and

mathematics?

• ‘Numeracy is what you develop when you learn

mathematics well’ Quote from Anita Straker

Useful ETI references/documents:

•Better Mathematics (2006)

•Commentary on post-primary

mathematics teaching (2007)

•Follow-up to Better Mathematics

(2010)

•Best Practice Survey (2013)

Better Mathematics (ETI 2006) identifies best practice

Effective T&L is in place when teachers: ( Suggestion

Use these as SC (success criteria) for TCN

• Share the intended learning with the pupils at the

start of the lesson (1)

• Recap and link the work to previous learning, or set

the work in an appropriate real-world context (2)

• Provide clear exposition involving, where

appropriate, multiple explanations, with board-work modelling what the pupils should do (3)

• Use a variety of activities, including ICT and

practical equipment, which entails the pupils

working individually, in pairs or in groups (4)

More characteristics GP to

use

• Provide opportunities for the pupils to problem-solve

• Integrate, when appropriate, the use of effective mental

mathematics strategies (5)

• Use skilful questioning, challenging the pupils’

understanding and requiring them to draw conclusions and justify their thinking (6)

• Highlight common misconceptions and exploit these in a

sensitive way (7)

More characteristics GP to

use

• Relate the ongoing work to other parts of the course to

encourage the pupils to make interconnections and think

of mathematics holistically (8)

• Engage the pupils fully by ensuring that the lesson had

appropriate pace, challenge and progression (9)

• Teach step-by-step algorithms only when necessary (10)

• Encourage the pupils to think and talk about how they

learn and what they have learnt, often through

appropriate plenary sessions at the end of lessons.(11)

ETI Best Practice Survey

(ETI 2013)

• The mathematics section of the Best Practice Survey

(2013) concludes:

Many of the characteristics of good practice illustrated in the case studies are not new and can be best summed up by teachers having high expectations for what the pupils

can achieve This is mainly achieved by:

• having well-planned progression in the Schemes of

Work;

• challenging questioning which involves all; and

• rigorous follow-through of support given to pupils.

Contexts for the learning-crucial for effective learning

The use of interesting and meaningful contexts for the learning is important for the promotion of numeracy

Key questions to ask and self evaluate as a mathematics department and an individual mathematics teacher

• When you the teacher are using a context as a

backcloth for teaching a maths lesson, is it appropriate for the maturity and ability of the pupils?

• Is the context engaging the pupils, or is it too contrived?

The role of the teacher

The role of the teacher when the pupils are engaging in

mathematics is crucial

Key questions (and statements below exemplify good

practice) to ask during self-evaluation and to use for TCN:

12 Is she/he circulating the room, providing ‘scaffolding’

support?

13 Is s/he intervening at whole class level when there

appears to be many of the pupils having the same

difficulty?

14 Are the whole-class questions open, challenging and leading to mathematical thinking and discourse?

Well focused lessons

The degree to which the focus of the lesson is on well-defined intended learning and has sharp success criteria including mathematical content , processes and skills is important Key questions and for use as SC for TCN or other forms of SE

• Are the pupils clear about not only what they are doing but

also what they will be able to do as consequence? (15)

• Does the plenary consolidate and build on the intended

learning? (16)

• Is the plenary focused on success criteria and is

differentiation taken into account when thinking of SC?(17)

• Is the quality of the mathematical discourse good, taking into

account the maturity and ability of the pupils? (18)

ABOVE ALL THE BIG PICTURE

Are all the pupils actively engaged in purposeful work through which they are learning appropriate

mathematics?

Now comes the big challenge for you

• What can you as senior leaders do with this information ?

• Make improvements!Close the loop!

• Disseminate best practice

• Take action through self evaluation either by yourself or

through your QACI ( Quality Assurance and Continous Improvement ) team

HOW?

• WHAT CAN I DO?

• TO MAKE A DIFFERENCE!

• TO IMPROVE THE PRACTICE!

• TO KNOW THAT I HAVE DONE THIS! (EVIDENCE!)

• NOT TO DESTROY ANOTHER RAIN FOREST!

Linkage of Indicators to use of TCN: hence DGP

• I have set out the possible SC for self evaluating best

practice – or at least some of them

• Now further develop your self evaluation this year using

TCN (or collegiate book monitoring or “the voice” (along

with data if needed) to link indicators to self

evaluation to DGP as just described

TCN proforma

Focus of lesson:

-Quality Indicators:

The pupils will be - well

The pupils will be - accurately

The pupils will be -

Strengths (6) Suggested adjsts to learning (1)

• The pupils could be

Tear up after use

IF TCN A “ BRIDGE TOO

FAR” AT THIS POINT

• USE ONE OTHER OF THE FOUR TYPES OF FIRST

HAND EVIDENCE?

• WHAT ARE THEY?

• BUT REMEMBER TO “CLOSE THE LOOP” EVALUATE

AGAIN TO SEE IF IMPROVEMENT!

The work in the books can be very informative:

1 Is the pupils’ self-marking being regularly monitored by the teacher?

2 Is there evidence that pupils’ errors are being identified and they are receiving feedback?

3 Is there evidence the pupils’ corrections are being monitored?