1. Best practice
Mathematics
Paddy Shevlin
ETI

2. 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

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

4. Better Mathematics (ETI 2006) identifies best practice
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)

5. 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)

6. 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)

7. 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.

8. 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?

9. 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?

10. 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)

11. ABOVE ALL THE BIG PICTURE
Are all the pupils actively engaged in purposeful work through which they are learning appropriate mathematics?

12. 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

13. 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!

14. 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

15. 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

16. 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!

17. 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?