1	Evaluating Mathematics DENI 1999
2	1. Ethos The ethos of the subject contributes effectively to the full development of the pupils when: i. the teachers work together effectively in a professionally stimulating, supportive and self-questioning manner;
3	1. Ethos The ethos of the subject contributes effectively to the full development of the pupils when: ii. mathematics lessons take place in a purposeful atmosphere where supportive teaching encourages all the pupils to participate in the lessons and to give of their best; the pupils’ ideas and approaches are built upon and their confidence in their ability to succeed in mathematics is reinforced; the sharing of ideas, collaborative learning and individual effort are valued and encouraged;
4	1. Ethos The ethos of the subject contributes effectively to the full development of the pupils when: iii. the teachers actively promote enthusiasm for mathematics in their pupils through their teaching, displays of pupils’ work and the use of stimulating materials and activities.
5	2.2 Pupil Responses can be considered good when the pupils: i. have a secure understanding of the mathematical concepts, knowledge and skills across their programme of study; they use and apply their mathematics in a variety of tasks and contexts, working to a standard broadly in keeping with their ability and stage of development;
6	2.2 Pupil Responses Responses can be considered good when the pupils: ii. understand and use patterns and relationships in their mathematics and make generalisations; they develop and use effective mental strategies in number and in other aspects of mathematics; they estimate sensibly in number and in measure, and they work to an appropriate degree of accuracy;
7	2.2 Pupil Responses Responses can be considered good when the pupils: iii. show enjoyment, growing self-reliance, and confidence in their ability to succeed in mathematics; they organise their work methodically and persevere when faced with difficulties or unfamiliar tasks;
8	2.2 Pupil Responses Responses can be considered good when the pupils: iv. discuss mathematical ideas and methods, ask thoughtful questions to develop their thinking and understanding and evaluate their methods and solutions;
9	2.2 Pupil Responses Responses can be considered good when the pupils: v. choose, and use effectively, a variety of appropriate resources for their mathematical learning; as they progress through the key stages, they use an increasing range of information and communications technology (ICT) tools to enhance their understanding and application of mathematics;
10	2.2 Pupil Responses Responses can be considered good when the pupils: vi. show, through their questions and responses in the classroom and through their approach to unfamiliar and more complex tasks, good development in their ability to reason mathematically.
11	2.3 Teaching Approaches The teaching approaches can be considered fit for purpose when: i. the teachers have realistically high expectations for their pupils and their teaching is thorough and systematic; they organise whole-class, group and individual work, as appropriate; they make effective use of a suitable variety of approaches such as direct teaching, investigation, consolidation activities, practical work, discussion, and open-ended, computer-based and mental activities;
12	2.3 Teaching Approaches The teaching approaches can be considered fit for purpose when: ii. the teaching consistently promotes progression in the pupils’ understanding of mathematical ideas and inter-relationships, their ability to apply mathematics in a variety of contexts and to reason and communicate mathematically, and their competence in essential mathematical skills;
13	2.3 Teaching Approaches The teaching approaches can be considered fit for purpose when: iii. the quality of the discussion between the teacher and the pupils, and amongst the pupils, enhances the pupils’ mathematical learning; the pupils have good opportunities to articulate, clarify and extend their thinking and to develop appropriate mathematical language;
14	2.3 Teaching Approaches The teaching approaches can be considered fit for purpose when: iv. lessons are purposeful, well organised and interesting; the pace of work, the level of challenge and degree of support given enable all the pupils to participate fully in the learning activities and to make progress; v. monitoring and evaluation of the pupils’ responses are integral to the day-to-day teaching and enable the teachers to adapt their teaching and match the work closely to the abilities and understanding of the pupils.
15	2.4 The Teachers’ Assessment of the Pupils’ Work The teachers’ assessment of the pupils’ work can be considered effective when: i. the pupils’ learning in mathematics is assessed through their day-to-day work and responses in the classroom and through specific assessment activities; the teachers assess the important aspects of the pupils’ learning across their programme of work in mathematics; they use appropriate criteria and standards to evaluate the pupils’ progress and achievements;
16	2.4 The Teachers’ Assessment of the Pupils’ Work The teachers’ assessment of the pupils’ work can be considered effective when: ii. the teachers use suitable assessment strategies; they observe and discuss the pupils’ responses effectively and make appropriate use of other forms of assessment, such as written, practical, oral/aural, mental, IT based and extended tasks; they diagnose specific difficulties identified in the pupils’ work and responses;
17	2.4 The Teachers’ Assessment of the Pupils’ Work The teachers’ assessment of the pupils’ work can be considered effective when: iii. the basis on which their work is assessed is explained to the pupils; their written, oral and practical responses are discussed and marked frequently, and specifically in ways which encourage them and help them to evaluate and improve their performance;
18	2.4 The Teachers’ Assessment of the Pupils’ Work The teachers’ assessment of the pupils’ work can be considered effective when: iv. the teachers use the outcomes of their assessment to inform future planning, in order to consolidate or extend learning and address areas of difficulty;
19	2.5 Planning Planning can be considered effective when: i. whole-school planning for mathematics provides clear guidance for the progressive development and application of important concepts, skills and knowledge and the processes of using mathematics, communicating mathematically and mathematical reasoning; the planning identifies appropriate contexts for mathematical learning and exploits the potential of other subjects and aspects of the curriculum to contribute to the pupils’ development and use of mathematics;
20	2.5 Planning Planning can be considered effective when: ii. within each year and key stage, an appropriate balance is maintained in the mathematics programme across the attainment targets of the programme of study; the planning brings together different areas of mathematics to give coherence to the pupils’ experiences;
21	2.5 Planning Planning can be considered effective when: iii. the planning identifies clearly the intended learning outcomes in mathematics and sets clear standards of work; there is coherence between the different levels of planning from whole-school to individual lessons; long-term and short-term planning build upon the pupils’ previous attainments and take account of their abilities, interests and levels of maturity;
22	2.5 Planning Planning can be considered effective when: iv. the teachers plan suitable classroom approaches, learning activities and assessment strategies to promote learning by all pupils; the teachers’ preparation ensures that individual lessons are purposeful and coherent and contribute effectively to the overall mathematics programme;
23	3.1 The evaluation of teaching and learning in mathematics can be considered good when: i. throughout the school, the teachers use agreed, significant criteria to monitor and evaluate the effectiveness of their teaching and the quality of pupils’ learning and standards of achievement in mathematics; the outcomes of statutory assessment and public examinations are judged against relevant norms; issues arising from evaluation are followed up as an integral part of planning for development in mathematics;
24	3.1 The evaluation of teaching and learning in mathematics can be considered good when: ii. the teachers put into practice an agreed and understood policy for assessment and marking which enables them to build up a picture of the pupils’ progress and attainment in all aspects of mathematics; iii. there is an agreed and manageable way of recording cumulatively the pupils’ progress across their programme of work; the records are consistently and accurately interpreted;
25	3.1 The evaluation of teaching and learning in mathematics can be considered good when: iv. the outcomes of assessment are used to identify strengths and weaknesses in the provision for mathematics and in the teaching or in the pupils’ learning; where appropriate, action is taken to modify provision and practice; v. parents are regularly informed about their children’s progress in mathematics; the written reports convey a clear and comprehensive picture of the pupils’ progress and achievement in mathematics.
26	3.3 Organisation of the Curriculum The organisation of the curriculum for mathematics can be considered good when: i. there is an agreed and well-informed statement of policy on mathematics in the school’s curriculum; the policy sets out a rationale, aims and principles for curricular provision in mathematics for all pupils and to guide teaching and learning at each key stage;
27	3.3 Organisation of the Curriculum The organisation of the curriculum for mathematics can be considered good when: ii. there is a coherent strategy for mathematical learning in the school’s curriculum which takes account of the taught mathematics programme and opportunities for using mathematics in other subjects;
28	3.3 Organisation of the Curriculum The organisation of the curriculum for mathematics can be considered good when: iii. the mathematical needs of all pupils are being met through effective curricular programmes and support arrangements; in post-primary schools, the mathematics courses provided reflect realistically high expectations for externally accredited achievement by pupils.