Improving Mathematics in Key Stages 2 and 3

We continually strive to develop the quality of teaching and learning, to ensure pupils are making consistent progress in Maths throughout the school. We acknowledge the key findings from the Education Endowment Foundation (November 2022), which highlights:

• “Use assessment to build on pupils’ existing knowledge and understanding”
• “Use manipulatives and representations”
• “Teach pupils strategies for solving problems”
• “Enable pupils to develop a rich network of mathematical knowledge”
• “Develop pupils’ independence and motivation”
• “Use tasks and resources to challenge and support pupils’ mathematics”
• “Use structured interventions to provide additional support”
• “Support pupils to make a successful transition between primary and secondary school.”

“The focus is on improving the quality of teaching. Excellent maths teaching requires good content knowledge, but this is not sufficient. Excellent teachers also know the ways in which pupils learn mathematics and the difficulties they are likely to encounter, and how mathematics can be most effectively taught.”

The research informs our practice in the following ways:

• Encouraging pupils to take responsibility for, and play an active role in, their own learning.
• Providing regular opportunities for pupils to develop metacognition by encouraging them to explain their thinking to themselves and others.
• When pupils arrive in Year 7, they are assessed and baselined, so that we are able to have a good understanding of their strengths and weaknesses.
• Using assessment of pupils’ strengths and weaknesses to inform the level and type of tasks set.
• Assessment is used not only to track pupils’ progress but also to provide teachers with information about what pupils do and do not know. This helps inform the planning of future lessons and the focus of targeted support.
• Pupils that are not making expected progress are selected for structured and targeted interventions.

 

Efficacy of Teaching Mathematics with Concrete Manipulatives

Concrete manipulatives are used effectively in lessons in order to support pupils with their understanding of key concepts in Maths and to encourage independent learning. We acknowledge the key findings from the Journal of Educational Psychology (March 2013), which highlights: “Math manipulative-based instructional techniques are approaches that include opportunities for students to physically interact with objects to learn target information (Carbonneau & Marley, 2012). As examples, at the elementary level, teachers use play money to help students learn basic arithmetic functions, and at the high school level, teachers use plastic algebra tiles to teach concepts associated with division and multiplication within an equation. The National Council of Teachers of Mathematics (NCTM, 2000) has recommended that students be provided access to manipulatives in order to develop mathematical understanding.”

We use concrete manipulatives to support pupils with their understanding within a range of topics, which include the following:

• Time - interactive analogue clocks
• Money - play money, supermarket items, cash register
• Weight - balance scales
• Capacity - measuring jugs and containers
• Temperature - thermometer
• Measuring length, area, perimeter - rulers, metre sticks, trundle wheels
• Other - 2D and 3D shapes, fraction tiles, geoboards, numicon, base ten blocks, cuisenaire rods, chalk, play dough etc.

Manipulatives are used purposefully and appropriately to ensure they have an impact. There is always a clear rationale for using a particular manipulative to teach a specific mathematical concept. Manipulatives can also be used as a temporary measure, acting as a ‘scaffold’ that can be gradually removed once independence is achieved

 

Learning from Errors and Misconceptions

Teachers and TAs are prepared for the potential errors and misconceptions that could arise during Maths lessons and they are addressed and managed productively in the classroom using a range of strategies. We acknowledge the key findings from Children's Mathematics 4-15: Learning from Errors and Misconceptions (April 2007), which highlights:

A teacher preparing to teach a topic might have very practical questions in mind: for example, ‘What does research say about the errors and misconceptions related to the topic I am about to teach?’ We have provided in Appendix 1, a fully indexed set of errors arising from a major survey; finding a particular topic and error there, a teacher might go to the indexed parts of the book where there is related discussion about such errors and how they might be understood or managed. A teacher with sufficient interest will then find in Chapters 1 and 2 a wide-ranging set of common diagnostic errors organised according to a typology, together with a pedagogical approach to handling these in the classroom. This approach provides a strategy for eliciting and handling errors in a relatively productive way, and offers a contrast to the typical approaches we have often seen in classrooms where errors are simply and unproductively corrected.

The research informs our practice in the following ways:

• Teachers and TAs provide regular verbal and written feedback, as a result they: set SMART targets; recap prior learning; regularly and systematically check for understanding; address errors and misconceptions.
• Discussions take place between the teacher and TA regarding the potential errors and misconceptions that could arise in lessons, in order to ensure that a consistent approach is used by both the teacher and TA.
• Knowledge of common misconceptions can be invaluable in planning lessons to address errors before they arise.
• Teachers not only have to address misconceptions but also understand why pupils may persist with errors.
• Strategies are put into place so that these errors and misconceptions can be managed productively in lessons.
• The Maths TA has sufficient subject knowledge and is confident modelling and demonstrating to pupils using a specific method or approach, as discussed with the teacher.

• Present an environment where all pupils can learn Maths to the best of their ability and where all pupils’ needs are addressed positively and sensitively.
• Offer a variety of approaches to teaching and learning to engage and motivate pupils, encouraging their active participation in Maths.
• Provide pupils with techniques so that they can investigate and solve problems in school Maths and other curricular areas.
• Develop and extend a pupil’s ability to express themselves clearly; to reason logically and to be able to generalise.
• Build a pupil’s confidence in their own ability and develop mathematical skills for their usefulness and applicability in the real world.
• Develop mathematical knowledge and oral, written and practical skill that encourages confidence and enjoyment.
• Utilise pupils’ interests and popular current events in the world to stimulate learning.
• Set realistic yet challenging targets, with high expectations for all pupils.
• To ensure all pupils leave Woodlane with a Maths qualification which reflects the best of their ability. 

Curriculum Delivery

• Pupils have full access to the Maths National Curriculum which is differentiated to meet pupils’ learning needs and styles.
• The Maths curriculum is designed to be challenging, appropriate to each pupil’s stage of development.
• The Maths Curriculum offers opportunities for cross-curricular learning, to ensure pupils make significant personal development, including:
  • Maths Theme days;
  • Maths parental engagement workshops;
  • Educational visits;
  • SaLT strategies/Word Aware integrated in to teaching;
  • Modelling and encouraging appropriate speaking and listening skills and encouraging pupils to interact with one another, extend and reflect on their responses;
  • Encouraging focused questioning and discussion skills;
  • Improving pupils’ reasoning and problem-solving skills;
  • Use calculators and other ICT resources appropriately and effectively to solve problems;
  • Developing pupils’ skills in handling information effectively and using the internet appropriately as a learning tool to find things out, develop ideas and exchange and share information.
• The KS3 Maths/Numeracy curriculum is taught through 3.61 hours (average) contact time per week (14% curriculum time).
• The KS4 Maths/Numeracy curriculum is taught through 2.92 hours (average) contact time per week (12% curriculum time). 
• Recovery Lessons are timetabled for all of KS3 (x3 lessons per week), and Year 10 (x1 lesson per week). These lessons ensure dedicated curriculum time is provided to identified areas need. The topics and subjects covered are based on the school’s data, teacher observation and assessment.
• The Maths curriculum is designed to build and expand on previous skills and subject knowledge, over a 5-year period.  It also plans for opportunities for repetition to embed knowledge, increasing the chance of information recall and to integrate new knowledge into larger ideas (view our Maths curriculum map in appendix). 
• We offer a wide range of qualifications in Maths, which are selected to appropriately challenge, based on each pupil’s stage of development, including:
  • Maths (GCSE)
  • Maths (Entry Level)
  • Maths Functional Skills (NCFE Level 1 and 2)
  • Non-Qualification Maths Units for learners below Entry Level (AQA Unit Award Scheme)
• The love of learning is incredibly important to us, we therefore also run an annual Maths Theme Day, where pupils participate in fun and engaging activities throughout the day.
• We provide additional extra-curricular activities at lunch time, including:
  • GCSE Maths support
  • Opportunities for homework support

 

Teaching and Learning

• Our pupils are taught by transition teachers in Year 7 and subject specialists from Year 8 to Year 11.
• Our Maths Subject Leader is well qualified, possessing a PGCE in Secondary Maths, a BSc in Maths with Physics and is a SpLD specialist teacher.
• The Maths curriculum is differentiated broadly into 3 levels of challenge, ‘all’, ‘most’ and ‘some’.  Further differentiation and personalisation is implemented when required.  
• Maths homework is provided on a standardised format and is differentiated to provide the appropriate level of challenge, using all’, ‘most’ and ‘some’.
• In Maths we have a 3-tiered approach to supporting a pupil’s learning, including:

Universal – this is the teaching your child will receive from the Maths subject teacher and will include adaptations to match learning needs.  All classes:

• are supported by a teaching assistant (TA);
• have a maximum of 12 pupils per class to ensure there is a high level of support available from the teacher and TA;
• are multi-sensory;
• are dyslexia friendly;
• integrate speech, language and communication support;
• are supported either directly or indirectly by speech and language therapists; and
• receive specialist streamed Numeracy and STEM lessons at KS3, based on standardised testing.

Targeted­ – it may be appropriate to consider making additional short term special educational provision to remove or reduce any obstacles to your child’s learning.  This takes the form of a graduated four-part approach of a) assessing your child’s needs, b) planning the most effective and appropriate intervention, c) providing this intervention and d) reviewing the impact on your child’s progress towards individual learning outcomes.

Interventions may include:

• Specific targeted numeracy small group activities run outside the classroom. These will be limited to a number of weeks to minimise disruption to the regular curriculum;
• Termly numeracy and SaLT targets;
• Maths parent-pupil workshops delivered every year to enable parents to best support their child and work in partnership with the school.

Specialist – it may be necessary to seek specialist advice and regular long-term support from a specialist professional in order to plan for the best possible learning outcomes for your child

• Maths parent-pupil workshops are delivered every year to enable parents to best support their child and work in partnership with the school.
• Maths homework is provided on a standardised format and is differentiated to provide the appropriate level of challenge.

Assessment

• Pupils collate Pupil Achievement Books, where they showcase their best work and progress over time in Maths.
• Our bespoke Flight Path is used to track the progress of pupils in Maths and determine expected outcomes from different starting points.
• Maths teachers use a range of formative and summative assessment procedures to assess progress and attainment, including:
  • daily marking (see teaching and learning policy);
  • self/peer assessment;
  • Maths (Hodder/MALT) age assessment;
  • Mathletics;
  • informal/formal examinations; and
  • B-Squared etc.

 

* Please see annual SEF/SIP for further details.