16.1 Terms Relating to Pedagogy and Mathematical Learning
Active Listening: A listening approach in which the listener gives full attention to the speaker and uses techniques such as encouraging, restating, reflecting and summarising to demonstrate understanding and support further communication.
Assertive Communication: A communication approach in which a person expresses their thoughts, feelings, needs and expectations clearly and appropriately while respecting the views and boundaries of others.
Adaptive Teaching: Adjusting teaching approaches, explanations, and learning activities in response to pupils’ needs while maintaining high expectations for all learners.
Assessment for Learning (AfL): Assessment used during learning to provide feedback that helps pupils improve their understanding and informs future teaching.
Assessment of Learning: Summative assessment used to judge what learners have learned, typically through examinations or end-of-unit tests.
Body Language: Non-verbal communication conveyed through physical signals such as facial expressions, eye contact, gestures, posture, personal space and voice or speech patterns.
Closed Questions: Questions that generally encourage a short, specific response, often a yes or no answer. They can be useful for collecting facts but may restrict discussion if used too frequently.
Cognitive Load: The amount of mental effort required to process information. Effective teaching seeks to reduce unnecessary cognitive load so that learners can focus on learning.
Conceptual Understanding: A deep understanding of mathematical ideas, relationships, and structures rather than simply memorising procedures.
Curriculum: The planned sequence of knowledge, skills, and experiences that learners are expected to learn during their education.
Differentiation: Adapting teaching, resources, or tasks to support learners with different levels of prior knowledge, ability, or learning needs.
Diagnostic Assessment: Assessment used to identify learners’ existing knowledge, misconceptions, or gaps in understanding before or during learning.
Feedback: Information provided to learners about their performance that helps them improve their understanding and future work.
Formative Assessment: Assessment carried out during learning to monitor progress and guide teaching and learning.
Higher-Order Thinking: Thinking that involves analysing, evaluating, reasoning, and creating rather than simple recall of facts or procedures.
Inclusive Practice: Teaching approaches that ensure all learners can participate meaningfully regardless of ability, background, or educational needs.
Inquiry-Based Learning: An approach in which learners develop understanding through investigation, questioning, and exploration of mathematical ideas.
Leading Questions: Questions that suggest or anticipate a particular answer, potentially influencing the respondent rather than allowing them to respond freely.
Manipulatives: Physical objects such as counters, algebra tiles, or fraction strips that help learners develop mathematical understanding.
Mathematical Communication: The clear expression of mathematical ideas through spoken language, writing, diagrams, notation, technology, and discussion.
Mathematical Literacy: The ability to interpret, communicate, and apply mathematics effectively in a range of real-world contexts.
Mathematical Reasoning: Using logical arguments to explain why mathematical statements are true and to justify mathematical conclusions.
Misconception: An incorrect understanding or belief about a mathematical concept that may hinder future learning if left unaddressed.
Open Questions: Questions that encourage a fuller response, allowing a person to explain their ideas, experiences or reasoning rather than giving a simple yes or no answer.
Oracy: The ability to communicate effectively through spoken language, including discussion, explanation, reasoning, and active listening.
Pedagogy: The theory and practice of teaching, including the methods and strategies used to support learning.
Peer Assessment: A process in which pupils evaluate one another’s work using agreed criteria to support learning and reflection.
Problem Solving: Applying mathematical knowledge and reasoning to unfamiliar situations or complex tasks.
Professional Conduct: The ethical and professional standards expected of individuals working in educational settings, including maintaining confidentiality, respect, and appropriate behaviour.
Reflective Practice: The process of critically evaluating one’s teaching and communication to improve future professional practice.
Scaffolding: Temporary support provided by a teacher to help pupils complete tasks independently as their understanding develops.
Self-Assessment: The process by which pupils evaluate their own understanding or performance against agreed criteria.
Self-Evaluation: A process in which an individual considers and assesses their own strengths, weaknesses, skills or behaviour in order to identify areas for improvement.
Summative Assessment: Assessment conducted at the end of a period of learning to evaluate what pupils have achieved.
Teaching for Mastery: An approach to mathematics education that emphasises deep conceptual understanding, reasoning, and fluency before progressing to new topics.
Universal Design for Learning (UDL): A framework for designing learning experiences that are accessible and engaging for all learners by providing multiple means of engagement, representation, and action.
Visualisation: The use of images, diagrams, graphs, or dynamic software to support mathematical understanding and communication.
Worked Example: A fully solved mathematical problem used to demonstrate methods, reasoning, and solution strategies.
Zone of Proximal Development (ZPD): Vygotsky’s theory describing the range of tasks a learner can accomplish with appropriate guidance but not yet independently.
16.2 Useful Educational Terms (England)
Academies: Academies are publicly funded independent schools. Academies don’t have to follow the national curriculum and can set their own term times. They still have to follow the same rules on admissions, special educational needs and exclusions as other state schools. Academies get money direct from the government, not the local council. They are run by an academy trust which employs the staff.
Free Schools: Free schools are funded by the government but are not run by the local council. They have more control over how they do things. They are ‘all-ability’ schools, so can’t use academic selection processes like a grammar school. They do not have to follow the national curriculum.
GCE A Levels: The A levels were reformed for first teaching in 2017. The new A levels are now linear and assessed at the end of Year 13. There is also an Advanced Extension Award (AEA) available in Mathematics, requiring them to think more widely and critically than at A level.
GCE AS Levels: An AS (advanced subsidiary) level qualification, equivalent to half a full A (Advanced) were introduced into the post-16 curriculum to encourage the take up of more subjects and to reduce the numbers dropping out with nothing to show for their efforts. Under the new curriculum AS level marks do not count towards A levels.
GCSEs and Key Skills Qualifications: In addition to the National Curriculum each school offers a variable range of different subjects for GCSE. GCSE courses are normally taken during years 10 and 11 and assessed at the end of year 11. Some schools offer GCSE Short Courses (equivalent to half a GCSE). In 2002 GCSEs in vocational subjects were introduced and are qualifications that relate to work in a particular vocational area, such as art and design or engineering, are practical and give you a chance to learn by doing, can be mixed and matched with a variety of other courses, are mainly assessed by coursework, and can lead on to a wide range of courses, qualifications and jobs after year 11. GCSEs in vocational subjects are double awards, worth 2 GCSEs (like the Double Award science GCSE). This means that they are usually given more time on the timetable than other GCSEs.
Head of Year (HoY): Teacher with responsibility for monitoring and managing the welfare, guidance and progress of all pupils in a year group.
In-Service Education and Training Days (INSET): Inset days are set aside to allow teachers to update their skills and knowledge in order to raise pupil achievement.
Key Skills: Qualifications in communication, application of number, and information technology can be studied at different levels according to individual needs and are studied separately alongside other courses at age 14–16. There are also 3 wider skills: working with others; improving learning and performance; and problem solving.
Key Stage: One of the phases of the National Curriculum in England. Key Stages divide compulsory education into age groups from Key Stage 1 to Key Stage 4, with Key Stage 5 covering post-16 education.
Lesson Plans: Lesson Plans set out in detail how a topic is dealt with in a lesson. Some useful links can be found at Mr Barton Maths.
Local Education Authority (LEA): Each area of the country is divided into local education authorities. They are responsible for the staffing and maintenance of all schools in the area, except Independent Schools and Voluntary Aided Schools (see below).
Maintained Schools: These are more commonly known as state schools. The Government provides this education free and 93% of children attend state schools
Modern Apprenticeships: Modern Apprenticeships are available in most occupational areas from the age of 16. These offer a chance to learn skills, gain practical experience and work towards qualifications, usually NVQs. Foundation Modern Apprenticeships train young people to NVQ level 2 (broadly equivalent to 5 GCSEs at Grade C and above). Job specific training is complemented by general skills in communication; problem solving; application of number; and information technology. Advanced Modern Apprenticeships train young people in skilled and technical employment to NVQ level 3 (broadly equivalent to 2 GCE A levels). They are an alternative to A levels as a route into Higher Education.
National Vocational Qualifications (NVQs): National Vocational Qualifications (NVQs) are usually offered in association with Further Education Colleges and business/industry. They are work-related, competence-based qualifications which reflect the skills and knowledge needed to do the job effectively. NVQs represent National standards recognised by employers throughout the country.
Newly Qualified Teacher (NQT): Teachers who have just completed initial teacher training and who are in their first year of teaching.
Office for Standards in Education (OFSTED): Inspectors assess a school’s performance regularly to ensure that standards of education are being maintained. A team of inspectors visit every school at least once every 3 years, though some schools may be monitored more regularly.
Safeguarding: The responsibility of schools and education professionals to protect children from harm and promote their welfare.
Special Educational Needs (SEN): A child is said to have Special Educational Needs when special arrangements have to be made for that child to learn successfully. About 20% of the school population has special educational needs of varying kinds. A Special Educational Needs Co-ordinator (SENCO) is the teacher in the school with responsibility for the special needs arrangements. For those children whose special educational needs cannot be met within the resources available to a school the LEA will make a statement specifying the educational provision the child should have and ensure that resources are available to meet this need.
Special Educational Needs and Disabilities (SEND): A term describing pupils who require additional or different educational provision because of learning difficulties or disabilities.
Standard Attainment Tasks (SATs): These are national tests that are taken by all school children at the end of Key Stages 1 and 2. All children will take the same tests. Children are tested in Maths, English and Science (Science from Key Stage 2) to assess their level of knowledge, skills and understanding.
STEM Subjects: Science, Technology, Engineering and Mathematics.
T Levels: T Levels are new two-year technical programmes, equivalent to 3 A levels. Their primary purpose is to prepare students for entry into skilled employment, or higher-level technical study. The first three T Levels will be available at selected colleges and schools (providers) across England in September 2020.
The National Qualifications Framework: The National Qualifications Framework (NQF) (Ofqual) sets out the levels at which qualifications can be recognized. It allows learners to compare the levels of different qualifications and to identify clear progression routes to their chosen career. It incorporates the general educational pathway (GCSE, A/AS level, Degree), vocational education pathway (First Diploma, Advanced Vocational Certificate of Education, Degree), and occupational pathway (NVQ levels 1, 2, 3, 4 and 5).
Voluntary Aided School: Those schools which are owned by trustees and jointly maintained by the trustees and the Council. They are often supported by a religious denomination (e.g. Roman Catholic).
16.3 Terms Relating to Accessible Design
Mathematical Markup Language (MathML): An XML-based standard for encoding mathematical notation so that software, including screen readers, can read and display it.
User Experience: How a person feels when using a product or interface. Accessible design and good user experience overlap heavily.
Web Content Accessibility Guildlines (WCAG): The international technical standard for making web content accessible to people with disabilities, published by the W3C. Public sector bodies in the UK meet level AA of WCAG.