The glossary
Education and mathematics glossary.
A working glossary for education, early grade mathematics and research. Read a definition, inspect an example and follow the original guidance.
Array
An arrangement in equal rows and columns that makes grouping and multiplication relationships visible. Specify what each row, column and individual object represents.
Barrier to learning
A condition that restricts access, participation or learning. Barriers can arise through the interaction of a learner’s circumstances with tasks, environments and systems.
Cardinality
The quantity of a collection. In counting, the cardinality principle means understanding that the final number word tells how many objects the whole collection contains.
Differentiation
Adapting content, teaching processes, responses or the learning environment to respond to learners’ needs. State the intended learning and the reason for each adaptation.
Foundation Phase
The South African schooling phase comprising Grade R and Grades 1–3. Early language, mathematical and other foundational learning develops across this phase.
Fraction
A number that can describe equal parts of a specified whole. The denominator names the size of the equal parts; the numerator counts how many of those parts.
Inclusive education
An approach that addresses exclusion and barriers across teaching, curricula, support and educational settings so learners can access learning and take part meaningfully.
Inverse operations
Operations that undo one another in a defined context. Addition relates to subtraction, and multiplication relates to division; the quantities and operation must remain clear.
Manipulative
An object or interactive representation used to explore a mathematical relationship. Its meaning must be connected explicitly to the diagram, language and notation.
Number line
A representation of numbers as positions on a line, with equal numerical differences shown by equal distances. A labelled scale establishes the unit and direction.
Number sense
Understanding numbers, quantities and their relationships well enough to represent, compare and work with them flexibly, rather than relying only on a memorised procedure.
One-to-one correspondence
Pairing each object in one collection with exactly one object in another. A complete pairing with none left over shows that the collections have equal quantities.
Participation
Meaningful involvement in learning: engaging with a task, contributing and showing understanding. Physical presence alone does not describe the quality of participation.
Place value
The value a digit represents because of its position in a numeral. In whole-number base ten, moving one position left makes its place value ten times greater.
Purposive sampling
Selecting participants or cases because their experience or characteristics can inform the research question. It differs from random sampling intended to support statistical population estimates.
Qualitative research
Systematic inquiry into meanings, experiences and context, often using interviews, observations or documents. It can explain how people understand a situation without estimating population prevalence.
Reasonable accommodation
A necessary, appropriate adjustment for a particular person with a disability to participate on an equal basis, without imposing a disproportionate or undue burden.
Regrouping
Representing the same quantity with different groupings. In base ten, ten units can be exchanged for one ten, or one ten for ten units, without changing the value.
Subitising
Recognising how many objects are in a small collection without counting them one by one. Recognisable arrangements can also reveal small groups within a larger quantity.
Technical and Vocational Education and Training (TVET)
Education and training connected to occupational knowledge, practical skills, employment and the wider world of work. Its institutions, programmes and qualifications vary by context.
Ten frame
A structured arrangement of ten spaces, usually two rows of five, used with counters to make quantities and relationships to five and ten visible.
Triangulation
Examining a question through more than one source, method or perspective. Agreements and differences can deepen interpretation; using several methods does not automatically establish truth.
Universal Design for Learning (UDL)
A planning framework that anticipates learner variability through options for engagement, representation, and action and expression. It encourages designing access into learning from the start.
These plain-language explanations and fictional examples were written for this website. They are reading aids, not quotations, diagnostic definitions, legal advice or methods claimed as invented or endorsed by Dr Sako. Sources provide the professional context. English only; no unreviewed Sepedi translations are supplied.