Mathematics year 1-10 (MAT01‑06)
Core elements

Exploration in mathematics is defined by pupils searching for patterns, finding relationships and seeking out shared understanding by means of discussion. Pupils should place more emphasis on their strategies and approaches than on the solutions themselves. Problem solving in mathematics is about pupils developing a method they were not previously familiar with in order to solve a problem. Algorithmic and computational thinking is an important part of the process to develop problem-solving strategies and approaches, and can entail breaking problems down into sub-problems that can be solved systematically. This also comprises an assessment of whether the sub-problems are best solved with or without digital tools. Problem solving also involves the analysis and reshaping of known and unknown problems, solving them and assessing whether the solutions are valid.

A model in mathematics is a description of reality using mathematical language. Pupils are expected to develop an understanding of how mathematical models are used to describe everyday life, work and society more generally. Modelling in mathematics is about the creation of such models. It is also about the critical assessment of whether the models are valid (as well as any limitations that apply to them), the assessment of these models in light of the original situations that gave rise to them, and the assessment of whether they can be used in other situations. The application of mathematics is about giving pupils insights into how use mathematics in different situations both in the classroom and further afield.

Reasoning in mathematics relates to the ability to follow, assess and understand mathematical sequences of thought. This should lead to pupils recognising that mathematical rules and results are not random but have clear rationale behind them. Pupils will develop their own reasoning both in order to understand and solve problems. Argumentation in mathematics relates to pupils’ ability to justify their approaches, reasonings and solutions, and to prove that these are valid.

Representations in mathematics are ways of expressing mathematical concepts, relationships and problems. Representations can be concrete, contextual, visual, verbal and symbolic. Communication in mathematics refers to pupils’ use of mathematical language in conversation, argumentation and reasoning. Pupils must be given the opportunity to use mathematical representations in different contexts through their own experiences and in mathematical discourse. Pupils must be given the opportunity to explain and justify their choice of representation. Pupils must be able to translate between mathematical representations and the vernacular, and to switch between different representations.

Abstraction in mathematics refers to pupils’ gradually developing formalisation of their thoughts, strategies and mathematical language. This development ranges from specific descriptions to codified mathematical notation and formal reasoning skills. Generalisation in mathematics refers to pupils’ discovery of relationships and structures without being presented with a finished solution. This empowers pupils to explore numbers, calculations and shapes to find relationships, and then formalise this through the use of algebra and appropriate representations.

The mathematical fields of knowledge include numbers and number sense, algebra, functions, geometry, statistics and probability. Pupils must acquire a strong grasp of numbers and develop a variety of numeracy strategies from an early stage. Algebra refers to exploring structures, patterns and relationships, and is an important prerequisite for enabling pupils to engage in generalisation and modelling in mathematics. Functions provide pupils with an important tool for studying and modelling change and development. Geometry is important building block in enabling pupils to develop a good spatial understanding. Knowledge of statistics and probability provide pupils with strong foundations to make decisions in their own lives, as part of wider society and in working life. These fields of knowledge constitute the essentials that pupils need in order to develop their mathematical understanding by exploring relationships within and between the mathematical fields of knowledge.