The Mathematics Curriculum in Primary and Lower Secondary Grades

The mathematics curriculum for students assessed in TIMSS 2015 was the Northern Ireland Curriculum, introduced in the 2007–2008 school year. The legislative basis for the curriculum is provided by the Education (Northern Ireland) Order 2006 and the Education (Curriculum Minimum Content) Order (Northern Ireland) 2007. The curriculum for Key Stages 2 and 3 is outlined below.

At Key Stage 2, the statutory minimum curriculum specifies seven Areas of Learning, and includes mathematics and numeracy as one area. The minimum content for mathematics and numeracy at this key stage is organized under the following domains,² in which teachers are expected to help students develop knowledge, understanding, and skills:

Processes in Mathematics
- Making and monitoring decisions
  - Taking increasing responsibility for selecting and using appropriate materials and mathematics for work
  - Identifying and obtaining information required for a task; suggesting appropriate information sources
  - Planning and organizing work, learning to work systematically
  - Developing a range of strategies for problem solving; looking for ways to overcome difficulties
- Communicating mathematically
  - Understanding mathematical language and using it to discuss work and explain thinking
  - Comparing their ideas and methods with others’
  - Interpreting situations mathematically using appropriate symbols or diagrams
  - Presenting information and results clearly
- Mathematical reasoning
  - Recognizing general patterns and relationships and making predictions about them
  - Asking and responding to open-ended questions and explaining their thinking
  - Understanding and making general statements
  - Checking results and considering whether they are reasonable
Number
- Understanding number and number notation
  - Counting, reading, writing, and ordering whole numbers
  - Developing an understanding of place value up to two decimal places and using this to multiply and divide numbers by 10 and 100
  - Estimating and approximating to gain an indication of the size of a solution to a calculation or problem
  - Understanding and using common fractions, decimal fractions, and percentages, and exploring the relationships among them
  - Understanding and using negative numbers in context
- Patterns, relationships, and sequences in number
  - Exploring and predicting patterns and sequences of whole numbers; following and devising rules for generating sequences
  - Understanding and using multiples and factors and the terms prime, square, and cube; understanding inverse operations
  - Interpreting, generalizing, and using simple relationships expressed in numerical, spatial, and practical situations; understanding and using simple function machines
  - Understanding that a letter can stand for an unknown number
- Operations and their applications
  - Developing strategies to add and subtract mentally
  - Knowing the multiplication facts up to 10 x 10
  - Engaging in a range of activities to develop understanding of the four operations of number; understanding the use of brackets; adding and subtracting decimals with up to two decimal places; multiplying and dividing decimals by whole numbers; using these operations to solve problems
- Money
  - Using the four operations to solve problems involving money
  - Discussing the value of money, how to keep money safe, ways to pay for goods, and the need for budgeting
  - Learning to plan and think ahead in terms of saving and spending money
  - Prioritizing spending with a limited supply of money; understanding how to assess best buys
  - Discussing foreign currency including the Euro
Measures
- Developing skills in the estimation of length, weight, volume/capacity, time, area, and temperature
- Understanding important concepts of measurement, including the continuous nature of measurement and the need for appropriate accuracy
- Understanding the relationship among units of measurement and converting one metric unit to another; using the four operations to solve problems
- Calculating perimeter, area, and volume of simple shapes
- Understanding and using scale in the context of simple maps and drawings
- Recognizing times on analog and digital clocks and understanding the relationship between the 12-hour and 24-hour clocks; using timetables
Shape and Space
- Exploration of shape
  - Constructing a range of regular and irregular two-dimensional shapes; classifying these by examining angles and sides; recognizing line and rotational symmetry; reflecting shapes in a line; exploring tessellations; naming and describing common two-dimensional shapes
  - Beginning to understand congruence in two-dimensional shapes; constructing three-dimensional shapes; investigating the number of faces, edges, and vertices on these shapes; naming and describing common three-dimensional shapes; exploring the relationship between two-dimensional and three-dimensional shapes
- Position, movement, and direction
  - Understanding the concept of angle in the context of turning; recognizing right angles; understanding clockwise and anti-clockwise; knowing the eight points of the compass; using Logo to understand movement and turning; learning about a programming language and using it to create pictures and patterns and to generate shapes
  - Developing language associated with lines and angles; recognizing properties of acute, obtuse, and reflex angles; investigating angles in triangles and quadrilaterals; measuring and drawing angles up to 360 degrees
  - Using coordinates to plot and draw shapes in the first quadrant
Handling Data
- Collecting, representing, and interpreting data
  - Collecting, classifying, recording, and presenting data drawn from a range of meaningful situations, using graphs, tables, diagrams, and Information and Communications Technology (ICT) software
  - Explaining work orally and/or in writing and drawing conclusions; interpreting a wide range of tables, lists, graphs, and diagrams; creating and interpreting frequency tables, including those for grouped data
  - Designing and using a data collection sheet; interpreting the results; entering information in a database or spreadsheet, and interrogating and interpreting the results
  - Understanding, calculating, and using the mean and range of a set of discrete data
Introduction to Probability
- Becoming familiar with and using the language of probability
- Understanding possible outcomes of simple random events
- Understanding that there is a degree of uncertainty about the outcome of some events, while others are certain or impossible
- Placing events in order of likelihood; understanding and using the idea of evens in probability (i.e., neither likely nor unlikely) and knowing whether events are more or less likely than this

At Key Stage 3, the statutory minimum curriculum specifies nine areas of learning, and includes mathematics and numeracy as one area of learning. The minimum content for mathematics and numeracy at Key Stage 3 is as follows.³

Mathematics and numeracy includes the contributory elements of mathematics and financial capability. Students should have opportunities through specified contexts to develop the following:

Knowledge and understanding of
- Number
- Algebra
- Shape, space, and measures
- Handling data
Knowledge and understanding of personal finance issues and skills to enable competent and responsible financial decision making
The application of mathematical skills in real life and work situations
The creative use of technology to enhance mathematical understanding, demonstrating
- Creative thinking in solving mathematical problems
- Increasing competence in mental mathematics skills
- Increasing competence using pencil and paper methods
- Increasing confidence in the use of mathematical language and notation
- Practical skills using technology

The minimum content sets out the contexts in which these opportunities should be provided, organized around three main objectives:

Helping students develop as individuals
Helping students develop as contributors to society
Helping students develop as contributors to the economy and the environment

The minimum content also specifies learning outcomes. At the end of Key Stage 3, students should be able to do the following:

Demonstrate mental mathematical capability with simple problems
Select appropriate methods and tools for solving problems (i.e., performing mental or written calculations, using a calculator or mathematical instruments, or a combination of these)
Demonstrate capability with financial problem solving in a range of relevant everyday contexts
Research and manage information effectively to investigate and solve mathematical problems, using ICT where appropriate
Show deeper mathematical understanding by thinking critically and flexibly, solving problems and making informed decisions, using ICT where appropriate
Demonstrate creativity and initiative when developing ideas, and follow through on them
Work effectively with others
Demonstrate self-management by working systematically, persisting with tasks, and evaluating and improving their own performance
Communicate effectively in oral, visual, written, mathematical, and ICT formats, showing clear awareness of audience and purpose

Using Mathematics is embedded as a cross-curricular skill throughout the Northern Ireland Curriculum at each key stage.^4,5 The CCEA provides guidance and additional resources to support teachers in implementing the curriculum, which they may follow if they wish.⁶