Ireland

The Mathematics Curriculum in Primary and Lower Secondary Grades

The mathematics component of the Primary School Curriculum⁷ is for all children from Junior Infant classes (preprimary) to Grade 6. The mathematics curriculum aims to help all children to:

• Develop a positive attitude toward mathematics and to appreciate its practical applications in life
• Develop problem solving skills and the ability to use mathematics in everyday life
• Use mathematical language effectively and accurately
• Understand mathematical concepts and processes at a level commensurate to their development and ability
• Become proficient in fundamental mathematical skills and in recalling basic number facts

In Grade 4, the curriculum is presented in five areas, known as strands—Number, Algebra, Shape and Space, Measures, and Data. The strands are interrelated, such that student understanding in one strand is dependent on and supportive of ideas and concepts in other strands. The strands are divided into strand units in which student learning is described using content objectives. Unlike the rest of the Primary School Curriculum—in which subject learning content is categorized at four levels, each of which consists of a two year grade band—the content in the Mathematics Curriculum is specified in single year grades.

Exhibit 1 shows the curriculum strands and strand units for Grade 4, and provides some specific examples of the types of skills students are able to develop through their mathematical work. These include Applying and Problem Solving, Understanding and Recalling, Communicating and Expressing, Integrating and Connecting, and Reasoning and Implementing.

Exhibit 1: Summary of Mathematics Curriculum for Grade 4, and Sample Skills

Strand	Strand Unit	Mathematical Learning Objectives
Number	Place value	Round whole numbers to nearest 1,000
	Operations	Solve word problems involving adding and subtracting within 9,999
	Fractions	Solve problems involving fractions
	Decimals	Order decimals on the number line
Algebra	Number patterns and sequences	Explore, recognize, and record patterns in number, 0–9,999; describe sequences
	Number sentences	Translate a one-step word problem into a number sentence, and solve
Shape and Space	2-D shapes	Identify, classify, compare, draw, tessellate, and make patterns with 2-D shapes
	3-D shapes	Identify, classify, and construct 3-D shapes Describe relationship of 3-D shapes with constituent 2-D shapes
	Symmetry	Use understanding of line symmetry to complete missing half of a shape, picture or pattern
	Lines and angles	Describe intersecting lines and their angles and classify angles as greater than, less than, or equal to a right angle
Measures	Length	Add, subtract, multiply, and carry out simple division of units of length (m, cm, km)
	Area	Estimate, compare, and measure the area of regular and irregular shapes (cm2, m2)
	Weight	Add, subtract, multiply, and carry out simple division of units of weight (kg and g)
	Capacity	Add, subtract, multiply, and carry out simple division of units of capacity (l, ml)
	Time	Work with times and dates; add and subtract hours and minutes
	Money	Add, subtract, multiply, and carry out simple division of money (euro and cent)
	Representing and interpreting data	Use data sets
Data	Chance	Identify and record outcomes of simple random processes

A revised syllabus for Junior Certificate Mathematics (lower secondary level) was introduced on a phased basis^a in September 2010 as part of the Project Maths initiative. The syllabus⁸ comprises five strands:

• Statistics and Probability
• Geometry and Trigonometry
• Number
• Algebra
• Functions

In September 2014, all students at the lower secondary level engaged with all five strands of the revised syllabus for the first time. The syllabus is set out in strands to provide continuity with the primary school curriculum. Teachers are encouraged to teach mathematics in contexts that allow learners to see connections within mathematics, between mathematics and other subjects, and between mathematics and its real life applications. In this way, students can achieve the objectives of lower secondary mathematics and develop proficiency in the following areas of mathematical competence:

• Conceptual understanding—Comprehension of mathematical concepts, operations, and relations
• Procedural fluency—Skill in carrying out procedures flexibly, accurately, efficiently, and appropriately
• Strategic competence—Ability to formulate, represent, and solve mathematical problems in both familiar and unfamiliar contexts
• Adaptive reasoning—Capacity for logical thought, reflection, explanation, justification, and communication
• Productive disposition—Habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence, perseverance, and one’s own efficacy

Problem solving (i.e., engaging in a task for which the solution is not immediately obvious) is integral to the lower secondary mathematics classroom. The syllabus stipulates that problem solving should not be met in isolation; rather, it should permeate all aspects of the teaching and learning experience. Problems may comprise purely mathematical matters or an applied context. In a mathematics problem solving environment, students are expected to:

• Make sense of the problem
• Make sense of the mathematics they can learn and use when doing the problem
• Arrive at a correct solution to the problem

In the lower secondary mathematics classroom, teachers focus on helping students to develop mathematical knowledge and skills through the process of solving problems, rather than on helping them to find solutions. They prioritize generating class discussion and facilitating mathematical reasoning as students engage in problem solving. Students learn to analyze problems and break them down into manageable steps, to reflect on their strategies and those of others, and to adjust their own approach where necessary.

Teachers play an important role in helping students develop these kinds of skills. By choosing tasks that present learners with a challenge, they activate learners’ mathematical thinking processes, as opposed to imitative thinking processes. By encouraging them to share, explain, and justify their problem solving strategies, those that work as well as those that do not work, teachers can help learners to develop robust and deep mathematical understanding as well as confidence in their mathematical ability.