“The development of mathematics has always gone hand in hand with the development of civilisation itself. A truly international discipline, it surrounds us and underpins so many aspects of our daily lives.”
Curriculum for Wales
Mathematics and Numeracy in a changing world
Our rapidly changing world and the challenges that face humanity highlight that there is a fundamental need for learners to develop mathematical reasoning and understandings which will enable them to be creative, critical and inventive in solving our world's problems.
As numerical information becomes more readily available and data plays an increasingly prominent role in our daily lives, manipulating and interpreting this information wisely and using it to make informed decisions will require knowledge, skills and values which will be developed in this Area.
Numeracy is the application of mathematics to solve problems in real-life contexts. Understanding this relationship between mathematics and numeracy will be essential for nurturing confidence, resilience and enthusiasm as learners develop a deep understanding of the relevance of this Area to their everyday lives.
Creating a shift in culture
“The aspiration is to deliver this Area so that there is a shift in culture towards learners fostering a positive and resilient attitude towards it.”
Curriculum for Wales
To realise this aspiration, schools will need to provide opportunities for all learners to engage positively with mathematics and numeracy.
Response and Reflection
Watch this short video of learners who are talking and thinking mathematically as they explore number patterns.
Consider the following questions:
How would you describe the attitudes towards mathematics displayed in this video?
What enables these learners to enjoy such attitudes?
To what extent would fostering similar attitudes require a shift in culture in your school?
“Mathematics is a subject that allows for precise thinking, but when that precise thinking is combined with creativity, openness, visualization, and flexibility, the mathematics comes alive.”
Jo Boaler
Response and Reflection
As you reflect on this shift in culture, you may wish to start imagining how learning in mathematics and numeracy could look in your school.
Look at the images and questions below and consider how they might serve as a starting point in facilitating this shift in culture.
How do you support learners to work together when they are exploring concepts, reasoning and problem solving?
How do you plan for learners to apply their numeracy skills to real-life situations?
How do you create an engaging and exciting learning environment?
How do you enable learners to make connections within and between mathematical concepts?
Creating a shift in culture will demand a change in the emphasis of learning and teaching, which considers not simply what we teach, but how and why we teach it in Mathematics and Numeracy.
A new approach - learning through the five proficiencies
Curriculum for Wales has developed five new proficiencies which will form a new approach to learning in this Area. All five proficiencies are highly connected and interdependent. There is no hierarchy as they are all of equal importance.
They are:
Conceptual understanding
Communication using symbols
Fluency
Logical reasoning
Strategic competence.
Progression in this Area is dependent on the development of these five proficiencies. Learners will develop them at different times and they may also develop several at the same time. For example, as a learner becomes more fluent in adding two-digit numbers, they will be developing their conceptual understanding of place value.
The revised non-statutory numeracy framework provides suggested learning progression for the five proficiencies. Learners must be supported to apply and connect them to each other in a range of real-life contexts across the curriculum.
Response and Reflection
The five proficiencies are fundamental in supporting learners to progress towards the four purposes and should underpin all decisions when designing mathematics and numeracy learning experiences.
Read the descriptions of each of the five proficiencies and match them to the correct heading.
Consider their implications for learning in mathematics and numeracy in your school.
Response and Reflection
This video shows one example of how the proficiencies might look when solving a linear equation.
You may wish to consider the following:
How does the video display the interconnectedness of the five proficiencies?
How do you think they will enable learners to gain a deeper understanding of mathematical concepts?
Working towards the four purposes in Mathematics and Numeracy
Response and Reflection
The vision of Curriculum for Wales is set out in the four purposes, enabling all learners to become:
Ambitious capable learners
Ethical informed citizens
Creative enterprising contributors
Healthy confident individuals.
Learning experiences in all Areas should provide opportunities for learners to progress towards these four purposes.
Consider the sentences in the resource on the right. They are adapted from the introduction to the Mathematics and Numeracy guidance.
To which of the four purposes is each sentence applicable?
Suggestions are offered here, but some apply to more than one and therefore your discussions may lead to different answers. This exemplifies the interconnected nature of Curriculum for Wales.
Response and Reflection
Consideration of the characteristics which lie beneath the headings of the four purposes will lead to an in-depth understanding of the vision of Curriculum for Wales. This conversation must take place within each Area.
Using the resource on the left, explore ways in which learning and experiences within Mathematics and Numeracy will support the development of each of the characteristics.
What matters in Mathematics and Numeracy?
The essential learning required to realise the four purposes in each AoLE is encapsulated in the statements of what matters.
They provide the key concepts for learning from age 3 to 16.
There are four statements of what matters in the Mathematics and Numeracy area of learning and experience. They are interconnected, and should be addressed in a holistic manner.
“What matters in this Area has been expressed in four statements which support and complement one another and should not be viewed in isolation. Together they contribute to realising the four purposes of the curriculum.”
Curriculum for Wales
Statements of what matters in Mathematics and Numeracy
The number system is used to represent and compare relationships between numbers and quantities.
Algebra uses symbol systems to express the structure of mathematical relationships.
Geometry focuses on relationships involving shape, space and position, and measurement focuses on quantifying phenomena in the physical world.
Statistics represent data, probability models chance, and both support informed inferences and decisions.
The first statement of what matters refers to the importance of the number system and the learning derived from this statement underpins learning within the other three statements. Curriculum for Wales states, “Algebra, geometry and statistics cannot be understood without a prior understanding of number and consistent reference to numbers, calculations and the number system.”
Response and Reflection
Read the rationale for this statement of what matters and create a visual which reflects your understanding of the learning required. You may choose to use pictures, diagrams, symbols and some key words.
The same activity could be done with the other statements of what matters, in order to ensure a balanced interpretation of the interconnectedness of all four.
Creating your vision for Mathematics and Numeracy
You may wish as a next step to start creating a shared vision for Mathematics and Numeracy in your school/setting. This could be presented as a statement which will express your ambitions and aspirations for all learners in your school/setting.
Using your understanding of the vision of this Area and your reflections from the activities above, start putting some ideas together as a basis for discussion with your colleagues as you build your vision.
Response and Reflection
These questions may provide a useful starting point:
What really matters for your learners in your context in this Area?
What do you want your learners to remember about Mathematics and Numeracy in their future lives?
How will the four purposes drive your vision?
Creating a vision for Mathematics and Numeracy
This vision workshop for the Mathematics and Numeracy AoLE has previously been offered as online training, a recording of which is available opposite.