At the Numeracy and the Australian Curriculum Conference over 300 teachers and leaders at the Fleurieu and Kangaroo Island SFD had the opportunity to listen to guest speaker Garry Costello (Head of Schools DECD) and keynote speaker Dr Thelmo Perso (Executive Director, Literacy and Numeracy Taskforce, NT Department of Education and Training)
Garry Costello spoke about numeracy in his address and of the need for teachers to develop a deeper understanding of students numeracy through improving their mathematical literacy and providing real life examples. Teachers need to not only provide these examples but, through explicit teaching and role modelling, show students how to break down these problems. He also spoke of the need for teachers to know where students are at in order for us to teach them effectively and improve student engagement by creating an inquiry approach to learning, by improving student attendance and fostering a strong learning culture within the school and the classroom.
‘All teachers are teachers of numeracy” and as such, Dr Thelma Perso challenged us all to look at numeracy deeper, across all curriculum areas and in real life examples. She explained that numeracy was a capability – you are numerate or not. It is not a subject you can learn or be taught. Rather in order to develop numeracy, students need to be taught some maths (the tool kit so to speak), they need to be shown how to use the maths in a broad range of contexts and they need to be given the opportunity to use it themselves, independently. Teachers need to ask them to make a choice about how they are going to do it. Finally they need to use it in ways which develop confidence and a willingness to try – this is the pedagogy.
“Numeracy is the capacity, confidence and disposition to use mathematics to meet the demands of learning, school, home, work, community and civic life.” ACARA, 2008
So how do we make students numerate? We have to realise that it is the responsibility of all teachers ( not just the maths teacher). As teachers we need to model the use of mathematics to students everyday and be more explicit when it happens – we need to tell them “I’m using maths here” and not assume they will know it. We need to ask “Will some maths help here?”
Teachers can best teach students to apply their mathematics independently by using an application framework such as the one Thelma Perso presented below;
- Clarifying is the first step in numeracy and involves students determining what is needed and asking “if some maths will help”. Teachers need to teach their students to ask questions so they know the context of the question. Students need experiences with real purposes and audiences that involve them reading and understanding the language used in context, so that they comprehend what they have read. They also need to understand that there are many answers to the same question. It is essential that students ask “Can I rewrite the problem in my own words?’ and “Would a sketch or drawing of the situation help?”
- Choosing gives students the opportunity to make a choice about what strategy they are going to use to answer problems. How are they going to use the mathematics that they know to solve the problem?
- Using. Students are given the time to apply the maths.
- Interpreting the answer or result enables the student to reflect on wether the answer makes any sense in the context given. The purpose and audience is just as important as the answer and so students need to think about the answer and check its validity. As teachers we need to ask them to see if they can visualise it?
- Communicating is vital to consolidate student learning as it gives them the opportunity to validate their results through having to explain or justify both the answer and the process used to get it through self reflection.
Thelma Perso adds that the Modelling, sharing and guiding of numeracy is the second component of developing numeracy. It is through the scaffolding and modelling of numeracy through speaking out aloud the ‘in the head choices’ that teachers make while problem solving, and using the above applications, that will guide students to become more numerate.
As teachers we are also accountable to ensure that our students are learning what they should be learning and that means developing methods to inform our pedagogy as well as intervening when we have students that are not. Thelma Perso looked at how Naplan is a tool for improvement through a numeracy lens and the place of literacy, problem solving and intervention has in this improvement. It is important for teachers to understand that the NAPLAN numeracy test requires a deep understanding of numeracy and as such, are mostly problem solving questions which use real life language. The questions can, for the most part, be done by estimating and no actual ‘correct answer’ is needed.However, students do need to be able to read, clarify and comprehend the context of the question through language in order to answer it. Thelma demonstrated this beautifully in her slide below of a numeracy question taken from the year 3 NAPLAN numeracy test.
The implications for teachers is that we need to be teaching the literacy in the questions our students need to answer and we need to teach them how to break each question down from the visual to the written to the notation.
In 2008, I led a group of Junior Primary Teachers in an Inquiry Project around “What is the meta- language of mathematics?” During this project, we looked at what the language is that we need students to know and understand when we are teaching mathematics. It was interesting that the JP teachers felt the need to simplify the language in the early years and I recall one teacher saying she never referred to one of the properties of a 2D shape as vertices. As teaches, we need to be aware that even young students can learn this language and a lot of relearning needs to happen later in their schooling if we don’t teach it from the start or make those connections later in their schooling for them. The JP teachers began to be more explicit in the teaching of the language of mathematics and its use. They also had a better understanding of where their students were going and what they needed to know before they moved into the middle primary years. We also looked at the then year 3 numeracy benchmarks test and broke down what each question was actually asking. This was a really useful exercise, as teachers developed an understanding of the complexity of problem solving questions and the need to role model the thinking needed to break down these questions.
The numeracy conference gave me the opportunity to reflect on the general capability “numeracy” in the Australian Curriculum. It reinforced for me, that my own teaching practice is sound. That I truly endeavour to understand what it is my students already know before I teach them. I look at how I will assess what they learn before I plan how I will teach what they need to learn. While I can not solely teach my students numeracy, I develop their numeracy through continuous exposure to experiences that will allow them to develop these skills across all curriculum areas. I am explicit in my teaching and role model my thinking whenever the opportunity will allow. I show my students how to unpack the language of a question so they can understand how to find a solution to the problem. I allow them many opportunities to practice these skills.
I was told at the beginning of the day, that if I took just one thing away from the conference then the day had been worthwhile. So what did I take away from the conference? I think it was a better understanding of how a framework for developing numeracy, can support students in understanding the context of a problem and not only allowing them to choose how to solve it but being able to use logic to understand if their solutions makes sense and then being able to communicate this.