Improving Primary Mathematics: The Challenge of Curriculum

Arguably one of the biggest challenges for most primary teachers is the struggle to address the many components of the mathematics curriculum within the confines of a daily timetable. How many times have you felt there just isn’t enough time to teach every outcome and every ‘dot point’ in the entire mathematics curriculum for your grade in one year? It is my belief that one of the biggest issues in mathematics teaching at the moment stems from misconceptions about what and how we’re supposed to be teaching, regardless of which curriculum or syllabus you are following.  The way we, as teachers, perceive the content and intent of our curriculum influences whether students engage and achieve success in mathematics. The way we experienced the curriculum when we were at school also influences how mathematics is taught in our own classrooms.

This struggle arises partially from the common perception that every outcome (in NSW) or Content Descriptor (from the Australian Curriculum) must be addressed as an individual topic, often because of the way the syllabus/curriculum is organised (this is not a criticism – the content has to be organised in a logical manner). This often results in mathematical concepts being taught in an isolated manner, without any real context for students. A result of this is a negative impact on student engagement. Students fail to see how the mathematics relates to their real lives and how it is applied to various situations. They also fail to see the connections amongst and within the mathematical concepts.

Imagine if you could forget everything you remember about teaching and learning mathematics from when you were at school. Now think about the three content strands in our curriculum: Number and Algebra, Measurement and Geometry, and Statistics and Probability. Where are the connections within and amongst these strands? If you could, how would you draw a graphical representation of all the connections and relationships? Would your drawing look like a tangled web, or would it look like a set of rows and columns? I’m hoping it would like more like a tangled web! Try this exercise – take one strand, list the content of that strand, and then list how that content applies to the other two strands. If you can see these connections, now consider why we often don’t teach that way. How can you teach mathematics in a different way that will allow students to access rich mathematical relationships rather than topics in isolation? How can we make mathematics learning more meaningful for our students so that maths makes sense?

This leads me to my second point and what I believe is happening in many classrooms as a result of misunderstanding the intention of the mathematics curriculum. If students are experiencing difficulties or need more time to understand basic concepts, you don’t have to cover every aspect of the syllabus. It is our responsibility as teachers to ensure we lay strong foundations before continuing to build – we all know mathematics is hierarchical – if the foundations are weak, the building will collapse. If students don’t understand basic concepts such as place value, it doesn’t make sense to just place the ‘strugglers’ in the ‘bottom’ group and move on to the next topic.

We need to trust in our professional judgement and we need to understand that it’s perfectly okay to take the time and ensure ALL learners understand what they need to before moving on to more complex and abstract mathematics. It most definitely means more work for the teacher, and it also means that those in positions of leadership need to trust in the professional judgement of their teachers. Most importantly, it means that we are truly addressing the needs of the learners in front of us – the most important stakeholders in education.

 

Using Contexts to Make Mathematics Meaningful

One of the most common questions children ask in relation to mathematics is ‘When will I ever use this?’ Often they don’t realise that we use mathematics in almost every aspect of our lives, from the minute we wake up each morning and estimate whether we should push the snooze button, to working out how many minutes or hours there are until we get to finish school or work for the day. The perception that mathematics has little or no relevance to their lives beyond the classroom is one of the reasons children begin to disengage from mathematics during the primary years. In order to bridge the gap between children’s lives and the mathematics classroom I firmly believe that all mathematics teachers should take every opportunity to make mathematics meaningful by using the real world where appropriate, whether through the use of objects, photographs or physically taking children into the world beyond the classroom and engaging them in rich, worthwhile activities. This blog post was originally posted in 2015 and I thought the messages here would be a timely reminder, given that I have continue to receive invitations to assist teachers and schools in engaging their students with mathematics.

So how can you make mathematics more meaningful? If you are new to teaching with contextual mathematics, I would suggest that you begin by designing a mathematics trail at your school or somewhere out in the community – it could even take place at the local shopping centre. Find points of interest that have mathematical potential, photograph them and then plan a set of activities. For example, if you have a giant chessboard in the school playground, you might pose the following questions:

  • Estimate the following and explain your thinking: The area of the chessboard, the perimeter of the chessboard, and the area of each tile
  • Use words to describe the position of the chessboard without coordinates and in relation to its surroundings.
  • Locate the chessboard on a map of the school grounds. What are the coordinates?
  • Investigate the total number of squares (of any size) in the chessboard.
  • Design a new maths game that can be played on the chessboard and write a set of instructions for another group to follow.

You will notice that the questions above are quite open-ended. This will allow for all students to achieve some success and provides an important opportunity for children to show what they can or cannot do. Open-ended questions are more engaging for students and often require them to think harder and more creatively about the mathematics they are engaging in.

Another idea for contextualising mathematics is to use objects or photographs of real life objects, items or events. It could be something as simple as a school lunchbox, with questions such as the following:

  • Explore the ways sandwiches are cut. What different shapes can you see? Can you draw them?
  • Before recess, compare the mass of your lunchbox with five other lunchboxes. Can you order the lunchboxes from lightest to heaviest?
  • List the types of food in the lunch boxes today. Can you sort them into different categories? What categories do you have? Is there another way to sort them?
  • Conduct a survey to find out the most popular recess or lunch food in your class. Do you think this is a healthy food?
  • How many Unifix cubes do you think would fit in your empty lunchbox? Write down your estimate and then test it out. Was your estimate close? Find someone with a different size or shape lunch box and repeat the activity.
  • Use a special bin to collect rubbish from your lunch boxes. How much rubbish did you collect?
  • Sort out the lunch box rubbish and organise it into a graph. What information does your graph give you?

Another idea is to collect interesting photographs from around the world. I took the photograph above recently in Oslo, Norway. What sorts of questions could you ask students to explore relating to the interesting shapes you see in the bridge and the building? Here’s another interesting photograph from Morocco.

OLYMPUS DIGITAL CAMERA

 

There are several interesting mathematical questions you could pose relating to the phtograph:

  • Can you work out the number of hats in the photograph without actually counting them one by one? How? Is there another way?
  • The hats at the top of the photograph are called a ‘fez’ or ‘tarboosh’. Investigate their history and construct a timeline.
  • If each fez cost 80 Moroccan Dirham, how much would each one cost in Australian currency? Would the entire contents of the shop be worth more than $200?

A great free resource (and one of my favourites) that often has fantastic mathematical potential is the website, Daily Overview (http://www.dailyoverview.nyc/). Each day Daily Overview post a different aerial photograph from somewhere in the world. The photograph is accompanied by background information that could also be explored within a mathematics lesson.

There are many ways to bridge the gap between school mathematics and children’s lives. If we can promote the relevance of mathematics to children while at primary school, then we have a much better chance of sustaining their engagement through the secondary years, when mathematics becomes more abstract. We want children to continue the study of mathematics beyond the compulsory years and this is more likely to happen when they no longer ask ‘When am I every going to use this?’.

Assessment and Mathematics: Where are we going wrong?

Thousands of children in Australian schools have recently sat the national literacy and numeracy test (NAPLAN), and many teachers have been busy administering a whole range of assessments because it’s report writing season and boxes need to be ticked. My question is, how often do we ask ourselves why we’re assessing? What are we doing with the results apart from using them for reporting purposes? I’ve spent quite a bit of time in schools lately, and after talking to lots teachers and seeing a range of mathematics assessment tasks and work samples, I’ve begun to reflect on some of the things we could do better.

“Effective pedagogy requires effective assessment, assessment that provides the critical links between what is valued as learning, ways of learning, ways of identifying need and improvement, and perhaps most significantly, ways of bridging school and other communities of practice” (Wyatt-Smith, Cumming, Elkins, & Colbert, 2010, p. 320)

It’s through our assessment we communicate most clearly to students those learning outcomes we value, yet it’s often held that no subject is as associated with its form of assessment as is mathematics (Clarke, 2003). Assessment practices in mathematics often consist of formal methods such as tests and examinations (Wiliam, 2007), and it’s believed that such strategies need as much consideration for renewal as does content and classroom pedagogy. Although lots of progress has been made in terms of improving mathematics teaching and learning and curriculum, many such improvements have failed due to a mismatch between assessment practices and pedagogy (Bernstein, 1996; Pegg, 2003). It’s been suggested that in mathematics, there should not be more assessment, but more appropriate assessment strategies implemented to inform learning and teaching as well as report on progress and achievement (Australian Association of Mathematics Teachers, 2008; Clarke, 2003). And this is the point I want to highlight – assessment to inform teaching. Regardless of the type of assessments we use, are we using assessment data in the right way?

What do you do with your assessment work samples? Do you simply use the scores to determine how students are grouped, or what aspects of a topic you need to cover? How often do we, as teachers, take the time to analyse the work samples in order to identify specific misconceptions? Imagine a scenario where students are grouped according to assessment scores. Each of those groups are then exposed to pedagogies intended to address the ‘level’ of the group. What if, within each group, there were a range of misconceptions? And what about the top groups? What if work samples that resulted in accurate answers exposed misconceptions despite being correct?

When students transition from one level of schooling to another, it’s not uncommon to hear teachers complaining about the broad range of abilities, and more specifically, those students who appear not to have achieved the most basic skills. How have these students managed to get to kindergarten/Year 3/Year 6/high school/university without knowing how to……? Mathematics content is hierarchical – when students miss out on learning concepts in the early years, the gaps in knowledge continue to widen as they progress through school. Whether caused by inattention, absence from school, or any other reason, students find it hard to catch up when they’re missing pieces of the mathematical jigsaw puzzle. It’s like building a house on faulty foundations.

So how can we fix this? A teacher recently told me that she didn’t have time to analyse the responses in an assessment task. Isn’t this our job? How can we manage workloads so that teachers have the time to really think about where students are going wrong, and how can teachers access professional learning to assist them in being able to identify and address students’ misconceptions?

I think one way we can address this situation is to think carefully about the design and the quantity of assessment tasks. Administer fewer, better quality tasks that are designed to assess both the content and the processes of mathematics. That is, tasks that require students to show their working, explain their thinking, and produce an answer. The more they show, the more we see. Another strategy to assist teachers is to provide time for teachers to look at assessment samples and analyse them collaboratively, discussing the identified misconceptions and planning strategically to address them.

The knowledge that teachers need to effectively teach mathematics is special. We need to know more about mathematics than the average person – we need to understand where, why and when our students are likely to go wrong, so we can either avoid misconceptions occurring, or address them when they do. This specialist knowledge comes from continued professional learning and collaboration with peers. Don’t just rely on the curriculum documents – we need to look beyond this to ensure we have that specialist knowledge.

This post posed more questions than answers in relation to assessment in the mathematics classroom. Hopefully it will spark some conversation and thinking about what we are doing with the assessment work samples we gather, regardless of why type of assessments they are. If we don’t try and change the way we use assessment, we’ll always have those students who will struggle with mathematics, and while there will always be a range of achievement levels in every group of students, that doesn’t mean we shouldn’t keep trying to close those gaps!

 

References:

Australian Association of Mathematics Teachers. (2008). The practice of assessing mathematics learning. Adelaide, SA: AAMT Inc.

Bernstein, B. (1996). Pedagogy, symbolic control and identity: Theory, research, critique. London: Taylor and Francis.

Clarke, D. (2003, 4-5 December). Challenging and engaging students in worthwhile mathematics in the middle years. Paper presented at the Mathematics Association of Victoria Annual Conference: Making Mathematicians, Melbourne.

Pegg, J. (2003). Assessment in mathematics. In J. M. Royer (Ed.), Mathematical cognition (pp. 227-260). Greenwich, CT: Information Age Publishing.

Wiliam, D. (2007). Keeping learning on track: Classroom assessment and the regulation of learning. In F. K. J. Lester (Ed.), Second handbook of mathematics teaching and learning (pp. 1053-1098). Greenwich, CT: Information Age Publishing.

Wyatt-Smith, C. M., Cumming, J., Elkins, J., & Colbert, P. (2010). Redesigning assessment. In D. Pendergast & N. Bahr (Eds.), Teaching middle years: Rethinking curriculum, pedagogy and assessment (2nd ed., pp. 319-379). Crows Nest, NSW: Allen & Unwin.

 

Primary Mathematics: Engaged Teachers = Engaged Students

“The first job of a teacher is to make the student fall in love with the subject. That doesn’t have to be done by waving your arms and prancing around the classroom; there’s all sorts of ways to go at it, but no matter what, you are a symbol of the subject in the students’ minds” (Teller, 2016).

A few months ago I published a post about the issue of teacher engagement and mathematics. The following is an updated version of that post. The issue of student engagement with mathematics is a constant topic of discussion and concern within and beyond the classroom and the school, yet how much attention is given to the engagement of teachers? I am a firm believer that one of the foundational requirements for engaging our students with mathematics is a teacher who is enthusiastic, knowledgeable, confident, and passionate about mathematics teaching and learning – that is, a teacher who is engaged with mathematics. Research has proven that the biggest influence on student engagement with mathematics is the teacher, and the pedagogical relationships and practices that are developed and implemented in day to day teaching (Attard, 2013).

A regular challenge for me as a pre-service and in-service teacher educator is to re-engage teachers who have ‘switched off’ mathematics, or worse still, never had a passion for teaching mathematics to begin with. Now, more than ever, we need teachers who are highly competent in teaching primary mathematics and numeracy. The release of the Teacher Education Ministerial Advisory Group (TMAG) (2014) report, Action Now: Classroom Ready Teachers, included a recommendation that pre-service primary teachers graduate with a subject specialisation prioritising science, mathematics, or a language (Recommendation 18). In the government’s response (Australian Government: Department of Education and Training, 2015), they agree “greater emphasis must be given to core subjects of literacy and numeracy” and will be instructing AITSL to “require universities to make sure that every new primary teacher graduates with a subject specialisation” (p.8). While this is very welcome news, we need to keep in mind that we have a substantial existing teaching workforce, many of whom should consider becoming subject specialists. It is now time for providers of professional development, including tertiary institutions, to provide more opportunities for all teachers, regardless of experience, to improve their knowledge and skills in mathematics teaching and learning, and re-engage with the subject.

So what professional learning can practicing teachers access in order to become ‘specialists’, and what models of professional learning/development are the most effective? Literature on professional learning (PL) describes two common models: the traditional type of activities that involve workshops, seminars and conferences, and reform type activities that incorporate study groups, networking, mentoring and meetings that occur in-situ during the process of classroom instruction or planning time (Lee, 2007). Although it is suggested that the reform types of PL are more likely to make connections to classroom teaching and may be easier to sustain over time, Lee (2007) argues there is a place for traditional PL or a combination of both, which may work well for teachers at various stages in their careers. An integrated approach to PD is supported by the NSW Institute of Teachers (2012).

Many teachers I meet are considering further study but lack the confidence to attempt a Masters degree or PhD. I am currently teaching a new, cutting edge course at Western Sydney University, the Graduate Certificate of Primary Mathematics Education, aimed at producing specialist primary mathematics educators – a graduate certificate is definitely less intimidating than a Masters, and can be used as credit towards a higher degree. The fully online course is available to pre-service and in-service teachers. Graduates of the course develop deep mathematics pedagogical content knowledge, a strong understanding of the importance of research-based enquiry to inform teaching and skills in mentoring and coaching other teachers of mathematics.

In addition to continuing formal studies, I would encourage teachers to join a professional association. In New South Wales, the Mathematical Association of NSW (MANSW) (http://www.mansw.nsw.edu.au) provides many opportunities for the more traditional types of professional learning, casual TeachMeets, as well as networking through the many conferences offered. An additional source of PL provided by professional associations are their journals, which usually offer high quality, research-based teaching ideas. The national association, Australian Association of Mathematics Teachers (AAMT) has a free, high quality resource, Top Drawer Teachers (http://topdrawer.aamt.edu.au), that all teachers have access to, regardless of whether you are a member of the organisation or not. Many more informal avenues for professional learning are also available through social media such as Facebook, Twitter, and LinkedIn, as well as blogs such as this (engagingmaths.co).

Given that teachers have so much influence on the engagement of students, it makes sense to assume that when teachers themselves are disengaged and lack confidence or the appropriate pedagogical content knowledge for teaching mathematics, the likelihood of students becoming and remaining engaged is significantly decreased, in turn effecting academic achievement. The opportunities that are now emerging for pre-service and in-service teachers to increase their skills and become specialist mathematics teachers is an important and timely development in teacher education and will hopefully result in improved student engagement and academic achievement.

References:

Attard, C. (2013). “If I had to pick any subject, it wouldn’t be maths”: Foundations for engagement with mathematics during the middle years. Mathematics Education Research Journal, 25(4), 569-587.

Australian Government: Department of Education and Training (2015). Teacher education ministerial advisory group. Action now: Classroom ready teachers. Australian Government Response.

Lee, H. (2007). Developing an effective professional development model to enhance teachers’ conceptual understanding and pedagogical strategies in mathematics. Journal of Educational Thought, 41(2), 125.

NSW Institute of Teachers. (2012). Continuing professional development policy – supporting the maintenance of accreditation at proficient teacher/professional competence. . Retrieved from file:///Users/Downloads/Continuing%20Professional%20Development%20Policy.pdf.

Teacher Education Ministerial Advisory Group (2014). Action now: Classroom ready Teachers.

Teller. (2016) Teaching: Just like performing magic. http://www.theatlantic.com/education/archive/2016/01/what-classrooms-can-learn-from-magic/425100/?utm_source=SFTwitter

Preparing for Term 2: Programming & planning in primary mathematics

This post was originally published last year, and I thought it timely to republish considering many teachers in Australia are busy spending the school holidays programming and planning for Term 2.Often when I work with teachers I am asked for advice regarding the design of a scope and sequence for mathematics. The programming and planning of mathematics seems to cause much concern, and often the reason is that there is no ‘magic fix’ or one-size-fits-all solution.

Traditionally, schools have planned their mathematics teaching using a topic-by-topic or strand-by-strand approach. Sometimes there is a formula for teaching the Number and Algebra strand for a certain number of days per week, with the other days dedicated to the remaining syllabus strands. Often, the strands are split into single, stand-alone topics. Unfortunately, there are issues with this approach. Teaching individual topics in mathematics hinders students in gaining a deep understanding of mathematics and the connections that exist between and among the strands. Teaching in this way can promote a traditional, rote learning approach where the opportunities for mathematical thinking are limited. Our curriculum places the Proficiencies (Working Mathematically in New South Wales) at the forefront of teaching and learning mathematics – teaching topics in isolation does not promote the Proficiencies.

So what’s the solution? Consider planning and programming using a ‘big idea’ approach. What’s a big idea? Big ideas are hard to define and different people have differing ideas on what the big ideas in mathematics actually are. However, all the definitions in literature have one thing in common – they all refer to big ideas as the key to making connections between mathematical content and mathematical actions, and they all link mathematical concepts. Take, for example, the big idea of equivalence. This relates to number and numeration, measurement, number theory and fractions, and algebraic expressions and equations. Connections can be made across the strands and these links should be made explicit to students.

Charles (2005) presents a total of 21 big ideas across the mathematics curriculum, however he states that these are not fixed – they can be adapted. He also states that a big ideas approach has implications for curriculum and assessment and professional development – teachers need to develop their pedagogical content knowledge to ensure they have a deep understanding of the connections within the curriculum if they are to teach mathematics successfully.

Of course, there are challenges to teaching using a big ideas approach. Teachers often feel under pressure to address all curriculum outcomes, and often this is the reason that the topic-by-topic approach is adopted. Using a big ideas approach can feel messy – it is not linear and in some ways feels as though it is conflicting with the organisation of our curriculum. However, we must remember that although our curriculum is separated into strands and sub-strands, this is simply an organisational tool and does not mean that mathematics should be taught in this same way.

My advice would be to take our curriculum, pull it apart and try seeing it differently – what areas of the curriculum have obvious links? How can you link aspects of measurement to the number strand? Where does measurement and geometry link? And how can you use the statistic and probability strand to teach number concepts? Making connections will make your teaching easier in the long run, and more importantly, will result in deeper learning and deeper engagement with mathematics.

Randall, C. (2005). Big ideas and understandings as the foundation for elementary and middle school mathematics. NCSM Journal, 7(3), 9-24.

Problem solving and mathematics: Promoting cognitive dissonance

A couple of weeks ago I came across the term ‘cognitive dissonance’ in relation to teaching and learning mathematics and I have been thinking about it ever since. It reminded me of something a colleague of mine talks about with his primary class – the idea of getting a ‘sweaty brain’ when something is challenging or difficult during maths lessons. It’s that uncomfortable feeling you get, that feeling of disequilibrium, when you’re grappling to learn something new – something that is slightly out of reach.

Do you celebrate cognitive dissonance or ‘sweaty brains’ in your classroom? I think this is something that we have to promote – we need our students to value the struggle that takes place as part of the learning process and particularly when we engage in the problem solving process. Problem solving is a central part of the mathematics curriculum, and explicitly listed as one of the four Proficiencies of the Australian Curriculum: Mathematics and as a Working Mathematically component in New South Wales schools.

Another important aspect of the problem solving process and one that is closely related to the idea of cognitive dissonance is the development of perseverance in our students – when tasks are challenging it’s important not to give up – what some might refer to as having ‘grit’. So how do students develop perseverance when it comes to problem solving? There are things we can do as part of our pedagogical repertoires that promote perseverance and help celebrate having a ‘sweaty brain’. First, we need to understand the struggle that students are experiencing. By knowing your students well and developing a positive pedagogical relationship where you have a strong understanding of the learning needs of each individual student, you can set tasks and problems that are at an appropriate level of cognitive challenge for each child – not too difficult, but not too easy!

Set up opportunities for your class to work collaboratively on challenging problems – this gives students a chance to share their thinking and hear you model the thinking processes that occur when tasks are challenging. Use a growth mindset approach and focus on the language of ‘yet’. Often in mathematics classes we expect to begin and end a task within one mathematics lesson – giving students a very limited amount of time to work on what could be a complex problem. Why not allow students to walk away from the problem and think about it overnight before continuing to work on it the following day?

Use reflection as a natural part of the learning process, and model reflection for your students – very often we assume students can ‘do’ reflection, yet often they don’t really engage in metacognition because they haven’t practiced it or seen someone else engage in the process of reflection.

Finally, consider where problem solving fits into your classroom routines – is it part of your daily routine, and do you use problem solving as an opportunity to provide purpose for learning mathematical concepts and processes? Do you promote a classroom culture where mistakes are regarded as learning opportunities and cognitive dissonance is celebrated?

Maths and Money: Engaging students in real world mathematics


Many children are consumers of financial services from a young age. According to Thomson (2014) it’s not uncommon for them to have accounts with access to online payment facilities or to use mobile phones during the primary school years, and it’s clear that financial literacy and mathematics skills would be of benefit when using such products. Prior to leaving school, young people often face decisions about issues such as car insurance, savings products and overdrafts. In fact, by the age of 15 to 18, many young people face one of their most important financial decisions: that is, whether or not to invest in higher education. Financial education programs for young people can be essential in nurturing sound financial knowledge and behaviour in students from a young age (Ministerial Council for Education Early Childhood Development and Youth Affairs, 2011).

This week (14th – 20th March) is Global Money Week, initiated by Child & Youth Finance International. What’s that got to do with maths and engagement? When integrated and contextualised to suit students’ needs and interests, mathematics and financial literacy education can be highly engaging for students. My current study into the use of Financial Literacy as a tool to engage students with mathematics has highlighted how teaching financial literacy through the mathematics curriculum improves students’ understanding of mathematical concepts, their engagement with mathematics and how important it is for all students to:

  1. Understand the importance and value of money;
  2. Recognise the mathematics that underpins consumer and financial literacy;
  3. Engage in real-world projects and investigations relating to consumer and financial literacy to understand how mathematics is applied in everyday decisions that could influence life opportunities; and
  4. Learn about consumer and financial literacy via the mathematics curriculum.

In this research project I worked with teachers from four different schools across the state of NSW. Each of the schools as situated in low socio-economic areas and each was a unique context. Initially the teachers were asked to explore the MoneySmart  teaching Units of Work to find and teach one that suited the needs of their learners and to familiarise themselves with the teaching of consumer and financial literacy concepts, including the National Consumer and Financial Literacy Framework  alongside the NSW mathematics curriculum. Following this, the research team worked with the teachers to develop context-specific units of work that responded to the needs and interests of the students in their classrooms. The results, which I will report on in forthcoming blogs and publications, were inspiring.

The teachers involved in the project went from knowing very little about teaching consumer and financial literacy and where it fit within the mathematics curriculum to disseminating their knowledge across and beyond their school communities. The children became ‘experts’ at financial matters and a range of rich projects emerged that included a fully functioning Money Museum, a Market Day that involved a range of ‘small businesses’, and the planning, financing and building of a school ‘buddy bench’. Once school had every single class involved in individual projects, and one class planned and financed their end-of-year excursion.

Over the coming months I will share some of the exciting work from this project and the project findings on this blog. In the meantime, consider how you might celebrate Global Money Week in your classroom.

References:

Ministerial Council for Education Early Childhood Development and Youth Affairs. (2011). National Consumer and Financial Literacy Framework. from http://www.mceecdya.edu.au/mceecdya/2011_financial_literacy_framework_homepage,34096.html

Thomson, S. (2014). Financing the future: Australian students’ results in the PISA 2012 Financial Literacy assessment. https://http://www.acer.edu.au/files/PISA_2012_Financial_Literacy.pdf