Tag Archives: Professional learning

Beyond Monday’s Maths Class: Making the Most of Teacher PD

Last weekend I travelled interstate to attend a professional development day for teachers of mathematics. It was a good day, with lots of ideas shared and great enthusiasm from the 500+ audience. The presenter was well informed and, in fact, created quite a lot of hype due to her international reputation. Everyone went home happy and the word on Twitter was that Monday’s maths lessons were going to be different. Fantastic! But what about Tuesday’s lesson, and what about next week’s, next month’s, and next year’s lessons? What about the lessons of other teachers in the school?

How do you make the most of professional development?

Too often teachers attend PD sessions, get enthusiastic, try a few new things, but quickly get bogged down in the day-to-day challenges of life in a busy school and the demands of administration and curriculum authorities. How can you translate the underlying philosophy being promoted in the professional development sessions into sustainable change that can be shared amongst colleagues to improve and transform mathematics teaching and learning?

PD is expensive, and it’s important that opportunities aren’t wasted. I’ve been talking and writing a lot recently about promoting critical thinking in the mathematics classroom. It’s equally as important for teachers to engage critically with professional development. The following list contains a few thoughts that might help teachers get the most out of PD opportunities.

  1. Choose the right PD

Do a little research on the person presenting the PD. What are their credentials? Are they a self-proclaimed expert or do they have an established reputation? A simple Google search should reveal some insights, and, if the presenter is an academic, you could search Google Scholar for some of their academic publications. Spending time researching the presenter’s background can save you from attending a PD session that may not be right for you, and can provide some good research background should you choose to go ahead with the session. You also need to consider what you want out of a PD session. If you want a ‘bag of tricks’ in the form of a handful of ready to go activities, then you probably shouldn’t be wasting your school’s money. Rather, think about PD that is going to cause you to think deeply about your practice, and have a long-term effect on students’ educational outcomes.

  1. Does the presenter understand the Australian school context and curriculum?

When you attend PD, you expect that the presenter is aware of the Australian school context, and more importantly, the Australian Curriculum. This assists you, the teacher, in applying the learning to your practice, and also makes the content of the PD more relevant to you and your students.

  1. Understand the structure of the PD session

Before you commit to attending a PD session, ensure you understand what is going to happen in that session. Nobody likes sitting down and being lectured to for hours on end, nor do you want to listen to a presenter talk about themselves for an entire day! Look for presentations that are interactive and allow participants to apply theory to practical activities. If we are going to ask our students to do something differently, we need to experience it ourselves first. It’s also a better way of retaining information.

  1. Active Participation

When you’re at the PD session, don’t be afraid to ask questions. It’s also important to think critically about the information you are receiving. Presenters are usually very happy to answer questions that spark discussion – this often results in deeper learning, and better value for your school’s money! If the presenter doesn’t welcome questions, this is a sign that they may not have expert knowledge.  During the PD session it’s important that you participate in any activities – there’s usually a good reason a presenter has asked you to engage in a task. Active participation gives insight into the student experience and possible challenges, and it’s a great way to make links between theory and practice.

  1. Use the session as a networking opportunity

Often one of the most valuable aspects of professional development sessions is the opportunity to connect with teachers from other schools. It’s a great opportunity to discuss practice, students and school procedures. Networks developed at PD sessions can be maintained easily using tools such as LinkedIn, Twitter, and Facebook.

  1. Reflection

Before you leave your PD session, pause and consider what you have learned (a good presenter will actually give you opportunity to reflect). Think about how you might apply what you have learned (not just the activities, but the educational philosophy underpinning them) to your classroom, and don’t limit yourself to just replicating the activities. What are the underlying messages? How can you use those messages to adapt your practice? What will be different in the way that you plan and implement lessons? It doesn’t have to be a big change. Often subtle differences have huge effects.

  1. Sustainability: Sharing the Learning

Finally, it’s important to share the learning. It’s difficult to sustain any kind of change that will have ongoing benefit for students if it’s not supported by others in your school. This may not be easy, but small changes are better than no changes. Sometimes it’s a good idea to try out new things in your own class first, then use evidence of your success to convince others.

When it comes to PD, one of the most important things to remember is the reason we do what we do. We want our students to be the best they can, and when it comes to mathematics, we want to give them confidence, skill, passion and excitement that will ensure they continue to study and use mathematics beyond their school education.

Promoting Student Reflection to Improve Mathematics Learning

Critical reflection is a skill that doesn’t come naturally for many students, yet it is one of the most important elements of the learning process. As teachers, not only should we practice what we preach by engaging in critical reflection of our practice, we also need to be modelling critical reflection skills to our students so they know what it looks like, sounds like, and feels like (in fact, a Y chart is a great reflection tool).

How often do you provide opportunities for your students to engage in deep reflection of their learning? Consider Carol Dweck’s research on growth mindset. If we want to convince our students that our brains have the capability of growing from making mistakes and learning from those mistakes, then critical reflection must be part of the learning process and must be included in every mathematics lesson.

What does reflection look like within a mathematics lesson, and when should it happen?Reflection can take many forms, and is often dependent on the age and abilities of your students. For example, young students may not be able to write fluently, so verbal reflection is more appropriate and can save time. Verbal reflections, regardless of the age of the student, can be captured on video and used as evidence of learning. Video reflections can also be used to demonstrate learning during parent/teacher conferences. Another reflection strategy for young students could be through the use of drawings. Older students could keep a mathematics journal, which is a great way of promoting non-threatening, teacher and student dialogue. Reflection can also occur amongst pairs or small groups of students.

How do you promote quality reflection? The use of reflection prompts is important. This has two benefits: first, they focus students’ thinking and encourage depth of reflection; and second, they provide information about student misconceptions that can be used to determine the content of the following lessons. Sometimes teachers fall into the trap of having a set of generic reflection prompts. For example, prompts such as “What did you learn today?”, “What was challenging?” and “What did you do well?” do have some value, however if they are over-used, students will tend to provide generic responses. Consider asking prompts that relate directly to the task or mathematical content.

An example of powerful reflection prompts is the REAL Framework, from Munns and Woodward (2006). Although not specifically written for mathematics, these reflection prompts can be adapted. One great benefit of the prompts is that they fit into the three dimensions of engagement: operative, affective, and cognitive. The following table represents reflection prompts from one of four dimensions identified by Munns and Woodward: conceptual, relational, multidimensional and unidimensional.

Picture1(Munns & Woodward, 2006)

Finally, student reflection can be used to promote and assess the proficiencies (Working Mathematically in NSW) from the Australian Curriculum: Mathematics as well as mathematical concepts. It can be an opportunity for students to communicate mathematically, use reasoning, and show evidence of understanding. It can also help students make generalisations and consider how the mathematics can be applied elsewhere.

How will you incorporate reflection into your mathematics lessons? Reflection can occur at any time throughout the lesson, and can occur more than once per lesson. For example, when students are involved in a task and you notice they are struggling or perhaps not providing appropriate responses, a short, sharp verbal reflection would provide opportunity to change direction and address misconceptions. Reflection at the conclusion of a lesson consolidates learning, and also assists students in recognising the learning that has occurred. They are more likely to remember their learning when they’ve had to articulate it either verbally or in writing.

And to conclude, some reflection prompts for teachers (adapted from the REAL Framework):

  • How have you encouraged your students to think differently about their learning of mathematics?
  • What changes to your pedagogy are you considering to enhance the way you teach mathematics?
  • Explain how your thinking about mathematics teaching and learning is different today from yesterday, and from what it could be tomorrow?

 

References

Munns, G., & Woodward, H. (2006). Student engagement and student self-assessment: the REAL framework. Assessment in Education, 13(2), 193-213.

 

 

 

 

When a Maths Curse is a Good Curse!

In one of my previous posts I wrote about the use of children’s literature to encourage rich mathematical investigations and improve student engagement with mathematics. One of my favourite books, Math Curse by John Szieska and Lane Smith, is described in the blog post as a great way to engage reluctant learners. Even better, Math Curse encourages children (and their teachers) to see the mathematics that is embedded in every aspect of our lives. In this post I am going to share some student work from a Grade 3 classroom. In this classroom, the teacher read the book to the students before challenging them create their own class maths curse. The children took their own photographs, and working in small groups, they came up with a range of mathematical problems and investigations, which they then gave to other groups to solve.

Here are some of the photos with their accompanying questions:

Beyblades:

  1. If one of the beyblades spins for 2 minutes and 31 seconds and the other one spins for 1 minute and 39 seconds what is the difference between the two times?
  2. If one of the beyblades spins for 1 minute and 1 second and another spins for 78 seconds, which beyblade spun for the longest and by how long?

Hair:

  1. If there are 31 people in the class (10 boys and 21 girls) and all of them have hair that is 30cm long. Half of the boys cut 10cm off their hair, the other half cut 20cm off their hair. How long is the classes hair now altogether? How long was it before? How much hair has been cut altogether?
  2. Check your friend’s hair. Estimate how long it is when it is out, how long it is when it is in a ponytail, and how long it is when it is in a braid. List some different ways you could check if your estimate is accurate? What are the potential problems with your methods?
  3. I’m 9 years old. I had really long hair for 6 years, then I cut it. How long did I have short hair for?
  4. I have 5 friends that are girls and 2 friends that are boys. All 5 girls have hair length of 50cm. The boys both have different lengths of hair. The 1st boy has 30cm of hair, the second has 25cm of hair. What is the difference between the 1st boy and the girls and the 2nd boy and the girls?

Birthday Balloons:

  1. Write down the dates of important celebrations. If you add all the dates together, what is the value of their numbers?
  2. How many days are there in 6 years?
  3. If everyone’s birthday occurred every three years (starting the year you are born) what years would your birthday fall on?
  4. If Lisa and Jane went on a holiday every 2 months, how many holidays could they take in a year?
  5. If you could rearrange the seasons, what months would you choose to be Spring? Why?
  6. What is the most popular letter in the days of the months?
  7. Why do you think there are 4 seasons in a year?

From Problem Solving to Problem Posing

What is the purpose of getting students to write mathematical problems? First of all, the problems give us good insight into whether students recognise mathematical situations, and whether they understand where, how, and what mathematics is applied in day to day situations. An added bonus is that the students are highly engaged because they have ownership of the mathematics they are generating, the topics they choose are of interest to them, and stereotypical perceptions of school mathematics are disrupted.

Student Reflection

The students who wrote the examples above completed a structured written reflection following the sequence of designing and solving each others’ maths curses. Here are some of reflection prompts and a sample of responses:

What did you enjoy about today’s learning?

“working with my team”
“working at the problems for a long time and then finally getting them after a long, hard discussion”

“solving questions that my friends wrote”

“I felt challenged and I learnt more about what maths is”

“working with my group, choosing our own questions and learning something new”

“I liked the chess card the best because we had to solve it together and use problem solving”

“having a go at tricky questions even if i got them wrong”

Did you learn anything new?

“how to work things out in different ways”

“working in groups helps you learn more skills”

“not every question uses just one skill like addition, division, multiplication or subtraction”

“when I am challenged I learn more”

“Maths is not always easy”

“how to work together”

“Everyone in the group has different responses so we needed proof to figure out the right one”

What surprised you about this task?

“It surprised me how hard my own questions were”

“I didn’t know that we could come up with so many interesting questions”
“I got a shock! We had to research to solve some problems, Adam even taught me how to add a different way”

“I got some questions wrong “

“It was hard but if we put our brains into gear we could figure it out”

“I was able to play while doing maths” 

Using activities such as this provides multiple benefits for students. Contextualising the mathematics using students’ interests highlights the relevance of the curriculum, improves student engagement, and makes mathematics meaningful, fun and engaging!

Australia’s Declining Maths Results: Who’s Responsible?

Once again, mathematics education is in the spotlight. The most recent TIMMS  and PISA results highlight a decline in Australia’s mathematics achievement when compared to other countries, which will no doubt perpetuate the typical knee jerk reactions of panic and blame. So, what are we doing about this decline? Who’s responsible? Typically, the first to get the blame for anything related to a decline in mathematics are teachers, because they work at the coal face, they spend significant amounts of time with students, and they’re an easy target. But shouldn’t we, as a society that considers it acceptable to proudly claim “I’m not good at maths” (Attard, 2013), take some portion of the blame?

Numeracy and Mathematics education is everyone’s business

As a society, we all need to take some responsibility for the decline in mathematics achievement and more importantly, we all need to collaborate on a plan to change the decline into an incline. From my perspective, there are three groups of stakeholders who need to work together: the general community, the policy makers and school systems that influence and implement the policies, and the teachers.

Let’s start with the general community. It seems everybody’s an expert when it comes to mathematics education because we all experienced schooling in some form. Many say: “I survived rote learning – it didn’t hurt me”. The world has changed, access to information and technology has improved dramatically, and the traditional ‘chalk and talk’ practices are no longer appropriate in today’s classrooms. Many hold a limited view of school mathematics as drill and practice of number facts and computation. Although it’s important that children build fluency, it’s simply not enough. We must promote problem solving and critical thinking within relevant contexts – making the purpose of learning mathematics visible to students. It is, after all, problem solving that forms the core of NAPLAN, TIMSS and PISA tests.

The community pressure for teachers to use text books and teach using outdated methods, along with a crowded curriculum and an implied requirement for teachers to ‘tick curriculum boxes’ causes significant tensions for teachers, particularly in the primary school where they are required to be experts at every subject. If we consider the limited number of hours allocated to mathematics education in teacher education degrees compared with the expectations that all primary teachers suddenly become experts on graduation, then we should understand that teachers need continued support beyond their tertiary education to develop their skills. In addition, rather than focusing on students’ learning, the crowded curriculum  leads them to focus on getting through the curriculum (http://v7-5.australiancurriculum.edu.au/mathematics/curriculum/f-10?layout=2#page=1) and this often leads to a ‘back to basics’ approach of text books, work sheets and lots of testing that does not create students who can problem solve, problem pose and problem find.

This is where the policy makers and school systems must come into play by providing support for high quality and sustained professional learning and encouraging primary teachers to gain expertise as specialist mathematics teachers. We already have a strong curriculum that promotes problem solving and critical thinking both through the Proficiencies and through the General Capabilities. The General Capabilities provide teachers with the opportunity to embed mathematics in contextual, relevant and purposeful mathematics. However, teachers need to be supported by all stakeholders, the community and the policy makers, to use these tools and focus less on the teaching of mathematics as a series of isolated topics that make little sense to students.

What can we do?

There are no easy solutions, but one thing is clear. We need to disrupt the stereotypical perceptions of what school mathematics is and how it should be taught. We need to support our teachers and work with them rather than against them. Let’s band together and make some changes that will ultimately benefit the most important stakeholders of all, the children of Australia.

 

 

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.

 

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

Programming & planning dilemmas in primary mathematics

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 amongst 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.

 

Professional Learning and Primary Mathematics: Engaging teachers to engage students

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 recent 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).

In anticipation of the TMAG recommendations for subject specialisation, I have been involved in the design and implementation of a new, cutting edge course to be offered by the University of Western Sydney, the Graduate Certificate of Primary Mathematics Education, aimed at producing specialist primary mathematics educators. The fully online course will be available from mid 2015 to pre-service and in-service teachers. Graduates of the course will 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. For those teachers who are hesitant to commit to completing a full course of study, the four units of the Graduate Certificate will be broken up into smaller modules that can be completed through the Education Knowledge Network (www.uws.edu.au/ekn) from 2016 as accredited PL through the Board of Studies Teaching and Educational Standards (BOSTES).

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.

M

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.