Category Archives: mathematics

Flipped learning in primary and secondary mathematics: Some lessons

Flipped classrooms and flipped learning approaches are fast becoming a popular practice in mathematics classrooms, providing opportunities for students to learn anywhere, at any time. A flipped pedagogical approach may go some way in addressing the continuing issue of student disengagement with mathematics, yet how do we know if it really works? And what are the advantages and disadvantages to flipped approaches? In this blog post I provide a brief explanation of flipped learning before sharing some of the lessons I’ve learned about the flipped approach from my research into the effective use of technology in mathematics classrooms.

First, let’s consider how flipped learning works. There are various approaches that range from the provision of direct instruction via the use of video recorded lectures, to those that allow teachers to individualise learning according to student needs. The fundamental reason flipped learning approaches evolved was to take advantage of new technologies that allow for the introduction of new knowledge via multi-media and shift passive learning (via direct instruction) to allow teachers and students to make better use of classroom time. Pre-lesson materials can take the form of prescribed readings, teacher-produced videos, screencasts that may incorporate resources created on software such as GeoGebra, videos sourced from Youtube, or resources created by others such as Khan Academy. Face to face lessons can then be freed up for more teacher/student and student/student interaction, collaboration, application of learning through problem solving and investigation, and opportunities to provide intervention where necessary (Bhagat, Chang, & Chang, 2016; Lo & Hew, 2017; Weinhandl, Lavicza, & Süss-Stepancik, 2018).  

Lessons from research

Through my various technology-related research projects I have seen a variety of models of flipped approaches from primary through to senior secondary classrooms. The most important lesson I’ve learned is, just like any other teaching resource, a flipped learning approach is only as good as the person driving it: the teacher. It’s the teacher and his or her understanding of student needs, along with the ability to address those needs, that can determine the effectiveness of any flipped approach. For example, in research I conducted approximately five years ago, a Year 3 teacher tried a flipped approach. Unfortunately, not all of the students understood the content that was covered in the pre-lesson videos, and the flipped approach failed. This leads me to lesson two: A one-size-fits-all approach very rarely works in the classroom and is even more precarious in a flipped approach where young students don’t have access to the teacher to seek clarification.

In the five years since that research project, the emergence of new technologies and software has meant that flipped learning in the mathematics classroom has evolved and become much more sophisticated. Apps such as SeeSaw provide different flipped learning opportunities that allow multi-directional communication between home and school, as well as the sharing of work samples.  Productivity packages such as OneNote and learning management systems such as Canvas or Echo allow for multimedia to be used rather than the simple use of video. Programs such as Matific and Prodigy allow teachers to allocate different levels of activity to different students and track student achievement.These applications have made it easier than ever to differentiate learning, view student progress, and collate assessment data, which leads me to lesson three: flipped learning is hard work for the teacher.

A successful flipped learning approach requires the teacher to be vigilant beyond the timetabled mathematics lesson. If students are accessing and responding to resources anywhere and anytime, this requires a substantial commitment on the part of the teacher. Similarly, if students are not accessing the set tasks in preparation for their lessons, the teacher must also be aware and adjust lessons accordingly. The issue of students failing to access material prior to lessons is a common one and was observed in my most recent research. It is important to carefully consider the students and their contexts beyond the mathematics classroom.  The fourth lesson, therefore, is to beware of assumptions about access. Not all students will have access to devices or internet. Sometimes a flipped approach may result in exclusion, depending on socioeconomic circumstances or location. For example, in one of the schools involved in my research, there were connectivity issues due to the location.  

The final lesson I’d like to share about flipped learning is perhaps the most important. It can help students, particularly those who are disengaged with mathematics. The teachers who use flipped learning effectively in my most recent research were able redefine mathematics learning spaces for their students. The flipped approach promoted self-confidence, built strong connections between teachers and students, and provided ‘just in time’ learning and support, and self-paced learning without the stigma usually associated with students who feel they just can’t do mathematics.

There is emerging evidence that a flipped learning approach in mathematics is achieving success in relation to increasing student engagement due to the increased autonomy that allows students more access to learning resources. However, the majority of research on flipped learning focuses on tertiary and secondary education, with little attention paid to the primary classroom. There is also a need to explore more deeply how and why flipped learning approaches improve student engagement, if we are to take advantage of the affordances of emerging technologies to enhance students’ learning experiences and ultimately improve outcomes and attrition in higher level mathematics. In my upcoming blog posts I will provide further detail about the different models of flipped learning I observed, and how they influenced student engagement and learning.

References

Bhagat, K. K., Chang, C.-N., & Chang, C.-Y. (2016). The Impact of the Flipped Classroom on Mathematics Concept Learning in High School. Journal of Educational Technology & Society, 19(3), 134–142.

Lo, C. K., & Hew, K. F. (2017). A critical review of flipped classroom challenges in K-12 education: possible solutions and recommendations for future research. Research and Practice in Technology Enhanced Learning, 12(1), 4. https://doi.org/10.1186/s41039-016-0044-2

Weinhandl, R., Lavicza, Z., & Süss-Stepancik, E. (2018). Technology-enhanced Flipped Mathematics Education in Secondary Schools: A Synopsis of Theory and Practice. K-12 STEM Education, 4(3), 377–389. https://doi.org/10.14456/k12stemed.2018.9

Don’t bank on Dollarmites to teach financial literacy: here are our alternatives

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Research shows combining maths education and financial literacy concepts is a better way to teach children good financial habits and boost numeracy. http://www.shutterstock.com

Catherine Attard, Western Sydney University

The recent royal commission into banking has revealed rampant wrongdoing by the big banks. As a result, there is renewed public interest in school banking schemes. The Commonwealth Bank’s Dollarmites program has once again come into the spotlight.

Dollarmites was awarded a 2018 Choice Magazine Shonky award. The program has over 300,000 active participants, and although it’s not the only school banking program, it’s the largest by far.


Read more: Should banks play a role in teaching kids about how to manage money effectively?


According to the Commonwealth Bank, the motive behind the Dollarmites program is to teach good savings habits and develop financial literacy. But I could find little independent research evidence it actually does.

On the surface, the Commonwealth Bank’s intentions are good. But research has found 40% of people develop loyalty to their banks and continue banking with them into adulthood.

We need to consider other options. Here are some research-backed alternatives.

Alternatives to school banking

Financial literacy can be taught both at home and at school, in practical and meaningful ways. If we consider the core business of schools to be learning, then our classrooms are not an appropriate place for the distractions of corporate marketing. There is definitely no time to be wasted on the logistics of organising school banking.


Read more: Financial literacy is a public policy problem


In fact, schools have several options when it comes to teaching financial literacy. There are a number of free resources already aligned to the curriculum.

In my research, using ASIC’s MoneySmart resources, financial literacy was combined with maths. Students did activities that allowed them to deal with real money while applying maths skills.

For example, some students borrowed money from the school principal to set up small businesses. They then ran their business at a school market day, and used their profits to buy Christmas gifts for underprivileged children.

Simple activities such as setting up classroom economies or allowing children to help plan events (such as class excursions) are also excellent at engaging children in financial literacy in a fun, realistic and interactive way.

Findings from my study showed learning about money and maths improved engagement, understanding of mathematical concepts and knowledge of financial concepts such as budgeting, profit and loss, lending and interest.

There are also resources such as Banqer, a free subscription-based app that allows students to manage fictitious money to budget and cover expenses (such as “renting” a desk). In my professional opinion, apps such as this are high quality. They may have corporate sponsorships, but are offered brand-free, which is preferable.

Parents can teach financial literacy too

Parents are one of the biggest influences on the financial habits of children. Parents have a responsibility to model good financial behaviours.

Involving children in shopping, having discussions about family budgeting and encouraging children to save some of their pocket money using a bank account of their choice all contribute to the development of financial literacy. These are really simple, everyday things parents can do to help their children learn financial literacy.


Read more: Teaching kids about maths using money can set them up for financial security


Catherine Attard, Associate Professor, Mathematics Education, Western Sydney University

This article is republished from The Conversation under a Creative Commons license. Read the original article.

Engaging children with mathematics: Are you an engaged teacher?

“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).

Teller (2016), makes a powerful point about teaching and engagement, and how important it is that we, as teachers, portray positive attitudes towards our subject and towards teaching it. Do you consider yourself an engaged teacher? Are your students deeply engaged with mathematics, and how do you know? In education we talk about student engagement every day, but what do we actually mean when we use the term ‘engagement’? When does real engagement occur, and how do we, as teachers, influence that engagement? In this post, I will define the construct of engagement and pose some questions that will prompt you to reflect on how your teaching practices and the way you interpret the curriculum, influences your own engagement with the teaching of mathematics and, as a result, the engagement of your students.

Student Engagement: On Task vs. In Task

In education, engagement is a term used to describe students’ levels of involvement with teaching and learning. Engagement can be defined as a multidimensional construct, consisting of operative, cognitive, and affective domains. Operative engagement encompasses the idea of active participation and involvement in academic and social activities, and is considered crucial for the achievement of positive academic outcomes. Affective engagement includes students’ reactions to school, teachers, peers and academics, influencing willingness to become involved in school work. Cognitive engagement involves the idea of investment, recognition of the value of learning and a willingness to go beyond the minimum requirements

It’s easy to fall into the trap of thinking that students are engaged when they appear to be busy working and are on task.  True engagement is much deeper – it is ‘in task’ behaviour, where all three dimensions of engagement; cognitive, operative, and affective, come together (see figure 1).  This leads to students valuing and enjoying school mathematics and seeing connections between the mathematics they do at school and the mathematics they use in their lives outside school. Put simply, engagement occurs when students are thinking hard, working hard, and feeling good about learning mathematics.

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There are a range of influences on student engagement. Family, peers, and societal stereotypes have some degree of influence. Curriculum and school culture also play a role. Arguably, it is teachers who have a powerful influence on students’ engagement with mathematics (Anthony & Walshaw, 2009; Hattie, 2003). Classroom pedagogy, the actions involved in teaching, is one aspect of a broader perspective of the knowledge a teacher requires in order to be effective. The knowledge of what to teach, how to teach it and how students learn is referred to as pedagogical content knowledge (PCK). The construct of PCK was originally introduced by Schulman (1986), and substantial research building on this work has seen a strong focus on PCK in terms of mathematics teaching and learning (Delaney, Ball, Hill, Schilling, & Zopf, 2008; Hill, Ball, & Schilling, 2008; Neubrand, Seago, Agudelo-Valderrama, DeBlois, & Leikin, 2009). Although this research provides insight into the complex knowledge required to effectively teach mathematics, little attention is paid to how teachers themselves are engaged with teachers.

Engaged Teachers = Engaged Students

It makes sense that teachers need to be engaged with the act of teaching in order to effectively engage their students. If we take the definition of student engagement and translate it to a teaching perspective, perhaps it would look something like Figure 2, where teachers are fully invested in teaching mathematics, work collaboratively with colleagues to design meaningful and relevant tasks, go beyond the minimum requirements of delivering curriculum, and genuinely enjoy teaching mathematics in a way that makes a difference to students. In other words, thinking hard, working hard, and feeling good about teaching mathematics.

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Are you an engaged teacher?

Teaching is a complex practice with many challenges. Teaching mathematics has the additional challenge of breaking down many stereotypical beliefs about mathematics as being difficult and only for ‘smart’ people, mathematics viewed as black and white/right or wrong, and mathematics as a simply focused on arithmetic, to name a few. However, there are elements of our day to day work that we can actively engage with to disrupt those stereotypes, make teaching more enjoyable, and promote deeper student engagement. The following section provides some thoughts and questions for reflection.

Curriculum

How do you interpret the curriculum? Do you view it has a series of isolated topics to be taught/learned in a particular order, or do you see it has a collection of big ideas with conceptual relationships within and amongst the strands? How do you incorporate the General Capabilities and Cross-curriculum priorities in your teaching? Do you make the Working Mathematically components a central part of your teaching?

Planning

How do you plan for the teaching of mathematics? Does your school have a scope and sequence document that allows you to cater to emerging student needs? Does the scope and sequence document acknowledge the big ideas of mathematics or does it unintentionally steer teachers into treating topics/concepts in isolation?

Assessment

How often do you assess? Are you students suffering from assessment fatigue and anxiety? Do you offer a range of assessment tasks beyond the traditional pen and paper test? Do your questions/tasks provide opportunities for students to apply the Working Mathematically components?

Tasks

What gets you excited about teaching mathematics? Do you implement the types of tasks that you would get you engaged as a mathematician? Do your tasks have relevance and purpose?  Do you include variety and choice within your task design? Do you take into account the interests of your students when you plan tasks? Do you incorporate student reflection into your tasks?

Grouping

How do you group your students? There are many arguments that support mixed ability grouping, yet there are also times when ability grouping is required. Is the way you group your students giving them unintended messages about ability and limiting their potential?

Technology

How do you use digital technology to enhance teaching and learning in your classroom? Do you take advantage of emerging technologies and applications? Do you use digital technology in ways that require students to create rather than simply consume?

Professional Learning

How do you incorporate professional learning into your role as an educator? Do you actively pursue professional learning opportunities, and do you apply what you have learned to your practice? Do you share what you have learned with your colleagues, promoting a community of practice within your teaching context?

There are many other aspects of teaching mathematics that influence our engagement as teachers, and of course, the engagement of our students. Many factors, such as other non-academic school-related responsibilities, are bound to have some influence over our engagement with teaching. However, every now and then it is useful to stop and reflect on how our levels of engagement, our enthusiasm and passion for the teaching of mathematics, can make a difference to the engagement, and ultimately the academic outcomes, of our students.

References:

Anthony, G., & Walshaw, M. (2009). Effective pedagogy in mathematics (Vol. 19). Belley, France.

Attard, C. (2014). “I don’t like it, I don’t love it, but I do it and I don’t mind”: Introducing a framework for engagement with mathematics. Curriculum Perspectives, 34(3), 1-14.

Delaney, S., Ball, D. L., Hill, H. C., Schilling, S. G., & Zopf, D. (2008). “Mathematical knowledge for teaching”: Adapting U.S. measures for use in Ireland. Journal for Mathematics Teacher Education, 11(3), 171-197.

Hattie, J. (2003). Teachers make a difference: What is the research evidence? Paper presented at the Building Teacher Quality: The ACER Annual Conference, Melbourne, Australia.

Hill, H. C., Ball, D. L., & Schilling, S. G. (2008). Unpacking pedagogical content knowledge: Conceptualising and measuring teachers’ topic-specific knowledge of students. Journal for Research in Mathematics Education, 39(4), 372-400.

Neubrand, M., Seago, N., Agudelo-Valderrama, C., DeBlois, L., & Leikin, R. (2009). The balance of teacher knowledge: Mathematics and pedagogy. In T. Wood (Ed.), The professional education and development of teachers of mathematics: The 15th ICMI study (pp. 211-225). New York: Springer.

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

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 mathematical inquiry to make mathematics meaningful

At the moment I’m involved in a project with the Sydney Metro (Transport for NSW), currently the largest infrastructure project in Australia. When complete, the Sydney Metro project is going to change the way many Sydney residents work, live and socialise. My involvement with this project has required me to design, deliver and research the effectiveness of a professional learning program. In this program, teachers from all stages of schooling and a range of curriculum areas learn about using inquiry based learning and then design, implement and evaluate units of work that use the Sydney Metro project as the stimulus for inquiry.  So what’s that got to do with engaging maths? My work in this project has confirmed what I’ve always believed – contextualising learning makes mathematics (and other disciplines, of course) more meaningful, purposeful and relevant for students. It shifts the traditional approach of ‘just in case’ learning to ‘just in time learning’.

Using contexts from student’s lives, such as Sydney Metro, makes mathematics come alive. For example, some of the students participating in the inquiry based units are looking at the social implications of having a rail station constructed in their community where there previously wasn’t one. This inquiry provides a purpose for designing survey questions, collecting, representing and analysing data that has meaning and purpose. Others are looking at the engineering aspects of the project relating to the tunnelling that is currently underway. Some are working on design aspects relating to the trains themselves or the stations and some are looking at mapping – planning future metro lines, or timing (the system won’t have a timetable).

The possibilities are endless, but for these units of work (or indeed, any inquiry based unit of work) to be successful, the teachers planning them have to consider carefully the potential directions that students will take their inquiry if the units are to be true inquiry based learning that is driven by students’ interests. This requires a strong knowledge of curriculum and a willingness to hand over some control of the learning to the students. It may even involve the introduction of content beyond the students’ current grade.
Another consideration when planning inquiry units is the inclusion of other aspects of our curriculum, beyond content. For example, in mathematics we have the Proficiencies (Working Mathematically in NSW) that represent the processes of mathematics. It’s impossible to conduct inquiry based learning without these processes and inquiry learning is a perfect opportunity to develop, refine and show evidence of these processes. Then we have the General Capabilities. Again, inquiry based learning provides an opportunity to access mathematics while accessing these capabilities, enhancing the relevance of the learning.

Where do you find resources for inquiry? Take a look around at what is happening in your community, in the media, or simply the things that your students are interested in. Consider how those things could spark curiosity in your students (or how you could promote that curiosity within  your students). Model how to ask good questions (students need to know how to do this – it doesn’t always come naturally). Be prepared for it to get messy, search for resources that the students might need or help them find resources. Be prepared to teach a range of mathematical concepts as the need arises.

I’ll you with an example of a resource that I believe would be a great stimulus for inquiry – take a look, at let me know what you think! Every Drop Counts

Teachers and Mathematics: Making the most of professional development

Over the past week I have been involved in a number of professional development events for primary and secondary teachers of mathematics. This included presentations at a primary and middle years conference and a number of sessions involving the development of teachers as action researchers. This weekend I will be travelling to the US to attend the NCTM Annual Meeting and Exposition in Washington DC and will be presenting a session there. All of these engagements with teachers reminded me of a post I published last year about what teachers do with the information they gain from attending professional development, particularly when it happens away from school. The following are some thoughts I wrote about last year – a timely reminder for those teachers who are taking time away from their students or in their personal time to deepen their knowledge about mathematics teaching and learning.

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 school context and curriculum in your state/country?

When you attend PD, you expect that the presenter is aware of the school/state/country context, and more importantly, the 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.

Tips for beginning primary teachers: What’s in your maths toolbox?

If you’re an early career teacher, chances are you spend lots of your spare time looking for good maths resources. Some of you may have your own class, while others are beginning their careers as a relief teacher, having to move from one class to another, and often between different schools. Many teachers who are starting out have to build their toolbox of resources from nothing. Where do you begin? How can you develop a bank of activities that suits lots of different levels and abilities, and engages children of diverse abilities?

One of the first things I would recommend would be to invest in a small range of materials that allow you to implement some simple tasks that could then be expanded into interesting and worthwhile mathematical investigations. For example, if you purchase around ten sets of playing cards (go to a cheap two dollar store), you could learn a few basic games (Snap, Making 10, Playing with Place Value – see my book Engaging Maths: Exploring Number) that could then be differentiated according to the students you are teaching. A simple game of Making 10 could be used from Grade 1 all the way to Grade 6 by simply changing the rules.

Other materials that are a ‘must have’ for beginning teachers are dice and dominoes. There are many simple investigations that could lead from simple explorations with these materials. For example, use the dice to explore probability or play a game of Greedy Pig. Play a traditional game of dominoes before adding a twist to it, or simply ask students to sort the dominoes (students have to select their own criteria for sorting)– an interesting way to gain insight into students’ mathematical thinking and a great opportunity for using mathematical language. Once students have sorted the dominoes conduct an ‘art gallery tour’ and ask other students to see if they can work out how others have sorted out their dominoes. Photograph the sorting and display then on an Interactive Whiteboard for a whole class discussion and reflection…the list goes on!

Another ‘must have’ for beginning teachers is a bank of good quality resource books. Don’t fall into the trap of purchasing Black Line Masters or books full of worksheets to photocopy. You don’t want your students to be disengaged! Books such as my Engaging Maths series (http://engagingmaths.co/teaching-resources/books/ ), or any of Paul Swan’s books or resources (http://www.drpaulswan.com.au/resources/) are a great place to start. Explore some of the excellent free resources available online such as http://nrich.maths.org/teacher-primary and http://illuminations.nctm.org/, but do be aware that some resources produced outside of Australia will need to adapted for the Australian Curriculum: Mathematics.

In my research on student engagement, I found that students would remember what they would recall as a ‘good’ mathematics lesson for a very long period of time. In fact, some of the students in my PhD study talked about a ‘good’ mathematics lesson two years after it had taken place. Whether you are lucky enough to have your own class or have to begin your career as a relief teacher moving from class to class, you can make an impact on the students in your care and the way the view mathematics by being prepared with your ‘toolbox’ of engaging and worthwhile activities.