Tag Archives: professional development

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

 

Setting up Your Students for Mathematical Success : Tips for Teachers

Many children begin the new school year with feelings of fear and anxiety. Will they like their new teacher or teachers? Will the work be difficult? What will the homework be like? As you prepare programming and planning for a new teaching year and new students, give some thought to the strategies and activities you and your students can do in the first few weeks of term to ensure everyone gets the most out of their mathematics lessons for the entire school year. Think about what you can do differently in 2017 to make your work more engaging for both you and your students. The following are some ideas to consider.

  1. Be a positive mathematical role model

I’m sure this won’t come as a surprise, but there are teachers in our schools who actually don’t like maths and don’t like teaching it. Why is this a problem? Student know! This knowledge perpetuates the common misconception that it’s okay to dislike mathematics, and worse still, it’s okay to be considered ‘bad’ at maths.  Unless the teacher is an award-winning actor or actress, it’s really difficult to hide how you feel about a subject – it’s obvious in body language, tone of voice and of course, the way you teach the subject and the resources you use. If you know someone like this, suggest they seek some support from a colleague or colleagues. Often the reason a person dislikes mathematics is related to a lack of confidence.

  1. Get to know your students as learners of mathematics

The foundation of student engagement requires an understanding of students as learners, in other words, the development of positive pedagogical relationships (Attard, 2014). Positive relationships require teachers to understand how their students learn, and where and when they need assistance. It’s also important to provide opportunities for ongoing interactions between you and your students as well as amongst your students.

Another way to get to know your students as learners is to use existing data. For example, if your school takes part in external testing such as PAT, you can use this data as a guide. However, keep in mind that things change quickly when children are young – what they knew or understood three months ago may be very different after a long summer holiday.

A great activity to do in the very first few maths classes of the year is to ask your students to write or create a ‘Maths Autobiography’. If required, provide the students with some sentence starters such as “I think maths is…” “The thing I like best about maths is…” “The thing or things that worry me about maths is…” They could do this in different formats:

  • In a maths journal
  • Making a video
  • Using drawings (great for young children – a drawing can provide lots of information)
  1. Start off on a positive note

Have some fun with your maths lessons. I would strongly recommend that you don’t start the year with a maths test! If you want to do some early assessment, consider using open-ended tasks or some rich mathematical investigations. Often these types of assessments will provide much deeper insights into the abilities of your students. You can even use some maths games (either concrete or digital) to assess the abilities of your students.

A great maths activity for the first lesson of the year is getting-to-know-you-mathematically, where students use a pattern block and then need to go on a hunt to find other students who have specific mathematical attributes. Encourage your students to find someone different for every attribute on the list, and change the list to suit the age and ability of your students. For example, in the younger years you could use illustrations and not words. In the older years, you could make the mathematics more abstract.

  1. Take a fresh look at the curriculum

Even if you’ve been teaching for many years, it’s always good to take a fresh new look at the curriculum at the start of each year. Consider how the Proficiencies or Working Mathematically processes can be the foundation of the content that you’re teaching. For example, how can you make problem solving a central part of your lessons?
Take a close look at the General Capabilities. They provide a perfect foundation for contextual, relevant tasks that allow you to teach mathematics and integrate with other content areas.

  1. Consider the resources you use: Get rid of the worksheets!

Think about using a range of resources in your mathematics teaching. Regardless of their age or ability, children benefit from using concrete manipulatives. Have materials available for students to use when and if they need them. This includes calculators in early primary classrooms, where students can explore patterns in numbers, place value and lots of other powerful concepts using calculators.

Children’s literature is also a great resource. A wonderful book to start off the year is Math Curse by Jon Scieska and Lane Smith. Read the book to your students either in one sitting or bit by bit. There are lots of lesson ideas within the pages. Ask your students to write their own maths curse. It’s a great way to illustrate that mathematics underpins everything we do! It’s also a great way to gain insight into how your students view mathematics and what they understand about mathematics.

  1. How will you use technology in the classroom?

If you don’t already integrate technology into your mathematics lessons, then it’s time to start. Not only is it a curriculum requirement, it is part of students’ everyday lives – we need to make efforts to link students’ lives to what happens in the classroom and one way to do that is by using technology. Whether it’s websites, apps, YouTube videos, screencasting, just make sure that you have a clear purpose for using the technology. What mathematics will your students be learning or practicing, and how will you assess their learning?

  1. Reach out to parents

As challenging as it may be, it’s vital that parents play an active role in your students’ mathematical education. They too may suffer from anxiety around mathematics so it’s helpful to invite them into the classroom or hold mathematics workshops where parents can experience contemporary teaching practices that their students are experiencing at school. Most importantly, you need to communicate to parents that they must try really hard to be positive about mathematics!

These are just a few tips to begin the year with…my next blog post will discuss lesson structure. In the meantime, enjoy the beginning of the school year and:

Be engaged in your teaching.

Engaged teachers = engaged students.

 

 

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.

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.

 

More tips for the new teaching year: Ability grouping and mathematics

A few months ago I posted a blog about ability grouping in the mathematics classroom. I am re-posting the blog here because the beginning of the school year is the perfect opportunity to set up routines and strategies that will promote mathematical learning and ensure the diversities of your new class group are addressed. I strongly recommend flexible grouping in mathematics and I hope this post causes you to think about how you will be grouping your students in 2016.

During the primary years students either experience mathematics lessons within mixed ability classrooms or are ability grouped across or between grade levels. In mixed ability classes and to a lesser degree in ability grouped classrooms teachers often have to cater for a range of students whose previous attainment varies considerably. The gap between low and high achievers is said to increase as students progress through school, with as much difference in performance within year levels as there is between Years 5 and 9 students overall (State of Victoria Department of Education and Training, 2004). This concurs with findings by The Middle Years Numeracy Research Project (Siemon, Virgona, & Corneille, 2001) that cites teachers in the middle years can and should expect a range of up to seven school years in numeracy-related performance. Australian TIMSS and PISA reports show our middle years students, when compared to students in other countries, are not keeping up with some aspects of mathematics (Lokan, Greenwood, & Cresswell, 2001). Among the strategies teachers implement in order to cater to the diverse needs of the classroom is the use of ability grouping and the incorporation of differentiated tasks.

Although there are arguments both in favour and against the use of ability grouping, it is not uncommon for primary and secondary schools in Australia and internationally to use such grouping in mathematics classrooms. The following is an exploration of both arguments. Clarke (2003) maintains teachers need to think carefully about reasons for choosing to place students into groups according to perceived ability. Teachers need to consider the potential impact upon students’ self-esteem, and the ‘self-fulfilling prophecy’ (Brophy 1963, as cited in Clarke, 2003), in which students perform to the level expected of them by their teacher. He concludes that ability grouping is used in mathematics for teacher convenience more than for student benefit. This is a sentiment echoed by Boaler, Wiliam and Brown (2000), who also believe ability grouping is one of the main sources of disaffection.

Ability grouping, such as that which is common in Australian secondary schools, became the focus of a study conducted in the United Kingdom (Boaler, et al., 2000). The grouping of students into ability ‘sets’ emerged as a significant factor that influenced students’ ideas, their responses to mathematics, and their eventual achievement. The study found that students in the school that used ability grouping were significantly disadvantaged by their placement and this disadvantage was not restricted to students in the lower ability groups. Approximately one-third of students in the highest ability groups felt disadvantaged because of high expectations, fast-paced lessons and pressure to succeed. Students from a range of groups were ‘severely disaffected’ by the limits placed upon their attainment. Students reported that they gave up on mathematics once they discovered their teachers had been preparing them for examinations that gave access to only the lowest grades. Large numbers of students, in the study by Boaler et al., experienced difficulties working at the pace of their particular class. For some the pace was too slow, resulting in disengagement, although for others it was too fast, resulting in anxiety. Both responses led to lower levels of achievement.

In addition to the findings above, there is research that claims ability grouping causes behavioural problems for some within the mathematics classroom. Teachers in a study conducted by Ventakatakrishnan and Wiliam (2003) found behavioural problems more common in mixed ability groups than in their fast-track, higher ability group. These behavioural problems were compounded by the weak literacy skills of some individuals in these groups in addition to peer self-management skills. Interestingly, placing students in ‘tracked’ groups had an effect on students’ perceptions of themselves as learners of mathematics. Those who were fast-tracked perceived themselves as ‘doing well’ while those in mixed ability groups perceived themselves as ‘low’ in mathematical ability. The teachers involved in the study also noted they had problems motivating the higher attaining students within the mixed-ability groups – students who had ‘just’ missed out on being placed in the fast tracked group. Ventakatakrishnan and Wiliam also note that mixed-ability grouping decreases the opportunities for higher-achieving students to interact constructively with peers although ability groups have the same effect on lower achieving students. The study found that advantages of grouping by ability are limited and restricted to higher achieving students while causing disadvantage to those who are the lowest attainers.

Although there are advantages and disadvantages in grouping students according to ability, it is also reasonable to expect that a result of such grouping is differences in teacher expectations and instructional techniques. There is a tendency for instruction in lower ability groups to be of a different quality to that of higher ability groups (Ireson & Hallam, 1999). There appears to be a concern that instruction in low ability groups is conceptually simplified with a higher degree of structured, written work, as in the traditional method of teaching mathematics. Higher ability classes appear to include more analytic, critical thinking tasks with pupils allowed greater independence and choice along with opportunities for discussion, reflecting a more contemporary style of mathematics lesson. Based on stereotypes and past experiences, some teachers hold low expectations for low ability groups, further decreasing students’ own expectations and self-esteem, and leading to decreased levels of engagement with mathematics (Ireson & Hallam, 1999).

At the primary level classroom, research suggests students in mixed ability classrooms display more positive attitudes towards school in general (Ashton, 2008; Ofsted, 2008). However, the more common practice of ability grouping in the secondary mathematics classroom is a complex issue. Although it appears to perpetuate the inequities associated with mathematics and the notion of mathematics being an elitist subject, it is often an attempt to address the needs of all students as well as the needs of mathematics teachers.

So what is the answer? Again, my advice is to group flexiblyThere are circumstances that require children to be grouped by ability, and other circumstances where it is more appropriate and beneficial for students to work in mixed groupings, where students can learn from each other. Another reason to have flexibility is that often children may excel in one area of mathematics, but may be challenged in other areas. Those who appear to struggle, may not necessarily struggle with all concepts. The key is knowing your students and their needs across all aspects of the mathematics curriculum, and ensuring that assessment of students’ ability informs teaching and the way students are grouped. And finally, have high expectations of all students!

References:

Ashton, R. (2008). Improving the transfer to secondary school: How every child’s voice can matter. Support for Learning, 23(4), 176-182.

Boaler, J, Wiliam, D, & Brown, M. (2000). Students’ experiences of ability grouping: Disaffection, polarisation and the construction of failure. British Educational Research Journal, 26(5), 631-649.

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.

Ireson, J., & Hallam, S. (1999). Raising standards: Is ability grouping the answer? Oxford Review of Education, 25(3), 343-358.

Lokan, J., Greenwood, L., & Cresswell, J. (2001). 15-up and counting, reading, writing, reasoning. How literate are Australia’s students? The PISA 2000 survey of students’ reading, mathematical and scientific literacy skills. Melbourne: ACER.

Ofsted. (2008). Mathematics: Understanding the score. London: Ofsted.

Siemon, D., Virgona, J., & Corneille, K. (2001). Final report of the middle years numeracy research project. Melbourne, Victoria: RMIT University and the Department of Education and Training (Victoria).

State of Victoria Department of Education and Training. (2004). Middle years of schooling overview of Victorian Research 1998-2004 Retrieved July 7, 2005, from http://www.sofweb.vic.edu.au/mys/docs/research/

Venkatakrishnan, H., & Wiliam, D. (2003). Tracking and mixed-ability grouping in secondary school mathematics classrooms: A case study. British Educational Research Journal, 29(2), 189-204.

 

 

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.

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