Tag Archives: professional development

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.

 

 

 

 

Promoting Creative and Critical thinking in Mathematics and Numeracy

What is critical and creative thinking, and why is it so important in mathematics and numeracy education?

Numeracy is often defined as the ability to apply mathematics in the context of day to day life. However, the term ‘critical numeracy’ implies much more. One of the most basic reasons for learning mathematics is to be able to apply mathematical skills and knowledge to solve both simple and complex problems, and, more than just allowing us to navigate our lives through a mathematical lens, being numerate allows us to make our world a better place.

The mathematics curriculum in Australia provides teachers with the perfect opportunity to teach mathematics through critical and creative thinking. In fact, it’s mandated. Consider the core processes of the curriculum. The Australian Curriculum (ACARA, 2017), requires teachers to address four proficiencies: Problem Solving, Reasoning, Fluency, and Understanding. Problem solving and reasoning require critical and creative thinking (). This requirement is emphasised more heavily in New South wales, through the graphical representation of the mathematics syllabus content , which strategically places Working Mathematically (the proficiencies in NSW) and problem solving, at its core. Alongside the mathematics curriculum, we also have the General Capabilities, one of which is Critical and Creative Thinking – there’s no excuse!

Critical and creative thinking need to be embedded in every mathematics lesson. Why? When we embed critical and creative thinking, we transform learning from disjointed, memorisation of facts, to sense-making mathematics. Learning becomes more meaningful and purposeful for students.

How and when do we embed critical and creative thinking?

There are many tools and many methods of promoting thinking. Using a range of problem solving activities is a good place to start, but you might want to also use some shorter activities and some extended activities. Open-ended tasks are easy to implement, allow all learners the opportunity to achieve success, and allow for critical thinking and creativity. Tools such as Bloom’s Taxonomy and Thinkers Keys  are also very worthwhile tasks. For good mathematical problems go to the nrich website. For more extended mathematical investigations and a wonderful array of rich tasks, my favourite resource is Maths300  (this is subscription based, but well worth the money). All of the above activities can be used in class and/or for homework, as lesson starters or within the body of a lesson.

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Will critical and creative thinking take time away from teaching basic concepts?

No, we need to teach mathematics in a way that has meaning and relevance, rather than through isolated topics. Therefore, teaching through problem-solving rather than for problem-solving. A classroom that promotes and critical and creative thinking provides opportunities for:

  • higher-level thinking within authentic and meaningful contexts;
  • complex problem solving;
  • open-ended responses; and
  • substantive dialogue and interaction.

Who should be engaging in critical and creative thinking?

Is it just for students? No! There are lots of reasons that teachers should be engaged with critical and creative thinking. First, it’s important that we model this type of thinking for our students. Often students see mathematics as black or white, right or wrong. They need to learn to question, to be critical, and to be creative. They need to feel they have permission to engage in exploration and investigation. They need to move from consumers to producers of mathematics.

Secondly, teachers need to think critically and creatively about their practice as teachers of mathematics. We need to be reflective practitioners who constantly evaluate our work, questioning curriculum and practice, including assessment, student grouping, the use of technology, and our beliefs of how children best learn mathematics.

Critical and creative thinking is something we cannot ignore if we want our students to be prepared for a workforce and world that is constantly changing. Not only does it equip then for the future, it promotes higher levels of student engagement, and makes mathematics more relevant and meaningful.

How will you and your students engage in critical and creative thinking?

 

 

 

 

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.