# Are you a beginning teacher? What’s in your maths toolbox?

Very recently one of my children began a career as a primary teacher. Like most early career teachers, she has had to begin working as a casual relief teacher. Fortunately for her, she has a ready supply of resources and mathematics activities (thanks to Mum) for those days when she walks into a classroom and has to deliver a day full of engaging activities. However, 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 you may never have met before?

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 and you want to be called back for more work! 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 early 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. Although you might only be in a classroom for a very short time while you begin your career as a relief teacher, 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.

# Professional Learning and Primary Mathematics: Engaging teachers to engage students

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

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

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

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

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

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

M

References:

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

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

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

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

Teachers.

# “If you like the teacher, you’ll ‘get’ maths more”: Students talk about good mathematics teachers

This post was originally published in 2010 on the UWS 21st Century Learning Blog. The discussion relates to my PhD research on the influences on student engagement in maths during the middle years of school and findings have subsequently been published in academic journals (see, for example, Attard 2011, 2012). I thought it would be interesting to revisit since things don’t seem to have changed much in relation to the issue of students ‘turning off’ maths.

Many students during the middle years of schooling (Year 5 to Year 8 in New South Wales) are experiencing emotional, social, physical, and cognitive changes that must be dealt with in the mathematics classroom. Mathematics curriculum and instruction must address the particular needs of these students because so many jobs and indeed the demands of everyday living now and in the future, require complex mathematical thinking. Over the last 20 years research has overwhelming documented an increasingly smaller percentage of students pursuing the study of mathematics at upper secondary level and beyond. The choice not to pursue mathematics has been seriously influenced by students’ attitudes towards and performance in mathematics, in turn deeply shaped by school mathematical experiences and the teaching they experienced in school (Nardi & Steward, 2003).

So, what makes a good mathematics teacher? There are several frameworks that address ‘good’ teaching including the Quality Teaching Framework (NSW Department of Education and Training, 2003) and the Standards for Excellence in Teaching Mathematics in Australian schools (Australian Association of Mathematics Teachers [AAMT], 2006). But how do the frameworks compare to what students think about the qualities of a good mathematics teacher? My PhD thesis was a longitudinal study on engagement in middle years mathematics and early in the study I asked a group of 20 Year 6 students at a Western Sydney school to name the qualities that make a ‘good’ mathematics teacher. The students perceived a good maths teacher to be someone who:

• is passionate about teaching mathematics;
• responds to students’ individual needs;
• gives clear explanations;
• uses scaffolding rather than providing answers;
• encourages positive attitudes towards mathematics; and
• shows an awareness of each students’ prior knowledge.

The study followed the same group of students through their transition to high school, and into Year 8. During their time in secondary school, the students’ experiences included a wide range of practices and teachers, and significant exposure to technology within the mathematics classroom (a one-to-one laptop program). Despite being exposed to an integrated curriculum and a school that was purpose built to cater for ‘next-practice’ learning and teaching, it was the teachers and the relationships that were developed within the classroom that had the most significant impact on student engagement in mathematics. It appeared that the introduction of technology during Year 7 had removed many of the opportunities for student/teacher and student/student interaction that are such an integral aspect of learning mathematics. During their time in Year 7 the students experienced lowered engagement as a result.

Two years after the study began, when the students were in Year 8, their secondary school underwent some significant changes in terms of its curriculum delivery (no longer integrated) and the use of technology in the mathematics classrooms. There was significantly less reliance technology and a much heavier emphasis on direct instruction. The students began to build relationships with their teachers and in turn, this saw their engagement in mathematics begin to build. The students spoke about how they now felt their teachers ‘cared’ about them and ‘knew’ them. This comment from one of the students indicates the importance of positive student/teacher relationships: “if you like the teacher, you’ll get maths more. You’ll know what’s going on more.”

Although some of the pedagogies these students experienced during the study were not necessarily considered ‘best practice’, it appears the students were able to overcome this where it was difficult for them to overcome the lack of positive interactions with some of their mathematics teachers. It is proposed that regardless of the school context, students in the middle years have a need for positive teacher-student and student-student relationships as a foundation for engagement in mathematics. This relationship is built on an understanding of students and their learning needs. Unless such a relationship exists, other pedagogical practices including the use of technology may not sustain engagement in mathematics during the middle years.

Attard, C. (2011). “My favourite subject is maths. For some reason no-one really agrees with me”: Student perspectives of mathematics teaching and learning in the upper primary classroom. Mathematics Education Research Journal, 23(3), 363-377.

Attard, C. (2012). The influence of pedagogy on student engagement with mathematics during the middle years of schooling. In A. L. White & U. H. Cheah (Eds.), Transforming School Mathematics Education in the 21st Century (pp. 140-157). Penang: SEAMEO RECSAM.

Association of Mathematics Teachers [AAMT]. (2006). Standards of Excellence in Teaching Mathematics in Australian Schools. Adelaide: Australian Association of Mathematics Teachers.

Nardi, E., & Steward, S. (2003). Is mathematics T.I.R.E.D? A profile of quiet disaffection in the secondary mathematics classroom. British Educational Research Journal, 29(3), 345-367

NSW Department of Education and Training. (2003). Quality Teaching in NSW Public Schools. Sydney: Professional Support and Curriculum Directorate.

# Making mathematics relevant: Putting the ‘home’ back into homework

I wrote this post a couple of years ago and it was published on the UWS 21st Century Learning Blog and a slightly modified version was republished in the online journal, Curriculum Leadership. I am republishing it again here as I think the message is as important as ever!

The start of a new school year is a perfect time to reflect on and perhaps make adjustments to the pedagogical practices we use in our day-to-day teaching of mathematics. If our goal is to produce successful learners of mathematics and students who choose to continue the study of mathematics beyond the mandatory years, then we need to ensure our students are engaged and motivated to learn both within and beyond the classroom. The purpose of this post is to argue that if we need to set mathematics homework, it should reflect ‘best’ practice and should provide students with opportunities to extend their learning in ways that highlight the relevance of mathematics in their lives outside school while practising and applying mathematical concepts learned within the classroom.

The pedagogical practices employed within mathematics classrooms cover a broad spectrum that ranges from ‘traditional’, text book based lessons, to more contemporary constructivist approaches that include rich problem solving and investigation based lessons, or a combination of both. When asked to recall a typical mathematics lessons, many people cite a traditional, teacher-centred approach in which a routine of teacher demonstration, student practice using multiple examples from a text book and then further multiple, text book generated questions are provided for homework (Even & Tirosh, 2008; Goos, 2004; Ricks, 2009).

Traditional, teacher-centred approaches have been found to result in low levels of motivation and engagement among students (Boaler, 2009), and although there is an abundance of research that promotes a more constructivist, student-centred approach, one study found traditional practices continue to dominate, occurring more often than student-centred approaches in mathematics education (McKinney, Cappell, Berry, & Hickman, 2009). If many teachers are continuing to teach in such way, then it is likely that many set mathematics homework that continues to be repetitious and merely a provision of further practice of concepts learned during lessons.

While it is critical that students are provided with many opportunities to practice mathematical concepts learned at school, perhaps we need to consider how homework can be structured so that it is motivating, engaging, challenging, and most importantly, relevant. One of the most common complaints from students with regard to mathematics education is the lack of relevance to their lives outside the school. It is an expectation of today’s students that learning is meaningful and makes sense to them (Australian Association of Mathematics Teachers, 2009; NSW Department of Education and Training, 2003). There needs to be a directional shift in the way we establish relevance and applicability in mathematical engagement because the type of mathematics that students use outside school is often radically different in content and approach to the mathematics they encounter in school (Lowrie, 2004). Homework provides the perfect opportunity for students to make connections between school mathematics and ‘home’ mathematics.

So what would motivating, engaging, challenging and relevant mathematics homework look like? That all depends on you and your imagination! When I was a Year 6 classroom teacher, one of the most popular homework activities amongst my students was based on Tony Ryan’s Thinker’s Keys. Students would be provided with a range of activities that included an element of choice. Each activity was much more creative than a typical mathematics task yet provided challenge for students and an opportunity for them to apply their understandings of mathematical concepts. For example, in a range of activities based on multiplication and division, one of the tasks, the Question Key, required students to respond to the following prompt: How is multiplication related to division? Write an explanation appropriate for a Year 4 child. Use an example to show how multiplication is related to division. The Brainstorming Key required students to make links to real-life: Brainstorm examples of everyday situations that require you to use multiplication and division. Record your responses in a mind map.

Another great idea for homework with younger students is to have them take photographs of their home environment that directly relate to the mathematics being learned at school. For example, in a study of 3D objects, students could photograph and label 3D objects found in their homes. Students could draw floor plans of their homes when learning about scale, position, area and perimeter. At a higher level, students could solve real-life problems that require the application of a number of mathematical concepts such as selecting the best mobile phone plan, comparison of household bills, budgeting, etc.

How much work would be involved in planning this type of homework? One approach to planning homework tasks would be to work within stage/grade teams to design a bank of tasks that could be re-used from one year to another. As with many things, once you begin to plan and design rich homework tasks, it gets easier. Often ideas also come from the students. Consider tasks that vary in length from quick, one-day homework tasks to longer term tasks that may take two or three weeks from students to complete. Also consider your priority: quality or quantity?

How hard would it be to assess and provide feedback on homework tasks? If we expect students to engage with and complete their mathematics homework, then we must provide constructive feedback. In my previous research on student engagement with mathematics, some students were frustrated when their teacher did not mark homework: “If they don’t give you feedback then you don’t know if you’re doing it right or wrong, or if you need improving or anything.” Marking and providing feedback on homework should not be viewed as a burden but rather a critical part of the teaching and learning process. The way feedback is delivered depends on the nature of the task.

Finally, when setting homework, we need to reflect on our purpose for doing so. Are we doing it to keep the parents happy and the students busy, or do we want to support students’ learning in a seamless link between school and home, providing opportunities for students to apply concepts in real-world situations?

References:

Australian Association of Mathematics Teachers. (2009). School mathematics for the 21st century: Some key influences. Adelaide, S.A.: AAMT Inc.

Boaler, J. (2009). The elephant in the classroom: Helping children learn and love maths. London: Souvenir Press Ltd.

Even, R., & Tirosh, D. (2008). Teacher knowledge and understanding of students’ mathematical learning and thinking. In L. D. English (Ed.), Handbook of international research in mathematics education (2nd ed., pp. 202-222). New York: Routledge.

Goos, M. (2004). Learning mathematics in a classroom community of inquiry. Journal for Research in Mathematics Education, 35(4), 258-291.

Lowrie, T. (2004, 4-5 December). Making mathematics meaningful, realistic and personalised: Changing the direction of relevance and applicability. Paper presented at the Mathematical Association of Victoria Annual Conference 2004: Towards Excellence in Mathematics, Monash University, Clayton, Vic.

McKinney, S., Cappell, S., Berry, R. Q., & Hickman, B. T. (2009). An examination of the instructional practices of mathematics teachers in urban schools. Preventing School Failure, 53(4), 278-284.

NSW Department of Education and Training. (2003). Quality Teaching in NSW Public Schools. Sydney: Professional Support and Curriculum Directorate.

Ricks, T. E. (2009). Mathematics is motivating. The Mathematics Educator, 19(2), 2-9.

# New Years Resolutions, primary mathematics, and technology

Welcome to the first blog post on my Engaging Maths site! I thought I’d try setting up a website that will host some of my resources, thoughts, videos, ideas and anything else I think of! I hope you enjoy 🙂

This year, for the first time, I volunteered to teach one of my primary mathematics units during the summer school session. That meant that I had to begin teaching in the first week of January….a shock to the system. As challenging as it was to summon my enthusiasm, the first week has been excellent and working with keen pre-service primary teachers has got me thinking about all the teachers still on holidays. Most of you would have already started thinking about and perhaps planning for your new class in 2015. I wonder if anyone made a new year’s resolution relating to teaching? I always enjoyed that period of planning new things to do with a fresh group of students, in fact, I still do, but it’s at the tertiary level. This year I am committed to integrating even more technology into teaching and learning, and making more use of the mobile technologies that students bring with them. Having said that, I need to make sure my use of technology is going to enhance what I do, and not distract students.

Can I use technology to make mathematics more relevant, and can this be replicated in primary mathematics classrooms? I think the answer is yes! An example of how I have done this occurred two days ago with my university students through the use of a maths trail. If you don’t know what a maths trail is, it’s really like an outdoor adventure/treasure hunt where students are taken out of the school environment and using maps, photographs, and all sorts of equipment, get to follow a trail and do some really engaging, relevant and real life mathematics activities. Here is an example from the maths trail I have designed at the UWS Bankstown campus based on the giant rabbit sculpture that sits outside the pre-school on campus (the students are provided with a photograph to help them find the site):

Somewhere on campus is a giant rabbit…..can you locate it?

1. How many times bigger than a normal rabbit do you think it is? Explain the mathematics you used to work this out?
2. If the university wanted to build a sculpture of a human adult to stand beside the rabbit, how tall would the sculpture have to be? Use your iPad to record the group’s working out and your findings.

Once the students have finished the maths trail and are back in the classroom, a follow-up activity based on the giant rabbit tasks is provided along with a QR Code:

If two newborn rabbits (one male and one female) are put in a pen, how many rabbits would be in the pen after one year? How many would be in the pen after 18 months?

Use the QR Code for extra help:

That is just one example of a number of different maths trail ‘stations’. The task above could be replicated in any number of ways, with many benefits for students and teachers. First, the original maths trail tasks require students to apply their knowledge, understanding, and higher order thinking skills rather than complete a simple computation or regurgitate a set of rules or facts. Secondly, the tasks are open-ended, allowing for creativity. The use of the iPad on site to record students’ responses promotes discussion and the use of mathematical language, and takes away the burden of having to use pen and paper to record absolutely everything – it can all be done on one device. Extending the task through the use of an interesting problem and some help (you need to access the QR code), allows you to promote sustained engagement.

So that’s one way I have kept my new year’s resolution to incorporate more technology into the teaching and learning of mathematics….more ideas coming soon!