Subject: Primary

Catherine Attard continues her guidance about making Maths come alive in your primary classroom…

What does it look like, feel like and sound like when your students are deeply engaged in a mathematics task? What is it like when they are disengaged? In my previous article for the JPL I provided a definition of engagement as a multidimensional construct, consisting of three domains: operative, cognitive and affective. The coming together of the three domains leads to students feeling good, thinking hard, and actively participating in their Mathematics learning (Fair Go Team NSW Department of Education and Training, 2006; Fredericks, Blumenfeld & Paris, 2004).

I also provided a discussion on the importance of establishing positive pedagogical relationships as a foundation for student engagement in Mathematics. In this paper I will move beyond pedagogical relationships to discuss what happens in practice – the pedagogical repertoires that promote positive student engagement.

The following figure (Figure 1) is an excerpt from the Framework for Engagement (FEM), (Attard, 2014), which provides a summary of the critical elements of engaging pedagogies.
 

In an engaging Mathematics classroom pedagogical repertoires mean:   there is substantive conversation about mathematical concepts and their applications to life; tasks are positive, provide opportunity for all students to achieve a level of success and are challenging for all; students are provided an element of choice; technology is embedded and used when appropriate to enhance mathematical understanding through a student-centred approach to learning; the relevance of the mathematics curriculum is explicitly linked to students’ lives outside the classroom and empowers students with the capacity to transform and reform their lives. Mathematics lessons regularly include a variety of tasks that cater to the diverse needs of learners

                         Figure 1: Engaging Repertoires (Attard, 2014)

What do these elements look like in practice? I will expand on each of the points illustrated in Figure 1, and provide some practical advice on how the pedagogies can be applied.

Firstly, how do we provide opportunities for substantive conversations between students and the teacher, and amongst students? If you consider a traditional approach to teaching where the Mathematics lessons are based on a drill and practice approach, it is difficult to see where important mathematical conversations can take place. However, consider an approach where collaboration is encouraged through problem solving and investigation, and where student reflection is an integral aspect of every Mathematics lesson, regardless of the types of tasks and activities implemented.

We must also consider the Working Mathematically components of our K-10 Mathematics Syllabus (Board of Studies New South Wales, 2012). Promoting substantive conversation allows students access to each of the five components: Reasoning, Communicating, Understanding, Fluency and Problem Solving, and provides teachers with opportunities to assess them.

The provision of tasks that provide opportunity for all students to succeed can be a challenge for teachers. It is often difficult to differentiate activities to ensure the diversity of academic ability is not only addressed, but provides sufficient challenge. Learners need to experience success and a sense of achievement if they are to develop a positive attitude towards Mathematics. One way of ensuring all learners are challenged is to provide open-ended, rich tasks rather than closed problems that only have one correct answer or limited opportunities to apply a range of strategies.

Allowing student choice in the Mathematics classroom is an important element of engagement and sends important messages relating to power and control. You can provide choice by having alternative activities within a specific mathematical content area, or you can have students choose how they present their work. Perhaps students may choose to work with concrete materials or interact with appropriate technology. This does not have to occur in every lesson, but allowing students the freedom to make choices every now and then can contribute to their overall engagement.

Technology has become an integral part of contemporary life, and as such, our curriculum requires us to use it meaningfully to enhance the teaching and learning of Mathematics. The challenge with using technology in Mathematics lessons, however, is to ensure that we promote a student-centred approach. If you take for example, the interactive whiteboard, consider how it positions the teacher. The whiteboard is fixed and usually located at the front of the classroom. Any interactivity usually occurs between one person (often the teacher), and the whiteboard. The teacher has control and students are generally passive (Attard & Orlando, 2014). How can this engage all learners?

Many schools have introduced 1:1 laptop or tablet programs, however there is a danger that the devices may be used simply as a replacement for a traditional textbook or as a word-processing device to replace pen and paper. Online Mathematics programs provide some functional improvement to textbooks, however the opportunities for students to collaborate and become involved in substantive mathematical conversations is limited.

Fortunately, the introduction of mobile technologies such as tablets has now provided us with rich opportunities to develop highly engaging, student-centred mathematical activities and tasks.

The use of contemporary technologies in Mathematics lessons provides opportunities to illustrate the relevance of Mathematics and bridge the digital divide between the school and students’ lives outside school. However, it does not necessarily mean students will be engaged. Caution must be taken to ensure the use of technology is driven by good pedagogy, rather than the technology becoming the focus of the lesson. Other ways to illustrate the relevance of Mathematics is to, where possible, embed mathematical concepts into real-life contexts and allow opportunities for students to apply Mathematics in meaningful and purposeful ways. This not only deepens mathematical understanding but will enhance engagement. Of course, as mathematical concepts become more abstract in the senior years it is not always possible or practical to apply all concepts to real-life contexts, however if students have developed a love of Mathematics through quality practices, their engagement will be sustained.

The final aspect of the FEM relating to pedagogical repertoires refers to the provision of variety within Mathematics lessons. Although young students do require some structure, variety can be provided within that structure. For example, in the primary classroom children can be presented with a range of tasks that use a range of resources. Sometimes Mathematics lessons can be conducted outside the classroom – consider running a maths trail at your school where students can participate in interesting mathematical investigations based upon their physical surroundings.  Explore the use of tools such as Thinkers’ Keys (Attard, 2013) to provide Mathematics tasks that are open-ended and creative, and set homework that takes advantage of the Mathematics in students’ lives, rather than drill and practice activities.

I have provided a brief exploration of engaging pedagogies that are listed in the Framework for Engagement with Mathematics (FEM), (Attard, 2014). Engagement with Mathematics during the compulsory years of schooling is critical if students are to develop an appreciation for and understanding of the value of Mathematics learning. Students who are engaged are more likely to learn, find the experience of schooling more rewarding, and more likely to continue with higher education. How can you adapt your practices so that your students value the Mathematics they are learning and see connections between the Mathematics they do at school and their own lives beyond the classroom now and in the future?

References:

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

Attard, C. (2013). Engaging maths: Higher order thinking with thinkers’ keys. Modern Teaching Aids: Brookvale

Attard C, & Orlando J, 2014, Early career teachers, mathematics and technology: device conflict and emerging mathematical knowledge. In J. Anderson, M. Cavanagh, & A. Prescott, Curriculum in Focus: Research Guided Practice, proceedings of the Mathematics Education Research Group of Australasia annual conference, pp 71-78. MERGA: Sydney

Board of Studies New South Wales. (2012). Mathematics K-10 syllabus.   Retrieved from http://syllabus.bos.nsw.edu.au/

Fair Go Team NSW Department of Education and Training. (2006). School is for me: pathways to student engagement. Sydney: NSW Department of Education and Training, Sydney, Australia.

  Fredricks, J. A., Blumenfeld, P. C., & Paris, A. H. (2004). School engagement: Potential of the concept, state of the evidence. Review of Educational Research, 74(1), 59 -110

  Dr Catherine Attard worked as a school teacher and proceeded to complete a PhD on student engagement. She has been a part of the Fair Go Project Team at the University of Western Sydney. She is also editor of the journal Australian Primary Mathematics Classroom.

Catherine Attard conducts a weekly blog at http://engagingmaths.co/about/?blogsub=confirming#blog_subscription-3  that has a number of resources that teachers are able to access and use.”

Catherine Attard explores some strategies to increase student engagement in Maths …

“I like having a teacher who is really passionate about maths”: Getting students to engage with mathematics through positive pedagogical relationships

How often do teachers of Mathematics hear the phrase “why do I need to learn this?” or “I’m no good at Maths”? Many people attribute anxiety or a dislike of Mathematics to their experiences during the middle years of schooling (Years 5 to 8) and although students are influenced to some degree by parents and peers, it is the teacher who has the most influence on students’ engagement with mathematics. This article explores the construct of engagement as it relates to Mathematics, and suggests that for deep and sustained engagement to occur, positive pedagogical relationships, the interpersonal relationships between teachers and students that optimise engagement, must first be established.

Defining engagement

As teachers, we use the term ‘engagement’ often, but do we really understand what real engagement looks like? When we see students who are ‘on task’, are they engaged, or are they just involved in busy work, and in getting the task done? Consider the difference between students who are ‘on task’, and students who ‘in task’. When students are ‘in task’, their minds and bodies are focused on what they are doing. They might be participating in substantive dialogue about the topic, or they might be working in silence, thinking deeply about Mathematics they are involved in – either way, they are engaged.

Many definitions of engagement are found in education literature. Some provide a narrow view that relates only to behaviour and participation. Others provide a deeper understanding that is multi-dimensional. Fredricks, Blumenfeld and Paris (2004), define engagement as a deeper student relationship with classroom work, multi-faceted and operating at cognitive, emotional, and behavioural levels. In this paper, I draw on work of the Fair Go Project (Fair Go Team NSW Department of Education and Training, 2006) and define engagement as the coming together of three facets – cognitive, operative, and affective, which leads to children valuing and enjoying, and actively involved with school mathematics, and seeing connections between the Mathematics they do at school, and their own lives beyond the classroom now and in the future.

Pedagogical relationships and mathematics

This paper is informed by a longitudinal study on the influences on engagement (for a more in depth description see Attard, 2011, 2013, in print). In the study, data were collected from a group of 20 children across three years of their schooling from Year 6 to Year 8. The major selection criterion for participation in this project was that the students had to identify themselves as being engaged with Mathematics (through the use of a Motivation and Engagement Scale (Martin, 2008).  Data were collected through individual student and teacher interviews, student focus groups, and classroom observations.

During the first phase of the study when the students were still attending primary school, they identified their current teacher as someone they perceived to be a good Mathematics teacher. They articulated several attributes directly relating to the pedagogical relationships the teacher had formed with her students, such as her ability to cater to individual needs through the differentiation of tasks, and her modeling of enthusiasm and passion towards Mathematics. Comments such as these were typical: “I like having a teacher who is really passionate about Maths” (Alison, Year 6), and “…while you’re doing the work she also has fun teaching the Maths as well” (Tenille, Year 6).

In the second phase of the study, things changed for this group of students. They began their secondary education, at a new school that was significantly different at the time from traditional secondary schools. At the time the school identified itself as a ‘ground breaking’ learning community in relation to its multi-disciplinary approach to curriculum, large open teaching spaces and a teaching structure that saw a group of Mathematics teachers rotate amongst classes, which meant each class group did not have one allocated teacher and saw each teacher every fourth lesson. These structures were not conducive to building relationships – the teachers had very limited opportunities to identify student needs and abilities, and as a result, students became disengaged: “everyone’s excited when there’s no Maths. I think it’s because, not having someone explain it to you and you don’t get it. If you don’t get it that means you don’t like it” (Kristy, Year 7).

Fortunately circumstances improved for the students in Year 8. Teachers were allocated a class group and the students were back on the path to engagement. They felt that they were now seen as individuals rather than a collective, and teachers cared more about their learning. They also felt that if they required assistance from their teachers, they felt safe in asking for help and felt the teachers now wanted to help them. The increased opportunity to develop pedagogical relationships also improved the level of feedback students received, which began to re-build their confidence as well as their engagement.

During the course of the study the students experienced a wide range of teaching and learning situations that resulted in significant fluctuations of their engagement levels. Although the data overwhelmingly confirmed the teacher was the strongest influence on these students’ engagement, this influence appeared to be complex, consisting of two separate yet inter-related elements: pedagogical relationships and pedagogical repertoires. Pedagogical repertoires refer to the day-to-day teaching practices employed by the teacher.

Results of this study suggest that it is difficult for students to engage with Mathematics without a foundation of strong pedagogical relationships. Positive pedagogical relationships exist when:

• students’ backgrounds and pre-existing knowledge are acknowledged and contribute to the learning of others;
• interaction among students and between teacher and students is continuous;
• the teacher models enthusiasm and an enjoyment of Mathematics and has a strong Pedagogical Content Knowledge;
• the teacher is aware of each student’s abilities and learning needs; and
• feedback to students is constructive, purposeful and timely.

It can also be argued that it is through engaging pedagogies that positive pedagogical relationships are developed, highlighting the connections between relationships and engaging repertoires. So what are considered engaging pedagogies in the Mathematics classroom? These will be explored in the next issue of The Journal of Professional Learning.

Catherine Attard worked as a school teacher and proceeded to complete a PhD on student engagement. She has been a part of the Fair Go Project Team at the University of Western Sydney. She is also editor of the journal Australian Primary Mathematics Classroom.

Catherine Attard, University of Western Sydney
c.attard@uws.edu.au

References:

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. (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.
Attard, C. (in print). “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.
Fair Go Team NSW Department of Education and Training. (2006). School is for me: pathways to student engagement. Sydney: NSW Department of Education and Training, Sydney, Australia.
Fredricks, J. A., Blumenfeld, P. C., & Paris, A. H. (2004). School engagement: Potential of the concept, state of the evidence. Review of Educational Research, 74(1), 59 -110.
Martin, A. J. (2008). Motivation and engagement Scale: High school (MES-HS) test user manual. Sydney: Lifelong Achievement Group.