During my pre-practicum visit, my cooperating teacher provided me with a copy of the term four program and asked what areas I would like to teach. One subject I chose was volume and capacity, not because I felt I had expert knowledge in this area, but because I believed I needed experience in this aspect of mathematics instruction. Over the four weeks, I taught six lessons about capacity to year 3 and in the process faced many unexpected challenges. I found myself questioning my effectiveness, content knowledge and patience, yet believed that I have emerged from these lessons with a better understanding of myself as an educator.
My first lesson on capacity followed on from an introduction to the topic given by my cooperating teacher. I had planned the lesson around stage 1 outcomes, as I wanted to ensure that all students were ready for stage 2 content. I had noticed in another maths lesson that many students were working beyond expectations for year three, while others (including some special needs students) needed considerable help. I realised that teaching capacity would allow me to use a range of materials and teaching styles, that would hopefully reach all learners. The school incorporated Gardner’s Multiple Intelligences, and Bloom’s Taxonomy into many of its programs – I hoped to do the same with my unit. I had planned my lesson in detail and my cooperating teacher had given me some pointers as to where I would need to consider behaviour management strategies. I had identified key focus areas for my lesson – estimation, comparison, justification, measurement and recording. I knew that in the early stages of teaching about measurement, it is important that students share estimation strategies, often using the language of comparison ( NSW Department of Education and Training: Curriculum K-12 Directorate, 2004) and had planned for students to work in pairs.
During the introduction to my lesson, I found that the same students were able to answer all of my questions, as well as discuss ideas beyond what I had expected. This threw me, as although they were moving themselves through my lesson sequence, they were leaving the rest of the class behind. I struggled to bring the rest of the class up to speed while still maintaining everyone’s interest. I found myself moving quickly through instructions that needed more explicit demonstration. I paired students according to the container they had chosen for estimation, but my lack of knowledge about social groups, behaviour and ability quickly became apparent. I had inadvertently paired the more capable students and sent them off to work while the slower workers were at their desks last. I found out later that I had paired several students who were ‘enemies’. I also discovered that as I paired the last few students, I had left myself with the more difficult children. I had no idea how to place them.
The lesson was, in many ways, a disaster. Students had no idea of how to record their answers. They changed their estimation to the correct answer after measuring. Some students simply played with their materials, or fought, while others complained that they could not accurately measure capacity without continuous materials. I realised that my understanding of the developmental sequence for this subject needed serious revision. I had allowed several students to lead the direction of the lesson, due to both knowledge and behaviour, and as result had left many students behind. My confidence at the end of this lesson was low, and I dreaded the having to teach the next lesson.
The feedback from my cooperating teacher was to focus on behaviour management and understanding the developmental sequence for learning about capacity. I created an overview of the students in the class and as the week went by, attempted to identify their areas of need. Examining friendship groups helped me to see who I could trust to support the more needy students and closely watching behaviour allowed me to identify disruptive patterns. As I only had six girls in a class of 21, I also realised that I needed to try not to always group them together. I was nervous about grouping the students the second time around, but took a more strategic approach. I created heterogenous cooperative groups (Latham, Blaise, Dole, Faulkner, Lang & Malone, 2007) that were based on personality, learning needs and abilities. The aim was to promote positive interdependence and individual accountability (McInerney and McInerney 2006). I took the time prior to the lesson to ask students whom they worked well with – this proved to be an effective technique, especially when grouping my students with anxiety, oppositional defiance and learning disabilities.
The school had a great focus on students taking control of their own learning and making positive choices, so I decided to work with aspects of the positive behaviour leadership model and Dreikurs democratic discipline model (Edwards and Watts, 2004). At the beginning of my next lesson I asked students to consider their learning space, moving away from people or objects that may distract them. We discussed the idea of taking control of our own learning and helping each other to learn. I re-introduced the idea of capacity, focusing on the necessary vocabulary and emphasising the concept of mathematical reasoning (NSW Board of Studies, 2002). I had spent a considerable amount of time acquainting myself with the levels of development for learning about volume and capacity (NSW Department of Education and Training: Curriculum K-12 Directorate, 2004, NSW Board of Studies, 2002) and found myself more able to determine the learning needs of particular students. I focused on direct instruction – explicit instruction, handover of responsibility and a focus on problem solving (McInerney & McInerney 2006, Dufficy 2005). The lesson worked well, and the majority of groups were able to complete the task with few problems. I was able to work with the groups who needed the most help, although this had its problems as I lost focus on the class as a whole. Learning where to position myself in order to see everyone took some practice.
Reflecting on my final lesson, I felt as though I had made great progress. Although I was a little apprehensive about the students using water to test capacity, I enjoyed the lesson and was confidant. I tried to regard the mistakes I had made as opportunities for learning (Groundwater-Smith, Ewing & Le Cornu, 2003), rather than signs of failure. Discussing my concerns with other teachers had helped to alleviate some of the pressure. Alongside this, I had also witnessed first hand the benefits of cooperative teaching (NSW Institute of Teaching, n.d). The year three classes were often combined for certain lesson and I was given the opportunity to contribute to joint planning sessions. The other teachers greatly assisted me with their understanding of content, student needs and behaviour management. Feedback from these teachers assisted me with the grouping of students for my final lesson. After each question, I allowed the students to discuss in pairs before reporting back to the class. This allowed them to formulate their understandings, and present when ready. After repeating this several times, I was able to see which students were working well together and grouped them accordingly. This technique also allowed me to step back and watch what direction the lesson was taking. At one point, after introducing a new concept, the silence of the class made me think I had confused them. However during a feedback session, my cooperating teacher reassured me that this was the sound of engagement – of all students taking the time to ponder the question posed.
I found myself taking a lot more ownership of the class during my third and fourth weeks, and believe that this was due to what I had learned during my capacity lessons. I learnt not to be afraid of feedback, to take it as an invaluable tool for development rather than a personal criticism. I learnt so much about my students in such a short period of time, mostly due the support and guidance of my cooperating teacher. She helped me to make the links between theory and practice – and showed that teaching can also be about pure luck and experience. I came to prac with little confidence, as I felt that the more I learned, the less I knew. The feeling of being overwhelmed did not entirely dissipate but became more manageable with every new experience. I feel incredibly grateful to have developed not only as a teacher, but as a learner too.
Edwards, C & Watts, V. (2004). Classroom discipline and management: An australasian perspective. Milton: John Wiley and Sons Australia, Ltd.
Dufficy, P. (2005). Designing learning for diverse classrooms. Sydney: Primary English Teaching Association
Groundwater-Smith, S., Ewing, R. & Le Cornu, R. (2003) Teaching: Challenges and dilemmas. Southbank: Thomson
Latham, G., Blaise, M., Dole, S., Faulkner, J., Lang, J., & Malone, K. (2007). Learning to teach: New times, new practices. South Melbourne: Oxford University Press
McInerney & McInerney (2006) Educational psychology: Constructing learning (4th ed). Frenchs Forest: Pearson Education Australia
NSW Board Of Studies (2002). Mathematics K-6 Syllabus. Sydney: Author
NSW Department of Education and Training: Curriculum K-12 Directorate, (2004). Teaching measurement: Stage 2 and stage 3. Sydney: Author
NSW Institute of Teachers (n.d). Professional teaching standards. Retrieved 11th November 2008 from: http://www.nswteachers.nsw.edu.au/Main-Professional-Teaching-Standards.html