Element 6 Milestones and Evidence



I HAVE… continually aimed to improve upon my own teaching over the past four years of my University degree. For instance, I have taken into consideration advice from cooperating teachers during practicums, I seek to increase professional knowledge through doing readings and training courses, as well as regularly reflecting upon my own teaching practice. My written lesson plans all include evaluation questions which allow me as a teacher to reflect on how inclusive the lesson was to all students, whether more scaffolding was needed and suggestions for future lessons. I have also written a critical reflection on the use of student grouping over three linked lessons, which demonstrates my ability to honestly analyse my teaching practice with the aim of improving it.            

 I have undertaken a number of courses for Professional Development in order to enhance my teaching knowledge and practice, including obtaining my Senior First Aid Certificate, Electoral Education Course by the Australian Electoral Commission, and SPARK training (St Vincent de Paul Society Assisting Refugee Kids). I have also complemented my time studying to be a teacher at University with teaching a Sunday School class every Sunday, as well as involvement in Scripture Teaching for a year.             Other ways in which I have improved professional knowledge and practice include collaboration with other pre-service teachers in designing Units of Work, preparing presentations on educational topics, writing research papers to explore subject content and becoming a member of professional teaching organizations such as E:Lit (formerly PETA).


 I WILL…seek to be informed of more opportunities for Professional Development. During practicum I will (to the extent I can), participate in staff meetings and Professional Development seminars as they arise. I will enquire into courses I could undertake during the University break to improve my teaching practice between practicum experiences this year. I will also seek to write written reflections on my own teaching and have the cooperating teacher do the same in order that I may consider ways in which to move forward as a quality teacher.   

GOAL FOR PRACTICUM: Utilise all opportunities for Professional Development, including staff meetings, reflection on my own teaching and accepting feedback from my Cooperating Teacher.  


 I NEED…to access information about Professional Development seminars for the second half of 2009 across a range of KLA’s. I need to allocate a specific time each week during practicum to use for reflection on my own teaching and to consider feedback from my Cooperating Teacher. It is through reflective practice such as this that my educational philosophy can be challenged and reconstructed (Latham et al., 2006, p. 97). I need to continually seek to improve my professional knowledge and practice in order to be a lifelong learner (Peters, 2001).                              

With this in mind, I can take the following steps towards my goals for practicum: 

1.      Consider professional development opportunities before practicum. Use available time before practicum to consult relevant resources which can enhance my time on practicum.

2.      Attend staff meetings and any professional development seminars offered during practicum.

3.      Keep a reflective journal which incorporates feedback from my Cooperating Teacher.

4.      Continue to read professional articles and use these to improve professional knowledge.

 I BELIEVE… Teachers are learners, an idea which is unpacked in detail in “Teaching Challenges and Dilemmas” (Groundwater-Smith, 2003, p. 152). I believe teachers should aim to improve the quality of their teaching through reflection, feedback and increased professional knowledge. Teachers have the responsibility of providing a quality education for their students, and must therefore identify mistakes, identify successes and identify quality pedagogy in their own (and other’s) teaching. Using documents such as the Quality Teaching Framework (NSW Department of Education and Training, 2003) as the basis of reflection on teaching is an easy and essential aspect of personal development. I believe teachers should maintain and feed the desire to continue to learn about teaching and learning, a process which is never-ending.

Element 6 Evidence

Annotations for the evidence 

I  have included as evidence of my achievement of Element 6: 

An excerpt of a Critical Reflection on my use of student grouping in a lesson. This demonstrates my ability to honestly reflect on my own teaching for improvement. As a teacher, it shows I can recognise mistakes and successes and use these to inform future teaching. Critical reflection is an important part of continuing to improve professional practice and this piece of evidence shows my capability to achieve this. 6.1.1 

A research paper focused on the content and teaching strategies of the Mathematics topic Fractions. This shows I have the capacity to contribute to teaching as a professional community by presenting conceptual ideas of Mathematics, common student misconceptions of Fractions and providing practical tasks based on research and theory to assist teaching and learning. The paper was designed for entry into a Professional Journal for Mathematics teachers in Australia. 6.1.6, 6.1.7 

Two examples of Professional Development Certificates I have obtained within the past year. The first is a SPARK certificate demonstrating my attendance at the training course which incorporated refugee training tips and Child Protection. I will be using the skills taught on this course in Term 3, 2009 by working in a school in South-West Sydney working exclusively with refugee students in an after-school program to support their learning needs. The second certificate is from the Australian Electoral Commission and demonstrates my attendance of their course about the processes of Australian Democracy, particularly the voting system. This included packs of information and activities to use in the classroom when and if I teach a Stage 3 class the HSIE topic on Australian government.  6.1.3 

Some evidence is scanned and thus appears on Wikispaces under "Element 6 Evidence" on http://anne87.wikispaces.com/

Critical Reflection on student grouping during a lesson:

One of the first lessons I taught on the Unit of Identity was focused on the significance of Edmund Barton and his contribution to Federation, and how this helped develop an Australian identity. The first thing I needed to know as a teacher was the students’ existing understanding of this topic, as I use this information to determine whether students will require scaffolding throughout the lesson or whether students may need to be challenged further than initially planned for, something I have learnt from the work of Paul Dufficy (2005). My introduction, therefore, was a whole-class discussion aimed to explore the main ideas of Edmund Barton and Federation through student dialogue. While grouping students as a whole class on the floor to facilitate a discussion may be a good way to easily manage and direct students, it is not always a useful way to engage all students. The difficulty of whole-class grouping in this manner was that not all students remained on-task (such as Michael or Asghar) and some students didn’t participate in the discussion (like Debra), with only a few key students providing the main dialogue. Further, it was tempting for me as the teacher to take control of the discussion and shift it from being student-based to teacher-based, which defeats the purpose of the introduction. Overall, I think whole-class grouping like this discussion can be helpful in introducing ideas and content of a lesson, however, they are not inclusive of a range of abilities or learning styles, and therefore should be used in conjunction with other learning activities, especially to support ESL students.     


Research paper and discussion about teaching content

Turning up the Volume:

Teaching Volume and Capacity concepts practically in the K-6 classroom

Anne Lewis discovers that teaching experiences of volume and capacity can be enhanced with a sound conceptual knowledge working together with practical pedagogy. 

Volume and capacity surround our everyday existence, from filling a jug of water at dinner, to packing a suitcase for a holiday, or baking a cake for a special occasion. Measurement, especially of volume and capacity, is a highly practical topic (NSW Department of Education and Training, 2004), with significant relevance to daily living, especially in regards to the skill of estimation (Thom, 2002). Students in New South Wales schools are expected to have a considerable amount of content knowledge and experience of the topic, with concepts of volume and capacity being taught from Early Stage 1 through to Stage 3, and then all through high school, as outlined in the Mathematics Syllabus (NSW BOS, 2000). While it is an important aspect of learning measurement, volume and capacity is an area of mathematics that many teachers feel unsure about teaching, either for lack of discipline knowledge or pedagogical knowledge. In her research on primary preservice teachers, Robyn Zevenbergen found that many students have weak content knowledge of volume and capacity, yet she also found strong content knowledge positively correlated with better teacher practice (Zevengergen, 2005, p. 5). Similarly, Curry & Outhred found that if teachers better understood the progress of students’ conceptual understanding, they would be better equipped to teach volume and capacity effectively (Curry & Outhred, 2005, p. 26). As such, the purpose of this article is to outline the main concepts of volume and capacity taught in K-6, identify some common misunderstandings of students, and present some engaging practical ideas to assist teachers in planning purposeful learning experiences in the classroom.

Conceptual Understandings

There are several key concepts to understand when teaching and learning about volume and capacity. Volume and capacity are concerned with the measurement of three dimensional shapes, namely, the amount of space occupied by an object, or the amount a container can hold (Zevenbergen, Dole & Wright, 2004). The Professional Support and Curriculum Directorate (2003, p. 82) has recognised that because there are different ways to measure volume and capacity the concepts can become quite complex, especially differentiating between measurements with liquid units, (eg. mL) and solid units (eg. cm³) in Stage 3.


Much of the conceptual understandings involved with volume and capacity require students to utilise “spatial visualisation skills”, such as estimating ‘which container will hold more?’ (Okun, 2003, p.19). Learning how units spatially fit together and being able to count them accurately has been identified as a basic concept for students to grasp (Professional Support and Curriculum Directorate, 2003, p. 7). Importantly, the relationship between one-dimensional, two dimensional and three dimensional shapes with length, area and volume respectively should be demonstrated to students, in order for them to understand what attribute they are measuring (see Figure 1 below), which is discussed and illustrated in the Queensland Mathematics Syllabus (Queensland Studies Authority, 2004).

The Learning Framework for Measurement, based on research and theory, has informed much of the NSW Syllabus documents for Mathematics, and suggests there are six levels of progressive understanding in measurement (Professional Support and Curriculum Directorate, 2003). In broad terms, students first recognise the attribute they are measuring, (volume or capacity, in this case) then move on to directly compare and measure the attribute with non-formal units, recording their findings. In the later levels, students are introduced to formal measurement units (such as cm³) and look at structure and unit iteration to best calculate volume or capacity. This is not restricted to NSW curriculum documents, but is evident also in the Queensland Mathematics Syllabus, which details the concepts of volume and capacity more intricately than the NSW syllabus, and also places an emphasis on the relationship between volume and capacity and Space and Geometry strands (Queensland Studies Authority, 2004). Similarly, the Victorian P-10 Maths Continnum (Victoria Department of Education and Early Childhood Development, 2000) outlines levels which closely resemble the Learning Framework in Measurement, as does the National Curriculum for England (Department of Education and Employment & Qualifications and Curriculum Authority, 1999).

 Common Misconceptions and Difficulties

Students and teachers can hold a number of misconceptions about volume and capacity. It is important to recognise these common misconceptions and difficulties listed below before teaching the topic, as to avoid communicating these ideas to students.

·                     The belief that the volume formula is always Volume = Length x Width x Height. This is only true for rectangular volumes, and it has been suggested that students are taught to “distrust formulas in constructive, investigative ways” (Gough, 2004, p. 11). The Volume formula is actually Volume = Area of Base x Height.

·                     Mass and volume is the same thing. Mass is a measure of the weight of an object, while volume is how much space an object occupies. For instance, two balls can be the same size (ie have the same volume), but have different masses (one is heavier than the other).

·                     Measuring volume and capacity inaccurately. American researchers Reece & Kamii (2001) found that if children could not understand a unit as part of a whole quantity, they would measure inaccurately. Students need to understand unit iteration before their measurements can become exact (Reece & Kamii, 2001, p. 357).

 Practical ideas for teaching Volume and Capacity

In all Mathematics topics, especially volume and capacity, students must be given opportunities to explore the concepts with hands-on activities, which is grounded in constructivist theory by theorists such as Piaget, who say children construct their own knowledge (Bobis, Mulligan, Lowrie, 2004). Much of these activities should be undertaken in pairs or small groups, which is part of Vygotsky’s social-constructivist theory, and this is especially important when developing the metalanguage of volume and capacity (Thom, 2002, p. 27). A particularly useful resource called “Teaching Measurement: Early Stage 1 and Stage 1” (Professional Support and Curriculum Directorate, 2003) gives many suggestions of simple, practical activities teachers could use in the classroom. For instance, making cardboard cylinders of different sizes and then filling them with rice to make direct comparisons of which cylinder has a greater volume. In fact, teachers can utilise a number of different informal units of measure, including; marbles, playdoh, water, sand, jelly beans, soft drink containers, paddle pop sticks, matchboxes and pegs to name just a few. Below are some practical ideas aimed to enhance learning of the main concepts of volume and capacity as discussed earlier in this article:

·         In Early Stage 1, focus on concepts in play situations, such as packing toys away and building sandcastles, as suggested by the NSW Board of Studies Mathematics K-6 Syllabus (NSW Board of Studies, 2000, p. 102).

·         Use literature to illustrate concepts in a fun way. An example is the children’s book Mr Archimedes’ Bath (Allen, 1980), which is suggested by Bobis et al (2004, p. 241) as a way to appreciate displacement of water in relation to volume.

·         Use Base-10 blocks when introducing standard formal units of measurement (Zevenbergen et al., 2004, p. 269). In particular, they show the relationship between single cm cubes and when they contribute to a block of 10, unit of 100 or cube of 1000. Unit iteration can be taught with Base -10 blocks, importantly, as they form a tessellating pattern, leaving no gaps or overlaps.

·         Develop and use classroom-based referents when estimating (Thom, 2002, p. 27), including such things as the capacity of the fish tank, or volume of a pencil case. Classroom cooking classes using measuring containers to follow the recipe can also be fun, practical ways of experiencing volume and capacity (Thom, 2002, p. 28).

·         Make boxes out of A4 paper/ cardboard and use these as the basis of direct comparison of volume. A great example of this is described by the NSW Department of Education and Training (2004), as seen below in Figure 2.                        


If teachers combine solid discipline knowledge of volume and capacity with practical and interesting activities, their classrooms will benefit from quality teaching practice. With simple materials teachers can help students to progress their understandings of volume and capacity, and avoid common misconceptions and difficulties.

 Helpful Resources

For teachers:

- Blake Education. (2001). Targeting Maths. Glebe, NSW: Author. (BOOK & CD ROM)

- PrimarySchool.com.au.(2008). Mathematics. Retrieved August 19, 2008 from: http://www.primaryschool.com.au/mathematics-lessonsresults.php?strand=Measurement&unit=Volume%20and%20Capacity&grade=56

- Zevenbergen, R., Dole, S., & Wright, R.J. (2004). Teaching mathematics in primary schools. Crows Nest, NSW: Allen & Unwin.

  For students:

- Allen, P. (1980). Mr Archimedes’ Bath. Sydney: HarperCollins

- Australian Broadcasting Corporation. (2008). Count us in games. Retrieved August 19, 2008 from: http://www.abc.net.au/countusin/games/game15.htm

- Educational Broadcasting Corporation. (2006). Can you fill it? Retrieved August 19, 2008 from: http://pbskids.org/cyberchase/games/liquidvolume/liquidvolume.html


Allen, P. (1980). Mr Archimedes’ bath. Sydney: HarperCollins 

Bobis, J., Mulligan, J., & Lowrie, T. (2004). Mathematics for children: Challenging children to think mathematically. (2nd Edn). Frenchs Forest, NSW: Pearson Education

  Curry, M., & Outhred, L. (2005). Conceptual understanding of spatial measurement. In P. Clarkson, A. Downton, D. Gronn, M. Horne, A. McDonough, R. Pierce & A. Roche (Eds.), Building connections : theory, research and practice : proceedings of the 28th annual conference of the Mathematics Education Research Group of Australasia. Volume 1, pp. 265-272. Sydney: MERGA 

Department of Education and Employment & Qualifications and Curriculum Authority. (1999). National curriculum for London. London: Qualifications and Curriculum Authority. 

Gough, J. (2004). Fixing misconceptions: length, area and volume. Prime Number 19(3), 8-14.  

NSW Board of Studies. (2000). Mathematics K-6 syllabus. Sydney: Author. 

NSW Department of Education and Training. (2004). Teaching measurement in the new syllabus. Curriculum support for Primary Teachers 9(2), 1-2.

 Okun, S. (2003). Measuring volume informally: Teaching notes. In G.W Bright & D.H Clements (Eds.), Classroom activities for learning and teaching measurement: 2003 Yearbook. Reston, VA: The National Council of Teachers of Mathematics.

 Professional Support and Curriculum Directorate. (2003). Teaching measurement: Early stage 1 and stage 1. Sydney: NSW Department of Education and Training. 

Queensland Studies Authority. (2004). Mathematics 1-10 Syllabus. Spring Hill, QLD: Author. 

Reece, C.S., & Kamii, C. (2001). The measurement of volume: Why do young children measure inaccurately? School Science and Mathematics, 101(7), 356-361. 

 Thom, R. (2002). Measurement? It’s fun! Didn’t you guess? AMPC 7(2), 26-29. 

Victoria Department of Education and Early Childhood Development. (2000). Mathematics developmental contiuum P-10 measurement, chance and data. Melbourne: Author.


Zevenbergen, R., Dole, S., & Wright, R.J. (2004). Teaching mathematics in primary schools. Crows Nest, NSW: Allen & Unwin.

 Zevenbergen, R. (2005). Primary preservice teachers’ understandings of volume: the impact of course and practicum experiences. Maths Education Research Journal 17(1), 2-23.