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Element 2

Element 2: Teachers know their students and how they learn.

I believe that in order to be a successful teacher who makes a difference in the lives of my students and assists them to achieve at school that I need to know them and their specific and  individual learning needs well. I believe that a crucial part of teaching is realising the unique learning style and needs of each child and catering to them in the way I teach. I believe that teaching is about assisting all students to access the curriculum and reach their full academic potiential. I believe that in order to assist students to do this that I need to be aware of the diverse backgrounds of students and that the learning opportunities I provide them with need to meaningful and significant to them.

I have demonstrated how I have found out students background knowledge and learning needs and then designed learning opportunities which cater to those needs on a number of different occasions. One such example is during an in-school teaching opportunity I had. Collaborately, I collegue and I had the opportunity to work with a small group of stage 3 students over the course of 3 weeks (1 hour per week) teaching them content from the volume and capacity strand of the K-6 mathematics syllabus. As we had not previously met the children and were unaware of their learning needs we spent time during our initial lesson ascertaining their prior knowledge and level of ability with working with the concepts of volume and capacity. Upon reflecting on the first lesson were were able to discuss the suitability of our tasks to students needs and use the knowledge we gained to inform further learning. As a result of this initial assessment of students prior knowledge, future learning experiences were planned specifically to allow students to work in their zones of proximal development (Vygotsky, 1978, pp. 38-39) and achieve learning outcomes.

A further example of how I have achieved this graduate standard stems from experience working as a teachers' aide (special). I had been working with a year 6 child with numerous learning difficulties especially in the area of literacy. This  child had given up hope of ever reading independently as he continued to fail at every stratey he tried. The only books he was able to read in any capacity were at Early Stage One level and he was put off by the content of the books, they just were not interesting to him and made him feel embarrassed that he was still reading books about fluffy bunnies and the colours of the rainbow. In order to motivate this child I completed a verbal survey of his interests and discovered he had a great interest in cars and one day wanted to be a mechanic. He loved playing a Playstation2 game about cars and was especially interested in finding out how to get better at the game to beat his older brother's high score. I wanted to use this interest to encourage him to read. I sought his fathers permission (as the content was from an M-rated game) to use information from the game's instruction manual to teach his son to read (I prepared an example to show him which included only age-appropriate terms and content). After just a week of reading my prepared material the child's interest in reading had greatly improved - he would seek me out and read to me during his lunch break as well as during our scheduled meeting times as he was so excited. After a term his reading had improved so much that he was able to read upper stage 1 books independently and by the end of the year was reading at a stage 2 level (most of the time). Although he was still not achieving reading outcomes at the same level of his peers he was excited about reading and believed that he now had the ability to succeed in reading tasks. [INCLUDED EVIDENCE: Volume and Capacity mini program of work: Excerpts from Assessment of Students' Learning, Reflective Evaluation; Personal Account: above account from my own experience of using student interests to teach a child to read]; [Other possible evidence for use in meeting this outcome: Classroom management assignment - Guise public school; Ed. Psych assignment showign theoretical knowledge and research of how students learn; 3rd year practicum reflection showing my use of different grouping of students and how these groupings assisted different students to access the curriuclum by catering to their individual learning preferences and needs; Mulitlingual Assignment on time demonstrating using curriculum differentiation and grouping strategies to meet the needs of students from NESB; Aboriginal Education Assignments showing affects of culture and health on learning; Special Education assignments demonstrating using different strategies to meet the needs of a child with Aspergers Syndrome in the classroom; Background research on common misconceptions from science unit on seeds (see Element 1 Evidence); Real life examples, e.g of implementing behaviour management strategies; etc].

I will endeavour to develop a deeper knowledge of different literacy strategies to use in meeting students' varied learning needs as this is an area I feel is not my strength. I need to especially research and practice using literacy strategies to meet the needs of Indigenous children, and those from NESB. I need to focus on taking opportunities during my upcoming practicum and intership to observe and use different literacy strategies which cater to such children - I need to especially take hold of such opportunities as I will be at a school in Western Sydney with a high Indigenous and multicultural population.

EVIDENCE:

  • Excerpt from reflection on lesson one of volume and capacity mini unit of work:

Suitability of Tasks

Although this lesson was intentionally designed to be basic and focus primarily on students’ prior knowledge, difficulties were still encountered. For example, our original mind-mapping strategy to elicit students existing understandings of capacity failed as students demonstrated no understanding (shown by blank expressions when asked to record everything they knew about the concept). Even after we altered this activity to focus on mind-mapping students’ understandings of volume instead, students still appeared to have a limited knowledge of the term (referring to volume as “music”) and as such this activity was further adjusted to include an ‘excursion’ around the playground to observe other groups. This adjustment assisted students in building their mind-maps and engaged them in the lesson. In light of students demonstrated limited understandings of capacity, we decided that students were not ready to move onto discussing the need for formal units in measuring capacity and so did not engage them in working towards the indicator “Recognise the need for formal units to measure capacity” during this lesson (refer anecdotal notes on Lesson Plan 1: Conclusion, included above on p. 9 of this assignment). 

Achievement of Indicators

Students were unable to achieve all the indicators included in this lesson. For instance, the indicator “Communicates prior knowledge of capacity through visual, textual and verbal communicative mediums and explains their ideas” could not be achieved by either student as it required students to possess a prior knowledge of capacity which they did not (as discussed above). However, upon altering the indicator to “Communicates prior knowledge of volume through visual, textual and verbal communicative mediums and explains their ideas”, students were able to demonstrate their limited existing understandings (although as previously discussed it was difficult to elicit whether Brianna’s communicated prior knowledge was her own). Furthermore, both students were unable to achieve the indicator “Recognise the need for formal units to measure capacity” as tasks which work towards this indicator were abandoned, as previously mentioned. Students however, did successfully achieve the indicator “Estimate and measure the capacity of various containers by packing with unifix cubes and other units” shown clearly on ‘students’ records of their findings’ (shown below in Figures 4 & 5), supported by photographic records (Figures 6, 7 & 8). 

Future Planning

As students have been identified as having a very limited understanding of volume and capacity, the subsequent lesson will focus specifically on capacity in order to clarify ideas and understandings of this concept. Future lessons will likely be based on “what is capacity?” and scaffold students’ measuring skills using informal units, working towards activities that require students to measure capacity with formal units. It is most likely that the concept of volume will not be addressed in remainder of this mini-program rather focusing on only capacity to consolidate understanding and promote deep knowledge (NSW DET, 2003, p. 11).  

  • Excerpt from reflection on lesson two of volume and capacity mini unit of work:

Suitability of Tasks

In light of what students demonstrated in the first lesson, this lesson was purposefully focused on capacity and aimed at student’s observed ability level. Although the students were unable to produce answers to all question posed, all set tasks were completed with some guidance, scaffolding and higher order questioning. For example, students struggled to answer the HOT question ‘Why do you think it is important to fill measuring devices to the top?’ however through further questioning ‘What might happen if we didn’t fill it to the top?’ students were able to deduce the answer. Based on the theoretical framework of Vygotsky’s (1978) Zone of Proximal Development (pp. 38-39), the main activity aimed to scaffold student’s understanding of the measuring process (refer to Lesson Plan 2: Activity 3, included on p. 12 of this assignment). It gave students the opportunity to observe, recall and then demonstrate their understanding of the process in a safe environment equipping them with a strategy they could later use to measure capacity independently.  

Achievement of Indicators

As result of eliciting students’ prior knowledge in lesson one and designing the activities in this lesson to reflect and build on the capabilities demonstrated by students, students comfortably achieved all the outcomes specified in this lesson. For instance, the indicator “Observes and records steps in the measuring process” was achieved by completing their ‘Measuring capacity’ worksheets and accompanying tasks as part of the activity (Activity 3) described above (refer to Figure 10).  Students were also able to recall and use mathematical terms appropriately demonstrating their understanding of the metalanguage associated with measuring capacity (some terms were misspelt however, e.g.: ‘estimate’, ‘measuring device’, ‘substance’) (refer to Figure 11).  By completing the activities in this lesson, students were able work towards working mathematically outcomes. For example, in Activity 2 (refer to Lesson Plan 2: Activity 2, included on p. 11 of this assignment) students brainstormed ideas about capacity and use these ideas to jointly construct an appropriate definition for capacity. This activity required students to reflect upon their prior knowledge, communicate their ideas and provide reasons when questioned about particular contributions, all key elements of working mathematically (Board of Studies, 2002, p. 19).  In the conclusion of the lesson, students were engaged in discussion, working towards the indicator “Recognises the need for formal units”. Although students appeared to understand and communicate the need for formal units, demonstrated by their ability to adequately answer the HOT questions posed, it would have been worthwhile to further explore these questions and discuss other units and examples beyond L and mL, however time did not permit.   

Future Planning

As a result of learning experiences engaged in during lessons one and two of this mini-program, students both appear to have a good understanding of capacity and how to measure it using informal units. To allow students to be better equipped to achieve their stage outcome in volume and capacity: Selects and uses the appropriate unit to estimate and measure volume and capacity, including the volume of rectangular prisms(Board of Studies NSW, 2002, p. 22), it would be appropriate that students transition from measuring capacity with informal units and apply learnt strategies to measure capacity with formal units in next week’s lesson.

 

  • Excerpt from reflection on lesson three of volume and capacity mini unit of work:

Suitability of Tasks

All activities were suitably designed, scaffolding information so that it progressed from the known (i.e. activation of prior knowledge – refer to Lesson Plan 3: Introduction, included on p. 16 of this assignment), to less familiar knowledge (i.e. investigating ‘containers’ that can be measured in L – refer to Lesson Plan 3: Activity 2, included on p. 16 of this assignment) to the unknown and never previously experienced (i.e. measuring capacity with formal units – refer to Lesson Plan 3: Activities 3 & 4, included on p. 17 of this assignment).  Throughout these activities students were able to draw on their experience of measuring capacity using informal units (from previous two lessons) and apply learnt strategies to assist them in measuring capacity using formal units.  The summative assessment given to students at the end of the lesson was also suitable and could be considered to be ‘valid’ in that it only asked students to recall information they had covered over the 3 lessons and allowed them to consolidate key concepts learnt (McInerney & McInerney, 2006, pp. 376-378), promoting deep knowledge (NSW DET, 2003, p. 11).  Students were required to complete this assessment without teacher support and while some in-built assistance mechanisms were included (i.e. sentence starter such as ‘Capacity is…’ and advanced organisers such as ‘Step 1’, ‘step 2’, etc.) there was notably less instruction and assistance given than in the formative assessment task used in Lesson 2 which gave both clear instructions, allowed students to watch a demonstration, seek teacher assistance and had in-built assistance mechanism (i.e. advanced organisers). This contrast between the assistance given in the two assessments was intentional and can be seen in Figures 16 & 17. The formative task ‘Measuring Capacity’ was designed to allow students to receive feedback as they learnt new strategies (assisted performance) (Dufficy, 2005, p. 80) and whereas the summative task ‘Capacity’ was intended to assess how well students could recall and apply learnt strategies. While students completed the summative assessment tasks without assistance (refer to Figures 18 & 19), they were asked to clarify some of their answers afterwards in order for teachers to ascertain their understandings, provide feedback and annotate their work.  We had intended to conclude this mini-program by asking students to create new mind-maps detailing what they now understood about capacity as a result of their learning over the three lessons. However, due to the extra time taken in moving students outdoors to complete the hand-on tasks, the inclusion of this final activity was not possible. While it was disappointing that time did not allow for this activity as it would have been an effective way to conclude the mini-program and a useful resource and record of learning that the students could have kept, we were still satisfied that both students had learned invaluable strategies and information that they can recall and use in understanding and measuring capacity. 

Achievement of Indicators

As result of careful lesson design, in which all activities were intentionally catered to students’ abilities and needs, both students were able to achieve all content indicators, successfully demonstrating their understandings of and capabilities in measuring capacity. Furthermore, each of the activities included in the lesson allowed students communicate, reason, investigate, reflect and or apply strategies and hence to demonstrate that they could work mathematically. For instance, during activity 3 (described above) students were engaged in substantive communication, investigation and application of strategies as they measured the capacity of containers with formal units.  Another example of students’ achievement can be seen in Figures 20 & 21, depicting lists they created of ‘containers’ that could be measured using litres (Activity 2). Following the compilation of their lists students were able to communicate that litres would not be the most efficient way of measuring everything on their lists, noting for example that ‘It would take ages to measure a pool with litres’ (refer to anecdotal notes on Lesson Plan 3: Activity 2, included on p. 16 of this assignment), deciding that kilolitres would be more efficient. In light of this suggestion students were asked to write next to each item on their list the unit (mL, L, kL) they thought to be the most appropriate to use in measuring the capacity of each ‘container’. Students then justified why they had selected particular units and gave examples to support their reasons (refer to anecdotal notes on Lesson Plan 3: Activity 2, “a litre would be too much to measure most tins, mL would be better”, “most cordial bottles come in 1L or 2L, so litres would be the right thing to measure them with”, included on p. 16 of this assignment) demonstrating clearly that they had met the indicator “Discusses and justifies reasons for selecting particular formal unites to measure capacity of different containers” using the working mathematically skills of reasoning and communicating. To encourage students and reward them for their hard work over the course of the program, we awarded them with certificates, shown below in Figure 22.  

Future planning

Over the course of this mini-program we have been able to elicit students understanding of volume and capacity, provide learning experiences scaffolding how to measure the capacity of containers using informal units, progressing to formal units, and have provided students with opportunities to work mathematically. It would be appropriate in future learning experiences (completed with their classroom teacher) for students to engage in further learning centred on the concept of capacity in order to develop deep understanding and deep knowledge. Following should be opportunities for students to learn about volume and eventually the relationship between the two concepts.

~ Reflective Evaluation ~

~ Cathie ~ 

I found the experience of co-teaching at North Newtown Public School to be both a valuable learning opportunity and an experience which will shape my future teaching career. 

In reflecting upon this experience I couldn’t help but think about how difficult it was to prepare a lesson for students whom I had no prior knowledge about. I did not know their abilities, weaknesses or existing knowledge of volume and capacity; I did not even know how many students we would have or whether they would be in year four or five. I was struck as I reflected upon this, of the difficult task that casual teachers must face almost every day.   

In light of this (i.e. planning for the unknown), my co-teacher and I focussed our initial lesson upon eliciting the students’ prior knowledge of capacity with a view of moving to volume in the following weeks. We incorporated mind-mapping into our lesson as a means of discovering what students already knew about capacity, a strategy we had observed in tutorials (Bobis, 2008). This strategy however had not been as successful as we had hoped as students appeared to have little or no knowledge of capacity. As a result of that lesson I realised that while mind-mapping is a useful strategy, it can only be successfully implemented if students have some prior knowledge about a topic or concept. In reflecting on this experience, I have come to realise that having a contingency plan and being able to improvise and adapt lessons on the spot are necessary ‘tools of the trade’ that I will need to employ in future teaching opportunities, especially in light of the fact that many graduate teachers do not find full time employment straight out of university and will be faced with planning for the unknown for the majority of their early careers (NSW Teachers Federation, 2007, section 4).  

Additionally, I have learnt several valuable lessons about co-teaching from this experience. For example, I have learnt that co-teaching requires not only careful collaborative planning of learning experiences but of “all stages of the teaching/learning process” (Bobis, 2007, p. 62) including careful consideration and discussion of the content knowledge required for each task. This hard lesson was realised especially in our second lesson where we discovered mid-teaching, after asking students to help us write a definition for capacity, that we had not come to a prior consensus on an appropriate definition. Subsequently we were left trying to ‘read each other’s minds’ as we discussed the appropriateness of students’ suggestions. 

Furthermore, the experience of co-teaching at North Newtown Primary School has allowed me to learn the benefit of scaffolding learning experiences for students. After ascertaining what prior knowledge students possessed my co-teacher and I were able to cater our teaching to allow students to work in their ‘Zones of Proximal Development (ZPD)’ (Vygotsky, 1978, pp. 38-39) where they were challenged by the nature of the learning but able to achieve learning goals with assistance. I discovered the importance of higher order questioning in providing students the opportunity to be challenged and work in their ZPD. I have come to realise that by asking merely closed questions which have definitive answers student are destined to either fail by giving incorrect answers or merely regurgitate information they already know. Also, closed questioning does not provide any real opportunities for students to work mathematically. By asking open-ended, higher order questions however to find out why or how students know (or think they know) something, they are challenged to reflect upon their learning and apply strategies in order to justify (reason) and communicate their understandings; allowing them to confront any misconceptions and also to work mathematically. As a result of this realisation our questioning style developed over the course of the program from closed questions requiring definitive answers such as ‘what is volume?’ (Lesson 1) to open ended higher order questions such as ‘why do you think it is important to fill measuring devices all the way to the top?’, (Lesson 2). 

Overall, I found the experience of co-teaching at North Newtown to be both challenging and rewarding, and an experience on which I will look back and reflect upon during my future teaching career. 

 

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