аЯрЁБс>ўџ 9;ўџџџ8џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџьЅС7 јПз!bjbjUU ..7|7|[нžџџџџџџllll:І,вввц8:NцŸ Жnn(–ЌЌЌЌЌ  $U u>D вЌЌЌЌЌD VввЌЌY VVVЌ(вЌвЌ VЌ VШV вв Ќb р4Ž A‰Уцд‚  o 0Ÿ  ГVГ Vццввввй Graduate Diploma in Secondary Education HEG1602: Educational Systems and Issues Case and Commentary by Graham Taylor The Case I was involved in the numeracy program at Maribyrnong Secondary College where I worked with a year 7 female student from Somalia whose name is Hamida. Initially I was surprised at the lack of knowledge Hamida had in mathematics but through questioning found that her schooling background was very limited having been a recent arrival to Australia. I was able to assess Hamidas’ level of understanding through questioning, tests and activities. The CSFII standard for year 7 students is a level 4 understanding in mathematics. I found that Hamida had mathematical knowledge that was in between level 1 and 2 of the CSF II. Hamida was able to count to 100, to add and subtract using her fingers, and to recognise number patterns. Her comprehension of English was OK, however she was of low ability in reading and writing. I knew that this would need to be taken into account in my teaching practice with her. Most of my time spent with Hamida was during maths class. Hamida was a hard working student and was eager to participate in the class exercises. The difficulty I encountered was that although Hamida wanted to complete the class work her knowledge would often not allow her to do the exercises and she constantly needed step by step instructions for each problem. I found that I was in fact supplying the answers for Hamida instead of letting her construct her own understanding and meaning. I quickly learned to not provide Hamida with answers and to ‘de-construct’ the problem to a level where she had an understanding of the task. At times I also found that Hamida was slightly embarrassed to admit her lack of knowledge in front of the other students. I thought this may be hindering her progress and have a negative impact on her confidence. On the few occasions I asked to remove her from the classroom we would work together in the library on key concepts. During these periods her feedback became more open and we where able to concentrate totally on the concept being taught. We had one particularly rewarding occasion that occurred after I discovered that Hamida had little understanding of division. I had asked her to mentally compute 12 divided by 3. She couldn’t answer the problem so I asked her to write down the problem and answer it. Again she was unable to solve the problem. I then introduced 12 matchsticks and asked her to divide the matchsticks into 3 groups. She was able to perform this task and then construct an understanding between the mathematical notation and the task. By using concrete tasks Hamida was also able to make the connection between division and multiplication. Commentary There where a few educational issues relevant to this case. The numeracy program that is running at Maribyrnong Secondary College, named RESTART, is an initiative of the Victorian Department Of Education. The program allocates resources to public schools to allow year 7 students who have deficiencies in numeracy to receive individual assistance. I needed to ensure that Hamida was able to receive the guidance she required to improve her numeracy skills. Although Hamida was not provided with an integration aid I felt that I needed to fulfil this role to some degree. Because of Hamidas’ Muslim background and short time in Australia she also required assistance in the areas of social recognition, integration into the classroom and acceptance amongst her peers. Hamida made significant progress in her numeracy skills as demonstrated by her ability to use concepts learned to solve problems. I believe this was because I was able to assess her level of ability in numeracy and literacy and respond effectively to create a plan to assist her attain the knowledge she required. The assessing of her ability was done by questioning, tasks, tests and monitoring work performed. The plan was to attempt to accelerate Hamidas’ numeracy knowledge without removing her from classroom activities and social interaction. I felt that although the goal was to improve Hamidas’ numeracy it was of equal importance to allow Hamida to feel like she was part of the class. Therefore I provided most of the aid during class time. I also used a range of teaching practices to introduce and reiterate mathematical concepts. These practices included open-ended questions, concrete tasks, real world problems and discussion.    Some examples of tasks used were the problems I created using matchsticks to teach multiplication and division, and a problem involving the division of a pizza to introduce fractions. While working with Hamida I was able to show my competence in a range of areas of teaching practice. Specifically, I used the knowledge I gained of Hamida and her history to assess her strengths and weaknesses. I displayed an awareness of Hamidas’ special requirements due to her social and ethnic background when devising a plan to improve her numeracy skills. I did this by not removing Hamida from social interaction gained in the classroom environment. I researched and used a variety of techniques for assessment and teaching numeracy to Hamida. I was able to communicate effectively with Hamida and build a rapport to make her learning program explicit and to set achievable goals. And, I gave Hamida a sense of satisfaction and relativity in the reaching of the goals. I believe that while working on the numeracy program I have displayed competence in the areas of ‘Communicating, Interacting and Working with Students and Others’, ‘Planning and Managing the Teaching and Learning Process’, and ‘Monitoring and Assessing Student Progress and Learning Outcomes’. I feel that our time spent doing one on one lessons where particularly rewarding, however, I would be reluctant to take Hamida out of the classroom too often as this would lead to her becoming isolated from her classmates and the classroom activities. I would of liked to have worked with Hamida individually more often outside of school hours to allow her the opportunity to progress more rapidly. I would suggest that Hamida requires a tutor that is able to perform this task with her.  Board of Studies (2000). Curriculum and Standards Framework II: Mathematics. Carlton. Victorian Department of Education.  Victorian Department of Education and Training (2002). The Victorian Government Three-Year Report On Education and Training.  HYPERLINK "http://www.deet.vic.gov/deet/resources/pdfs/3yr_report.pdf" http://www.deet.vic.gov/deet/resources/pdfs/3yr_report.pdf [viewed 18th June 2003].  Department of Education (1997). Multicultural Policy for Victorian Schools. Carlton. Victorian Department of Education.  Taylor, G (2003). Teaching Number Sense (poster presentation). Footscray. Victorian University of Technology.  Grimison, L. & Pegg, J. (1995). Teaching Secondary School Mathematics: Theory into Practice. Sydney. Harcourt Brace.  Gates, P. (2001). Issues in Teaching Mathematics. London. RoutledgeFalmer.  Sobel, M. & Maletsky, E. (1999). Teaching Secondary School Mathematics. Theory into Practice. Sydney. Harcourt Brace.  Vale, C. (2003). Graduate Diploma of Education, Mathematics Method Course Material. Footscray. Victorian University of Technology.  Australian Teaching Council (1996). National Competency Framework for Beginning Teachers. National Program on the Quality of Teaching and Learning. Graduate Diploma in Secondary Education HEG1602: Education Systems and Issues Case and Commentary Graham Taylor - 3002472 Page  PAGE 4  DATE 3/10/03 lq‹јљХžбвVWƒ„…†‡ˆ‰ŠpqrZ[\wЉзиVWŸ ЁлміїBpq„Арс=WXkŠЄЅЧ   / p Ё Ђ Ч ћ 8!™!›!И!Й!П!§њіьіххххххххіхсхсмдмбмхсхсхсхсхсхсхсЮЧМЧjCJUmH sH  CJmH sH CJ0JjU jU6] j0JUj0J5U\5\CJCJ J-./WXYmnopq‹Œh УФХабеCrњњњњјјјјјјјјјјјјјѓѓѓѓѓѓѓѓёёё$a$$a$[8!ж!§§§rZ[зіpрWЄ Ё 7!8!`!†!š!›!д!е!ж!з!њјіііііііііјёёёјяјјј$a$$a$П!Р!С!Т!У!Ф!Ъ!Ы!в!г!д!з!єъєуєуєъєрCJ CJmH sH CJmHnHsH ujCJUmH sH  ,1hА‚. 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