SCHOOL CONTEXT
Harrington Park Public School was established in 2002 and has 704 students currently enrolled. The school implements a PBL strategy of ‘Be Safe, Be Kind, Be Fair, Be Great’ which is seen around the school and in classrooms. Teachers’ base their classroom expectations on this PBL strategy. Technology can be found in every classroom and teachers implement collaborative learning and ‘talk for learning’ in the classroom as they have recently done research on the 21st Century Pedagogy of Dialogic Classrooms and Robin Alexander's theory on using dialogic teaching in the classroom.
Harrington Park Public School was established in 2002 and has 704 students currently enrolled. The school implements a PBL strategy of ‘Be Safe, Be Kind, Be Fair, Be Great’ which is seen around the school and in classrooms. Teachers’ base their classroom expectations on this PBL strategy. Technology can be found in every classroom and teachers implement collaborative learning and ‘talk for learning’ in the classroom as they have recently done research on the 21st Century Pedagogy of Dialogic Classrooms and Robin Alexander's theory on using dialogic teaching in the classroom.
- 36.4% of the community attends primary school with 20.5% in government schools
- 80.7% of homes speak English
- The community has a moderate-high economic status with most families having both parents employed full time.
CLASSROOM CONTEXT
5/6W
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To protect student identities, pseudonyms of student A, B and C is used throughout this case study. Parent/carer's consent was also received through permission notes given by the University stating that I was conducting a case study for an assignment and their child was chosen as a participant.
Links to:
Standard 7.1.1 - Meet professional ethics and responsibilities
Standard 7.3.1 - Engage with parents/carers
Links to:
Standard 7.1.1 - Meet professional ethics and responsibilities
Standard 7.3.1 - Engage with parents/carers
ADJUSTED (emergent)
Student A
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CORE (working at expected level)
Student B
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EXTENSION (advanced)
Student C
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Links to:
Standard 1.1.1 - Physical, social and intellectual development and characteristics of students
Standard 1.2.1 - Understand how students learn
AITSL, 2011
Standard 1.1.1 - Physical, social and intellectual development and characteristics of students
Standard 1.2.1 - Understand how students learn
AITSL, 2011
Aim:
The aim of this unit of work is to build upon existing knowledge of area and acquire the skills to measure and calculate shapes accurately. Specifically, students will be required to calculate the area of squares, rectangles, triangles and compound shapes in the measurements of mm2, cm2, m2, hectares and km2.
Learning sequences throughout the unit of work will be differentiated accordingly to cater for students' learning abilities, interests and needs.
Prior to lesson sequences:
Prior to teaching the lesson sequences, students completed a pre-assessment on Essential Assessment to gather data on what they know/can improve on. Analysing the assessment results, I was able to identify concepts students showed deep understanding in therefore a quick recap was needed and concepts that they lacked knowledge in, indicating that explicit teaching was needed in those areas.
Links to:
Standard 2.2.1 - Content selection and organisation
Standard 2.3.1 - Curriculum, assessment and reporting
Standard 3.2.1 - Plan, structure and sequence learning programs
AITSL, 2011
The aim of this unit of work is to build upon existing knowledge of area and acquire the skills to measure and calculate shapes accurately. Specifically, students will be required to calculate the area of squares, rectangles, triangles and compound shapes in the measurements of mm2, cm2, m2, hectares and km2.
Learning sequences throughout the unit of work will be differentiated accordingly to cater for students' learning abilities, interests and needs.
Prior to lesson sequences:
Prior to teaching the lesson sequences, students completed a pre-assessment on Essential Assessment to gather data on what they know/can improve on. Analysing the assessment results, I was able to identify concepts students showed deep understanding in therefore a quick recap was needed and concepts that they lacked knowledge in, indicating that explicit teaching was needed in those areas.
Links to:
Standard 2.2.1 - Content selection and organisation
Standard 2.3.1 - Curriculum, assessment and reporting
Standard 3.2.1 - Plan, structure and sequence learning programs
AITSL, 2011
WALT: Calculate the areas of rectangles and squares using familiar metric units.
WILF: Understand and use length x width to calculate the area of rectangles and squares. Visualisation of arrays, ship counting, factor multiplication. Teaching and Learning Cycle: Analysing student data from the pre-assessment showed that students did not understand the difference between perimeter and area calculations. Thus, this lesson I explicitly taught and demonstrated how to calculate the area of squares and rectangles using the formula and distinguishing the difference between perimeter and area. Students demonstrated a clear understanding of using the formula to calculate the area of various squares and rectangles through observation, verbal and written work. Theorists/Teaching Strategies used: Number talk - encourages mathematical thinking and skills (Humphreys & Parker, 2015) Repetition - repeating the same phrases and processes transfers knowledge from short to long term memory (Lykins, 2015; Lominbao & Ombay, 2017) Dialogic Classrooms/ Talk for learning - encourages collaborative work between students to share ideas and knowledge (Alexander, 2020) Explicit Teaching - going through the process step by step (Tella, 2013; Doabler & Fine, 2013) |
Links to:
Standard 1.2.1 - Understanding how students learn Standard 3.2.1 - Plan, structure and sequence learning programs Standard 3.3.1 - Use teaching strategies Standard 4.1.1 - Support student participation Standard 5.1.1 - Assessing student data AITSL, 2011 |
WALT: Partition irregular shapes to calculate total area.
WILF: Separation of 2 (or more) regular shapes. L x W. Correction addition. Teaching and Learning Cycle: Analysing student work samples in calculating the area of squares and rectangles, I know students have an understanding of this concept. Thus, for this lesson I focused my explicit teaching on finding the missing lengths on regular shapes and applied learnt knowledge of using the formula to calculate the area. Students demonstrated an understanding of partitioning irregular shapes and calculating the area, however a few adjusted students struggled with finding the missing lengths. Theorists/Teaching Strategies used: MeE framework - engagement in mathematics through high cognitive, operative and affective elements (Attard, 2012) Number talk - encourages students to build on peer's ideas (Humphreys & Parker, 2015) Dialogic Teaching - gaining an understanding of the concept through dialogue (Bakker, Smit & Wegerif, 2015) Explicit Teaching - breaking down the process step by step ensuring students understand each step before moving on (Tella, 2013; Doabler & Fine, 2013) Repetition - repeating the same phrases and processes transfers knowledge from short to long term memory (Lykins, 2015; Lominbao & Ombay, 2017) Scaffolding - partition shapes for students to make finding the missing lengths easier (Bakker, Smit & Wegerif, 2015) |
Links to:
Standard 1.2.1 - Know how students learn Standard 1.5.1 - Differentiate teaching to meet specific learning needs of students with all abilities Standard 2.5.1 - Understand numeracy strategies Standard 3.2.1 - Plan, structure and sequence learning sequences Standard 3.3.1 - Use teaching strategies (AITSL, 2011) |
WALT: Solve a variety of problems involving the areas of triangles.
WILF: To use the CUBES model to identify parts of the word problem. To use the 'draw a diagram' strategy to help solve the problem. Teaching and Learning Cycle: Analysing student work samples in the previous lesson of word problems with area of squares and rectangles and in area of triangles, I know that students have an understanding of working with word problems however some students misunderstood the area of a triangle. Thus, my explicit teaching is focused on revising the area of triangles, highlighting the importance of the 1/2. Students demonstrated a deep understanding of using CUBES and diagrams to solve word problems and gained an understanding of finding the area of triangles. Theorists/Teaching Strategies used: CUBES - helps student break down and understand how to solve the problem. Little to no research found on the effectiveness of this strategy Dialogic Teaching/Talk for Learning - students scaffolding each other's learning through sharing ideas and knowledge (Alexander, 2020) Explicit Teaching -going through the process step by step (Tella, 2013; Doabler & Fine, 2013) |
Links to:
Standard 1.5.1 - Differentiate teaching to meet specific learning needs of students with all abilities Standard 2.5.1 - Understand numeracy teaching strategies Standard 3.1.1 - Establish learning goals Standard 3.3.1 - Use teaching strategies (AITSL, 2011) |
Student A
Learning Goal: Maintain in the year 5 level and/or achieve year 5.75 level.
Achieved: Student A achieved her learning goal of 5.75 year level as she made a 13% improvement in her post-assessment. Working Towards: Student A is working towards building confidence and reducing anxiety in mathematics as she engaged in collaborative work with her peers and communicated her understanding of concepts one-on-one with the teacher. Growth: 0.25 year level Outcome Achieved: MA3-10MG |
Student B
Learning Goal: Reach working at a year 5 level.
Achieved: Student B achieved her set learning goal of working at a year 5 level as she made a 38% improvement in her post-assessment. Working Towards: Student B is working towards building confidence in participating in class discussions during mathematics. She showed signs of increasing confidence in verbally sharing ideas through interacting with peers and teacher during independent activities. Growth: 1.25 year level Outcome Achieved: MA3-10MG |
Student C
Learning Goal: Achieve working at year 5.75 level or higher.
Achieved: Through observations, class discussions and work samples, Student C showed an understanding and capability of calculating the area of various shapes throughout the unit of work. Working Towards: Student C did not achieve her set goal of working at year level 5.75 or higher as she maintained the same as there was a slight decrease from her pre-assessment of 3%. These results may be due to performance anxiety as she was not surrounded by her peers during the post-assessment and/or she did not read the questions correctly. Growth: -0.25 year level Outcome Achieved: MA3-10MG |
Goal 1: Differentiate to cater all student's needs, abilities and strengths
Goal 2: Behaviour management strategies
Goal 3: Deepen understanding of pedagogical practices
Goal 4: Inclusive education
Links to:
Standard 6.1.1 - Identify and plan professional learning needs
Standard 6.2.1 - Engage in professional learning and improve practice
Standard 6.3.1 - Engage with colleagues to improve practice
Standard 6.4.1 - Apply professional learning and improve student learning
Standard 7.4.1 - Engage with professional teaching networks and boarder communities
(AITSL, 2011)
- More research on implementing effective differentiation.
- More experience in differentiating lessons and activities.
Goal 2: Behaviour management strategies
- More research on effective behaviour management strategies for all stages.
- Implement researched strategies in casual teaching for experience and practice.
- Follow teacher Facebook groups and Instagram's
Goal 3: Deepen understanding of pedagogical practices
- Research pedagogical practices and what is effective in each stage.
- Participate in professional development through online courses and/or schools.
- Follow teacher Facebook groups and Instagram's.
Goal 4: Inclusive education
- Become more familiar with the Universal Design for Learning through research.
- Study inclusive education courses in the future: -
- Western Sydney University offers Masters of Inclusive Education
- University of NSW offers Master of Education (Special Education)
Links to:
Standard 6.1.1 - Identify and plan professional learning needs
Standard 6.2.1 - Engage in professional learning and improve practice
Standard 6.3.1 - Engage with colleagues to improve practice
Standard 6.4.1 - Apply professional learning and improve student learning
Standard 7.4.1 - Engage with professional teaching networks and boarder communities
(AITSL, 2011)
References
Alexander, R. (2020). (1st ed.). A Dialogic Teaching Companion. Routledge. https://doi-org.ezproxy.uws.edu.au/10.4324/9781351040143
Attard, C. (2012). Applying a Framework for Engagement with Mathematics in the Primary Classroom. Australian Primary Mathematics Classroom,
17(4), p.22-27. Australian Association of Mathematics Teachers. http://web.b.ebscohost.com.ezproxy.uws.edu.au/ehost/pdfviewer/pdfviewer?vid=1&sid=0b0576e2-2e84-40fa-8337-d9e884cb46e8%40sessionmgr102
Australian Bureau of Statics. (2016, October). 2016 Census QuickStats: Harrington Park.
https://quickstats.censusdata.abs.gov.au/census_services/getproduct/census/2016/quickstat/ssc11859
Australian Curriculum Assessment and Reporting Authority [ACARA]. (n.d.). Harrington Park Public School, Harrington Park, NSW. My School.
https://www.myschool.edu.au/school/41523
Australian Institute for Teaching and School Leadership [AITSL]. (2011). Australian Professional Standards for Teachers. Education Services
Australia, Melbourne: New South Wales. Retrieved from: https://www.aitsl.edu.au/docs/default-source/national-policy-framework/australian-professional-standards-for-teachers.pdf
Bakker, A., Smit, J., & Wegerif, R. (2015). Scaffolding and dialogic teaching in mathematics education: introduction and review. ZDM Mathematics Education, 47, 1047-1065. doi: 10.1007/s11858-015-0738-8
Bartlett, J. (2013). Becoming an outstanding mathematics teacher. ProQuest Ebook Central
https://ebookcentral.proquest.com/lib/uwsau/detail.action?docID=1323370#
Booker, G., Bond, D., Sparrow, L., & Swan, P. (2015). Teaching Primary Mathematics (5th ed.). Pearson Australia.
Doabler, C. T., & Fien, H. (2013). Explicit Mathematics Instruction: What Teachers Can Do for Teaching Students With Mathematics Difficulties.
Intervention in School and Clinic, 48(5), 276-285. doi: 10.1177/1053451212473151
Harrington Park Public School. (2021). 2020 Annual Report. Harrington Public School. https://s3-ap-southeast-2.amazonaws.com/doe-nsw-
schools/annual-report/2020/4628/2020_Harrington_Park_Public_School_Annual_Report.pdf
Hemphreys, C., & Parker, R. (2015). Making number talks matter: Developing mathematical practices and deepening understanding, grades 4-10.
ProQuest Ebook Central https://ebookcentral.proquest.com/lib/uwsau/detail.action?docID=2032800#
Lomibao, L. S., & Ombay, S. O. (2017). Does Repetition with Variation Improve Students’ Mathematics Conceptual Understanding and Retention?
International Journal of Science and Research (IJSR), 6(6), 2131-2137. doi: 10.21275/ART20174479
Lykins, A. N. (2-15). Using Repetition to Make Ideas Stick. The Mathematics Teacher, 108(8), 622-625. doi: 10.5951/matheteacher.108/8.0622
Munns, G. & Martin, A. J. (2005). Its all about MeE: A Motivation and Engagement Framework.
https://www.aare.edu.au/data/publications/2005/mun05400.pdf
NSW Education Standards Authority [NESA]. (2019). NSW syllabus for the Australian curriculum: Mathematics K-10 syllabus. Sydney, Australia.
http://educationstandards.nsw.edu.au/wps/portal/nesa/k-10/learning-areas/mathematics/mathematics-k-10
NSW Education Standards Authority [NESA]. (n.d.). Working Mathematically. https://educationstandards.nsw.edu.au/wps/portal/nesa/k-10/learning-areas/mathematics/mathematics-k-10/organisation-of-content/working-mathematically
Poduska, J. M., & Kurki, A. (2014). Guided by Theory, Informed by Practice: Training and Support for the Good Behavior Game, a Classroom-Based Behavior Management Strategy. Journal of Emotional and Behavioral Disorders, 22(2), 83-94. doi: 10.1177/1063426614522692
Stoehr, K. L. (2017). Mathematics Anxiety: One Size Does Not Fit All. Journal of Teacher Education, 68(1), 69-84. doi: 10.1177/0022487116676316
Tella, A. (2013). The Effect of Peer Tutoring and Explicit Instructional Strategies on Primary School Pupils Learning Outcomes in Mathematics.
Bulgarian Journal of Science and Education Policy, 7(1), 5-25. https://www-proquest-com.ezproxy.uws.edu.au/docview/1435832680?accountid=36155&pq-origsite=primo
Whitton, D. (2015). Teaching and Learning Strategies. Port Melbourne, Australia: Cambridge University Press.
World Health Organization. (2020). Physical Activity. https://www.who.int/news-room/fact-sheets/detail/physical-activity
Attard, C. (2012). Applying a Framework for Engagement with Mathematics in the Primary Classroom. Australian Primary Mathematics Classroom,
17(4), p.22-27. Australian Association of Mathematics Teachers. http://web.b.ebscohost.com.ezproxy.uws.edu.au/ehost/pdfviewer/pdfviewer?vid=1&sid=0b0576e2-2e84-40fa-8337-d9e884cb46e8%40sessionmgr102
Australian Bureau of Statics. (2016, October). 2016 Census QuickStats: Harrington Park.
https://quickstats.censusdata.abs.gov.au/census_services/getproduct/census/2016/quickstat/ssc11859
Australian Curriculum Assessment and Reporting Authority [ACARA]. (n.d.). Harrington Park Public School, Harrington Park, NSW. My School.
https://www.myschool.edu.au/school/41523
Australian Institute for Teaching and School Leadership [AITSL]. (2011). Australian Professional Standards for Teachers. Education Services
Australia, Melbourne: New South Wales. Retrieved from: https://www.aitsl.edu.au/docs/default-source/national-policy-framework/australian-professional-standards-for-teachers.pdf
Bakker, A., Smit, J., & Wegerif, R. (2015). Scaffolding and dialogic teaching in mathematics education: introduction and review. ZDM Mathematics Education, 47, 1047-1065. doi: 10.1007/s11858-015-0738-8
Bartlett, J. (2013). Becoming an outstanding mathematics teacher. ProQuest Ebook Central
https://ebookcentral.proquest.com/lib/uwsau/detail.action?docID=1323370#
Booker, G., Bond, D., Sparrow, L., & Swan, P. (2015). Teaching Primary Mathematics (5th ed.). Pearson Australia.
Doabler, C. T., & Fien, H. (2013). Explicit Mathematics Instruction: What Teachers Can Do for Teaching Students With Mathematics Difficulties.
Intervention in School and Clinic, 48(5), 276-285. doi: 10.1177/1053451212473151
Harrington Park Public School. (2021). 2020 Annual Report. Harrington Public School. https://s3-ap-southeast-2.amazonaws.com/doe-nsw-
schools/annual-report/2020/4628/2020_Harrington_Park_Public_School_Annual_Report.pdf
Hemphreys, C., & Parker, R. (2015). Making number talks matter: Developing mathematical practices and deepening understanding, grades 4-10.
ProQuest Ebook Central https://ebookcentral.proquest.com/lib/uwsau/detail.action?docID=2032800#
Lomibao, L. S., & Ombay, S. O. (2017). Does Repetition with Variation Improve Students’ Mathematics Conceptual Understanding and Retention?
International Journal of Science and Research (IJSR), 6(6), 2131-2137. doi: 10.21275/ART20174479
Lykins, A. N. (2-15). Using Repetition to Make Ideas Stick. The Mathematics Teacher, 108(8), 622-625. doi: 10.5951/matheteacher.108/8.0622
Munns, G. & Martin, A. J. (2005). Its all about MeE: A Motivation and Engagement Framework.
https://www.aare.edu.au/data/publications/2005/mun05400.pdf
NSW Education Standards Authority [NESA]. (2019). NSW syllabus for the Australian curriculum: Mathematics K-10 syllabus. Sydney, Australia.
http://educationstandards.nsw.edu.au/wps/portal/nesa/k-10/learning-areas/mathematics/mathematics-k-10
NSW Education Standards Authority [NESA]. (n.d.). Working Mathematically. https://educationstandards.nsw.edu.au/wps/portal/nesa/k-10/learning-areas/mathematics/mathematics-k-10/organisation-of-content/working-mathematically
Poduska, J. M., & Kurki, A. (2014). Guided by Theory, Informed by Practice: Training and Support for the Good Behavior Game, a Classroom-Based Behavior Management Strategy. Journal of Emotional and Behavioral Disorders, 22(2), 83-94. doi: 10.1177/1063426614522692
Stoehr, K. L. (2017). Mathematics Anxiety: One Size Does Not Fit All. Journal of Teacher Education, 68(1), 69-84. doi: 10.1177/0022487116676316
Tella, A. (2013). The Effect of Peer Tutoring and Explicit Instructional Strategies on Primary School Pupils Learning Outcomes in Mathematics.
Bulgarian Journal of Science and Education Policy, 7(1), 5-25. https://www-proquest-com.ezproxy.uws.edu.au/docview/1435832680?accountid=36155&pq-origsite=primo
Whitton, D. (2015). Teaching and Learning Strategies. Port Melbourne, Australia: Cambridge University Press.
World Health Organization. (2020). Physical Activity. https://www.who.int/news-room/fact-sheets/detail/physical-activity