St Ruislip School, Leederville
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Santa Clara School
91 Coolgardie Street, Saint James, WA, 6102.
Ph: 9251 0400
Principal: Mr Richard Win Pe
CPL Consultant: Julie Kay CPL: Evelyn Temmen and Amy Perinski Literacy and Numeracy Plan 2013-2014
This plan is in four sections. The first section provides an overview of our school including its context and direction, ending with a statement of our main focus over the past year. The second section presents an outline of the strategies we have used to achieve the goals we set through our focus. The third section of this report presents data relating to our focus and data that, while not related to our focus, is of interest or concern to us. The final section outlines our plans for the future, in relation to our current focus and potential shifts in focus. In this section we identify changes in our data that we expect to find as a consequence of our renewed or realigned focus for the school.
SCHOOL PROFILE
Santa Clara School is a single stream co-education Catholic primary school of approx. 240 students from Kindergarten to Year Six. The school is located in St James and was established by the Dominican Sisters in 1954. Inspired by the Dominican way, Santa Clara is founded on the principles of Truth and the Christian way of living, and seeks to nurture the individual qualities of each person in a caring and accepting environment. Santa Clara is an active community with school receiving great support from parents.
FOCUS
At Santa Clara School we are committed to the cognitive development of all students. The 2012 focus was based on the Professional Learning Community’s understanding that the building blocks of literacy are fundamental to literacy success. As part of this commitment to excellence the focus was on Reading Comprehension throughout the school.
In 2013, whilst maintaining and continuing to embed Reading Comprehension and Guided reading, our focus moved to Problem Solving in Numeracy with a lens of Critical and Creative Thinking investigated through the following question:
Focus Question 2013:
How do we ensure that our students have a repertoire of specific strategies to develop critical and creative thinking in the proficiency strand/ Problem Solving in Numeracy?
In 2014, the focus will remain on developing critical and creative thinking in the proficiency strand, in particular Problem Solving in Numeracy with the aim of embedding supportive structures, whole school processes and strategies. In addition to this the Professional Learning Community will focus on specifically developing mathematical language or vocabulary. Therefore the focus question for 2014 whilst continuing our problem solving focus will focus specifically on the development of mathematical vocabulary. OUR STRATEGIES Literacy and Numeracy Strategies. The following supportive structures have been continued or implemented this year for our literacy and numeracy strategies. It is the intention of the professional learning community to continue to support these structures with the aim to embed strategies, processes and beliefs for the added growth and development of all students across year levels: Enabling shoulder to shoulder learning. Appointment of a Coordinator of Professional Learning, who is provided with two days of professional learning in 2013 and regular onsite support from our school support consultant, Julie Kay. Staff engaged in professional learning readings and activities to encourage and analyse whole school teaching and learning practices, school data and whole school academic improvement. Using shoulder to shoulder strategies to support and learn from each other. A proforma to guide teachers in preparing and implementing shoulder to shoulder sessions with reflection proformas to further inform future sessions. Developing models of effective practice in numeracy: Appointment of two key teachers in numeracy who attended four days of professional development in 2013 and engaged in reporting back to staff and sharing mathematics teaching and learning strategies with staff. The continuation of an EMU (Extending Mathematical Understanding) teacher for Year Two students. The attendance by the EMU teacher at a professional learning day and the sharing with staff of EMU strategies and MAI techniques and scripts. Examining and implementing a whole school problem solving processes and strategies. Whole professional development, run by Catholic Education Numeracy consultant, in problem solving and mathematical language. A focus on the development of mathematical vocabulary and a whole school common language across year levels. The identification of specific vocabulary to be introduced or revised in the form of a scope and sequence booklet. Collaborative learning in the form of mathematics problem solving day with multi age groups and the whole school involved in rotating learning activities. A continuation of the use of Mathletics across year levels with the possibility of reviewing the use of this program in the early years based on staff reviewing the effectiveness of Mathletics for our school at that level.
Developing models of effective practice in Literacy: Maintaining guided reading groups as part of literacy hour in all classrooms. The introduction of Reading Eggs across all year levels in late 2013 with a three year ongoing commitment to the program. A three year commitment to implementing Diana Rigg phonics-language development approach in K-1 in 2014, sourcing current and adequate resources and accessing professional development for teachers and support staff in the early years. A further examination of phasing in this approach in subsequent years. The sourcing of new current guided reading resources, funded by the P&F, to the value of $7,000.
Developing models of effective practice across other curriculum areas: Appointment of a key teacher in ICT attending four days of professional development in 2013. The sharing of knowledge learned and modelled in the Key Teachers classroom and to staff in both PLC meetings and through classroom support. Acquisition of i-pads for teaching staff with the aim of teachers becoming competent users in preparation for 2014 implementation of iPads with students. Key teacher ICT reviewing technology in the school.
Distributing Leadership Data analysis and decision regarding focus involved all staff. Whole school testing schedule (Appendix 1), upgrading of diagnostic testing resources and collection and recording of school based data has been implemented with the aim of collecting and monitoring school data and student progress over time.
Key teachers driving areas of curriculum development particularly in ICT and mathematics. Ownership of decisions regarding implementation of our investigation to rest with the Professional Learning Community. A re-examination of optimum teaching beliefs and values as a Professional Learning Community. (Appendix 2).
Engaging in Action Learning Use of evidence to identify a singular focus for investigation. Commitment to Collaborative Professional Learning in Action model process. Collecting school based data on current school practises and actions, followed with actioning of determined aims in order of identified needs. Professional Learning Community Regular gatherings held to investigate and discuss implementation of focus.
Professional Learning Ongoing commitment to professional reading from a wide range of sources. Provision of professional development as required in focus area including key teacher numeracy learning and whole school professional development days. Relief provision for teachers to visit other schools to view a variety of models of practice in our focus area.
In addition to these supportive structures we will be continuing or implementing the following strategies: Whole School problem solving in mathematics continued focus. The addition of mathematical vocabulary and language to our focus question. Literacy and Numeracy Dedicated time continued. EMU teacher and daily EMU sessions in Year Two with the intention of reviewing outcomes by comparing NAPLAN results of previous EMU students. In 2014 Emu teacher will divide time between EMU activities with students, tracking and supporting previous EMU students and supporting teachers to implement small group work and support structures within the classroom. The school has renewed the 2014 EMU training commitment of 30 minutes a day with EMU over a minimum of 20 weeks. On-going tracking of students, reporting and analysis of students and support for teachers in the school. The provision of an additional hour for EMU teacher release to provide teacher support, on- going tracking and recording of EMU and at risk students’ achievement in mathematics and following up support provisions for these students. MAI to be introduced for at risk students across year levels.
Our Investigation During 2013 our focus question for investigation has been: How do we ensure that our students have a repertoire of specific strategies to develop critical and creative thinking in the proficiency strand/ Problem Solving in Numeracy?
PREPARING: The initial preparation for our 2013 focus took place at the end of 2012 with whole school involvement in analysis of school data and the identification of areas requiring renewed focus or improvement. It was a whole school decision that the guided reading focus had progressed to the stage of embedding the now agreed whole school practices. This would continue to be revisited and supported. In the early part of 2013 the professional learning meeting agenda was focused on QCS. Our meetings then became focused on our question the end of term two with our first PLC focus dedicated meeting in late May. Using the Professional Learning in Action model our learning our investigation has progressed through the stages discussed below and examined in terms of content, students and pedagogy. In term of content, we wanted to investigate the progression of learning in this area and identify common needs and existing knowledge. In terms of our students, we wanted to find out where our students are in terms of the use of understanding of problem solving strategies and processes and diagnostic and formative assessments we had in place or could implement that would allow us to track this. Finally in terms of pedagogy, we wanted to investigate effective strategies for teaching problem solving skills, processes and strategies.
During the year we committed to the Collaborative Professional Learning in Action Model process. We started by looking out at what the research was telling us in our focus area and investigating how our focus area was addressed in other schools. We then looked in and, in order to find out what quality teaching and learning practice looked like in our school, we organised shoulder to shoulder visits, shared discussions and data collection of what teachers were already doing in our school through a staff survey (Appendix 3). We investigated the current collection of student data in the school and data collection in general. We investigated the resources within the school to assist in the teaching of problem solving skills in mathematics and what we could do to improve these resources. This included the enlisting of support from the C.E.O. mathematics consultant to review mathematics equipment and resources in the school. We discussed and investigated the need to further develop and implement shoulder to shoulder learning within our school and how powerful a medium this would be in our school community. We re-examined our key beliefs and values in regard to learning, identified areas needing renewal or focus and asked ourselves what obstacles there have been in these areas.
REFINING. In the refining phase of the Action Learning Cycle we wanted to investigate ways to act on the results of our looking in and looking out from the preparation stage. We implemented several initiatives within the school including a whole school tabloid mathematics problem solving day, a weekly mathematics problem in the newsletter and a professional development day with the C.E.O. mathematics consultant with the following goals:
To investigate Problem Solving in the AC_M Content and Proficiency Strands. To develop a shared definition of what Problem Solving means at Santa Clara. To explore a range of problems To learn about Polya’s Four Steps. To decide whether the Newman Analysis would be useful. To appreciate the value of context in Problem Solving.
A maths audit was held and mathematics equipment has been reviewed with the assistance of the mathematics consultant, organised into boxes for each year level with the remaining equipment organised into kits or boxes and stored in a central easy access and use. A wish list of mathematics resources and equipment was prepared and all of these have subsequently been acquired.
Through our PLC meetings, PD and professional conversations we have decided a whole school language and a whole school scope and sequence is needed. We have created a mathematical vocabulary checklist and based on our professional readings and, with the support of the EMU teacher, have identified language and questioning that can help extend children’s thinking. This is being compiled as a whole school mathematical language and vocabulary scope and sequence booklet (Appendix 5). Our final CPLiA focus meetings and actions for 2014 will be to begin the development of a whole school scope and sequence across year levels based on our identified student needs and the Australian Curriculum. As a whole school we have introduced a model for problem solving R.U.C.S.A.C. (Read, Understand or underline, Choose, Solve, Answer, Check) from Years One to Six to ensure we have a common language and process across year levels. Posters highlighting and describing this process are displayed in classrooms and in the staffroom along with problem solving strategies.
As a result of our PLC examination and analysis of school based data, we have reviewed our standardised testing schedule and updated resources with the acquisition of current Progressive Achievement Tests for Maths. School based data will now be stored in in one location on the shared drive, as student cohorts progress through the year levels school based data along with NAPLAN, WAMSE and other forms of state or National testing will be used to track progress of individuals and groups. EMU (Extending Mathematical Understanding) data will be collected and used to track students inform the future structure of the EMU program. Previous EMU students will be identified and supported beyond Year Two and EMU data will be stored with other school based data on the shared drive.
We have used our 2013 NAPLAN and PAT-M school based data to identify at risk students and will trial multi-age grouping three days a week. The following arrangements will be implemented: two groups of Year One and Two students (with the possibility of some at risk Year Three students) and a further four ability groupings from Years Two to Six.
Key teachers for mathematics, the EMU teacher and in fact all teachers have supported each other to further develop our teaching and learning practices in mathematics. We plan to continue to support our own and each other’s learning as teachers come together and share their strategies, initiatives and success on a regular basis through our PLC meetings.
EMBEDDING. We are now moving between the refining and embedding phase of our Action Cycle where we will continue to investigate and work on the sustainability of our initiatives. Our Professional Learning Community has agreed that in 2014 we need to continue refining and embedding the practices and initiatives that have come out of our 2013 work. We agree that, based on our diverse and multi- cultural community, that language development must also be a part of all initiatives driving student’s needs and therefore have restructured our focus question to include mathematics language development. We have agreed that we have made considerable in roads as a teaching staff into the development of whole school strategies, procedures and attitudes towards problem solving in mathematics. As we continue to engage in the Action Cycle in 2014 by embedding the initiatives introduced in 2014, we will also move between the refining and embedding stage by continually assessing and reviewing our student needs and teaching actions.
CHECKING:
In 2014 we would like to continue our initiative by analysing our data and developing grade level plans for the teaching of problem solving strategies, ensuring that all teachers are using the R.U.C.S.A.C. approach to the problem solving process in their classrooms. We will follow through with the incorporation of the Mathematical Vocabulary and continue to monitor student progress with the collection and storing of whole school data. We will continue to maintain and revisit whole school and agreed guided reading. We will revisit our Optimal Teaching Beliefs and Values (Appendix 2) and PLC Policy and Procedures (Appendix 4) to ensure all staff agree and are committed to the Action Learning model for our professional learning community and school improvement through our literacy and numeracy action plan.
OUR DATA:
In Term Four of 2013 PAT-M was used to collect mathematics data. We have reviewed the 2013 NAPLAN data and school based Pat-M data and all agree that mathematics as a whole is an area requiring whole school focus. An analysis of the PAT-M data has been carried out and will be used in 2014 to inform teachers of individual and student cohort needs. We will further highlight priority areas, develop our school scope and sequence needs and monitor identified individuals and concepts. Furthermore with the introduction of a whole school testing schedule the cycle of data collection will continue in future years. In Term Four of 2014 our school data will be used to measure improvement and progress.
STATE AND NATIONAL TESTING:
In this section reference is made to NAPLAN, WAMSE and Bishops Literacy Test data.
Religious Education: Bishops Literacy Test.
Observations: In 2012 our results showed our Year Five group mean to be slightly above the state mean. In 2013 our results have remained stable or improved slightly against the state mean. Science Observations: In 2011, our Science results are slightly above all Schools Mean and in Science Investigating our results were above the all Schools Mean. In 2013, our Science results are slightly below the All Schools Mean and similar results can be seen in Science Investigating with our school mean 8 points below the All Schools Mean. Society and the Environment
Society and the Environment ICP
Observations: In 2011, our SOSE results were above the all Schools mean in both SOSE and ICP. Our results in 2013, SOSE results remain slightly above the All Schools mean and in ICP our results were almost equal to but slightly below the state mean.
Reading. 1019 Santa Cl ar a School Readi ng
800 780 760 740 720 700 680 660 640 620 600 580 560 540 520 500 Year 5 480 Year 7 460 Year 3 440 420 400 380 360 340 320 300 280 260 240 220
2006 2007 2008 2009 2010 2011 2012 2013
Observations: 2013 Reading results indicate that our Year 3 students are above Similar School with an upward trend. The Year 5 results are below similar schools. However, they do show an upward trend over time and we intend to monitor these results in the future. With our whole school focused on Guided Read and reading comprehension we would expect to see these results further improve. In 2014 we intend to revisit, continue to embed and enhance our reading comprehension focus. The P&F have committed funds for guided reading books and resources across year levels. We also have Reading Recovery teacher who will provide valuable support in the area of reading. Spelling 1019 Santa Cl ara School Spel l i ng
800 780 760 740 720 700 680 660 640 620 600 580 560 540 520 Year 7 500 Year 5 480 460 440 Year 3 420 400 380 360 340 320 300 280 260 240 220
2006 2007 2008 2009 2010 2011 2012 2013
Observations: 2013 Spelling results indicate that our Year 3 students are above Similar School with an upward trend. The Year 5 results are below similar schools. However, they do show a upward trend over time and we intend to monitor these results in the future. With our whole school focused on Guided Read and reading comprehesnion we would expect to see these results further improve
Grammar and Punctuation
1019 Santa Cl ar a School Gr ammar & Punctuati on
800 780 760 740 720 700 680 660 640 620 600 580 560 540 520 Year 5 500 Year 7 480 Year 3 460 440 420 400 380 360 340 320 300 280 260 240 220
2006 2007 2008 2009 2010 2011 2012 2013
Observations: 2013 Grammar and Punctuation results indicate that our Year 3 students are above Similar School with an upward trend. The Year 5 results are below similar schools. However, with a steady trend over time and we intend to monitor these results in the future. Writing
1019 Santa Cl ar a School Wr i ti ng ( Per suasi ve)
800 780 760 740 720 700 680 660 640 620 600 580 560 540 520 500 Year 5 480 460 440
420 Year 3 400 380 360 340 320 300 280 260 240 220
2006 2007 2008 2009 2010 2011 2012 2013
Observations: In 2013 Year 3 are significantly below Similar Schools, with an even trend. Yr 5 results are below Similar Schools and are aclosing the gap, moving closer to Similar Schools. They are on an upward trend. As many of our students come from background where English is not their first language we acknowledge that writing in the early years will continue to be a challenge.
Numeracy
1019 Santa Cl ar a Sc hool Numer acy
800 780 760 740 720 700 680 660 640 620 600 580 560 540 520 500 Year 7 480 Year 5 460 440
420 Year 3 400 380 360 340 320 300 280 260 240 220
2006 2007 2008 2009 2010 2011 2012 2013
Observations 2013 Numeracy results indicate that our Year 3 students are above Similar School with a downward trend. The Year 5 results are below similar schools, with a steady trend. Of concern is the when our Year 5 students were in Year 3 they were well above similar schools and now in Year 5 they have dropped to below similar schools. We are concerned about this and will investigate further. FOCUS AREA DATA for 2014. Numeracy
After much discussion and analysis of data, the Professional Learning Community at Santa Clara believes that our data indicates Numeracy continues to be an area of need.
School Over Time Year 3
Year 5 Our Year 3’s continue to be above the mean of Similar schools, while our Year 5 students continue to be below the mean. In Year 3 we are reducing the number and range of students in the 5 th to the 20th percentile and moving our upper average students into the 80th to 95th percentile. We are catering well for our lower and middle achieveing students. In Year 5 our students in the 60th to 80th percentile (dark blue) and our students in the 80th to 95th percentile are not scoring as high as students from similar schools. We need to ensure that our highest performing students are being catered for and also ensure that we are cateringand extending all our stlduents. This indicates a need to examine how we are differentiating the curriculum in order to cater for our more able students. 1019 Santa Cl ar a School 1019 Santa Cl ar a School 2013 Numer acy Year 3 Al l Austr al i an School s Mean: 396.9 2013 Numer acy Year 5 Al l Austr al i an School s Mean: 485.9 NAPLAN NAPLAN School Mean: 415.1 School Mean: 478.7
518 622 B a B n a d n
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498 8 School 602 21% School 478 15% 582 2 B 0 B a 458 % a n 562 2
n d o 0 d
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418 t n u 522
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School d
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School 378 482 63% 6 0 %
358 o B 462 B f a
a A n 6 n u d 0 d s
% 3 t 5 r
o 338 a f l 442
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i 22% i n n o o i i n n m m a 258 a 362 u l u l B B B B m m 2 a a e 0 e
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2 o w a 1 w a 3 0 238 f 342 n n
% A d d u a a o s r r f t
d d r A a u l i s a t r n a
S l i a t u n d
S e n t u t s d e n t s Distribution Observations: Our Distributions graphs indicate that our Year 3 mean is above the mean of the Nation or All Australian Schools. Year 5 Mean are is below the all Austrlaian mean. In Year 3 it is pleasing to note that we do not have any students at or below minimum benchmark, with the majority of our students stitting in the middle bands. In Year 5, our Distribution graph is negatively skewed. 22% of our students are at or below minimum standard when compared to the nation. With less that the nation in the top bands. Once again indicating a need to ensure we cater for our highest achieving students. Bands As we are concerned about our middle years of schooling we examined our bands to see where our students were sitting in comparision to similar, state and national schools. Year 5 2012 Year 5 2013
1019 Santa Cl ar a School 1019 Santa Cl ar a School 2012 N umer ac y Year 5 2013 N umer acy Year 5
40.7 %
36.4 % 37.4 % 31.4 % 27.6 % 26.4 %26.8 % 26.0 %26.7 % 27.3 %26.9 % 26.9 %27.5 % 25.7 %24.5 % 22.2 % 17.3 % 18.5 % 17.6 % 15.4 % 15.7 % 18.2 % 17.1 % 14.8 %14.6 % 15.7 % 15.5 % 15.7 % 11.2 % 13.5 % 12.9 % 10.1 % 9.3 % 9.6 % 7. 3 % 9.1 % 8.3 % 9.1 % 4.7 % 3.7 % 6.9 % 6.8 % 1.9 % 2.6 % 4.6 % 0.0 % 1.1 % 0.3 % 0. 0 % 0.0 % 1.3 % 2.0 % 1.3 % 0.0 % 0.0 % 0.0 % School StateN ati onalSi mi l ar Sc hool St ateNati onalSi mi l ar Sc hool StateNati onalSi mi l ar School StateNati onalSi mi l ar Sc hool Stat eNati onalSi mi l ar School StateN ati onalSi mi l ar Sc hool St ateNati onalSi mi l ar School StateN ati onalSi mi lar Sc hool StateNati onalSi mi l ar Sc hool StateNati onalSi mi l ar School StateNati onalSi mi l ar School StateNati onalSi mi l ar School StateNati onalSi mi l ar Sc hool StateN ati onalSi mi l ar Exempt Band 3 Band 4 Band 5 Band 6 Band 7 Band 8 Exempt Band 3 Band 4 Band 5 Band 6 Band 7 Band 8
Observations: Our Band percentage distribution graphs indicate that in Year 5 we have more students in bands 3 and 4 than Similar Schools which shows our weaker students and lower average are in need of more support. The upper average students are not being challenged to move into the higher bands as we have fewer students in Bands 7 and 8. This indicates that we need to ensure that we are catering for our more able students in numeracy. Our bands grapshs onceagain Indicates the need for a differentiated curriculum to cater for all our students. Cohort Over Time
1019 Santa Cl ara School 1019 Santa Cl ar a School Year 5 Numeracy Students assessed at thi s school and are stil l here / Compared agai nst SimiSimil l ar Schools data 2012 Year 5 Numeracy Students assessed at thi s school and are sti l l here / Compared ag ai nst Si mil ar School s data
B 610 B a n a
d n 600 d
8 590
8 580
B 570 B a n a d n 560 d
7 550
7 540 530
B 520 a 510 B n a d n
d 6
500 490 6
480 470 B a B
n 2013 a
d 460
450 n
5 d
5 440 430
B 420
a 410 B
n a d n
4 390 d 400
4
370 380 B a B n 350 360 d a n 3 d
330 3 340
B 310 320 B a n a d n d
2 290 300
2
Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 2007 2008 2009 2010 2011 2012 2008 2009 2010 2011 2012 2013
Observations: We looked at our Cohort Over Time graph for the past few years to gain a clearer picture of the needs of our students. The above Cohort Over Time graphs indicates that when our Year 5 students were in Year 3, their mean was above the mean of Similar Schools and their mean is now below Similar Schools. This indicates that the students have not moved as expected. The narrower spread of students in the 80th to 95th percentile on the Year 5 graph indicates that we were not able to cater for our more able students as effectively as when they were in Year 3. The need for a differentiated curriculum is highlighted by this data collection.
Progress and Student Progress
1019 Santa Cl ar a School 1019 Santa Cl ar a School 2013 Numer ac y Year 5 2013 Numer acy Year 5 Compar ed ag ai nst Si mi l ar School s data B a
n 640 d 120
9
B 620 a Si mi lar Schools Mean Gr owth: 100 n 100 d
8 600
80 580 B a
n 560 d 60
7 540 40 520 B a n d
500 20 6
480 School Mean Gr owth: 1 0 B
a 460 n d
5 - 20 440
420 - 40 B a n
d 400
4 - 60 380
- 80 B 360 a n d
3 340 - 100
320 B a - 120 n d 300
2 Observations: Our Student Progress graph indicates that almost 50% of students have gone backbards. With very few of our students making expected progress. Generally, the students at the top of the scale have made only very small gains between Year 3 and Year 5. Once again, this indicates that we need to investigate how we can ensure that we are differentiating the curriculum in order to cater for all students. We also note that our expected progress was 100 while our schools actual progress was only 1. When examining graphs from previous years progress (from 2010, 2011 and 2012) our students achieved close to expected growth.
Regression PP- Yr 3 Year 3 - 5
1019 Santa Cl ar a School 1019 Santa Cl ar a School 2007 Numer acy ( PIPS) Pr e- Pr i mar y - 2010 Numer acy Year 3 2008 Numer acy Year 3 - 2010 Numer acy Year 5
622 518 B B SchoolAl l Students a School a n n d d
8 602
6 498
582 478 Al l Students B a
B 562 n a 458 d n
7 d
5 542 438 522 B
418 a n B d
a 502
6 n
d 398
4 482
378 B 462 a n d B
358 5 a 2
n 442 0 d 1
0 3
2
338 N 0
u 422 1 m 0 B e
N r a a
u 318 n
c 402 d m y
B e 4 Y r a e a n a
c 298
d 382 r y
5 2 Y e
a 362 278 B r
a 3 n d
258 3 342 B a n d
1 238 218 249 280 312 343 374 405 436 468 499 530 2008 Numer acy Year 3
35 41 47 53 59 65 71 77 83 89 95 2007 Numer acy ( PIPS) Pr e- Pr i mar y
Observations:
Our PIPS graph indicates that most students have progressed as expected between Pre Primary and Year 3. We still need to ensure that all students especially our lower achievers are still being supported. Yet again emphasising the need for a differentiated curriculum. Our Regression graph for Year 3 to 5 also shows that many of our students are not making expected progress and these students appear to be in the middle to upper average groups of students.
2013 (> 5% below expected mean) Year 3 Space Recognises a cylinder Interprets geometric properties to identify a triangle Identifies corresponding faces given two different views of a model Recognise designs that are not symmetrical Counts the edges of a given hexagonal prism Identifies the shape resulting from folding a rectangle along its diagonal MEASUREMENT, CHANCE and DATA Find the total value of coins in a column graph ALGEBRA Matches a given addition fact to an inverse operation. (Q15)
NUMBER Interprets decimal in a money context Solves a multistep problem involving Compares amount of money in a decimal form Calculates the distance for 3 laps given the amount for 4 laps Applies subtraction and multiplication to solve a multistep problem Year 5 SPACE Identifies the names in a specified cell of an alpha numeric grid Identifies the coordinates of a point on an alpha numeric grid Recognises symmetrical shapes Uses and informal scale to estimate distance on a grid Calculates the number of edges of a prism Calculates the number of blocks in a prism given its scale diagram MEASUREMENT, CHANCE and DATA Identifies a true statement for data in a table. Recognises the angle closest to 100 and 45 degrees. Identifies data to evaluate the likelihood of an event. ALGEBRA Recognises division of a decimal by ten NUMBER Applies understanding of a fraction Applies subtraction of two digit numbers to solve problems Solves a problem involving multiplying by ten and subtraction. Determines the four notes needed to make a total of $57 Multiplies and subtracts small amounts of money to solve a problem Solves a problem involving multiplication and subtraction of money.
The table above shows an analysis of our 2013 NAPLAN results in the area of Numeracy for Years 3 and 5. We examined our Data to identify particular concepts that repeatedly came up below the expected mean for our school. We found that problem solving is an area that our students have struggled with repeatedly over time.
THE FUTURE After much discussion and exploration of school level data, the Professional Learning Community believes that there is a need to continue to focus on the area of Numeracy. Our school data collected supports the need to expose, immerse and explicitly teach our children the vocabulary used in working mathematically as well as providing many opportunities for them to use this vocabulary orally. Therefore we determined that this was an area that we would explore further while continuing with our problem solving focus from 2013. We will explore the question: How do we ensure that all students have a deep understanding and the ability to use mathematical vocabulary when developing the Numeracy proficiencies of problem solving and reasoning? While we explore this question we will keep in mind different learning styles and pedagogies as identified through our QCS observations and assessment
We will explore: Content What do students need to understand about problem solving? What language do we need to teach? What are the common misconceptions in the teaching and learning of problem solving?
Students How do we identify the point of need for our students in their understanding of problem solving? How do we identify through our formative assessment the level of understanding of our students in their understanding of problem solving? How do we assess students’ use of mathematical vocabulary?
Pedagogy What are the most effective strategies to teach problem solving?
How do we ensure that we cater for all students during Maths session?
Research and develop effective resources to support and encourage mathematical language and problem solving.
The following supportive structures will assist our investigation: 1. Revisit and enforce our non- negotiable of Numeracy Dedicated Time 2. Use our Vocabulary of Mathematics booklets and closely monitor that we are explicitly teaching and providing opportunities for students to engage and use this vocabulary. 3. Continue to expect and ensure manipulates are used during Maths sessions 4. Enforce that Mental Computation is part of the daily routine in every classroom. 5. To continue to use the ENI assessment tool in Year 1 and 2 and the PAT Maths Test in years 3 to 6 to develop a highly diagnostic classroom teaching program in Numeracy. 6. Continue with EMU teaching in Year Two whilst ensuring that EMU students are tracked, results are recorded in the whole school data collection central location and teachers are supported to continue to support these students. 7. Conduct research into best known practice and engage in professional reading and development. 8. Explore and use Literature that promotes and incorporates the vocabulary of Mathematics. 9. Continue to ensure that our investigation is lead by our Coordinator of Professional Learning.
APPENDICES
Appendix 1: WHOLE SCHOOL TESTING SCHEDULE. (Included at the end of this document).
Appendix 2: OPTIUMUM TEACHING BELIEFS AND VALUES (Separate to this document). Appendix 3: STAFF SURVEY: What we are already doing – What we would like to see happening in our school or
clusters. (Included at the end of this document).
Appendix 4: POLICY AND PROCEDURE FOR PROFESSIONAL
LEARNING COMMUNITY. (Included at the end of this document).
Appendix 5: SANTA CLARA SCHOOL MATHEMATICAL VOCABULARY -SCOPE AND SEQUENCE BOOK.
APPENDIX 1. SANTA CLARA SCHOOL
WHOLE SCHOOL TESTING SCHEDULE. SANTA CLARA SCHOOL – WHOLE SCHOOL TESTING AND DATA COLLECTION SCHEDULE. Version 2. At Santa Clara School testing is carried out with the purpose of collecting data to monitor student achievement over time, for diagnostic purposes and to inform our teaching and learning programs.
In the interest of avoiding over-testing standardised whole class testing will take place once a year in term four for Years Two and up. This will help us create whole class profiles and individual profiles which will enable tracking over time. This data can inform end of year reporting and allow us to identify patterns or changes in student achievement. By testing at the end of year, the beginning of the next school year can be used to follow up students identified at risk or with changes in their achievement levels.
Data gathered from the testing schedule below will be collated and stored in the shared drive in the “WHOLE SCHOOL TESTING” folder. Results can be matched up with previous standardised test results to measure growth for individuals and whole class. YEAR FEB ( Term One) FEDERAL,STATE OR OCT/NOV (Term Four) OTHER TESTING. Kindy CONCEPTS OF PRINT HEALTH NURSE SCREENING CONCEPTS OF PRINT Pre-Primary PIPS TEST PIPS TEST Year One Observation Survey assisted MAI by Helen Jackson.
Year Two Observation Survey at risk Pat R Comprehension Book 1 students. S.A. (Westwoods) Spelling Test S.A (Westwoods) Spelling A. Test B. PatMaths Book 2. Maths Assessment Interview Year Three Observation Survey at risk NAPLAN – TERM TWO Pat R Comprehension Book 2. students. BISHOPS LITERACY – TERM Pat R Vocabulary Book 1. TWO S.A. (Westwoods) Spelling Test A. PatMaths Book 3. Year Four Pat R Comprehension Book 2. Pat R Vocabulary Book 2. S.A. (Westwoods) Spelling Test A. PatMaths Book 4. Year Five NAPLAN – TERM TWO Pat R Comprehension Book 3. BISHOPS LITERACY – TERM Pat R Vocabulary Book 3. TWO. S.A. (Westwoods) Spelling Test WAMSE – TERM THREE. A. PatMaths5 Year 6 CIVICS AND CITIZENSHIP TERM PatR Comprehension Book 3. F0UR PatR Vocabulary Book 3. S.A. (Westwoods) Spelling Test A. MTS – ACM APPENDIX 2.
(A separate addendum to this document). APPENDIX 3.
LOOKING IN AND GATHERING INFORMATION.
1. The Survey
2. The Collated Results.
3. A Review Of Actions. THE SURVEY.
Looking In: Below is a summary of our brainstorming session on 21st May to establish what we are already doing as a school and what we would like to be doing. All contributions have been recorded and there is space to add additional information if you would like to. The next step is to disseminate this information. Please indicate with a yes or no by writing your particular year level in the appropriate column on “What We Are Already Doing Math Problem Solving”. Please indicate with your year level and/or comment next to the suggestions that you agree with or would like to see happening in the What we would like to be doing as a whole school or in clusters (ECE, junior, middle or upper). WHAT WE ARE ALREADY DOING IN MATH PROBLEM SOVLING. Numeracy Block YES NO Maths Assessment Interviews (EMU) Teaching Problem Solving Strategies Diagnostic Naplan Whole Part Whole Teaching Do Talk Record Using Interactive Whiteboard Using Hands on Resources Using Open Ended Investigations/Inquiry Based Learning
What we would like to see happening in our school or clusters. Year Level / Comment Whole School Scope and Sequence Organised central resource area Common maths language Maths library Using i-pads Whole school timetabled literacy blocks Collaborative learning Multi-aged activity centres Maths incursions Whole school data collection (Diagnostic) current and useful Maths focus days Emu dedicated person Parent education Problem of the Day Maths challenge in the newsletter Focus problem solving strategies in classroom Common language Resource making Parent help / involvement Community involvement THE COMPILED SURVEY RESULTS.
Based on input from all teaching staff
: Looking-In Maths P.S. Looking In: After brainstorming together on 21st May we listed things that we are already doing and things we would like to see happening as a whole school or cluster focus. We then marked in with our year levels to determine what is happening as a whole school or clusters and what we would like to see happening as whole school or clusters. Below is a summary with the things you indicated you would like to see happening most (the most number of year levels) highlighted as follows: Everyone would like this. Almost everyone would like this (7 out of 8). WHAT WE ARE ALREADY DOING IN MATH PROBLEM SOVLING. YES NO Numeracy Block PP - 6 N/A Maths Assessment Interviews (EMU) YR 2 K-1, 3-6. Teaching Problem Solving Strategies K-6 Diagnostic Naplan YR 3 AND 5 Whole Part Whole Teaching K-6 Do Talk Record YRS 2,3,5,6 Using Interactive Whiteboard K-6 Using Hands on Resources K-6 Using Open Ended Investigations/Inquiry Based Learning K-6 Maths focus days (planned) Yrs. 4,5,6. Collaborative Teaching Yrs 5,6.
What we would like to see happening in our school or clusters. Year Level / Comment Whole School Scope and Sequence Everyone would like to have this. Organised central resource area Everyone would like to have this. Whole School common maths language All classes except one would like to have this. Maths library Four of eight year groups would like to have this Using i-pads Everyone would like to be doing this. Whole school timetabled literacy blocks Two year groups would like to have this. Collaborative learning All classes except one would like to have this – some year groups are doing this. Multi-aged activity centres (across clusters) Five of eight year groups would like to have this. Maths incursions Five of eight year groups would like to have this. Whole school data collection (Diagnostic) current and useful All year groups would like to have this. Maths focus days (Whole school, clusters – year groups) Six of eight year groups would like to have this. Emu dedicated person Three year of eight year groups would like this. Parent education All year groups would like this. Problem of the Day Four year groups would like this. Maths challenge in the newsletter Four groups would like this. Focus problem solving strategies in classroom All classes except one would like to have this. Resource making Five out of eight year groups would like this. Parent help / involvement Three out of eight year groups would like this Community involvement Four out of eight year groups would like this A REVIEW OF OUR ACTIONS.
: Looking-In Maths P.S. Looking In - Below is the summary presented to staff in Term Two with implemented or in progress points now highlighted as below We have done this. This is happening. WHAT WE ARE ALREADY DOING IN MATH PROBLEM SOVLING. YES NO Numeracy Block PP - 6 N/A Maths Assessment Interviews (EMU) IN YEAR TWO YR 2 K-1, 3-6. Teaching Problem Solving Strategies K-6 Diagnostic Naplan YR 3 AND 5 Whole Part Whole Teaching K-6 Do Talk Record YRS 2,3,5,6 Using Interactive Whiteboard K-6 Using Hands on Resources K-6 Using Open Ended Investigations/Inquiry Based Learning K-6 Maths focus days (planned) Yrs. 4,5,6. Collaborative Teaching Yrs 5,6.
What we would like to see happening in our school or clusters. Year Level / Comment. Everyone would like this. Almost everyone would like this (7 out of 8).
Whole School Scope and Sequence Language scope and sequence Everyone would like to have this. in progress. Organised central resource area Everyone would like to have this. Whole School common maths language In progress, All classes except one would like to have this. Maths library – resource area in board room. Four of eight year groups would like to have this Using i-pads staff only to date. Everyone would like to be doing this. Whole school timetabled literacy blocks Two year groups would like to have this. Collaborative learning All classes except one would like to have this – some year groups are doing this. Multi-aged activity centres (across clusters) Five of eight year groups would like to have this. Maths incursions Five of eight year groups would like to have this. Whole school data collection (Diagnostic) current and useful All year groups would like to have this. Maths focus days (Whole school, clusters – year groups) We have Six of eight year groups would like to have this. had one with students and one with staff – term 3. Can we have another? Emu dedicated person Sue Hawkins. Three year of eight year groups would like this. Parent education All year groups would like this. Problem of the Day - Four year groups would like this. Maths challenge in the newsletter Larry is doing this. Four groups would like this. Focus problem solving strategies in classroom RUCSAC All classes except one would like to have this. Resource making Five out of eight year groups would like this. Parent help / involvement Three out of eight year groups would like this Community involvement Four out of eight year groups would like this APPENDIX 4.
SANTA CLARA SCHOOL.
POLICY AND PROCEDURES
FOR
A COLLABORATIVE LEARNING COMMUNITY. 1. Purpose and Rationale.
Santa Clara school, as part of Catholic Education in Western Australia, follows the Bishops Mandate which states “… the work of school leaders, teachers and school officers (support staff) requires a sophisticated array of knowledge, skills and attributes, which, in the face of constant and rapid social, economic, technological and educational change, requires continual enhancement.” At Santa Clara school we believe that through our professional learning community and the development of a shared vision and goals we can achieve optimum learning and development for students, teachers and others in our school community.
This policy explains what constitutes the collaborative professional learning community at Santa Clara School and sets out a framework and procedures for engagement and active participation. The overarching aim is to ensure that students receive the highest quality learning experiences through interaction with teaching staff who are recognised for their professional expertise and who, through close collaboration with other members of staff, are able to build increased capacity for teaching and learning in our school community.
The objectives of this policy are to:
• articulate what constitutes collaborative learning in our school
• outline the principles that underpin collaborative learning
• encourage partnerships that recognise expertise and promote collaborative teaching practices that are relevant to the learning outcomes of students
• support the negotiation of collaborative teaching partnerships and arrangements and shoulder to shoulder learning between teachers that meet the needs of all stakeholders.
2. Definitions, Terms, Acronyms.
PLC – professional learning community, committed educators working collaboratively in an ongoing process of collective inquiry and action research to achieve optimum results for students.
CPLiA – collaborative professional learning in action, this outlines a collaborative process that guides our school to develop, refine and embed solutions to pedagogical questions that build on the strengths already present in our school.
KT – key teacher - a key teacher is a practicing classroom teacher who provides a model of effective practice within a particular learning area and who seeks opportunities to make connections across learning areas and general capabilities and integrates their focus area across the curriculum.
CPL – coordinator of professional learning - the coordinator of professional learning enables and supports professional learning within the school. They work with the leadership team to guide and support teachers by providing opportunities and time for authentic professional learning. They support teachers to deepen their knowledge of content, pedagogy and students and integrate this knowledge in their classroom through a process of collaborative professional learning.
Aitsl – Australian Institute For Teaching and School Leadership – The Australian Charter for the Professional Learning of Teachers and School Leaders describes the characteristics of high quality professional learning in improving teacher and school leader practice.
3. Who Is This Policy For?
This policy applies to all current teaching staff and education assistants including designated leaders, teachers and others involved in the education of students at Santa Clara. It is relevant to all new and returning staff members.
4. Policy Statement
4.1 The principles that underpin this policy are:
• Teachers need to work collaboratively, where their strengths are acknowledged and promoted and they are given opportunity to learn from each other in order to develop deeper knowledge and understanding of education and gain higher levels of expertise.
• Teachers are professionals who have the expertise to sustain their own enquiry and practice and therefore can be responsible for stimulating productive pedagogies that will lead to improved student learning.
• Time needs to be allocated for close collaboration between designated leaders, CPL, key teacher leaders and others who contribute to improved educational outcomes of students.
• All staff members are responsible for meeting relevant professional standards as outlined in the Australian Charter for the Professional Learning of Teachers and School Leaders (aitsl, 2013). As professionals teachers are responsible for actively engaging in professional learning in order to build their capacity and that of others.
• Teachers engage in reflecting critically on practices and achievements individually and collectively to build their capacity and that of others.
• All staff are encouraged to participate in wider networks and professional organisations.
• All staff including designated leaders, teacher leaders and others need to be fully committed and engaged in the development of collaborative actions and articulating and documenting our shared goals and vision for whole school improvement.
• Leaders are engaged in and model learning and are committed to supporting and facilitating support structures and professional learning opportunities to enhance, improve and develop teachers’ pedagogical skills, knowledge and practice and the development of a learning culture. 4.2 Arrangements for Collaborative Teaching and Learning
To ensure quality collaboration, teaching staff and leadership must work together with a shared commitment to open communication, mutual respect and valuing of the views and expertise of each other.
Teachers with particular experiences and expertise will share resources, encourage dialogue and provide opportunities for shoulder to shoulder learning. Dialogue between teachers in partnership or clusters will enable agreement to be reached on appropriate models of sharing for year levels.
Shoulder to shoulder learning will be governed by agreed protocols. Observation theme will be agreed upon prior to engaging in shoulder to shoulder learning and will be followed by two way feedback between teacher partners.
5. PROCEDURES:
1. The professional learning community will meet regularly and engage in both formal and informal dialogue based on our defined requirements.
2. Teachers and participants will actively participate in PLC meetings by chairing, sharing resources and ideas, contributing professional readings, share professional learning opportunities and engaging in dialogue and discussion.
3. School data will be analysed and areas for potential improvement will be identified as a team. This will form the basis of an agreed instructional inquiry question that will become the school focus for improvement.
4. The PLC will articulate and document as a community optimum teaching and learning beliefs and values and agree on non-negotiable behaviours and teaching practices. This will be revised and shared at the commencement of each school year.
5. All members of the teaching community agree to acknowledge and respect the contributions, knowledge and expertise of other members in the spirit of suspension of judgement and a positive approach.
6. Key teachers will be appointed in core or focus learning areas to model effective practice and actively contribute their expertise to the professional learning community.
7. Teachers will work with teaching partners or clusters to engage in collaborative planning and teaching and shoulder to shoulder activity. APPENDIX 5.
SANTA CLARA SCHOOL.
Mathematical Vocabulary Development. Santa Clara School
Santa Clara School. Mathematics Vocabulary Development. Santa Clara School
Mathematical Vocabulary Scope and Sequence Book INTRODUCTION Who is this book for?
The purpose of this book is to identify the words and phrases children need to understand and use if they are to make good progress in mathematics. It is based on the Australian Curriculum (http://www.australiancurriculum.edu.au/Mathematics/Curriculum/F-10) and the Australian Curriculum; Western Australia (http://www.acwa.wa.edu.au/keyareas/mathematics). This book has been reviewed by teaching staff at Santa Clara School and aims to assist teachers to monitor and evaluate the introduction and understanding of mathematical vocabulary at our school. Why do we need this book?
Teaching staff at Santa Clara School, as a professional learning community, have engaged in examination of current curricula, academic readings and individual and group reflection on classroom practices in relation to mathematical vocabulary. As a result teachers at Santa Clara School have articulated the belief that children need to acquire appropriate vocabulary so they can participate in the activities, lessons and mathematical concepts encountered in daily life. We believe the acquisition and understanding of mathematical language is crucial to children’s development of thinking and reasoning mathematically, mathematical fluency and ability to solve problems as described in the proficiency strand of the Australian Curriculum. Current school and state data indicates the need for school improvement in mathematics. Teachers have observed and articulated the concern that our students need to further develop “the language of mathematics” in order to raise achievement levels in this learning area. How is this book organised and how can we use it?
To assist teachers to introduce, monitor and reinforce appropriate mathematical language to students at Santa Clara, this book in organised into checklists for student year groups. Within the year groups it is further organised into mathematical areas: Number and Algebra, Measurement and Geometry and Statistics and Probability as described in the Australian Curriculum. Using and applying mathematics is integrated throughout this book and at the each year group concludes with language commonly used when giving instructions about mathematical problems.
The words listed for each year level include vocabulary from the previous year, with new vocabulary printed in red. Some words may appear under different strands in different year levels as the meaning is expanded or becomes more specific.
Class teachers can use these lists to identify the vocabulary relating to teaching points and include in specific planning. They can make provision for the introduction of new vocabulary and the consolidation of familiar terms and existing vocabulary. The EMU support teacher, support staff and parents can also emphasise this vocabulary. The checklists are not intended to be exhaustive and teachers can add appropriate new vocabulary during the year to be added in the annual review of mathematical vocabulary at Santa Clara School. How do children develop their understanding of mathematical vocabulary?
Teachers often use informal, everyday language in mathematics lessons before or alongside technical mathematical vocabulary. Although this can help children to grasp the meaning of different words and phrases, a structured approach to the teaching and learning of vocabulary is essential to facilitate mathematical development and the understanding and correct use of mathematical terminology. Children come to Santa Clara School with varying understanding of mathematical words when used formally in either English or a home language. It is therefore important for teachers to establish the extent of mathematical vocabulary and the depth of the students understanding as soon as possible in order to begin with the students’ needs. Teachers can then plan the introduction of new words in context, explain meanings and provide opportunities to use and reinforce the words. Every opportunity to draw attention to new words or symbols with the whole class, in groups or with individuals can be used to reinforce new mathematics vocabulary. The use of word walls, reading and writing the new vocabulary in a range of circumstances and including new mathematics words within spelling lists are strategies that can be employed as children progress through year levels.
Regular, planned opportunities for the development of mathematical vocabulary are nee ded at all levels of primary school. A cycle of oral work, reading and writing which is compatible with the “do, talk, record” model which requires students to first experience visually or through tactile experiences, discuss and articulate understandings and processes before attempting to record through drawing or abstract form.
Oral work, based on practical work, allows students to have visual images and tactile experiences of what mathematical words mean in a variety of contexts. Other forms of oral work can include:
listening to adults and other children using the words correctly
acquiring confidence and fluency in speaking, using complete sentences that include the new words and phrases, individually and in groups
describing, defining and comparing mathematical properties, positions, methods, patterns, relationships, rules
discussing ways of tackling problems, collecting data, organising work
hypothesising or making predictions about possible results
presenting, explaining and justifying methods, results, solutions
reasoning to whole class, groups or partners
convincing others
generalising or describing examples that match a general statement
Reading aloud and silently, sometimes as a whole class and sometimes individually can include reading:
numbers, signs and symbols
expressions and equations from whiteboard, posters or other shared media
instructions and explanations in books, web-sites, aps and other media
texts with mathematics references in fictions and non-fiction books
rhymes during literacy hour and mathematics hour
labels and captions on classroom and school displays, diagrams, charts, graphs and tables
definitions in illustrated dictionaries, websites, posters and signs.
synonyms, origins or words, words that include the same letter patterns in spelling lessons, word study activities and literacy lessons
Writing and recording in a variety of ways, progressing from words, phrases and short sentences to paragraphs and longer pieces of writing such as:
writing prose in order to describe, compare, predict, interpret, explain, justify… writing formulae, first using words, then symbols
sketching and labelling diagrams in order to clarify their meaning
drawing and labelling graphs, charts or tables, and interpreting and making predictions from the data in them, in mathematics and other learning areas The Skill of Questioning.
Children do not learn the meaning of words in isolation, the use of questions is crucial in helping them to understand mathematical ideas and use mathematical terms correctly. It is important to ask questions in a variety of ways and stages of lessons and activities to cater for different needs and learning styles. A full range of question types will give students the best opportunity to expand and explain their thinking and develop vocabulary and grammatical structures through mathematics. Types of questions.
Recalling facts: What is 3 add 7? How many days are the in a week? How many centimetres are the in a metre? Is 31 a prime number?
Applying facts: Can yell me two numbers that have a difference of 12? What unit would you choose to measure the width of the table? What are the factors of 42?
Hypothesising or Predicting: Estimate the number of marbles in this jar? If we did this survey again, how likely is it that our graph would be the same? Roughly, what is 51 times 47? How many rectangles in the next diagram?
And the next?
Designing and Comparing Procedures: How might we count this pile of sticks? How could we subtract 37 from 82? How could we test a number to see if it is divisible by 6? How could we find the 20th triangular number? Are there other ways of doing it?
Interpreting Results: So what does that tell us about numbers that end in 5 or 0? What does the graph tell us about the most common shoe size? So what can we say about the sum of the angles in a triangle?
Applying Reasoning: The seven coins in my purse total .85c; What could they be? In how many different ways can four children sit at a round table? Why is the sum of two odd numbers always even? Further examples of questions of promote good dialogue and interaction in mathematics discussion.
Below are examples of closed questions (with just one correct answer) and open questions (with a number of different correct answers). Open questions give more children a chance to respond and provide greater challenge and opportunity to develop or extend understanding in mathematics.
CLOSED QUESTIONS. OPEN QUESTIONS.
Count these cubes. How can we count these cubes?
A bag of chips costs $1.25. A lolly pop costs .35c. A bag of chips and a lolly pop cost $1.60 altogether. What do they cost altogether? What could each item cost?
What is 6 – 4? Can you name two numbers with a difference of 2?
CLOSED QUESTIONS. OPEN QUESTIONS. Is 16 an even number? What even numbers lie between 10 and 20?
What are four threes? Tell me two numbers with a product of 12.
What is 7 x 6? If 7 x 6 = 42, what else can you work out?
How many centimetres are there in a metre? Tell me two lengths that together make 1 metre?
Continue this sequence: 1, 2, 4…… Find different ways of continuing this sequence 1, 2, 4….
Write eight different ways of adding two numbers to make 1? What is one fifth add four fifths? Find ways of completing …% of …= 30. What is 10% of 300? Sketch and label some different triangles. What is this shape called?
QUESTIONS THAT CAN HELP TO EXTEND CHILDRENS’ THINKING.
Basic skills: the “big 10” before embarking on problem-solving exercises, children need to be able to: Make sense of what the problem means. Identify and understand key vocabulary. Break the problem down into easier steps. Identify the maths needed to solve the problem. Decide what number operation(s) is (are) needed. Select the most efficient method of calculation. Choose suitable units to work in. Estimate what an answer is likely to be. Check the solution by using another method. Ensure the answer makes sense. At Santa Clara School the R.U.C.S.A.C. approach to problem solving is used throughout the school. The children follow the process with appropriate assistance according to their year level. The R.U.C.S.A.C. problem solving strategy begins with: READ – the problem (this will happen with the teacher for younger students. UNDERSTAND – the problem by understanding or underlining the maths in the problem. CHOOSE – the operation and/or strategies to solve the problem. SOLVE – the problem using the operations selected. ANSWER – the question/problem (children need to recognise that the answer to the problem is not always the answer to a “sum”). CHECK – the answer reasonableness or the answer or use inverse strategies to check working out. Questioning can be used as children work through this strategy at the commencement, during and after the problem solving process. As a professional learning community the teachers at Santa Clara are actively involved in sharing teaching and
Questions for children getting started. Questions for children who are stuck.
How are you going to tackle this? Can you describe the problem in your own words?
What information do you have? What do you Can you talk me through what you have done so far? need to find out? Have you solved a similar problem before? What did you What operation(s) are you going to use? do last time? What is different this time?
Will you solve this mentally, with pencil and Is there something that you already know that might paper, using a number line, a calculator…? Why? help? Could you try it with simpler numbers…..fewer What method or strategy will you use? Why? numbers…..using a number line…?
What equipment will you need? What about putting things in order?
What questions will you need to ask yourself? Would a table or diagram help? The teacher? Your team? Why not make a guess and check if it works? How are you going to record what you are doing? Have you compared your work with anyone else’s? What do you think the answer or result will be? Can you estimate or predict?
Positive interventions to check progress. During the lesson ask…
Can you explain what you have done so far? How did you get your answer? What else is there to do? Can you describe your method/pattern/rule to the class? Why did you decide to use this method? Can you explain why this works?
Can you think of another method that might What could you try next? work? Would it work with different numbers? Could there be a quicker way of doing this? What if you had started with …. rather than….? Can you explain what you mean by….? What if you could only use….? What did you notice when…? Is it a reasonable answer/result? What makes you say Why did you decide to organise your results like so? this? How did you check it? Is there a pattern or a rule here? What have you learned or discovered today? Do you think that this would work with other numbers? If you were doing this again, what would you do differently? Have you consider all factors? …thought of all possibilities? How can you be sure? Having done this, when could you use this method, information, idea again?
Did you use any new words today? What do they mean? How do you spell them?
What are the key points or ideas that you need to remember for next lesson?
At Santa Clara school specific problem solving strategies are named and taught. Strategies such as those included as Appendix 1 are named, reinforced, described and displayed. Students are exposed to mathematical terms and symbols in a variety of ways and visual reminders and stimulus for both teachers and students are displayed in classrooms, staffroom, workrooms and other common areas. The following section is a mathematical vocabulary checklist for year levels.
SANTA CLARA SCHOOL.
Mathematical Vocabulary Checklists
Kindergarten to Year 6. EARLY YEARS: Kindergarten and Pre- primary.
Students at this level will use much of this vocabulary through play in keeping with the play-based philosophy of early years’ education.
Counting and recognising numbers. Adding and subtracting.
Counting Adding and subtracting
Number Add, more, and
Zero, one, two, three….to twenty and beyond. Make, sum, total
None Altogether
How many…? One more, two more, ten more…
Count, count up to How many more to make…?
Count on … from… to How many more is… than…?
Count back … from… to Take away, leave
Count in ones How many are left/ left over?
More, less, many, few How many have gone?
Every other One less, two less…ten less…
How many times How many few is…than…?
Pattern, pair Difference between
Guess how many, estimate Is the same as
Nearly, close to, about the same as
Just over, just under
Too many, too few, enough, not enough Problem Solving Measurement and Geometry. pattern Measure, Size, Compare puzzle Guess, estimate, enough, not enough answer More, less, too much, too little, too many, too few right, wrong Nearly, closes to, about the same as, what could we try next? Just over, just under
How did you work it out? Length, width, height, depth, Long, short, tall
Count, sort High, low, wide, narrow, deep, shallow, thick, thin
Group, set Longer, shorter, taller, higher….etc.,
Match Longest, shortest, tallest, highest…etc.,
Same, different Far, near, close
List Weigh, weight, weighs, balances, heavy/light, heavier/lighter, heaviest/lightest Compare Balance, scales, weight Double, half, halve Full, half full, empty, nearly full, nearly empty, Pair Container Count out, share out Time Days of the week; Monday, Tuesday… Lef, left over Day, week, Money, coin, dollar Birthday, holiday, weekend Price, cost Morning, afternoon, evening, night, bedtime, dinnertime, Buy, sell playtime
Spend, spent Today, yesterday, tomorrow,
Pay Before , after, next, last, now, soon, early, late, quick, quicker, quickest, quickly, slow, slowly Change Old, older, oldest, new, newer, newest, takes longer, takes Dear, costs more less time
Cheap, costs less, cheaper Hour, o’clock, clock, watch, hands How much,…? How many….? total
Exploring Patterns, shape and space Position, direction and movement
Shape, pattern, Position, over, under, above, below\
Flat, curved, straight, round, Top, bottom, side, on, in
Hollow, solid, Outside, inside
Corner Around, in front, behind, Face, side, edge, end Front, back, before, after,
Sort, Beside, next to, opposite, apart
Make, build, draw Between, middle, edge,
Cube, pyramid, sphere, cone, Corner,
Circle, triangle, square, rectangle, star, hexagon, Direction, left, right, up, down rhombus, diamond, Forwards, backwards, sideways, Size, bigger, larger, smaller Across, Pattern, repeating pattern Close, far, near, match Along, through
To, from, towards, away from
Movement,
Slide, roll, turn, stretch, bend
Instructions General
Listen, join in, say Same number(s), different number(s), missing number(s) number facts, Think, imagine, remember Number line, number track, number square, number Start from, with, at cards,
Look at, point to, show me Counters, cubes, blocks, rods,
Put, place, fit Die, dice, dominoes,
Arrange, rearrange, change, change over Peg, peg board,
Split, separate Same way,
Carry on, continue, repeat, Different way, best way, another way
What comes next? In order, in a different order,
Find, choose, collect Not, all, every, each Use, make, build
Tell me, describe, pick out, talk about, explain,
Show me
Read, write, trace, copy, complete, finish, end
Fill in, shade, colour
Tick, cross
Draw, draw a line between
Join up,
Ring, Cost, count, work out, answer, check