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Donna Forster Written Action Project Proposal S00113908 Written Action Research Proposal STUDENT NAME: Donna Forster STUDENT NO: S00113908 TITLE OF RESEARCH PROJECT: KEEP IT OPEN: THE EFFECT OF OPEN-ENDED TASKS IN MATHEMATICS IN A YEAR 5 CLASSROOM Introduction/Problem/Statement/Research Context: Teachers have a challenging role in their ability to balance adequate learning with their students in all areas of the curriculum. In the key learning area of mathematics, each classroom will present a variety of learning abilities and thus it is difficult to provide a task or assessment that will cater for the range of abilities. The ‘No Child Left Behind’ policy advocates high expectations and all students are provided with the opportunity to reach the curriculum standards (Pacific Resources for Education and learning, 2005). One of the most effective strategies for this is the implementation of open-ended rich mathematical tasks which create no limitations for students to demonstrate their knowledge (Ferguson, 2009). The context of this issue relates to a year 5 class where students are easily becoming off task during the delivery of mathematics lessons. Students are disengaged and the results on assessment tasks are becoming significantly lower, especially for those students who are already placed below the academic standards of the year. The teacher has been utilising a knowledge delivery method and administering several mathematics worksheets, including extension worksheets to those students who are early finishers. For many years students have been given repetitive tasks and problems that require one solution, and focused on only one path to arrive at this solution (Kwon, Park & Park, 2006). The aim of 1

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Donna Forster Written Action Project Proposal S00113908

Written Action Research ProposalSTUDENT NAME: Donna ForsterSTUDENT NO: S00113908TITLE OF RESEARCH PROJECT: KEEP IT OPEN: THE EFFECT OF OPEN-ENDED TASKS IN MATHEMATICS IN A YEAR 5 CLASSROOMIntroduction/Problem/Statement/Research Context:

Teachers have a challenging role in their ability to balance adequate learning with their

students in all areas of the curriculum. In the key learning area of mathematics, each classroom will

present a variety of learning abilities and thus it is difficult to provide a task or assessment that will

cater for the range of abilities. The ‘No Child Left Behind’ policy advocates high expectations and

all students are provided with the opportunity to reach the curriculum standards (Pacific Resources

for Education and learning, 2005). One of the most effective strategies for this is the

implementation of open-ended rich mathematical tasks which create no limitations for students to

demonstrate their knowledge (Ferguson, 2009).

The context of this issue relates to a year 5 class where students are easily becoming off task

during the delivery of mathematics lessons. Students are disengaged and the results on assessment

tasks are becoming significantly lower, especially for those students who are already placed below

the academic standards of the year. The teacher has been utilising a knowledge delivery method and

administering several mathematics worksheets, including extension worksheets to those students

who are early finishers.

For many years students have been given repetitive tasks and problems that require one

solution, and focused on only one path to arrive at this solution (Kwon, Park & Park, 2006). The

aim of open-ended tasks is to provide opportunity for student’s to actively construct their

knowledge through divergent and creative thinking approaches whether it is constructed

individually or cooperatively with peers. Implementation of an open-ended task approach needs to

be accompanied through a variety of strategies including personalisation of problems, cooperative

learning groups and effective teaching strategies such as questioning in these inquiry based lessons.

This action research project will focus on the implementation of personalised open-ended tasks to

improve academic achievement in mathematics.

Research Question:

Will implementing open-ended questions in the year 5 classroom improve academic achievement in

mathematics?

Supporting questions:

How can I effectively use open-ended mathematics tasks to improve academic achievement?

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Donna Forster Written Action Project Proposal S00113908

How will personalising the open-ended tasks improve academic achievement?

Literature Review

The research into alternative methods of delivery of mathematics has been a challenging

area for teachers over the last 40 years. The role of the teacher is to keep students engaged while

creating collaborative learning environments harnessing divergent thinking. One solution to this

challenge is the use of open-ended problems, which are distinguished by the multiple solutions and

the ability to offer students numerous approaches to the methods of obtaining the solution

(Hancock, 1995). However as Pehkonen suggests, it is important to implement open-ended tasks in

more than merely assessment tasks (Pehkonen, 1997). Mack’s research heavily opposes traditional

knowledge delivery approaches that is most common in classrooms, showing the interference that

rote memorisation and repetitive procedures had when attempting to solve problems in real-world

situations (Mack, 1990). Students often draw on incorrect explanations when reasoning their use of

strategies as these were not understood but rather memorised (Mack, 1990).

Although conducting her research in the USA, Gullie states that many students leave

primary school with a disconnected understanding of mathematics, where they find difficulty in

applying their mathematics knowledge in different situations (Gullie, 2011). Gullie implemented

open-ended tasks as a predictive measurement of achievement on a high-stakes test and thus was

able to include that high achievement on the open-ended test correlated with high achievement on

the later high-stake testing/assessment (Gullie, 2011). Assessment of learning is essential to

understand student’s mathematical knowledge both pre and post teaching. Assessment gives

teachers information on students understanding and effectiveness of their programs and instruction

(National Council of Teachers of Mathematics, 1995). In addition the use of personalised word

problems within these open-ended tasks ignites student’s motivation and their attentiveness to

remain on task (Bates & Wiest, 2004).

Benefits of open-ended tasks generally lie in the different approaches to thinking. An ability

to solve open-ended problems effectively develops the human ability of creativity and the skill of

thinking of something new (Kwon, Park & Park, 2006). Kwon, Park & Park furthermore suggested

that an advantage is that students can answer the problem in their own meaningful way and in return

provide a sense of achievement despite their mathematical ability (Kwon, Park & Park, 2006).

Negatives for open-ended tasks include the lengthy time they require in order to reach the solution

(Hancock, 1995). In some cases, the open nature of the tasks also allow students to explore multiple

areas of mathematics and thus can veer learning from a specific content area the teacher is

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Donna Forster Written Action Project Proposal S00113908

addressing (Sullivan, Warren & White, 2000). Overall, open-ended tasks with personalisation show

positive and negative implications for academic achievement of students.

Methodology:

Evidence-based practices such as action research are highly encouraged through government

initiatives and programs especially for beginning teachers (Foreman-Peck & Murray, 2008). Action

research is defined as an inquiry or investigation that is carried out by teachers to reflect on their

own practice or the environment in which they are practicing (Ax, Ponte & Brouwer, 2008).

Essentially it works towards teachers becoming effective reflective practitioners, those who learn

through their experiences and transform to become better educators (Johns, 2009).

This research project of investigating open-ended tasks in improvement of academic

achievement for year 5 students will utilise John Creswell’s action research model. Creswell (as

stated in Mills) describes action research as a “…dynamic and flexible process…” which can be

broken into the following steps: determining if action research is appropriate, identifying a problem

to focus on, finding resources to help address this problem, collecting necessary information,

implementing the data collection, analysing the data, designing an effective plan for action or

intervention and implementing this plan, and finally reflecting on whether or not the intervention

was successful (Mills, 2014, p.18). This model is most effective for this study, emphasising

collecting data prior to implementing action and thus suggesting the use of a pre-test and post-test

method. The only negative of this model is that there is no emphasis on the repetition of the

process; the process of research is cyclical and thus new questions arise from results enhancing the

role of the teacher as the reflective practitioner (Somekh, 2006). This can be achieved by continuing

to repeat the process designed by Creswell when problems, questions or issues arise.

As Mills states, “The decision about what data is collected… is largely determined by the

nature of the problem” (Mills, 2014, p.83). The goal of this action research is largely based on

academic achievement and results in preferring the method of quantitative collection of data

through teacher made tests. Quantitative data allows the researcher to come to generalized

conclusions and statements when they have found trends in data of a considerably larger sampler

size where more than one class is used, however, it does not provide observational data directly of

the students experiences, struggles and achievements (University of South Alabama, 2013).

Unfortunately, with quantitative methods of data collection and maintaining the ethical nature of

school-based testing, other variables will come into play such as differentiated teacher instruction

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Donna Forster Written Action Project Proposal S00113908

(Mills, 2014). The Appendix in this action research project is key for teachers to understand the

process that will be undertaken and the type of tasks delivered to students.

Planning of your research data collectionSample:

In order to be able to obtain the generalized statements that can be concluded from

quantitative data it is important to have quite a large sample size. Sample size is important because

too large presents ethical issues such as waste of time of participants, and too small may lead to

results that are not transferable to the larger context and thus a waste of participants time (Francis et

al., 2010). The sample size will therefore be obtained from 3 different year 5 classes (total of 90

students) at the same school in order to keep the other variables to a minimum. The main focus will

be on the change in results of the pre and post-tests conducted. The reason for using the same

school is to allow for planning of curriculum content together reducing discrepancies that things

will be taught for longer periods of time or not taught at all, as well as allowing teachers to have

regular contact during the implementation of open-ended tasks throughout the different

mathematics strands.

Methods:

This action research project will utilise the use of teacher-made tests in the pre and post test

form (Appendix 2 & 3). Mills suggests that teacher-made tests do not rely on textbook companies

and allow teachers to adapt curriculum materials as a valid measure of the academic performance of

their students (Mills, 2014). These questions will be open-ended, those that in general elicit more

information than closed tasks which will allow teachers to gain an overall understanding on the

processes their students have grasped in particular mathematics content strands (Cohen, Manion &

Morrison, 2011). To ensure the tests are effective in their purpose of determining academic

achievement the questions will be different on the pre and post tests, however, they will address the

same content and the level of difficulty will remain the same (Cohen, Manion & Morrison, 2011).

In order to address the concept of personalisation of mathematics problems, the teachers will use

common names and items in the wording of questions, which have been identified previously in a

survey (Appendix 1). The process of surveying and testing will begin at the end of Term 1(see

timeline). Teachers will then introduce 2 open-ended tasks per content area being taught providing

guidance and assistance as students work through them. Teachers will reflect after each task is

given and demonstrate some effective methods of solving these tasks. At the end of term 3, students

will be administered the post-test. The results from the pre and post-test will then be interpreted and

results/further questions identified.

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Intervention:After the pre-test and survey is administered, in week 2 students will take part in a 2 hour

development session as a grade on how to best answer open-ended tasks using modelling from other

students and students. In this session teachers will utilise 2 open-ended warm-up activities, one

known as the broken calculator activity and the second will be general number busting (Appendix

4). The reason why we have chosen these questions is so they are not similar to the layout of the

pre-test but still allows students to think about the multiple answers available to answer the problem

(criteria of an open-ended task). Once students have completed the activity in their group the

teacher will bring students together to share responses that they discovered in their activities with

the guidance of teachers questioning. A grade session will reduce variables as all students are

exposed to the same content.

The second form of intervention will be during the teaching of mathematic content from

term 2 week 3, until term 3 week 8. In this case teachers will continue to teach maths content as per

the syllabus, however, integrated into their planning is 2 open-ended tasks per topic covered (a total

of 18 open-ended tasks over the 16 week period –Appendix 5). These tasks are used from the same

textbook “Investigations, Tasks and Rubrics to Teach and Assess Math” by Liburn & Ciurak and

will also be used as a basis for the questions for the pre- and post- tests. Teachers will ensure there

is a focus on discussion and reflection at the conclusion of these tasks.

Proposed Analysis:The pre- and post-test results will need to be analysed so conclusions can be made. Marking

of the test will occur by the researcher, questions will be worth 3 marks each, 2 marks for the

working out and 1 mark awarded for the right answer. Initially, the researcher should collect and

collate data into column graphs in order to group results together and bring to attention outliers.

There after, analysis of this data will be done so using descriptive statistics where mainly the central

tendency (mean, median, mode and range) and variability (standard deviation) will be compared in

both the pre and post-tests (Sage Publications, n.d.). The spread out of scores can be shown using

the standard deviation; a larger value for standard deviation may cause the researcher to rethink

whether general statements can be made in relation to achievement in the academic concept (Mills,

2014). It will also be important for the researcher to report on the statistical significance in order to

conclude findings and allow for a meaningful relationship between the pre- and post- test to be

drawn (Sage Publication, n.d.). An additional recommendation is the comparison of each student’s

results using a chart form (Appendix 5). Here the students may be numbered from 1-90 and their

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Donna Forster Written Action Project Proposal S00113908

results inputted on a computer as a pre-test and post-test comparison. This will assist an

understanding on whether an improvement in academic achievement is made in individual students.

Ethics:

The ethical nature of this project is adhered to in the data that is collected but also in the

nature of the research question to improve teaching, also known as beneficence (Vallance, 2005).

As mentioned above, the size of the sample is reasonable enough to produce effective results and

valid statements that can be concluded from this study ensuring that the test is not considered a

‘waste of time’. Sieber, as cited in Vallance’s article suggests five principles expanded from

Belmont’s three, including: “Valid research design, competence of the researcher, identification of

consequences, selection of subjects, voluntary informed consent and compensation for injury.”

(Vallance, 2005). The first is addressed in beneficence whilst the second can be addressed through

the researcher’s role as the classroom teacher and the purpose of the action research to prove

academic achievement of students within their school setting. Identification of consequences and

selection of subject is addressed within the action research plan where all institutions require ethical

clearance, usually through a board of members in order to satisfy institutional standards (Vallance,

2005). The most essential of the five principles is the voluntary informed consent because of the

intimate nature of action research (Mills, 2014). This is addressed within this action research

proposal through the ethical documentation attached. The principal will be given information

(Appendix 7) to ensure they are aware of the process that will be taking part in their school, which

needs to be signed and returned (the principal will also maintain a copy). In addition, parents will be

administered with both an information form (Appendix 8) and consent form to be signed and

returned for each participant (Appendix 9), to ensure they are aware of the process occurring with

their child’s learning and the use of the results from this study. Parents will however be ensured

confidentiality, no names will be disclosed in any results or findings. With the study using

quantitative data, it is much easier to exclude personal details in the research process (Mills, 2014).

Moreover, all teachers taking part in this study will also be given information for participant’s form

(Appendix 10) and an adult consent form (Appendix 11). All participants will have their own copy

following signing.

Reliability and Validity:Reliability and validity ensures the quality of the action research project that is being

undertaken (Sage Publications, n.d.). Reliability, according to Mills, is the degree to which a test

consistently measures what it has aimed to measure usually through repetition of tests (Mills, 2014).

In essence, reliability is the replication of similar results ensured with the sample of 90 students

(Winter, 2000). To prove reliability in reporting, the researcher should use a reliability coefficient

using the scale of 0-1, the closer the coefficient is to 1, the more reliable the test. As mentioned 6

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Donna Forster Written Action Project Proposal S00113908

above, the standard deviation will measure variability and whether or not the scores are consistent,

the higher the standard deviation, the less reliable the results are.

Validity is the most important concept to ensure in the planning of action research as “A

valid test is always reliable, but a reliable test is not necessary valid.” (Mills, 2014, p. 120).

Moreover, Winter agrees with this relationship in stating that validity is firstly whether the

measurements are accurate and secondly whether they measure what they intended to measure

(Winter, 2000). Ultimately, a perfect testing environment would ensure that there is no interference

from other variables in the testing procedure and will utilise the use of a control group. Within a

classroom and school environment the interplay between the many factors that influence students

lives is virtually impossible to remove and unethical to do so, however, in this project as only one

concept (open-ended tasks) is being used as the independent variable. The concept of validity also

relates to the initial research question and intervention techniques (Winter, 2000). The intervention

within this proposal aims to introduce students to open-ended tasks (the independent variable) and

the pre- and post- test is utilised to measure what it is intended to measure, the academic

achievement, if any.

Timeline:Term Week Activity1 10 Students will be administered a survey in regards to their interests (Appendix 1).

11 & 12

Teachers and teacher-researcher will collaboratively design the pre- test and post-test (Appendix 2 and 3) for their year 5 students, integrating the topics they will cover in term 2 and 3. These topics will include those shown in Appendix 5. This planning will ensure the pre-test and post-test contain the same strands in the KLA and that these strands are integrated into planning time.

2 1 Students will be administered the pre-test with open-ended tasks. Researcher will collect data and display in graphs to show the range of marks.

2 Teachers will provide a grade session on open-ended mathematic tasks explaining what is expected of students in their answers, what is needed and how to best address and open-ended task when it is given

3-10 Teacher continues to teach mathematic content as listed in planning time and integrates the use of open-ended questions/tasks 2 times per topic or content area covered. These open-ended tasks are planned prior to teaching and included in programs.

3 1-8 Teacher continues to teach mathematic content as listed in planning time and integrates the use of open-ended questions/tasks 2 times per topic or content area covered. These open-ended tasks are planned prior to teaching and included in programs.

9 Students will be administered the post-test with open-ended tasks and questions. Researcher will collect data and display to show the range of marks.

10 Teacher-researcher will analyse data using statistical figures such as mode, median, mean, significant difference etc. Teacher-researcher will then compare the difference between pre- and post-tests to come to conclusions on the effectiveness. This discussion time will also give teachers time to discuss the responsiveness, perceived attitude and ability of students in their class.

Figure 2 Timeline of Action Research Project

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Donna Forster Written Action Project Proposal S00113908

ReportingThis action research project will provide insightful information for the principal, teachers,

parents, students and further educators extending the immediate community. In order to ensure the

action research project maintains high ethical standards it is important to report findings to the

stakeholders in an easy to understand manner to ensure they are able to understand the success of

the findings. This may be achieved in a simple 2-page summary of the project sent home to parents,

or an invitation to an information night where the parents may be shown evidence in the form of

pictures and samples of the tests the students were involved in. Sharing this information to fellow

colleagues is also encouraged. The project fits into the big picture of research into increasing

academic achievement of students in mathematics through a variety of approaches and thus writing

up this project in a journal form helps the researcher to better understand what occurred within the

project, and creates an accessible article for fellow colleagues and educators to access (Mills, 2014).

ConclusionThis action research project will equip teachers with a better understanding on the

effectiveness of personalised open-ended tasks on increasing academic achievement. This study

provides only a small insight into the complex nature of the variables that interplay teaching open-

ended tasks and thus leaves further areas for study such as the frequency of exposure to open-ended

tasks for students. As discussed in the “big picture” of this action research proposal were additional

interventions for divergent and creative thinking approaches, however, within this study, the

independent variables were kept to a minimum by only changing the type of tasks to personalised

and open-ended. Limitations of this study include limited professional development of teachers into

correct questioning techniques as well as limited focus on the types of questioning needed. The use

of three different classes also required three different teachers to teach students content, increasing

the factors that will influence the results as each teacher approaches content in different manners.

Inoue & Buczynski in their research study of open-ended tasks created a camp setting where there

was a focus on only maths and thus reduced the interplay of other variables; this may be a

consideration in further studies (Inoue & Buczynski, 2011).

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List of references

Ax, J., Ponte, P. & Brouwer, N. (2008). Action research in initial teacher education: an explorative

study. Educational Action Research, 16(1), 55-72. DOI:10.1080/09650790701833105

Cohen, L., Manion, L. & Morrison, K. (2011). Research Methods in Education. 7th ed. Oxon:

Routledge.

Educational Policy Institute (2005). The No Child Left Behind Act of 2001 and the pathways to

college network framework: mutually supportive visions and complementary goals. Pacific

Resources for Education and Learning. Retrieved from:

http://www.educationalpolicy.org/pdf/PREL_NCLB.pdf

Ferguson, S. (2009). Same Task, Different Paths: Catering for Student Diversity in the Mathematics Classroom.

Australian Primary Mathematics Classroom, 14(2), 32-36.

Foreman-Peck, L. & Murray, J. (2008). Action research and policy. Journal of Philosophy of

Education, 42(1), 145-163.

Francis, J. J., Johnston, M. Robertson, C., Glidewell, L., Entwistle, V., Eccles, M. P. & Grimshaw,

J. M. (2010). What is an adequate sample size? Operationalising data saturation for theory-

based interview studies. Psychology and Health, 25(10), 1229-1245.

DOI:10.1080/08870440903194015

Gullie, K. A. (2011). Open-ended (extended/constructed) response questions as predictors of

success on subsequent state mathematics examination: the influence of mathematical

awareness and conceptual knowledge. Pro Quest Dissertations and Theses, 136. Retrieved

from: http://search.proquest.com/docview/867093379?accountid=8194.

Hancock, C. L. (1995). Mathematics learning with open-ended questions. The Mathematics teacher,

88(6), 496-499. Retrieved from: http://www.jstor.org/stable/27969418

Hetzler, N. (2004). Analysis of Pre- and Post-Tests: A Kindergarten Unit on Patterns. In McAllister,

D. A. & Bothman S. M (Eds), Culminating Experience Action

Research Projects (pp. 126-138). Retrieved from: http://files.eric.ed.gov/fulltext/ED490030.pdf9

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Johns, C. (2009). Becoming a reflective practitioner. United Kingdom: Wiley-Blackwell.

knowledge. Journal for Research in Mathematics Education, 21, 16–32.

Kwon, O. N., Park, J. S. & Park, J. H. (2006). Cultivating divergent thinking in mathematics through an open-

ended approach. Asia Pacific Education Review, 7(1), 51-61.

Liburn, P. & Ciurak, A. (2010). Investigations, tasks, and rubrics to teach and assess math. California, USA:

Math Solutions Scholastic Inc.

Mack, N. K. (1990). Learning fractions with understanding: Building on informal

Mills, G. E. (2014) Action Research: A guide for the Teacher Researcher. 5th ed. USA: Pearson

Education.

Sage Publications. (n.d.). Part I “What is Action Research?”. Retrieved on 3rd October 2013 from

http://www.sagepub.com/upm-data/38973_1.pdf

Somekh, B. (2006). Action Research: a methodology for change and development. New York,

USA: Open University Press.

University of South Alabama. (2013). Strengths and weaknesses of Quantitative Research.

Retrieved on 1st October 2013 from

http://www.southalabama.edu/coe/bset/johnson/oh_master/Ch14/Tab14-01.pdf

Vallance, R. J. (2005). Research ethics: reforming postgraduate information. Issues in Educational

Research 15(2), 193-205. http://www.iier.org.au/iier15/vallance.html

Winter, G. (2000). A comparative discussion of the notion of ‘validity’ in qualitative and

quantitative research. The Qualitative Report, 4(3). Retrieved from:

http://www.nova.edu/ssss/QR/QR4-3/winter.html

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Appendix 1 – Personalisation SurveyWhat do you like to do?

List three of your favourite activities you enjoy doing after school:

1) ____________________________________________2) _____________________________________________3) _____________________________________________

List three things you do not like to do:1) ____________________________________________2) _____________________________________________3) _____________________________________________

List three of your favourite foods:1) ____________________________________________2) _____________________________________________3) _____________________________________________

Where are your 3 favourite places to visit:1) ____________________________________________2) _____________________________________________3) _____________________________________________

What do you enjoy doing on the weekend?________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

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Appendix 2: Pre- Test

Name:________________ Date:1. Rebecca took out 1/6 of the M&M’s that were in the packet. How many M&M’s could have been in the packet to start off with?

2. In a long-jump competition Sarah jumped 2.4 metres and Jessica jumped 2.04 metres. Sarah came first and Jessica came third. What distance might the girl who came second have jumped? What distance might the girl who came fourth jumped? What was the total of the 4 jumpers?

3. Three schools raised a total of $125,750 for charity. Each school raised a different amount but were within $3000 of each other. What amount might each school have raised?

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4. When I tossed two eight-sided dice and multiplied the results I got a product that was an odd number. What numbers might have been on the dice?

5. Farmer Luke needed to build a pen on his property to keep his sheep in. He had 150m of fencing to use. What could his pen have looked like?

6. Freya measured the area of a shape and found it to be 48 centimetres squared. It was not a rectangle. What could her shape have looked like?

7. During the recent bake sale Keely’s mum made 24 brownies. How many different ways could she pack the brownies to fit into a box?

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8. Mrs Edward’s collected the scores on the recent spelling test. The mean and the median of 9 scores was 12. What might the numbers have been?

How do you think you went?

Appendix 3: Post-testName: __________________ Date:1.Indiana and Jules were given a bag of gobstoppers. If Indiana takes ¼ of the chocolates and Jess takes 1/5 of the bag, how many chocolates may have been in the bag and how many might still be in the bag?

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2. 10 students in 5 blue were measuring their heights to see who was the tallest student in the class. The tallest student was 1.55m and the shortest was 1.05m. What could the 10 measurements of students have been? What could be the total

height of the 10 students?3. Jason was comparing the cost of three motorbikes that he was going to buy. The total of the three motorbikes was $36

650. What could the cost of each motorbike have been?

4. Lee used a pack of cards and took out the K, Q, J and A. Using the numbers he multiplied 3 numbers together to get a number bigger than 50. What 3 numbers could he have multiplied together?

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Donna Forster Written Action Project Proposal S00113908

5. Joshua was helping his dad build a pen to keep his rabbits in. Each 10 centimetre of fencing costs $1.50. He only had $80 to spend. How might he have designed his rabbit enclosure?

6. Mr Frost was designing his new kitchen to be built. He only had 32 metres squared of tiles to use. What might his kitchen have looked like?

7. A prism was made with four layers of 9 cubes. What other ways can you make a prism with the same volume as this one?8. Keegan opened a packet of skittles with 5 different colours:

red, green, purple, yellow and orange. He had ¼ chance to

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Donna Forster Written Action Project Proposal S00113908

receive a green skittle. How many skittles did he have altogether? What chance did he have to receive a red skittle?

How do you think you went?

Appendix 4: Session Activities

Broken Calculator ChallengeThe number 7 and 5 appear to have broken on your calculator. Your challenge is to make the following numbers on you’re the calculator:

7577557

757 575

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Donna Forster Written Action Project Proposal S00113908

Joel wants to calculate 757 + 575 on his calculator, but the buttons are still not working. How can he do this without using 2 & 5?

Jen wants to calculate 24 X 42 on her calculator, but the buttons 2 & 4 appear to be broken. How can she calculate the answer to her problem?

Number BustingTo become a great mathematician, you need should

know how to use the 4 operations effectively.

How many different ways can you number bust 36?

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Donna Forster Written Action Project Proposal S00113908

How many times can you number bust 424?

How many times can you number bust 2500?

Appendix 5:Brief Overview of Maths ProgramTerm 2 Week 3 & 4 Fractions

Week 5 & 6 Decimals & Percentages

Week 7 & 8 Multiplication & Division

Week 9 Addition & Subtraction

Week 10 REVIEW WEEK19

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Term 3 Week 1 & 2 Length & Perimeter

Week 3 & 4 AreaWeek 5 & 6 Volume &

CapacityWeek 7 & 8 Data & Chance

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Donna Forster Written Action Project Proposal S00113908

Appendix 6: Suggested Graph

Figure 2 Proposed Chart to compare individual students (Hetzler, 2004).

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Donna Forster Written Action Project Proposal S00113908

Appendix 7: Information to the Principal

Appendix 8: Information for the participants

Appendix 9: Consent form for caregivers/parents

Appendix 10: Information for teachers

Appendix 11: Adult consent form for teachers

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