Gifted and Talented Research Project

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Gifted and Talented Research Project
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• Program
• Outline

• Students
• and their
• Work

• Teaching
• Project

• Teachers Diary
• and Reflection

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Program Outline

• How the students were identified
• Mathematics area of the C.S.F.

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How the G.L.I.M. students were identified

• S.I.N.E Clinical Interview and Diagnostic Test
• One of the children completed the D.A.R.T.
  assessment.
• Identification and Assessment of Gifted Students
  (Bright Futures 1999)

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• Mathematics Area of the C.S.F.

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• Measurement

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Measuring and Estimating

• Level 4
• At this level students focus on the
  identification of attributes which can be
  measured and select and use appropriate units
  when estimating, describing, comparing and
  measuring length, perimeter and area. They choose
  appropriate measuring instruments and use them
  accurately.

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• Level 5
• At this level students become familiar with
  metric units used to measure a range of
  quantities and common rates and choose units
  appropriate to the purpose of measurement.
• They choose instruments to measure to the
  required accuracy, devising ways to extend
  capabilities of the instruments and using their
  knowledge of fractions and decimals to read
  scales in which not all graduations are labelled.
• They relate metric units to quantities in their
  everyday experience and use this knowledge to
  make reasonable estimates of other quantities as
  required.

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Using Relationships

• Level 4
• At this level students understand and use
  relationships between different attributes in
  measurement situations involving the perimeter
  and area of polygons.
• Level 5
• At this level students investigate the
  relationship between the dimensions of
  two-dimensional shapes and three-dimensional
  solids and their areas and volumes. They use
  these relationships to determine perimeters,
  areas and volumes of a range of shapes and
  objects. They use and calculate rates in their
  everyday experience.

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Mathematical Reasoning

• Level 4
• At this level students continue to formulate and
  test conjectures in the areas of space, number,
  measurement and chance and data. The emphases are
  on providing evidence for conjectures and
  arguments, systematically testing these
  conjectures and arguments for exceptions,
  completeness and reasonableness and making
  modifications as appropriate. As well, students
  decide when to use mathematical models
  appropriate to this level and to check the
  reasonableness of the results obtained by using
  these models. They discuss and write about
  mathematical situations, relationships and models
  using mathematical terms, symbols and notations.

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• Level 5
• At this level students continue to develop the
  skills and dispositions associated with the
  formulation and testing of conjectures in all
  areas of the curriculum. An emphasis is on the
  development of general statements in symbolic
  form. Students also consider the assumptions and
  constraints which underpin the mathematical
  models they use and develop. As well, they
  consider the reasonableness of the results
  obtained by using these models in relation to the
  context.

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Students And Their Work

• Students
• Demographics of the Group

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(No Transcript)
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L Bs Profile

• Age 12
• Grade 6
• People in family 5 people in family. Mum and dad
  older brother and younger sister.
• Pet Golden Labrador called Jackie.
• Favourite subject Maths
• Favourite sport Football and tennis.
• Favourite hobby surfing.
• I like to go to school see my friends and to work
  hard. On the weekends I play my two favourite
  sports tennis and footy. I play for a club. I
  hope to be an A.F.L footy player but I also want
  to go really well in school to be a vet.

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L Bs Work

• Amazing Arrays 1
• Amazing Arrays 2
• Find The Area Of .
• My Area Worksheet
• House Plan
• My Dream Bedroom
• Bedroom Expenditure
• Area is 100cm² and Perimeter is 66cm
• Evaluation

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J Cls Profile

• Favourite Hobby Surfing.
• Favourite Subject Maths.
• Favourite Sport Lifesaving.
• Age 12
• What you would like to be when you are older
  Pilot in the Air force.
• My name is Jack and I am 12 years old I enjoy
  Maths because I like being challenged in areas of
  learning. I wanted to be apart of this maths
  group because I thought it would be a great
  experience and seeing that I want to be a pilot
  in the air force it would help me be closer to my
  dream job as a pilot. I also enjoy sport and I
  just competed in the state Cross Country
  championships which I came in the place 4th. My
  other favourite subjects are English and History.

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J Cls Work

• Amazing Arrays 1
• Find The Area Of .
• My Area Worksheet
• House Plan
• My Dream Bedroom
• Bedroom Expenditure
• Area is 100cm² and The Perimeter is 66cms
• Evaluation

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J Fs Profile

• I am 9 years old. I am an only child.
• Things that I enjoy doing are maths, reading,
  playing games and working on the computer.
• The sports I enjoy are cricket, basketball,
  tennis, swimming and soccer.
• When I grow up I want to be a doctor,
  specializing in surgery.

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J Fs Work

• Amazing Arrays 1
• Amazing Arrays 2
• Find The Area Of .
• My Area Worksheet
• House Plan
• My Dream Bedroom
• Bedroom Expenditure
• Evaluation

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Demographics of the Group

• The group consisted of nine boys eight were
  year six students and one was a year four
  student. This student who was a new admission to
  our school this year. The boys are being taught
  in six different grades, but we met at least once
  a week for an hour session while working on the
  project.

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• Teaching
• Project

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Teaching Project

• Learning Needs To Be Targeted
• Links to Other Curriculum Areas

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Learning Needs To Be Targeted

• My focus for these children was to review and
  extend their understanding of the measurement
  strand of the Mathematics K.L.A particularly the
  topic of area and perimeter. I wanted the boys to
  see that so many of our daily activities are
  influenced in some ways by measurement
  procedures. I aimed to provide them with rich
  mathematical investigation that would generate
  meaningful problem solving strategies that they
  could use in their project.

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• My plan was to provide explicit teaching on how
  to find the area and perimeter of regular and
  irregular polygons and then lead the children to
  investigate ways they could solve the area of
  parallelograms, quadrilaterals, triangles and
  circles. Throughout our sessions together my
  endeavor was to provide tasks that challenged and
  engaged the children. Many of the tasks were
  designed to promote discussion and lead to
  further inquiry and sorting out of formulas. The
  children needed to have a solid understanding of
  this topic before they could springboard into
  their individual projects.

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• The project while having parameters was aimed at
  providing opportunities for the children to be
  creative and put their individual mark on the
  task. The project outline was composed in
  consultation with the children after we had
  agreed what were to be basic inclusions. The use
  of technology was to be incorporated throughout
  this project.

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Links To Other Curriculum Areas

• This work while essentially a Mathematics unit
  does have links with the Technology K.L.A.
  Throughout the project the use of software,
  digital imagining and programming was used to
  enhance and modify tasks. The boys were asked to
  explain and create solutions as well as plan,
  construct and modify their designs and report on
  them using different materials.

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• The boys were asked to investigate house plans
  from a variety of sources and see why houses are
  built in many different ways. We talked about
  materials used and how designs have changed over
  the years. This area could have been expanded
  and the children chosen a dwelling from another
  part of the world and investigated size,
  materials used and why, age of dwelling, design
  structure, permanency and if construction relates
  to environment, climate or availability of
  materials. Unfortunately time did not allow for
  such investigations.

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• Teachers
• Diary

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Session One

• In this session the children came together and
  discussed what the project was about and where it
  might be leading. We discussed what the words
  area and perimeter meant to them as individuals
  as well as linking them to everyday life. We
  brainstormed various occupations that might use
  this form of measurement in their work. Some of
  the jobs that were proposed were builders,
  landscape gardeners, pool construction, carpet
  layers, interior designer, surveyor, picture
  framer, plumbers, glaciers, surfboard makers,
  architects and farmers. Following this discussion
  the children created individual mind maps and
  shared their ideas with the group.

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Session Two

• This was an explicit teaching session where the
  children reviewed/discovered how to work out the
  perimeter and area of a regular polygon.
• The children brainstormed with the teacher their
  knowledge about how to work out the perimeter and
  the area of a shape. They then worked on a sheet
  that was designed for them to discover if there
  was any correlation between the sides of a
  regular shape and its area. Squares Following
  this task we discussed their findings. Every
  child in the group had input here. I posed the
  question Is there a more efficient way to
  calculate the area of a square or rectangle than
  just counting the squares in the grid? Feed back
  was automatic from all the boys and I was able to
  gauge that each of them had a solid understanding
  of the formulas for finding the perimeter of a
  shape and calculating the area of squares and
  rectangles.

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Session Three

• As a review of the work from the last session
  the children were asked to calculate the area and
  perimeter of specific polygons using grid paper.
  This task was completed easily by all the group.
  The next aspect of this lesson was to have the
  children use a computer program devised by Mark
  Hennessey called amazing arrays. This program
  reinforced their understanding of how we multiply
  length x width to calculate the surface area of a
  regular polygons. The children were all
  successful at completing this task.

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Session Four

• This was an explicit teaching session on how to
  measure the area of irregular shapes. From this
  point on, I did not do any specific teaching on
  perimeter but the feedback from the children via
  their work and reflection indicated to me that
  this area was well established.
• The lesson began with the children being
  presented with a number of irregular shapes and
  we discussed in twos how we might calculate their
  areas. Irregular Shapes activity allowed the
  children to test their understanding and arrive
  at an efficient method of calculation.

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• After completing the task we checked their
  calculations by counting the squares in the shape
  and using the number sentences composed by each
  child. All of the children choose to break each
  shape into regular polygons (squares and
  rectangles), calculate the length and width,
  multiply together and then add the answers
  together. The way they broke up the shapes
  varied.
• Shape 3 for example was broken up in the
  following ways.
• (5 x 7) (4 x 3) (4 x 7)
• 35 12 28
• Answer 75 cm2

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• Another answer provided by a child was
• (5 x 2) (5 x 2) (13 x 3) (4 x 2) (4 x 2)
• 10 10 39 8
  8
• Answer 75 cm2

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• One child however chose to view the shape as a
  rectangle that was calculated as
• 13 x 7 and he then subtracted 2 x (2 x 4)
• Therefore he recorded the sum as
• 13 x 7 2 x (2 x 4)
• 91 - 16
• Answer 75 cm2

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• The work allowed for valuable discussion and the
  children were able to conclude that breaking the
  shape into regular polygons and calculating the
  answers was a much more efficient method to work
  out the area of a shape. They also decided that
  in some cases it was more efficient to calculate
  the outside perimeter of the shape and subtract.

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Session Five

• This session began with a review of what we had
  learnt about calculating the area of a regular
  polygon and irregular shapes. They completed a
  task called New Boundaries. In this task the
  children were asked to divide mainland Australia
  into six states of equal area and redraw the new
  state boundaries. (Examples of the childrens
  work is attached) This was also to be an explicit
  teaching session on calculating the area of a
  parallelogram and a triangle. The children shared
  their understandings of what constituted a
  parallelogram and triangle. They drew the shapes
  to show a visual representation of their
  understanding.

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• The children were then given a sheet and asked
  to find the area of these shapes. Parallelograms
• The discussion and solutions presented indicated
  the various ways each child arrived at a solution
  to the areas of the shape.
• Some cut out the shape and made into a regular
  polygon, others shaded and calculated the area
  they all used the grid squares to affirm their
  calculations.

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• We then took this further and I asked them to
  look at a regular polygon I had drawn and asked
  them to calculate its area. All completed easily
  by multiplying length x width. I then handed out
  the following sheet Parallelogram 2 and asked
  then to answer the sheet and write about their
  findings. We spoke of new terminology base and
  height. It was a great way for them to discover
  that the area of a quadrilateral is calculated
  using a formula similar to a regular polygon
  base x height

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• Some of the drawn diagrams of the children
  showed that they had constructed triangles in
  their effort to calculate the area of a
  parallelogram. I lead a discussion about how we
  could calculate the area of a triangle. Two of
  the children said that their triangles were
  right-angled triangles and half of the new
  polygon that they had drawn. After some teacher
  input the children came up with a formula for
  working out the area of a triangle.
• Area of a Triangle base x height or ½
  (base x height)
• 2

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• The question was posed Does this formula work
  for all triangles?
• - Isosceles triangles
• - Equilateral triangles
• - Scalene triangles
• - Right-angled triangles.
• Children tested this discovery using grid paper
  and formulas using the following task. Triangles

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• While most children counted the squares one
  child coloured the parts of squares to prove the
  formula.
• Another child cut up the part squares and
  rearranged into whole squares.

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Session Six

• The session began with the children going on a
  computer and opening a word document and
  formatting a table. The children were to go to
  clip art and insert a picture. The others in the
  group where challenged to try and work out the
  area of that picture.
• Area Pictures Informal lesson on how to measure
  a circle.
• Working On Area Pictures

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• The House Project was introduced to the
  children. They were given a design outline of
  what was expected to be included in their house
  plan which was negotiated with the group. House
  Project

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Session Seven

• When the children first heard that their homes
  were to be 42 squares, all of them imagined 42
  square metres. They had all made newspaper square
  metres as part of their homeroom class lessons.
  The Square Metre
• The task for the children in this lesson was to
  make a house square that equalled 9.6 square
  metres. The children loved this task and were
  amazed with the size.
• House Square

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Session Eight

• This session began with a lesson on how to work
  out the area of a circle. Reference Curriculum _at_
  Work.
• The children then had the following problem put
  forward to them Design a shape that has an area
  of 100cm² and a perimeter of 66cms.
• The children began by inserting a 10 by 10 array
  on a grid and then moved parts to increase the
  outside perimeter from 40cms to 66cms. Teacher
  Examples. The childrens work showed that
  solutions to this problem are not limited to just
  one answer.

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• The rest of the time was devoted to the children
  designing their house plans. There are two groups
  and four individual projects. The children looked
  at plans from newspapers as a guide to the set
  out of a plan and symbols used to note fixtures,
  doors etc.

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• One of the groups wanted to double their house
  size to be 84 squares. This was allowed but it
  could cause problems when blocks of land are
  given out, so house design needs to be
  considered. We used this session also to talk
  about areas that are included in the plans like
  verandas, garages, carports.
• We spoke about a staircase and what type of
  staircase would take up the most room. Position
  of rooms is also important while we are not
  doing plumbing and gas plumbing quotes, have all
  your wet areas on one side of a house cuts costs.
  Children reflected where in their homes, wet
  areas are located.

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Session Nine

• This session began with the allocation of house
  blocks for their plans. House blocks are not
  measured in house squares but in square metres.
  We had a walk around the local area and using a
  trundle wheel measured house blocks to gauge the
  average size of blocks.
• Measuring A House Block
• Our school is situated in an older area but has
  a new housing estate close by. The measuring that
  took place allowed the children to see that not
  all blocks are the same, or regular in their
  shape and that newer homes while being bigger
  have less free land. The children opted to
  construct their homes on blocks found in an older
  area.

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Session Ten

Working To Scale In this session the childrens
plans were discussed and they were presented with
a 6 x 7 grid. This grid was to be cut up and
rearranged by the grid to represent their plans.
No piece was to be discarded in the completion of
this task. Photo
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Session Eleven

• The children were shown a computer image of a
  house plans and then commenced transferring their
  drawn plans on to the computer and shading in the
  relevant rooms of their houses. These will be
  imposed on to their house blocks for final
  presentation.
• House plan on Computer

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Session Twelve

• This session was where the children costed the
  furnishing of their bedroom. There were lots of
  furnishing and electrical catalogues produced.
  Teacher also brought in paint cans for children
  to gauge the cost of painting and carpet / timber
  flooring brochures. This session also needed some
  explicit teaching about the way carpet is quoted
  and measured linear metre which is
  approximately 3 metres x 1 metre. The children
  had a budget of 8000 to spend. Their designs
  indicate their creativity and dreams of the
  perfect room.

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Session Thirteen

• Birds-Eye View Model
• Children worked on their scaled birds-eye view
  model of their house and placed on their
  allocated block. My original plan was to have the
  children build a 3D model of their house using
  any medium they choose, but time and the access
  to the children did not allow for this part of
  the project to evolve. (Six of these children
  have lead roles in our school musical and they
  were often called away for rehearsals. This is
  also the reason why some of them do not have all
  the work requirements in their folders.)

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• I also wanted them to reflect on our sessions
  together and have the opportunity to video their
  oral presentations but once again time and
  access to the children put a halt to these plans.
  The children have however, written an evaluation
  of the project and these reflections can be found
  in the individual student folders. As the teacher
  of this project I feel very affirmed and pleased
  that the students have enjoyed our time together.
  

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• Teachers Reflection

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• My biggest hurdle in doing this project was
  finding time to gather all the children from the
  different classes at one time to complete the
  tasks. Trying to co-ordinate time where other
  programs were not being interrupted was a huge
  hurdle and did mean that on occasions lessons
  were a little rushed.

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• While the enthusiasm by the children for this
  task has been fabulous, I would be hesitant to
  continue with such a project with children coming
  from so many grades. It is not the class
  teachers reluctance but finding time where we
  are not timetabled for specialists, sporting
  commitments and musical rehearsals. I was very
  lucky to have the vice-principal come and relieve
  me of my classroom commitments, so that I could
  work with all of these boys, but her time was
  also limited.

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• While I dont believe that individual grades
  should be streamed with like abilities, my
  recommendation would be to timetable a class
  session weekly where children of like abilities
  are grouped together for enrichment or remedial
  help. This type of structure would overcome the
  dilemma I had with finding regular time to
  complete this project.

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• I would also recommend that in each grade there
  is at least a pair of like abilities. While a lot
  of careful planning goes into grade placements,
  this year two of the senior grades have children
  whose abilities far outweigh any of their
  classmates having a peer with a similar ability
  in a particular subject area would challenge and
  help to further develop ideas on topics being
  studied.

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• Mathematics
• Unit

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• While I was released to work with these children
  the rest of the grade 5/6 classes worked through
  the prepared Mathematics Unit on Investigating
  The Relationship Between Length, Perimeter and
  Area.
• The unit I composed and followed, used a
  template adopted from a model developed by Cath
  Murdoch. This template is what we use to plan our
  Integrated Studies Units. Area Planner

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• My time with Dr. Munro has affirmed my teaching
  practice and the approach adopted by my team at
  school. We aim to have open-ended enquiry based
  tasks and research projects that foster
  self-directed learning. For me personally, the
  sessions had me reflecting on how I as a teacher
  impart this type of learning in my classroom.
  While I encourage the children in my care to be
  thinkers, risk takers and creative in their
  problem solving and questioning of tasks I have
  been made aware of the importance of teaching and
  unpacking the creative thinking of each child.