SCAFFOLDING NUMERACY IN THE MIDDLE YEARS

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SCAFFOLDING NUMERACY IN THE MIDDLE YEARS A
Linkage Research Project 2003 - 2006
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Research Schools Mid-term Teachers
Day February/March, 2005

• Project Update
• Elaborating the Learning Assessment Framework

Support for this project has been provided by the
Australian Research Council, RMIT University, the
Victorian Department of Education and Training,
and the Tasmanian Department of Education.
TASMANIAN Department of Education
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RESEARCH TEAM

• Associate Professor Dianne Siemon, Project
  Director, RMIT University
• Ms Jo Virgona, Senior Project Officer RMIT
  University
• Ms Margarita Breed, Ph.D student, RMIT
  University and
• Professor Peter Sullivan (Latrobe University), Dr
  Shelley Dole (University of QLD), and Adjunct
  Professors John Izard and Max Stephens (RMIT
  University) Consultants
• Ms Denise Neil (Tas DoE) and Mr Maurie Sheehan
  (DET) Industry Partner Representatives

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PROJECT AIM
In broad terms, the project will investigate the
efficacy of a new assessment-guided approach to
improving student numeracy outcomes in Years 4 to
8. In particular, it will identify and refine a
Learning Assessment Framework for the
development of multiplicative thinking using
authentic assessment tasks.
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RECAP
Why the middle years/Years 4 to 8?
Why multiplicative thinking?
Why an assessment-guided approach?
What is a Learning Assessment Framework?
Why authentic tasks?
For more details, see the Project Information
handout distributed at the Teachers Day in
Feb/March 2004 and Project Notes 1 to 5.
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WHAT WEVE ACHIEVED TO DATE

• Identified research and reference schools 1 in
  Tasmania, 2 clusters in Victoria
• Developed a set of rich tasks and scoring rubrics
  to evaluate multiplicative thinking in Years 4 to
  8
• Assessed 3172 students in Term 1, 2004

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WHAT WEVE ACHIEVED TO DATE

• Analysed the initial and subsequent trial data
  and identified a draft Learning Assessment
  Framework for multiplicative thinking
• Established Learning Plan teams
• Developed and trialled initial Learning Plans for
  each Level of the Learning Assessment Framework

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WHAT WEVE ACHIEVED TO DATE

• Learning Plans revised and distributed for other
  teachers to use (Round 1)
• Round 1 Implementation Reports completed and
  returned to Cluster Coordinators
• Identified who will develop Authentic Tasks and
  how this process will be supported

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WHAT WEVE LEARNT
Research Schools 2004
Adjusted Mean Scores 2(L5)
Adjusted Means by Year Level and Gender
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WHAT WEVE LEARNT
Reference Schools 2004
Adjusted Mean Scores 2(L5)
Adjusted Means by Year Level and Gender
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WHAT WEVE LEARNT

• There are little or no gender differences evident
  at any Year level in either the Research schools
  or the Reference schools this may be a function
  of the form of assessment which privileged
  explanations over answers alone
• Multiplicative thinking clearly improves with
  time, although, consistent with other middle
  years data, this appears to level off in Years
  7 and 8, suggesting that school transition is a
  factor impacting achievement at this level
• Although the levels of achievement are comparable
  at Year 8, reference school students appear to be
  starting from a lower base than the research
  school students

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WHAT WEVE LEARNT

• In terms of the Learning and Assessment Framework
  for Multiplicative Thinking (LAF), the average
  level of achievement for both research and
  reference schools ranges from Level 2 or 3 of the
  Framework in Year 4 to about Level 5 in Year 8,
  ie,

This suggests that, for many students,
multiplicative thinking may be much more
difficult than previously recognised and may take
many more years to acquire than is typically
assumed in curriculum documents. But this only
shows differences across Year levels, what about
the differences within Year levels?
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WHAT WEVE LEARNT
Research Schools 2004
Proportion of Students at each Level of the LAF
by Year Level
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WHAT WEVE LEARNT
Reference Schools 2004
Proportion of Students at each Level of the LAF
by Year Level
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WHAT WEVE LEARNT

• There are students at each level of the Learning
  and Assessment Framework for Multiplicative
  Thinking in each Year level this does not
  equate to every class but it does illustrate the
  enormous range of achievement within each Year
  level

• A significant number of Year 4 to 8 students
  appear to rely on additive thinking or naïve
  notions of multiplication (LAF Levels 1-3)

Proportion of Victorian sample at corresponding
levels of LAF and CSF for multiplicative thinking
in 2004
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WHAT WEVE LEARNT

• Overall, the vast majority of students appear to
  have little difficulty using additive thinking
  strategies to solve problems involving relatively
  small whole numbers
• Students can work with sharing division, simple
  proportion, and simple Cartesian product problems
  earlier than expected
• While initial ideas for multiplication and
  division appear relatively early, students may
  take many years to develop a flexible capacity
  for multiplicative thinking.

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WHAT WEVE LEARNT

• Detailed item analysis suggested additional tasks
  were needed to tease out the upper end of the LAF
  (Year 7 Trial, October 2004)
• Classroom observations suggest that students
  identified at LAF Levels 1 or 2 may need
  considerably more support than anticipated, eg,
  Poly Plug Activity with group of Year 4 (LAF 1)
  students (Tas) and 0-99 Number Chart Activity
  with Year 4 (LAF 1/2) students (Vic) and that
• We need to find ways to engage under-performing,
  older students.

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WHAT WEVE LEARNT

• School/Cluster visits and discussions have
  identified a number of useful ideas and resources
  which will be developed and shared as
  appropriate, eg, Easy Quezy, a similar game to
  Multiplication Toss that uses Cuisennaire Rods to
  reinforce the countability of the group.

1 one
6 fives

4 threes
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ELABORATING THE LAF
The Learning and Assessment Framework for
Multiplicative Thinking (Feb 05) was developed on
the basis of the detailed item analyses conducted
on the May and October 2004 data and relevant
research. It attempts to bring together, in a
loose hierarchy, all the key ideas, strategies
and representations of multiplication and
division needed to work flexibly and confidently
with whole numbers, fractions, decimals, and per
cent across a wide range of contexts.
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THE LEARNING ASSESSMENT FRAMEWORK (LAF)
The LAF is organised in terms of 8 Levels from
initial explorations with concrete materials
through to the confident use of a wide variety of
multiplicative structures and symbolic forms. It
is linked to the rich assessment tasks used to
evaluate multiplicative thinking and contains
explicit advice on teaching implications. It also
reflects the growth of problem-solving skills and
higher-order cognitive thinking.
See the Draft Learning and Assessment Framework
for Multiplicative Thinking (February, 2005)
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WHAT DOES THIS MEAN FOR ME?
On-going professional support (Professional
Development) Opportunity to work with colleagues
to plan focused learning activities (Learning
Plans) Experience in developing and using
authentic tasks (Task Development) Experience in
using rich assessment tasks (Testing)
For more details, see the Calendar of Events in
Project Note 5 (22 October, 2004)
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LEARNING PLANS

• Teachers to revise, share and implement Learning
  Plans with identified students
• Cluster Leaders to collect and distribute
  Implementation Reports
• School grants can be used to support teacher
  release and/or for the purchase of materials,
  resources, or additional professional
  development.
• Classroom/school visits by members of the
  research team should be used to support the
  further development of the Learning Plans

For further details see Project Note 5 (Oct 2004)
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TASK DEVELOPMENT

• Each cluster is expected to develop a small
  number of Authentic Tasks that embody key aspects
  of the Learning and Assessment Framework
• Guidelines for the preparation of authentic tasks
  have been provided and research team members will
  help facilitate the process
• The authentic tasks will be used to evaluate the
  Learning Plans and student progress against the
  Learning Assessment Framework during 2005.

See Authentic Task Guidelines (July 2004) and
Project Note 5 (Oct 2004)
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FINAL TESTING

• Research schools will be provided with booklets
  of rich assessment tasks, scoring rubrics, and
  instructions in October, 2005
• Teachers will be expected to implement the tasks
  over a period of 2-3 weeks in late October/early
  November 2005 and assess students work using the
  scoring rubrics provided.
• Coordinators are expected to collect all data and
  send it to Jo Virgona as required.

Further details later in the year
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AUTHENTIC TASK EXAMPLE
Title Not Enough Twine School Blackmans Bay PS
(Tas) Context/prompt School litter
problem Activity Lunch-box audit (3 times/week
for 3 weeks), data recorded, analysed and
communicated Resources Coloured dot stickers,
reference material from the NSW Canteen
Association
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