Scaffolding Numeracy in the Middle Years: Resource Library

This section is a library of all documents referred to within the site as well as additional resources related to the Scaffolding Numeracy in the Middle Years 2003-2006 (SNMY) research project.

The library includes the following sections:

Research project description

Scaffolding Numeracy in the Middle Years (SNMY): Research approach and rationale for the use of Rasch analyses (pdf - 60.83kb)

Authors: Dr John Izard, Adjunct Professor, RMIT University and Professor Dianne Siemon, RMIT University

Summary: Describes the research approach in more detail, in particular, the decisions and assumptions made in relation to each research question, the development of the instruments, and the rationale for the use of Rasch analyses including the use of summary statistics and effect sizes for the evaluation of student progress.

Assessment materials

Authors:SNMY Research Team

Summary: The following are additional assessment tasks

(pdf - 109.21kb) (pdf - 109.21kb)
• Computer Game (pdf - 109 (pdf - 109.21kb)
• Fencing the Freeway (pdf - 69.7kb)
• Filling the Buses (pdf - 46.93kb)
• How Far Is It (pdf - 156.68kb)
• Missing Numbers (pdf - 30.44kb)
• Orange Juice Task (pdf - 24.96kb)
• Pizza Party (pdf - 81.33kb)
• School Fair (pdf - 32.35kb)
• Swimming Sports (pdf - 32.73kb)

Support materials

Support Materials - Introduction (pdf - 15.43kb)

Authors: SNMY Research Team

Summary: Learning plans and authentic tasks along with games and other activities were used by project teachers in their classrooms to develop and consolidate multiplicative thinking in their students. These games and activities form the basis of the support materials.

The following documents are available as additional support materials:

• Multiple Patterns (pdf - 18.5kb)
• Multiplication Toss (pdf - 48.7kb)
• Place Value Game (pdf - 16.36kb)
• How Many Wholes Can You Make (pdf - 14.17kb)
• Supermarket Packer (pdf - 30.16kb)
• Target Practice (pdf - 35.57kb)
• Factor Cross (pdf - 54.57kb)
• Max’s Matchsticks (pdf - 27.6kb)

Subitising materials

The following documents are available as subitising materials resources:

• Subitisation Dice and Card Set (pdf - 39.29kb)
• Subitisation Two Collections 1-5 (pdf - 48.8kb)
• Ten Frame Doubles Set (pdf - 38.12kb)
• Ten Frame Build on Five Set (pdf - 39.97kb)
• Subitisation Two Collections 1-7 (pdf - 47.73kb)
• Ten Frame Random Set (pdf - 60.65kb)
• Two Ten Frame Set (pdf - 72.47kb)
• Subitisation Three Collections 1-5 (pdf - 103.05kb)
• Subitisation Three Collections 1-7 (pdf - 158.74kb)
• Subitisation Four Collections 1-5 (doc - 118.5kb)
• Subitisation Four Collections 1-7 (doc - 135kb)

Research papers and presentations

Multiplicative Thinking (pdf - 303.74kb)

Authors: Dianne Siemon, Professor of Mathematics Education, RMIT University

Summary: Discusses concepts, strategies and representations of multiplication (and division) as they occur in a range of examples. Includes advice for building fraction knowledge and confidence.

From Additive to Multiplicative Thinking – The Big Challenge of the Middle Years (pdf - 149.29kb)

Authors: Dianne Siemon, Margarita Breed and Jo Virgona, School of Education, RMIT University

Summary: Material from a workshop exploring some of the tasks used in the Scaffolding Numeracy in the Middle Years (SNMY) research project to identify steps in the development of multiplicative thinking from Years 4 to 8.

The Key Ideas and Strategies that Underpin Multiplicative Thinking (ppt - 3.61mb)

Author: Dianne Siemon, Professor of Mathematics Education, RMIT University

(pdf - 43.21kb)

Summary: Extensive set of examples demonstrating strategies for the development of multiplicative thinking and the key ideas within the SNMY project. Contains sections on early number, mental strategies for addition and subtraction, concepts for multiplication and division, mental strategies for multiplication and division and fractions and decimals

Scaffolding Numeracy in the Middle Years (pdf - 43 (pdf - 43.21kb)

Authors: Professor Dianne Siemon and Margarita Breed, School of Education, RMIT University

Summary: Describes the use of Cuisenaire Rods to model the number of groups as a way that prevents counting by ones. This is one way to support the development of more efficient mental strategies for the multiplication facts based on the array or factor idea.

Partitioning - The Missing Link in Building Fraction Knowledge and Confidence (pdf - 199.51kb)

Author: Dianne Siemon, Professor of Mathematics Education, RMIT University

Summary: Presents material from the Middle Years Numeracy Research Project (MYNRP), conducted in Victoria from November 1999 to November 2000. This project used relatively open-ended, 'rich assessment' tasks to measure the numeracy performance of approximately 7000 students in Years 5 to 9.

Teaching and Learning for, about and through Problem Solving (pdf - 462.19kb)

Authors: Professor Dianne Siemon, RMIT University and George Booker, Griffith University

Summary: Article from Vinculum, Volume 27, No.2, 1990.

There’s More to Counting than Meets the Eye (pdf - 100.88kb)

Author: Dianne Siemon, Professor of Mathematics Education, RMIT University

Summary: Research paper exploring what is needed to develop a sense of number and encourage early numeration. Topics include introducing and consolidating place-value ideas, developing mental strategies for addition and subtraction facts to 20, supporting and recording mental computation and representing multiplication and division facts.

From Their Point of View – Middle Years’ Students Perceptions of School Mathematics (pdf - 52.13kb)

Authors: Professor Dianne Siemon and Jo Virgona, School of Education, RMIT University

Summary: Summary paper prepared for the SNMY Teacher Days in July and August, 2004.

The Derivation Of A Learning Assessment Framework For Multiplicative Thinking (pdf - 93.27kb)

Authors: Professor Dianne Siemon, Dr John Izard, Margarita Breed & Jo Virgona, RMIT University.

Bibliography and references

References and further readings (pdf - 56.68kb)

Authors: SNMY Research Team

Summary: A list of sources cited through the project reports and this website plus references to related research.