Cognitive Diagnostic Assessment Tasks - CDAT (1 PDF)
The following book was developed in a cross-sectoral project, Cognitive diagnostic assessment in numeracy, funded by the Australian Government, Education Queensland, Queensland Catholic Education Commission and Independent Schools Queensland, and was provided free to all schools in Queensland in 2008.
Developing Mathematics Understanding Through Cognitive Diagnostic Assessment Tasks (PDF file, 6.8MB)
The book contains Cognitive Diagnostic Assessment Tasks (CDAT) to elicit students' understanding of the important mathematical concepts and processes required for processing whole numbers, decimal numbers, fractions and probability effectively. The CDAT tests are designed to give teachers insight into what their students know before teaching has taken place (entry knowledge) and after teaching has been completed (exit knowledge). Each test is administered to students before new learning to elicit each student's entry knowledge and is then repeated after teaching has been completed to determine each student's exit knowledge. These latter tests indicate those students who need more support.
CDAT can provide a vehicle for deepening teachers' understanding of core ideas in elementary mathematics and consequently for modifying or extending their instruction. As one teacher said when given a CDAT to trial with her class: "Oh, that's what I haven't been doing!". CDAT can also provide teachers with insights into how students learn those ideas, particularly when students' solution strategies are discussed. Thus, CDAT provide a springboard for intervention and prevention.
Number – MAST (8 PDF files)
The eight booklets below were written for ARC Discovery Indigenous project DI0668328, Indigenous world view, algebra pedagogy and improving Indigenous performance in secondary mathematics, conducted at Dunwich on Stradbroke Island from 2006–08 and known as the Minjerribah Maths project.
The project used an approach to maths learning called Maths as Story Telling (MAST). It is an attempt to work from the storytelling world of the Indigenous student through to the formal world of algebra by experiences with the creation of symbols that have personal meaning. The storytelling starts with simple arithmetic but moves quickly to algebraic thinking. It enables Indigenous students to bring their everyday world of symbols into mathematics.
Primary – addition
MAST Booklet Pr.P: Using Created Symbols to Develop Addition Stories (PDF, 0.9MB)
This booklet was developed for students in Prep and is designed so that the students can investigate the nature of symbols and develop their own to create addition stories. As students progress through the booklet they should develop their understanding of addition and begin to explore the nature of compensation and balance.
MAST Booklet Pr.4: Using Created Symbols to Develop Addition Principles (PDF, 1.0MB)
This booklet was developed for students in Year 4 and begins by introducing students to the concept of symbols, and how they can create and use their own symbols to write mathematical stories. As the students progress through the booklet they should develop a deeper understanding of the nature of addition and use balancing and compensation to solve for an unknown.
Secondary – addition and subtraction
MAST Booklet S.1: Creating Symbols for Addition and Subtraction Stories (PDF, 1.0MB)
This booklet was developed for students in secondary school, and is the first of six secondary booklets. Across the four lessons students explore symbols in the real world, and then focus on addition and subtraction by creating their own symbols. The last lesson enables students to read others' symbols and make sense of their stories; it then moves to linking addition and subtraction and concludes by focusing on the formal symbols for addition and subtraction.
MAST Booklet S.2: Using Created Symbols to Develop the Addition and Subtraction Principles (PDF, 1.0MB)
This booklet extends on booklet S.1, beginning with recapping symbols, then guiding students to an understanding of balance and compensation, and concluding with the rules that determine addition and subtraction in that setting.
MAST Booklet S.3: Creating, Using and Solving Unknowns in Addition and Subtraction Stories (PDF, 1.0MB)
This booklet is the last of the addition and subtraction lessons and focuses on working out the unknown in a given situation. Through the four lessons it covers the notion of 'unknown' and then moves into looking at unknowns in both addition and subtraction settings. It concludes by reinforcing this learning through using the formal mathematical symbols.
Secondary – multiplication and division
MAST Booklet S.4 Creating Symbols for Multiplication and Division Stories (PDF, 1.0MB )
This booklet is the fourth of six secondary booklets and the first of the booklets that focus on multiplication and division. This booklet follows a similar structure to booklet S.1, by introducing students to symbols in the real world, then giving them an opportunity to develop their own symbols for multiplication and division, and create their own mathematical stories. From here the booklet concludes by relating what they've learnt to the formal symbols of multiplication and division.
MAST Booklet S.5 Creating Symbols for Multiplication and Division principles (PDF, 1.0MB)
This booklet extends on booklet S.4 through recapping symbols and then guiding students to an understanding of compensation and balance, exploring the rules for these two principles with regard to multiplication and division. It then concludes by relating the content taught with using the formal mathematical symbols.
MAST Booklet S.6 Creating, Using and Solving Unknowns in Multiplication and Division stories (PDF, 1.0MB)
This booklet is the last of the multiplication and division lessons and is designed to follow on from booklets S.4 and S.5. It looks at finding the unknown in a multiplication and division setting. It links the principles for balance and compensation to the notion of the 'unknown' and then concludes by reinforcing and relating this new understanding to the formal mathematical conventions.
Number and operations – finance and virtual manipulatives (3 PDF
and 11 PowerPoint (Zipped) files)
The following three booklets and six virtual mathematics activities (11 PowerPoint files) were developed using funding from a Financial Literacy Grant from the Commonwealth Bank Foundation, for a 2008 project at Shalom Christian College in Townsville called Shalom Accelerated Numeracy. The booklets and virtual activities are based on financial mathematics material trialled by the researchers as part of a 2007 Australian Studies in Science, Technology and Mathematics (ASISTM) project, Using finance and measurement applications to improve number understanding of Indigenous students, conducted at schools in Aboriginal communities in central and southern Queensland.
The aim of the finance booklets and virtual manipulatives is to use money activities to reteach and reinforce students' understandings of number and operations.
Finance Booklet A: Creating a Shop (PDF, 2.1MB)
This booklet focuses on two-digit numbers, addition and subtraction, and the mathematics of shopping.
Finance Booklet B: Planning a Party (PDF, 1.9MB)
This booklet focuses on three-digit and decimal numbers, the four operations and the mathematics of planning a party.
Finance Booklet C: Developing a Family Budget (PDF, 740KB)
This booklet focuses on variables, multi-step problem solving and the mathematics of family budgets.
Virtual Finance (zipped file, 4.82MB)
These materials are designed to equip students with the ability to relate money (material) to the language and symbolic ($10, etc.) representation of it. The materials then continue on with practical applications of money that students would come across in the real world. This zipped folder contains the following PowerPoint files:
- VFA 1A: Place ValueLanguage to Materials
- VFA 1B: Place Value Materials to Language
- VFA 2A: Place Value Symbols to Materials
- VFA 2B: Place Value Materials to Symbols
- VFA 3A: Operations Addition
- VFA 3B: Operations Subtraction
- VFA 4: Operations Shopkeeper Subtraction
- VFA 5A: Operations Multiplication
- VFA 5B: Operations Multiplication and Subtraction
- VFA 6A: Operations Division
- VFA 6B: Operations Division and Subtraction
Number – ratio, proportion and percentage (1 PDF file)
Old ratio, proportion and percentage book
Ratio, Proportion and Percentage in the Primary School (PDF, 3.6MB)
This old book from 1993 focuses on the three concepts of ratio, proportion and percentage, which are some of the most important new ideas to be taught in the upper primary and lower secondary school years. The real world of mathematics involves the application of proportion and percentage extensively. The basis for both of these aspects is the concept of ratio.
The booklet considers a teaching sequence that can be used to establish each of the concepts of ratio, proportion and percentage. A model is shown which demonstrates how the two concepts of rate and ratio are related, but at the same time quite different.
Measurement (4 PDF and 9 Power Point files)
Measurement assessment tasks
The following booklet was developed as part of the 2009 Tagai Mathematics for Employment project funded by Tagai State College, Queensland.
Measurement: Interview-based Assessment – Prep to Year 6 (PDF, 1.0MB)
This booklet comprises interview-based assessment tasks for Measurement at Prep to Year 6 level and is designed as a tool to diagnose students' current knowledge and understanding. It contains assessment tasks and response recording sheets for the Measurement attributes of length, perimeter, area, volume (solid), volume (capacity), angle, mass, time, money and temperature.
Using measurement to teach number and operations
The following two measurement booklets and nine PowerPoint files with measurement games and activities were developed as part of an Australian Studies in Science, Technology and Mathematics (ASISTM) project, Using finance and measurement applications to improve number understanding of Indigenous students, conducted at schools in Aboriginal communities in central and southern Queensland in 2007.
Measurement Activities Booklet MA: Using Measurement to Teach Numeration and Operations (PDF, 1.8MB)
The aim of this booklet is to use measurement to reinforce the teaching of number and operations. This booklet is accompanied by a second booklet on teaching measurement, Measurement Background Booklet MB, and also nine PowerPoint files, Measurement Games MG1 to MG9.
Measurement Background Booklet MB: Teaching Measurement Processes in School Years P–10 (PDF, 4.3MB)
This booklet acts as a background booklet to Measurement Activities Booklet MA and Measurement Games MG1 to MG9. The booklet is in three sections: Section 1 provides an overview of measurement; Section 2 outlines a 5-step process for teaching measurement, with a chapter for each step; finally, Section 3 takes each attribute in turn and summarises how the 5 steps affect them and also looks at some teaching implications.
Measurement Games and Activities (zipped, 1.9MB)
These measurement games can be used with students to reinforce and strengthen their understanding of numbers and their applications. The games cover a variety of topics, from writing and recognising numbers and place value, through to multiplication and division. These materials are designed to be printed off and used as hands-on activities. Further instructions are included in each PowerPoint file. This zipped folder contains the following files:
- MG1: 2-Digit Comparison
- MG2: 3-Digit Comparison
- MG3: Reading and Writing 3-Digit Numbers
- MG4: Movement Left and Right
- MG5: 2-Digit Addition
- MG6: 2-Digit Subtraction
- MG7: 2-Digit with 1-Digit Multiplication
- MG8: 3-Digit with 1-Digit Division
- MG9: 3-Digit, Numbers and Zeros
Old measurement book
Teaching Measurement Processes in the Primary School (PDF, 1.7MB)
This old book from 1988 (reprinted 1993) focuses on the basics of measurement. The purpose of the book is to develop students' understanding of the concepts of length, area, volume, mass, time, money, temperature and angle, the units used and the formulae applied; and to develop students' competence in the process of measuring, using instruments and choosing appropriate units.
Geometry (2 PDF and 1 PowerPoint files)
Modulo art and tangrams
Mathematics and Modulo Art (PDF, 3.6MB)
The ideas presented in this booklet have been trialled with a large number of groups ranging from Years 6 and 7 in primary school through to students at tertiary level. In all cases they have generated considerable interest and enthusiasm and are presented in this booklet in a form which could be easily adapted to suit the needs of most year levels.
The worksheets in this booklet are based on Modulo Arithmetic or generated Latin Squares. The worksheets outline the theory of Modulo Arithmetic as a basis to construct standard, converging segment, kaleidoscopic patterns and circular residue designs. After completing the material students should be capable of producing large and intricate patterns from mathematical relationships both demonstrating and enhancing an appreciation of mathematical order. Your classroom, too, will look much more interesting.
Tangrams (PowerPoint, 140KB)
This PowerPoint file looks at how shapes are made up of other shapes.The slides are designed to be printed off and used as hands-on activity.
Old geometry book
Space and Shape in the Primary School (PDF, 3.7MB)
This old book from 1986 contains ideas for teaching geometry in primary mathematics classrooms. It presents a wide range of activities for teaching geometry in a stimulating and active way.
Problem solving (1 PDF file)
Old problem solving book
Developing Children's Problem Solving Ability in Mathematics (PDF, 2.3MB)
This old book from 1988 (reprinted 1993) is a collection of ideas and materials on problem solving and includes sections on the components of problem solving, how to teach problem solving, and problem solving examples and resources.
Statistics and probability (1 PDF file)
Old statistics and probability book
Statistics, Graphs and Probability in the Primary School (PDF, 1.7MB)
This old book from 1987 focuses on statistics, graphs and probability in primary mathematics. It covers statistical procedures and measures (including range, mean, median, mode, deviation), techniques for interpreting and constructing graphs, processes for understanding graphs, and both qualitative and quantitative concepts of probability.