numeracy program for middle school students

The National Centre of Science, Information and Communication Technology, and

Mathematics Education for Rural and Regional Australia

QuickSmart

Numeracy Program for

Middle School Students

User Guide

COPYRIGHT/ISBN:

QuickSmart Numeracy

User Guide

Edition 2

© SiMERR, University of New England 2017

This manual is copyright. Except as permitted under the Copyright Act of 1968 (Cth), no

part of this publication may be reproduced by any process, electronic or otherwise,

without the specific written permission of the copyright owner. Neither may information

be stored electronically in any form whatsoever without such permission.

Enquiries should be addressed to SiMERR, University of New England.

ISBN: 978-1-921597-17-2

i

QuickSmart Numeracy User Guide

FOREWORD 1

CHAPTER 1 2 Background to the QuickSmart Program 2

CHAPTER 2 3 The QuickSmart Numeracy Program 3 QuickSmart as a Fourth-Phase Intervention 3 QuickSmart Instruction 4 Assessment in the QuickSmart Program 4 Structuring for Success 5 Overview of the QuickSmart Program 5

Length of Instructional Phase 5 Selection of Targeted QuickSmart Students 5 Comparison Students 5 Standardised Testing 6 Preliminary OZCAAS Computer Testing 6 Mid-Phase OZCAAS Assessments [Optional] 6 Final Assessments 6 Reporting to Stakeholders – Parent Meetings 6

CHAPTER 3 7 Setting up the QuickSmart Numeracy Program 7

Location 7 Staff Required 7 QuickSmart Co-ordinator 7 Role Description for QuickSmart School Co-ordinator 7 QuickSmart Instructor 9 Role Description for QuickSmart Instructor 9

Timetable 10 The Yearly Planner 10 Implementing the QuickSmart Numeracy Program 10 Lesson Timetable 11

Stakeholder Communication and Involvement 11 Installation of the OZCAAS Software 12 Participant Selection 12 Selection of Comparison Students 12 Gaining Permission 13 Pairing of QuickSmart Students 13 Preparation of Material for QuickSmart Lessons 13 Preparation of Student Folders 13

CHAPTER 4 14 Commencement of Instruction 14

Conducting Baseline Testing (Pre- and Post-testing) 14 Create an Individual File for Each Student 15 Choose an Individual Task 15

Contents

ii

Pre-test – Establishing a Starting Point 15 Post-test 16 Run the Task 16 Score Student Responses 16 View and Discuss Results 17 Collecting Mid-Intervention, Post-Intervention and Maintenance Data 17 Standardised Tests 17

CHAPTER 5 19 The QuickSmart Numeracy Lesson 19

Numeracy Lesson Format 19 The Hundreds Club 23 QuickSmart Lesson Triangle 24

CHAPTER 6 25 Assessment for Learning and Record Keeping 25

Record Keeping 25 QuickSmart Lesson Activities 25 The Cognitive Aptitude Assessment System (OZCAAS) 26 Standardised Tests 26 Stakeholder Evaluation 26 Comparison Student Data 26 Long Term Data Collection – Follow up Testing 27

CHAPTER 7 28 Commencement of Instruction 28

CHAPTER 8 29 Using Additional Resource Materials 29

CHAPTER 9 30 Problem Solving 30

Word Based Mathematics Problems 30 Problem Solving / Strategy Development and Mathematics Language

Mastery Lesson Format 32

CHAPTER 10 34 Problematic Students 34

The Importance of Regular Attendance 35 Ideas for Dealing with Student Absences 35

CHAPTER 11 36 Conclusion of the QuickSmart Numeracy Program 36

Students Exiting QuickSmart 36 Final Testing of Students 36 Graduating QuickSmart Students 36 Conclusion of QuickSmart Program – Celebration of Success 36 During the QuickSmart Instructional Phase 36 Sharing / Recording Data 37 Transition to Secondary Setting 37 Alternative School Placement 37

APPENDIX I 38 Pre- and Post-intervention Testing for QuickSmart Numeracy 38

iii

APPENDIX II 39 Numeracy Lesson Format 39

APPENDIX III 41 Numeracy Glossary of Terms 41

APPENDIX IV 49 Why you can’t divide by zero 49

APPENDIX V 50 Case Studies: QuickSmart Numeracy Students 50

User Guide – Numeracy Program

1

Foreword

Middle school students who have problems with learning basic number facts face many difficulties

at school. These students often need intensive support to bring them ‘up to speed’ with basic

skills such as the recall of number facts and problem solving.

The QuickSmart Numeracy Program is an educational intervention designed to support numeracy

skills development. QuickSmart was developed by a research team from the National Centre of

Science, Information and Communication Technology, and Mathematics Education for Rural and

Regional Australia (SiMERR) which is based at the University of New England (UNE).

QuickSmart allows a focus on low-achieving students’ characteristics as learners and their

efficiency of cognitive processing. It also facilitates the delivery of instruction that emphasises

deliberate practice and provides extensive feedback on task performance.

The program is called QuickSmart to encourage students to become “Quick” in their response

speed and “Smart” in their strategy use when learning the basic skills required in numeracy. It

focuses on the role of automaticity in developing students’ understanding and quick recall of basic

academic facts. Ultimately, QuickSmart aims to free up the working memory of students so that

they can engage meaningfully in demanding school activities like problem solving and multiple

computations.

The User Guide for the QuickSmart Numeracy Program has been developed to assist anyone

involved in supporting students with learning difficulties in numeracy – classroom teachers,

support teachers, teacher assistants, parents and carers. The lesson activities, sample worksheets,

assessment strategies and resources (both hard copy and electronic) included in this program are

designed to support learners who require careful and explicit instruction.


2

Chapter 1

Background to the QuickSmart Program

QuickSmart is a theory-based instructional intervention designed to improve students’ information

retrieval times to levels that free up working memory capacity from an excessive focus on simple,

routine tasks.

There are two independent aspects to the overall QuickSmart Program. The first, QuickSmart

Numeracy, is discussed in the following pages. The second is referred to as QuickSmart Literacy

and targets those students who are performing poorly on reading and comprehension tasks. Both

these individual programs share a common theoretical basis, a similar structure, and an equivalent

extensive professional learning program for teachers, teacher assistants and school executive

staff. In addition, each program incorporates the Cognitive Aptitude Assessment System (OZCAAS)

computer assessment tool within the QuickSmart lesson structure.

The QuickSmart Program is based on a substantial body of research related to the importance of

particular skills in numeracy and literacy. In particular, students who develop fluency and

confidence in basic skills have more cognitive capacity to direct their efforts to higher-order

processes involved in reading meaningfully and being able to solve problems in mathematics.

Specifically for numeracy, becoming faster and more confident in recalling basic mathematics facts

(with understanding), can mean that students have more time, energy and attention available for

tackling more challenging mathematical problems. In the case of the QuickSmart Numeracy

Program the focus is on the four operations with whole numbers up to and including 12.

This User Guide sets out in detail the educational approach of the QuickSmart Numeracy Program.


3

Chapter 2

The QuickSmart Numeracy Program

The aim of the QuickSmart Numeracy program is to increase fluency in basic mathematics skills

for middle school students with learning difficulties. These students generally perform in the

bottom 30% of the national achievement spectrum.

The program focus is on basic mathematics content with instructional material that is planned to

meet individual students’ learning needs. Teaching time allows students to self-monitor and to

receive immediate, informative feedback. Students participate in targeted practice activities to

increase their understanding and to develop effective strategies.

Lessons follow a structured format based around a “focus set” of number facts. Explicit strategy

instruction; instructor and peer modelling; discussion; questioning; guided, deliberate and

independent practice and appropriate feedback form the basis of the QuickSmart lessons. Lessons

include an assessment on the OZCAAS system to provide the student and instructor with

information about accuracy and speed of recalling number facts. Students aim to increase their

accuracy and decrease response times, which demonstrate increased automaticity. They aim to

become both “Quick” and “Smart.”

QuickSmart as a Fourth-Phase Intervention

QuickSmart has accrued an extensive evidence base since 2001 indicating that there is an

alternative to failure for many middle-school students not meeting National Minimum Standards in

numeracy. The program provides a fourth, and potentially last, phase intervention that enables

students to proceed satisfactorily with their studies. Many teachers who have been involved in the

program believe that QuickSmart is their last realistic chance of being able to help low-achieving

students in a sustained, and for these students, sustainable, way.

The four phases referred to are:

Phase One: Teacher teaches. Students are included in the regular class program but make

little progress. The achievement gap widens between low-achieving students and their

peers.

Phase Two: Teacher provides differentiated activities to overcome learning obstacles. The

teacher notices the students’ difficulties and adapts and modifies classroom-learning

activities to make them suitable for students with a wide range of abilities. It remains

difficult, however, to organise sufficient practice experiences to ensure all students are

confident and fluent in their learning.

IMPORTANT: Instruction and assessment form a continuous learning and

teaching cycle in the QuickSmart program.


4

Phase Three: Teacher is supported through collaborative

consultation or with an in-class instructor – either

another teacher or teacher aide. The teacher collaborates

in order to meet low-achieving students’ needs in the

classroom setting.

Phase Four: Students receive a more deliberate and

focused small class instructional program in pairs for

some of their school day.

QuickSmart provides an alternative approach to improving

numeracy outcomes. The QuickSmart program offers a

structured way to provide tailored instruction that is of sufficient

intensity and duration to make a lasting difference to the

performance of low-achieving middle-school students.

QuickSmart Instruction

The QuickSmart program emphasises the usefulness and relevance of number facts to regular

classroom activities. This feature of the program is important for developing transfer of learning

to other settings. For example, the utility of basic academic understandings and skills can be

presented to the students by relating basic mathematics facts to money or other mathematical

situations in the independent practice and problem solving sections of the QuickSmart lessons.

Once students’ recall of basic academic skills becomes truly automatic, they cannot help but recall

this information and have it available for use in other settings and on more complex tasks. It is

particularly important that middle school students have ready access to basic academic skills that

enable them to fully engage with challenging academic work.

The rationale behind the QuickSmart program is that developing automaticity of basic

mathematics skills frees working memory resources and allows middle school students to engage

successfully with more challenging tasks such as those involved with problem solving.

Assessment in the QuickSmart Program

Observations and information gained from questioning students about their basic knowledge and

strategy use are the basis of instructional decision-making and individualisation of instruction in

the QuickSmart Program. Assessment information can also be collected from many of the

activities in the program such as Flash Cards, Speed Sheets, and independent worksheets.

Importantly, the OZCAAS assessment system provides on-going data related to students’ accuracy

and speed of recall.

An important feature of the program is that much of the assessment information obtained during

QuickSmart lessons is very accessible and understandable to the participating students. Students

are able to evaluate their own learning through recording information, such as how many Flash

Card number facts they can recall accurately in one minute.

Students are encouraged to use this information to set their own realistic future goals. Also

assessment information obtained from the flash card activities and OZCAAS is plotted onto

individual graphs in order to provide students with a motivating visual representation of their

progress.


5

Structuring for Success

The QuickSmart program follows a structured lesson sequence based on a “focus set” of number

facts. An important underlying goal of each lesson is to “structure for success” by providing

students with regular and predictable learning sequences. Instructional time is made available for

students to practise and improve on what they already know, and to learn and practise new

knowledge.

Such circumstances provide potent opportunities for students to become more successful in every

QuickSmart lesson as the result of enjoyable, achievable and personally challenging practice

activities. Frequent but genuine praise of students for their efforts to learn and improve their skills

is an important motivator. Often this

praise is also an opportunity for

reinforcement of effective strategy

use, for example, “Wow, you got 35

Flash Cards in a minute, very

impressive! One reason I can see that

you’ve improved so much is that

you’re now adding whole tens instead

of counting them as ten ones”.

Throughout the entire QuickSmart

program every effort should be made

to ensure that students spend the

majority of lesson time actively

engaged with learning and practice

activities.

Overview of the QuickSmart Program

Length of Instructional Phase

The instructional phase for each student should be 30 weeks of three half hour lessons per week.

Planning instruction over a 30-week period provides important benefits for students, particularly

those students who (i) need the additional time to reach acceptable levels of automaticity in recall

of basic number facts in all four operations; and (ii) need to undertake enough work on problem

solving to allow them to develop good problem solving work habits and to be able to see a way

forward for themselves in mathematics.

Selection of Targeted QuickSmart Students

Allocating time to select your targeted QuickSmart students at the beginning of your program is

important. Factors to be considered in choosing students to take part are detailed in Chapter 3:

Participant Selection

Comparison Students

The comparison students are average-achieving peers from the same years as those selected for

the QuickSmart program. They do the same testing as the QuickSmart students at the beginning

and end of the program but do not participate in the program. Having a comparison group gives a

baseline against which the improvement of the QuickSmart students can be measured. See

Chapter 3: Selection of Comparison Students


6

Standardised Testing

Before the program begins and after it is finished, both the QuickSmart and comparison students

are assessed using tests such as the ACER Progressive Achievement Test in Mathematics (PATM).

These independently developed tests assess mathematics content that is not directly taught in the

program. These measures are able to show the effectiveness of QuickSmart in developing a wide

range of academic skills. See Chapter 4: Commencement of Instruction

Preliminary OZCAAS Computer Testing

Once students are selected, a bank of OZCAAS tests for each QuickSmart and comparison student

should be completed. Results in both speed and accuracy on these tests provide a starting point

for instruction, goal setting and improvement. See Chapter 4: Commencement of Instruction

Mid-Phase OZCAAS Assessments [Optional]

Half way through the instructional phase, testing of targeted QuickSmart students using the

original bank of computer tests could be attempted, but it is optional. Results from this testing

should indicate that automaticity is becoming established. Difficulties may also be revealed which

will inform future instructional directions. This assessment is optional.

Final Assessments

At the end of QuickSmart intervention, both targeted QuickSmart students and comparison

students should once more be tested on the OZCAAS tasks used at the beginning of the program.

The standardised tests used at the beginning of the program should also be readministered. This

will provide information about progress for both comparison and targeted QuickSmart students on

higher order thinking tasks.

Reporting to Stakeholders – Parent Meetings

Regular reporting to parents/carers and classroom teachers about individual student progress

should be timetabled into the QuickSmart year. Parent meetings and observations by classroom

teachers are encouraged but should be delayed until the QuickSmart students feel comfortable

with the program and are able to demonstrate their new numeracy skills.

Such occasions should be seen as times of celebration and provide the students with the

opportunity to share their new learning with confidence and pride.


7

Chapter 3

Setting up the QuickSmart Numeracy Program

Location

The ideal setting for QuickSmart instruction is:

a quiet area of the school;

a permanently designated space (room) where the QuickSmart materials and the students’

work folders can be stored appropriately;

a computer (or computers) on which the OZCAAS software has been installed; and

a moderate sized desk with three chairs for each QuickSmart group working at any one time.

Staff Required

QuickSmart Co-ordinator

The trained and designated QuickSmart Co-ordinator needs to take responsibility to meet and

communicate with their QuickSmart Instructors on a regular basis. If at all possible, the

QuickSmart Co-ordinator should endeavour to instruct at least one QuickSmart pair in the first

year of the QuickSmart program. Regular meetings between all Instructors and the Co-ordinator

will facilitate discussion about program activities and individual student learning needs, and

provide an opportunity for further clarification and professional development through team

sharing and collaboration.

Role Description for QuickSmart School Co-ordinator

As Teacher Co-ordinator for QuickSmart in your school, your tasks may include:

(i) At the beginning of the QuickSmart year:

a. identifying target students;

b. organising and/or administering pre-program assessments to QuickSmart and

Comparison students;

c. ensuring the safe storage of results and uploading of data to the QuickSmart website;

d. organising student/Instructor timetables;

e. locating and organising the learning space, equipment (including a computer for

OZCAAS), individual student folders and resources as required.

(ii) Around the middle of the QuickSmart year:

a. coordinating preparation of mid-program Progress Report Evaluation report for

Workshop 2 (first year only); and

b. ensuring that pre-intervention results are uploaded to QuickSmart (using the dashboard

to access the data upload tool).


8

(iii) At the end of the QuickSmart year:

a. organising and/or administering post-program assessments to QuickSmart and

Comparison students;

b. uploading the QuickSmart and Comparison student data to QuickSmart; and

c. coordinating preparation of end-of-Program Evaluation report for Workshop 3 (first year

only);

(iv) and in general:

attending the six days of Professional Development required in the first year of

implementation of QuickSmart at your school, and the relevant Professional Development

in subsequent years;

liaising with relevant people as appropriate: class teachers, QuickSmart Instructors,

SiMERR/UNE staff, parents/caregivers, and other colleagues, including the School

Executive;

organising/facilitating the public acknowledgement of student success;

communicating on a regular basis with the various stakeholders as appropriate. This can

include organising information sessions for parents/caregivers and for classroom

teachers, held at mutually convenient times, to discuss the intervention and students’

progress;

facilitating effective teamwork between those involved: the Instructors, relevant

members of the school community, the Cluster Co-ordinator and the UNE SiMERR team;

troubleshooting problems that may arise;

monitoring student attendance/participation and following-up on poor

attendance/participation;

meeting regularly with QuickSmart Instructors to facilitate discussion about program

activities and individual student learning needs and providing an opportunity for further

clarification and professional development through team sharing and collaboration;

representing the needs of the QuickSmart intervention in planning discussions at your

school;

supporting the Instructors who deliver the intervention by identifying starting points for

students, providing guidance in planning lessons and tracking student progress when

needed; and

co-ordinating workshop application forms for staff at your school and co-ordinating

their travel to QuickSmart workshops.


9

QuickSmart Instructor

Ideally, all QuickSmart Instructors should have attended the 2 days of the initial implementation

workshop. Each Instructor should be allocated a period of time for preparing lesson material,

marking worksheets, record keeping and data entry. For every 12 QuickSmart students [6

groups of 2 students], one hour per week is suggested as the minimum time required for

this preparation. Making use of the proforma summary sheets provided in the QuickSmart

materials will assist in maintaining student records and data in a timely fashion.

Role Description for QuickSmart Instructor

As an Instructor for QuickSmart your tasks will include:

attending the six days of Professional Development required in the first year of

implementation of QuickSmart at your school, and the relevant Professional Development

in subsequent years;

gaining knowledge and understanding about the theoretical underpinnings of the

QuickSmart program;

gaining knowledge of the QuickSmart lesson structure and content and the resources that

are available;

gaining knowledge of instructional strategies and questioning skills;

delivering QuickSmart lessons to pairs of students;

preparing the materials required for QuickSmart lessons;

recording assessment data and evaluative comments;

providing feedback, both corrective and complimentary, to students for completed

QuickSmart activities;

making decisions as to how to adapt aspects of the QuickSmart lesson to achieve learning

for students;

making decisions on when to move on with new learning;

developing management strategies for working successfully with pairs of students;

collaborating frequently with the other QuickSmart Instructors and the QuickSmart Co-

ordinator to resolve, advance and promote QuickSmart within the school culture;

working closely with the QuickSmart students’ class teachers to resolve individual

timetabling issues; and

communicating with parents/carers of the QuickSmart students to provide knowledge of

the QuickSmart program and its focus, and information about student progress and

achievements.

Significantly, we ask Instructors to dismiss any reported record of poor previous performance of

the students with whom they are working. Instructors should have expectations that each child

under their care will improve. Instructors should believe, and show by their words and actions,

that their students can achieve and improve to levels that their classroom peers take for granted.

Part of this sense of “can do” is the celebration of growth in achievement, speed and

understanding whenever it occurs.


10

Timetable

The Yearly Planner

Implementing the QuickSmart Numeracy Program

You can use the QuickSmart Yearly Planner below as a guide to broadly plan the intervention

phase of the QuickSmart program for your school over a period of 40 weeks. It is possible that in

your first year of implementing the program you may not be able to reach the goal of 30 weeks of

instruction. However, the pre-testing and post-testing would still be completed as indicated.

QuickSmart Planner

School: Year

WEEK DATES PROGRAM FOCUS

1 Testing - Targeted & Comparison Students Standardised Tests

2 Testing - Targeted & Comparison Students - OZCAAS


4 Week 1 - Intervention






10 Week 7 - Intervention - Parent Meetings

11 Week 8 - Intervention - Parent Meetings








19 Testing - Targeted Students - OZCAAS [optional]

20 Testing - Targeted Students - OZCAAS [optional]


















38 Testing - Targeted & Comparison Students – Standardised Tests

39 and Submit all data to website

40 and send Completed Stakeholder Surveys


11

Lesson Timetable

How each school organises and timetables QuickSmart lesson times for students will vary

according to individual contexts, the availability of staff, and the overall timetable constraints of

the whole school. Primary, central and secondary schools will face different timetabling situations.

Following are some considerations that may influence timetabling of QuickSmart in your school:

Establishing a regular timetable for the QuickSmart students is important as it gives the

students a feeling of independence and responsibility. It also assists classroom teachers with

forward planning, enabling them to know when students will be missing from their classes.

Primary Schools - Rotating the timetable throughout the day means that students do not

miss the same lesson every QuickSmart day.

Secondary Schools - Withdrawing students from three single and different subject lessons

across the timetabled week assists by ensuring that students do not regularly miss

important learning in the same subjects. Issues to do with practical lessons and double

periods should be worked through at a school level.

Avoid having QuickSmart lessons during whole school commitments such as sports periods

or whole school assemblies.

Some students draw much enjoyment out of certain school lessons or activities. It would

seem fair, within limits, t hat students do not miss out on what they enjoy to attend a

QuickSmart lesson.

With the knowledge that maximum learning occurs in morning sessions, it would be ideal if

QuickSmart lessons could be scheduled before the lunch break. If this is not practical, at

least try to ensure that students get a mix of lessons before and after lunch.

Working with classroom teachers around whole-class activities, such as excursions and

whole-class testing, is important. Also, being flexible in rescheduling lesson times for

student priorities and accommodating class teachers’ needs or school events, if at all

possible, is recommended.

Stakeholder Communication and Involvement

When implementing QuickSmart in the school, it is important that all stakeholder groups have

enough information about the program to feel informed and included. The Principal, QuickSmart

Co-ordinator, and QuickSmart Instructors need to decide how the information about QuickSmart is

shared in the school community. Some ideas include:

providing information and regular updates to the school staff at staff meetings;

addressing a parent meeting;

inviting classroom teachers to observe a QuickSmart lesson;

providing regular updates about student growth and success to class teachers;

inviting parents of QuickSmart students to visit and observe their child in a QuickSmart

lesson; and

regular reporting to parents/carers about individual student progress throughout the

QuickSmart program.

Taking time to arrange these occasions can promote ownership of the QuickSmart program

throughout the school. Some schools have chosen Education Week while others have set up special

times for parents/carers (and grandparents) to visit. Many schools set up a series of work-stations


12

so that parents/carers can experience (and students can test their parents/carers on) different

aspects of a QuickSmart lesson such as Flash Cards, Speed Sheets and OZCAAS. Parents/carers

can also explore their child’s folder that contains evidence of their child’s successes.

Installation of the OZCAAS Software

The OZCAAS program can be downloaded from the website. Instructions for accessing this site

would have been sent by email.

Participant Selection

Students most likely to succeed and benefit from the QuickSmart Numeracy program are those

who:

• experience persistent difficulty in numeracy;

• display a good attitude to learning in small groups;

• attend school regularly; and

Additionally, students may benefit from the QuickSmart Numeracy Program if they:

• do not have major attention difficulties, problem behaviours or intellectual disabilities;

have recorded low performance in NAPLAN; or

have below average results in school or class administered tests.

Teacher observations are also important for identifying students who may benefit from the

QuickSmart program. Those students who experience a lack of confidence in participating in

classroom activities could also improve their performance when given the opportunity to be part

of a focused QuickSmart program.

Selection of Comparison Students

The selection of a small number of average achieving students at the beginning of the program

will facilitate the gathering of comparative information about the performances of targeted

QuickSmart Students and students not undertaking the QuickSmart intervention. Results on both

the standardised tests and the OZCAAS computer assessments from before and after the

intervention will provide this information.

It is important to select the group of Comparison Students from amongst the average- achieving

students who are the peers of the QuickSmart Students. Do not choose the comparison group of

students from those who are achieving well above the QuickSmart cohort of students as this will

not give a clear comparative snapshot of what is really happening back in the classroom for the

QuickSmart Students.

We recommend selecting about six Comparison Students with students chosen from the

same school years as the QuickSmart Students.

IMPORTANT: The inclusion of students with an intellectual disability needs

to be considered carefully. The research has shown that these students

enjoy and become more automatic in their basic numeracy fact recall but

have difficulty in transferring and using this learning to solve more complex

mathematical problems on standardised tests and back in their classroom.


13

Gaining Permission

Written permission for the collection of data for both QuickSmart and Comparison Students is

required to fulfil the ethical guidelines of the implementation of the QuickSmart program in your

school. Approved proformas for Permission letters are on the website.

Note: no student should be excluded from QuickSmart because they do not provide a

consent form, but their data must not be shared with the University of New England.

Pairing of QuickSmart Students

For QuickSmart instruction, targeted students need to be grouped in pairs. Knowledge of

friendship groups and personality and behavioural attributes should be considered.

Overall, instruction is more effective if both students are at a similar level in their learning. Pairing

students at a similar level of learning helps to promote good and beneficial discussion as these

students are often confronting the same difficulties in their mathematics learning. There is some

value in selecting pairs from the same class, as this minimises disruption and facilitates students

starting the lesson on time.

Preparation of Material for QuickSmart Lessons

Once all the baseline information from the Standardised Tests and the OZCAAS baseline testing is

available, and the QuickSmart Students have been paired, decisions should be made as to the

appropriate starting point for the instructional phase for each pair of QuickSmart Students. The

starting point is determined by considering the OZCAAS results. Students should experience

success when they begin the QuickSmart program, so adjustments may be necessary. See Chapter

4: Conducting Baseline Testing

Preparation of Student Folders

Before the instructional phase of the QuickSmart program commences, individual student folders

need to be prepared. Use the Example Student Folder that was supplied as part of the package of

resource material at the Implementation Workshop as a model for the setting up of these folders.

An examples of a student folder can also be found in the Numeracy Private Area website.

A ring binder is a very efficient way of storing the accumulated material for each student. If

everything is dated, corrected and graphed where appropriate, the student folder provides a

powerful history of achievement for each student. In the QuickSmart Numeracy Resources and

Organisation Manual (Section 9), there is a proforma that can be used as the front cover of these

folders. Including a photo of the student on the cover personalises each student’s folder.

Time needs to be allocated for photocopying the material needed for the first week of lessons. The

student folder should contain the appropriate Focus Fact sheet, Flash Card graph sheet, Speed

Sheet, and some appropriate independent worksheets. An individual summary sheet for collecting

information about lesson achievements and OZCAAS results is also handy.

IMPORTANT: If individual students who are initially paired together

experience different rates of progress throughout the intervention, it is

possible to re- group these students for a more compatible arrangement.


14

Chapter 4

Commencement of Instruction

Conducting Baseline Testing (Pre- and Post-testing)

The importance of baseline testing and data gathering in providing evidence-based information on

the success of the QuickSmart program in a school and information of its success for individual

students cannot be overestimated. It is important to schedule time for this testing before the

intervention commences.

Standardised tests used to measure higher-order thinking skills should be administered at the

beginning and at the end of the program to supply comparative data on progress in conquering

tasks that require higher-order thinking skills. It is important that the assessment measures

chosen for this purpose are rigorous, independent of the instructional program, and relevant to

the Australian student population.

The Progressive Achievement Tests in Mathematics (PATM) has been widely used by the

QuickSmart program and participating schools to measure student growth in the six strands of

Mathematics: Number; Algebra; Geometry; Measurement; Statistics; and Probability.

OZCAAS Testing provides a starting point for collecting data throughout the QuickSmart Program.

The Cognitive Aptitude Assessment System (CAAS), a computer-assisted assessment system, is a

unique component of the QuickSmart program. Developed by researchers from the Laboratory for

the Assessment and Training of Academic Skills (LATAS) at the University of Massachusetts to

obtain reliable assessments of student performance, the assessment tasks used are designed and

sequenced in order to target and identify the exact nature of the literacy and numeracy issues a

student is experiencing. In the case of QuickSmart Numeracy, it allows QuickSmart

Coordinators/Instructors to identify an appropriate place at which to commence the program.

Further research and changes have led to the current OZCAAS version and you can access this

program through the QuickSmart Numeracy Private Area website. There are five (5) tests to

complete:

• Number Naming,

• Addition or Basic Addition,

• Subtraction or Basic Subtraction,

• Multiplication or Basic Multiplication,

• Division or Basic Division.

Time is needed for conducting and marking the standardized tests and for conducting the

OZCAAS tests with individual students. About 45 minutes on average is needed to carry out the

bank of OZCAAS tests for each student.

IMPORTANT: It is important to use the same level of Pre- and Post-test

to measure improvement.


15

Create an Individual File for Each Student

An individual file needs to be created for each student at the beginning of the QuickSmart

intervention phase. This file cumulatively records both speed and accuracy for this student for all

assessment tasks throughout the QuickSmart intervention.

Choose an Individual Task

Once the individual student’s file has been opened, click on Run Activity on the menu at the top

right of the screen. Choose Numeracy Assessment in the next window. Choose the task the

student is to be tested on from the list of tasks available.

Pre- and Post-OZCAAS tests to be completed include:

• Number Naming,





When completing the OZCAAS during the QuickSmart lesson, only complete the level the student

is working through.

Pre-test – Establishing a Starting Point

Highlight all the student results and tick both speed and accuracy for the student to see. Discuss

with the student where he/she will be commencing.

The profile of results from the OZCAAS testing will give the best indication of where students

should begin working with the resources provided.

QS Tip

When administering the tasks for baseline assessment, it may be necessary to stop

some tasks before they are completed because the student is consistently failing.

Save your results for these tests. Encourage students to attempt OZCAAS

assessments on all operations if possible.

IMPORTANT: Care needs to be taken to check that you have the right file

open for a particular student.

Contact technical support on:

(02) 6773 5061 or email: [email protected]

for assistance with the OZCAAS program. This includes installing and using

the program etc.


16

Post-test

At the conclusion of the program, retest the student on the five tests, using the same level of

assessment as used for the pre-test:

• Number Naming,





Highlight all the student results and tick speed and accuracy for the post-test. Discuss with the

student the journey they have taken and celebrate the success.

Run the Task

Follow the instructions as displayed on the screen. Read all instructions to the student or have the

student participate in doing this until they are familiar with how to complete the OZCAAS

assessments. Try all the practice examples. These can clarify any difficulties the student may have

before proceeding to the OZCAAS assessment.

Score Student Responses

Once the student responds, the computer indicates that the item can be scored. (See the rectangle

in the top right hand corner of the OZCAAS screen.)

• If the student’s response is correct, the instructor needs to press the Left mouse button. If

the response is incorrect, press the Right mouse button.

• If the student has inadvertently set off the response mechanism by coughing, sneezing, or

breathing heavily, the result can be erased by pressing both mouse buttons simultaneously.

This is referred to as “flushing” the result.

• If the item has been marked incorrectly, the result can be fixed by pressing the correct mouse

button within about half a second of the original scoring.

IMPORTANT: Commence at the level the student demonstrated less than

100% accuracy and/or had an over 2 seconds response time.

IMPORTANT: Immediate Self-Correction when supplying answers to OZCAAS

tasks should be accepted and scored as correct. This is a natural learning

response that everybody makes occasionally when pressured to make a

quick response. Reassure students that this is acceptable. You need to be

careful that this does not become a feature of a student’s response where

the student uses a first quick response as an opportunity to gain “thinking

time”.


17

View and Discuss Results

Results can be viewed by returning to the menu at the top of the screen and clicking on Graphs,

then on By Task/Date.

• To view results of the current task, locate task and the day’s date. ‘Speed’ and ‘Accuracy’ can

be viewed on the same page by selecting both and clicking ‘OK’.

• To view a graph of all attempts at the same task, click on the top task entry and scroll down

highlighting all the dates for that task. Decide on whether ‘Speed’ or ‘Accuracy’ or both are to

be viewed then click ‘OK’. Viewing this graph presents a great opportunity to discuss results

over time for both ‘time’ and ‘accuracy’, and to highlight students’ improvements in response

time reduction and improved accuracy.

Slight dips in results can be discussed and explained in terms of difficulties with the random

selection of task items, the health of the child or the time of the day when the assessment may

have been completed. The immediate feedback provided by the results can also facilitate realistic

goal setting by the student.

To attain a summary of the speed and accuracy results in a table: click on reports; click By Task;

and select the results by highlighting the required dates. This is not visually as powerful but is a

useful numerical summary that displays accuracy and speed results on the one screen. Use this

format to get student assessment data to provide to UNE.

Collecting Mid-Intervention, Post-Intervention and Maintenance Data

Collecting OZCAAS assessment data during the intervention phase and at the end of the program

is important. Test each student on all OZCAAS tests that were attempted at the initial (baseline)

testing and add any tests that students have progressed to since. Mid Intervention testing is

optional, and maintenance testing at regular intervals after the program has been completed is

recommended, to see if students’ improvements in basic academic skills have continued.

Standardised Tests

Standardised tests are used as measures of higher-order thinking (e.g., problem solving) and are

administered at the beginning and at the end of the QuickSmart Program. This testing provides

data related to student progress in applying QuickSmart learning to their classroom demands. It is

important that the assessment measures chosen for this purpose are rigorous, independent of the

instructional program, and relevant to the Australian student population.

The Progressive Achievement Tests in Mathematics (PATM) have been selected by the QuickSmart

Program as a measure of this important instructional outcome. This multiple choice test is

QS Tip

The OZCAAS software automatically cleans the data by eliminating,

as outliers, responses two standard deviations from the mean, such

as impossibly fast or unusually slow scores. This can sometimes

mean that results can show 100% accuracy even though a response,

which is an outlier, has been marked incorrect.


18

available as pencil and paper tests or online through ACER. All PAT tests are normed on Australian

school children. All assessments need to be administered and scored according to the instructions

detailed in the test manual.

Many schools now use the PATM tests annually for all students, towards the end of the school

year. This result can used as their pre-test early in the following year.


19

Chapter 5

The QuickSmart Numeracy Lesson

Pairs of QuickSmart Students participate in three half-hour lessons each week, ideally with the

same instructor. Where possible, both students should have similar learning needs.

QuickSmart lessons consist of a variety of practice and recall strategies designed to develop

understanding and fluency with basic mathematics skills. Instruction in the QuickSmart Numeracy

program is delivered by focusing on a particular number fact or group of number facts. Each

lesson involves:

• revision of the previous session’s learning;

• explicit teaching of number facts;

• completion of a number of guided practice activities;

• discussion and practise of memory and retrieval strategies;

• timed and independent activities and worksheets; and

• strategies to assist in mathematical problem solving (during the second 15 weeks).

Games and worksheet activities are used to reinforce learning and allow for extra practice.

Working on independent worksheets allows for extra practice for one student while the other

student does an OZCAAS assessment on the computer.

Numeracy Lesson Format

1. Focus Facts – Knowledge / Understanding Check (5 minutes)

The lesson focuses on a targeted set of Focus Facts for either addition and subtraction or

multiplication and division. This encourages and directs the student’s attention to a limited and

controlled amount of learning and understanding.

Review and discuss the current set of Focus Number Facts. Examine patterns in the number facts

and how they make sense. Review errors and consolidate understanding.

When checking understanding consider, for example:

• the inverse nature of the + and - operations and the x and ÷ operations. (Strategies 2

and 10)

• the ‘grouping in tens’ strategies. (Strategies 3 and 7)

• skip counting strategy. (Strategy 14)

Explanations for these strategies can be found in the QuickSmart Numeracy Resources and

Organisation Manual (Section 3: Focus Facts, Pages 11-15)

• the use of number lines, see QuickSmart Numeracy Resources and Organisation Manual

(Section 2: Miscellaneous)


20

2. Flash Cards - Automatic Recall of Focus Number Facts (5 minutes)

Continue to develop the automatic recall of the focus number facts through the use of the Flash

Cards.

Use a pack of Flash Cards of current focus number facts to challenge each student to see how

many number facts they can get correct in one minute. Utilise the student’s QuickSmart buddy to

do the timing, if appropriate.

Count correct responses and have the student record their result on the graph in their work folder.

Discuss errors and establish understanding in gaining correct responses. Record the number of

errors on the bottom of the graph in each student’s work folder.

Celebrate speed and accuracy improvements.

Initially, use a pack that focuses on a single operation and number fact e.g., +4. Follow this by

moving to another set of flash cards in addition.

Each pack of +, -, and x number facts contains 65 cards made of 5 sets of the basic facts. There

are 60 cards in each pack of division facts (because it is not valid to divide by 0, see Appendix IV).

3. Speed Sheet Challenge (5 minutes)

The Speed Sheet begins to expand the confidence of the students to use their basic number

knowledge to incorporate larger numbers and more complex representations of the same number

facts.

Students work as fast and accurately as they can, answering the questions on the Speed Sheets of

the current set of Focus Number Facts, for two minutes. When the time is up, correct completed

work, give feedback on errors and record results.

Improvements in either speed or accuracy need to be celebrated.

IMPORTANT: It is important to note that the Focus Facts for each unit,

through the use of the Speed Sheets, also contain related facts such as 3 +

7 = 10, 30 + 70 = 100; 2 x 12 = 24, and 24 ÷ _ = 12 and 1/2 x _ =12. These

variations or extensions to the basic number facts facilitate students’

observations and understandings about relationships between numbers

and operations. The actual selection of the set of Focus Facts for each

student pair is matched to their learning needs. The Focus Facts for each

pair of students are then used in games and activities and practised using

Flash Cards.

IMPORTANT: Move your student on to a new set of Focus Facts when

they have achieved:

30 or more cards in a minute with

100% accuracy on

at least two consecutive occasions.


21

4. OZCAAS Assessment (5 minutes: one Student)

The OZCAAS task tests the facts for the operation that the student is working on. Under normal

circumstances, the OZCAAS task being assessed will match the operation on the current set of

Flash Cards. Because of the random nature of item selection in each OZCAAS task, students are

tested not only for facts that are currently the focus of attention but also on facts that have been

mastered, and facts that will be the focus of attention in subsequent QuickSmart lessons. This

encourages transfer and generalisation of learning.

Viewing the graphs of the tasks by looking at both response times and levels of accuracy is very

reinforcing and powerful for each student, particularly if improvement is noted. Less successful

results can often be justified by the students themselves or may be due to a student’s state of

health, time of day or other personal reasons.

Immediate self-correction in responding to an OZCAAS task item is to be acknowledged as a

regular strategy used when learning new material. If this occurs, the student’s answer can be

marked as correct.

5. Independent Worksheet (5 minutes – Student not doing OZCAAS task)

The independent worksheet requires students to use pen and paper to complete worksheets that

include the current number facts and extensions, or worksheets that relate the basic number facts

to other aspects of mathematics. The independent worksheet is completed by one student during

the time that his/her QuickSmart buddy is working on an OZCAAS computer assessment task with

the QuickSmart Instructor. Students are expected to work quickly and efficiently on their own

(without disruption) for five minutes on an independent worksheet.

IMPORTANT: SPEED SHEET GENERATOR – QuickSmart schools have access

to the QuickSmart website that allows you to generate extra Speed Sheets

for each set of Focus Facts. Over the period that instruction focuses on a

particular Focus Facts set, instructors can utilise this software to provide

extra Speed Sheets in addition to those that are provided in the QuickSmart

Numeracy Resources and Organisation manual. The use of the Speed Sheet

Generator is explained in Workshop 2.

QS Tip

Because of the time delay available in the OZCAAS program, after the student has

responded and before the instructor has scored the response, wonderful discussion

and teaching moments present themselves.

IMPORTANT: Move your student on to a new a new operation when

they have achieved:

an average response time of 2 seconds or less per item with

100% accuracy on

three consecutive occasions.


22

The focus of the worksheets might be different at different schools and for different pairs of

students at the same school. Collaborate with classroom teachers to source appropriate

independent worksheets. Be resourceful and make use of the many commercially available

Mathematics books that target the recall of basic number facts. The internet also provides a

wonderful source of mathematics activities that can be printed, photocopied and used. It is

important that these worksheets be at an appropriate level of difficulty for students to complete

independently.

Correct and give appropriate feedback. Students swap between activities 4 and 5 so each student

completes both activities. (5+5=10 minutes)

It is important to develop a routine to correct these worksheets and give appropriate and helpful

feedback. “Self-correcting” activities can be valuable at this point in the QuickSmart lesson. Some

of the commercially available mathematics activities are self correcting e.g. provide a coded

message or allow the student to journey though a maze or shade an area which becomes a

recognisable object.

Value this time for independent work. Frequently, QuickSmart students find it extremely difficult

to work independently on written tasks. The short and precise timing of this activity provides an

opportunity for quiet and independent application of their numeracy skills.

6. Games (5 minutes)

Play some mathematics games to help students become quick and accurate at automatically

recalling Number Facts. Games include Three-in-a-Row, Same Sums, Double O, QuickSmart Bingo

or QuickSmart Dominoes. These games provide opportunities for using extension facts,

approximations and the application of number facts to real life situations.

The games supplied in the Numeracy Resource folder, kit and games pack are examples of fun

ways to conclude each QuickSmart lesson. Requiring fast and accurate calculations, they target the

current Focus Facts or require automatic responses to basic number fact calculations. The use of

the games provided and commercially available games encourages the application and

generalisation of basic number facts and operational skills to broader mathematics concepts and

extension numbers.

IMPORTANT: Do not underestimate the importance of feedback, discussion

and clarification for QuickSmart students. This should be included as part

of all QuickSmart lesson elements. With only two students in each

QuickSmart group, the availability of time to receive specific feedback is a

luxury that is rarely available to these students back in the classroom.

IMPORTANT: In expecting students to work quietly and without disruption

on independent worksheets, it is important to explain fully what the

worksheet requires. This eliminates the need to disrupt the OZCAAS testing

of the other student and thus compromise the results of the test.


23

The Hundreds Club

This activity can be substituted instead of a numeracy game. Besides providing a

fun and friendly competitive activity, it can result in feeling what automaticity is

really like.

This great idea was developed by a QuickSmart Instructor and presented at a

workshop in the North Coast Region of NSW. The idea has been taken up by many

schools. There are, at least, three separate “ Hundreds Clubs”.

In the first Hundreds Club the instructor combines the 65 plus zero and the 65

minus zero Flash Cards forming a deck of 130 cards. These are shuffled. The

students have to provide the answers to as many cards as they can in one minute.

If they get between 50 and 74 they become a bronze member of the Hundreds

Club. If they can reach between 75 and 99, they become a silver member. If they

score 100 or more, they become a gold member of the Hundreds Club and do not

need to attempt this activity again. Once students have gained entry to the

Hundreds Club their names can be recorded on a chart in the QuickSmart room.

This activity is carried out in the games component at the end of a QuickSmart

lesson.

Two other Hundreds Clubs that can be attempted are: (i) combine the plus 1 and

minus 1 Flash Cards together, and (ii) combine the multiply by 1 and the multiply by

10 cards together. Success at this activity sensitises the student to what

automaticity feels like and the idea that it can be fun.


24

QuickSmart Lesson Triangle

This Lesson Triangle demonstrates how the QuickSmart lesson moves and broadens its focus from

concentrating on a selected Focus Fact set through the various lesson components to applying

newly learnt basic number facts to problem solving exercises. Mathematics language mastery and

strategy development are incorporated across all lesson elements.


25

Chapter 6

Assessment for Learning and Record Keeping

To assess the progress in the QuickSmart Program, on-going assessment of each student needs to

take place at a number of levels. Because QuickSmart emphasizes the development of automatic

responses on basic skills, a considerable amount of regular assessment focuses on response time

and accuracy levels. Data are collected before, during and after the QuickSmart intervention.

Assessment information can be collected from:

• QuickSmart lesson activities;

• OZCAAS assessments;

• standardised tests;

• stakeholder evaluation comments;

• Comparison Student data; and

• national assessment results.

This information helps instructors make decisions about what to focus on in lessons as well as

when to move on to a new set of number facts. It will also enable students to set their own goals

for improvement.

Record Keeping

QuickSmart Lesson Activities

As part of each lesson, students will be involved in a number of timed activities, e.g., Flash Card

Number Fact Recall and Speed Sheets. The completion of other worksheets can also be timed,

particularly if these sheets are repeated as practice activities. Graphing results or comparing

previous results by focusing on response times and accuracy can provide valuable assessment

information for both learners and QuickSmart Instructors. This visual display of individual

improvement is very powerful for students who may have rarely felt that they had control over the

outcomes of their learning. Graphing successful performance is important to the success and

appeal of the program.

Using the blank graphs in the final section of each student’s folder, students graph the number of

Flash Card number facts correct in one minute. This allows them to see and appreciate their

improvements and begin to value the success achieved through repeated practice. Also, knowing

that beginning a new set of Focus Card number facts will lead to a temporary decrease in

performance helps students understand that new learning is difficult and will take practice over

time to master. (Refer to QuickSmart Numeracy Resources and Organisation Manual (Section 8:

Numeracy Graphs))

IMPORTANT: SETTING INDIVIDUAL LEARNING GOALS – Reviewing students’

OZCAAS results presents a great opportunity to reflect on their

achievements and to set new learning goals. In general, QuickSmart

students are not used to setting themselves educational goals. The OZCAAS

results and QuickSmart lesson achievements provide evidence of

improvement and can allow students to set appropriate goals.


26

The Cognitive Aptitude Assessment System (OZCAAS)

This computer program enables measurement of average information retrieval times and gives

immediate feedback through its graphing of response time and accuracy for tasks. It will also

show the cumulative results for individual students on each task. Watching the columns becoming

shorter as response time decreases, and the columns becoming taller as accuracy increases, is

very affirming for both students and their instructor and shows that improvement is being

achieved.

Standardised Tests

The use of standardised tests for both the targeted QuickSmart Students and a group of

Comparison Students provides valuable data and information about improvements achieved for

both groups.

Standardised tests are used as measures of higher order thinking and are best administered at the

beginning and at the end of the program thus supplying comparative data on progress in

conquering tasks that require higher-order thinking skills. It is important that the assessment

measures chosen for this purpose are rigorous, independent of the instructional program, and

relevant to the Australian student population.

The Progressive Achievement Tests in Mathematics have been widely used by the QuickSmart

program and participating schools to measure student growth in mathematics. These tests are

multiple-choice pencil and paper tests normed on Australian school children.

These standardised tests measure mathematics performance across the range of National Profile

strands – Number, Space, Measurement and Chance and Data. All assessments need to be

administered and scored according to the instructions detailed in the test manual.

For the purposes of the QuickSmart program, higher-order thinking in numeracy is conceptualised

as knowing how to problem solve effectively using quickly and accurately recalled basic number

facts and strategies. Therefore, students’ improvement in higher-order thinking processes, such as

problem solving, can be shown by their improved performance on standardised tests.

Stakeholder Evaluation

In order to monitor the effects of participation in the QuickSmart Program, qualitative data should

be collected regularly. This consists mainly of interviews, teacher observations, and comments

from students, parents/carers and teachers recorded during the program. Instructors should also

note their own observations of student progress in attitude, understandings and strategy use

during the intervention.

Information about students’ perceptions of the usefulness and importance of their QuickSmart

learning experience can also be gathered at the conclusion of the intervention. Questionnaires for

students and other stakeholders such as parents/carers and class teachers have been included in

the QuickSmart Numeracy Resources and Organisation Manual (Section 9: Essential Features).

Comparison Student Data

In order to gain a clearer indication of the effectiveness of the QuickSmart intervention, OZCAAS

data should also be collected from other students in the same grade as the participants in

QuickSmart. In general, the group of Comparison Students consists of six average-achieving

students nominated by class teachers. These Comparison Students complete the same OZCAAS

sub-tests in numeracy and also the standardised test at the beginning and the end of the

intervention.

These data from the Comparison Students can then be compared with the results of the


27

QuickSmart Students. Expectations are that following the QuickSmart intervention the learning

gap between the QuickSmart Students and the Comparison Students will have lessened markedly.

Long Term Data Collection – Follow up Testing

Conducting the OZCAAS tests with past QuickSmart Students at varying times following

completion of the QuickSmart intervention has value in informing the school about the effect of

the program for both the school and the individual students. Too often interventions do not gather

longitudinal data to assess the value of particular programs. In QuickSmart we have conducted

numerous studies where we have assessed student performance up to five years after students

have completed the QuickSmart program. The good news so far is that these studies report that,

in general, QuickSmart Students continue to either maintain the gains made or even improve,

often at an above average rate.


28

Chapter 7

Commencement of Instruction

The QuickSmart Numeracy program aims to narrow the achievement gap in learning for

currently low-achieving students by developing automatic responses in basic number fact recall so

that working memory can be freed for application to higher order thinking tasks. Consequently,

the starting point for each student can be different.

Decisions on an effective starting point can be influenced by:

classroom teacher reports;

grade level and curriculum expectations;

the results of any pre-testing; and

the profile of results from the OZCAAS testing.

For younger students whose class program does not include all four operations, a natural starting

point is to commence with the operations of addition and subtraction. For older middle-school

students (those particularly at the end of primary school and those in secondary school) whose

class program concentrates more on the operations of multiplication and division, focusing on

these operations seems more applicable than starting with addition and subtraction.

To achieve the feeling of what automaticity feels like, there may be benefits in starting with low

numbers for addition or subtraction to demonstrate to a student what it feels like to respond

automatically to a series of calculations. Slavishly following the sequential number order of any

operation may be less successful than skipping to the Focus Fact sets that include calculations

which provide patterns, e.g,, 1’s, 2’s, 5’s and 10’s.

IMPORTANT: Success for each student is the principal goal of QuickSmart

instruction. The starting point for instruction should recognise this need for

success. Commence instruction at the level where the student is achieving a

moderate level of achievement and build on this.

QS Tip

If QuickSmart instruction commences with the operations of multiplication and

division, QuickSmart research has shown that improvement in the automaticity of

addition and subtraction fact recall can happen alongside the improvement

experienced in the recall of multiplication and division facts. This is especially

relevant if expectations of increased speed and accuracy are paired with strategy

instruction and instruction that supports students’ metacognitive development.


29

Chapter 8

Using Additional Resource Materials

As the QuickSmart program aims to meet the learning needs of individual students and fit within

the learning culture of different schools and systems, the resource materials in the QuickSmart

Numeracy Resources and Organisation Manual need to be used flexibly. Using the basic scaffold of

a QuickSmart instruction session, materials can and should be developed and modified according

to the learning needs of individual QuickSmart Students.

The materials contained in all QuickSmart documents can be modified to meet the individual

learning needs of students and schools. New resources should be generated and added to the

QuickSmart Numeracy Resources and Organisation Manual to meet individual needs.

Be creative and develop your own materials and games. For example, the use of the many faceted

dice and the dice with the four operations on them can provide speedy activities that encourage

automatic recall of number facts. Remember that the overarching operative words for QuickSmart

are Response Time and Accuracy when developing new material. Activities should be fun and

focused and they should provide important practice opportunities.

You will need to source extra appropriate materials, particularly for the Independent Practice

section of the QuickSmart lesson. Classroom teachers, the school library and commercially

available educational materials as well as the internet are all great sources of the extra material

and games that further enhance QuickSmart lessons. Some examples of sites and resources

follow. Many resources have been shared by QuickSmart schools and may be found in the Private

Area of the QuickSmart website.


30

Chapter 9

Problem Solving

Word Based Mathematics Problems

The problem solving approach used in QuickSmart draws heavily on the seminal work of Polya and

his four phases of problem solving. These phases describe different aspects of the problem

solving process. They are:

understand the problem;

develop a plan;

carry out the plan; and

check the answer.

It is important to note that taking time to “understand the problem” is often not attempted by

struggling students for a variety of reasons, including poor literacy skills. In practice, the four

steps as identified by Polya may be visited and revisited as students engage with the question and

its requirements.

The QuickSmart approach utilises the 6S Strategy for Problem Solving. To be good at problem

solving a number of abilities need to be in place. Students need the appropriate reading skills,

understanding of the underpinning mathematics content, and the willingness and confidence to

make an attempt. QuickSmart Students need a framework to help them get started and to offer

them guidance on that journey. Such an approach can be explicitly taught. The 6S Strategy draws

on the work of Kate Bricknell (Bricknell, K.L. (1997). 5S Strategy: A comprehension strategy for

mathematics. Paper presented at the New England Mathematical Association Conference,

Problem Solving

This component of the QuickSmart program should not be introduced until

automatic response skills for recall of basic number facts has reached an effective

level for the student. This is often about ten to fifteen weeks into the program.

There are three basic possibilities for problem solving to be included within the

30-minute QuickSmart lesson. Problem solving can be addressed by:

1. Replacing the Games component on one occasion each week. This frees up five

minutes.

2. Replacing an OZCAAS and independent worksheet component once a week. This

frees up ten minutes.

3. Setting aside one QuickSmart lesson per week for solving Mathematics problems

that include well known basic number facts and complement and broaden these

consolidated number facts in an applied way. This frees up 30 minutes. More

details about a QuickSmart Problem-Solving Lesson are provided below.


31

Armidale) who first developed such a problem solving strategy while working with her middle

school students at Peel High School in Tamworth, NSW.

The purpose of including the 6S Strategy for Problem Solving, is to provide you with a framework

for QuickSmart Students that meets their needs but also provides a basis for them to develop

good problem-solving work habits. These habits will place them in a good position to address

Mathematics problems for the rest of their lives.

By using the 6S Strategy for Problem Solving scaffolding sheet found in the QuickSmart

Numeracy Resources and Organisation Manual (Section 6: Problem Solving), planning and

confidence in attacking mathematical problems can be established. Explicit instruction and

modelling of each step to ensure understanding should form part of lessons until the students can

demonstrate their own effective planning and knowledge of solving problems.

Students need to be able to talk through their plan of attack and to justify the decisions they make

in solving word-based mathematics problems.

Several sheets of simple mathematical word problems are provided in the QuickSmart Numeracy

Resources and Organisation Manual (Section 6: Problem Solving). A variety of commercially

available material is also available and should be used to supplement resources in this section.

Problem Solving Approach

When problem solving with QuickSmart Students:

explicitly teach the 6S Strategy for Problem Solving;

share and model your approach to problem solving using the 6S Strategy with your

students;

encourage peer discussion and modelling of approaches and strategies;

provide opportunities for students to undertake problem solving on their own; and

have students talk about (reflect) what they have done and the processes they

have used in solving specific problems.


32

Below is a copy of the Lesson Plan for Problem Solving, Strategy Development and Mathematics

Language Mastery that is used if the decision is to allocate a whole lesson for Problem Solving.

Problem Solving / Strategy Development and Mathematics Language Mastery

Lesson Format

The lesson will generally follow this format:

A. Creating a Context for Success/Mathematics Language Mastery [5 minutes]

Establish an environment of success in this section of the lesson. This may include

reviewing errors from previous lessons, introducing mathematics language that will

be useful and consolidating understanding of the 6S Strategy.

B. Modelled Response to simple Mathematics Word Problems [10 minutes]

Use the 6S Strategy for Problem Solving framework and relevant mathematics word

problems.

1. Search: Students read the problem and think about what to do

• QuickSmart Instructor clarifies any vocabulary/comprehension difficulties.

• Students search to find what the problem is asking.

• Have the students underline (highlight) the question that they are to solve.

2. Sort: Students identify what information seems most important for solving the

problem

• Highlight key words that indicate the operations required to solve the problem.

• Have students circle the numbers to be used.

• Discuss what information is included in the problem but may not be needed to

solve the problem (optional).

3. See: Students visualise, sketch, tabulate, or document information relevant to the

problem

• Discuss how to ‘visualise’ the problem. Demonstrate ways of developing effective

representations of the information in the problem.

• Encourage students to do their own ‘sketches’.

[We interpret the word ‘see’ in the broadest possible way. It could mean a

simple sketch on paper or visualisation of the problem, or it could be some

other form of documenting information such as tabulating using a number

line or time line, or using graphic organisers like tree diagrams or Venn

diagrams.]

4. Select: Students decide what operations are necessary for solving this problem

• Discuss what actions or operation(s) should be used in solving the problem.

5. Solve: Students solve the problem

• Discuss the need to convert all measurements to the same unit, if necessary.

• Model how to solve the problem for the students if necessary.

6. Sense: Encourage students to provide their working out for calculations that

extend beyond basic number facts.

• Request that students reread the problem.

• Discuss what the problem required, the process used and whether their solution

makes sense.


33

C. Independent Problem Solving [10 minutes]

Encourage students to independently solve mathematics problems using the 6S

Strategy.

D. Correction and Feedback [5 minutes]

It is important to correct all completed problems, give necessary feedback and praise

good thinking and problem solving.

When implementing the 6S Strategy, the QuickSmart Instructor needs to provide:

• clear modelling and demonstration of strategies;

• “thinking aloud” while identifying various aspects of the problem;

• “thinking aloud” while selecting and applying appropriate procedures; and

• reflecting on the effectiveness of the procedure used and the solution obtained.

(Westwood, P. (2008). What teachers need to know about Numeracy. Camberwell,Vic: ACER

Press.)

In conclusion, our data indicate that through using the 6S Problem Solving approach students

become more strategic. When confronted with problems, students do not give up. Instead, reports

suggest that they:

• trust their heads;

• know there is more than one way to do problems;

• acknowledge their mistakes and take steps to rectify them;

• evaluate their answers and behaviour;

• show enhanced memory and are excited by their increases in learning;

• report increases in their own feelings of self worth; and

• become more responsible for their own learning.


34

Chapter 10

Problematic Students

Not every student can appreciate that his/her numeracy will benefit from their inclusion in the

QuickSmart program. For many students, regular failure in learning at school has been a constant

of their formal schooling. By the time these students reach middle school, many have also

experienced a number of different interventions aimed at helping them succeed in their learning

but without noticeable success. As a result, another intervention, such as the QuickSmart

Program, can be viewed very sceptically by these students.

In order to seek commitment from this group of students, it can be beneficial to offer them an

option to leave the program after a designated period of time – e.g. four weeks of three lessons

per week. It may also be helpful to offer such a contract to a QuickSmart Student displaying

reluctance to continue. Sometimes reviewing the achievements of a QuickSmart Student at the end

of this period by looking through their QuickSmart Student folder may result in a positive turning

point and a commitment to continue in the program.

If problem behaviour does occur throughout QuickSmart lessons, it may be beneficial to review

the following:

• The grouping of the QuickSmart pairs – are there personality clashes, too much difference in

levels of learning, a problem with grouping female and male students, or friendship issues?

• The timetabling of the QuickSmart lessons – is there evidence of clashes with more favoured

lessons back in the classroom, being removed from the same lesson each day, or are

QuickSmart lessons always scheduled after the lunch break?

• The way QuickSmart is viewed in the school – are there difficulties related to the attitude of

the classroom teacher to the withdrawal of students from the classroom, the attitude of

fellow students to the students being withdrawn for support, or the value placed on the

QuickSmart program by the whole school and its community, including parents or carers?

• The lesson structure – is there evidence that the suggested structure may not appeal to some

struggling learners? In some instances starting with a Numeracy Game may act as a good

lead-in to the more structured activities that are part of the QuickSmart lesson.

• The personal issues of the student – the personal lives of some QuickSmart Students may be

fraught with complications of a temporary or permanent nature.

• Attendance issues – regular attendance is crucial to improvement. Poor attendance can mean

that a student loses momentum and confidence in the benefits that accompany involvement

in the QuickSmart Program.

Consultation with other stakeholders – Principals, QuickSmart Coordinators, classroom teachers or

parents/carers of the QuickSmart Student may assist in addressing and finding solutions to these

issues. If the situation still does not improve, the only solution may be to end the student’s

involvement in QuickSmart and offer the opportunity to another struggling student.

The QuickSmart Co-ordinator should have a major role in assisting Instructors to resolve issues

with problematic students.

Despite the careful thought that is given to student selection for QuickSmart, it is possible that

some students cause concern. While we have never made the claim that QuickSmart can work for

all students, we know that it does work for the vast majority of students.


35

The Importance of Regular Attendance

For obvious reasons, it is critical that students attend QuickSmart lessons. Schools report that the

attendance of many students undertaking QuickSmart improves as a result of their involvement in

the program. For those students, who were already regular attendees, some parents report that

their children wake earlier on QuickSmart days and that even when students are sick there is

discussion on whether they can attend their QuickSmart lesson.

Nevertheless, there are students for whom the QuickSmart program alone does not guarantee, at

least in the early weeks, improved attendance. Hence, it is important to have strategies in place

that encourage and support regular attendance.

It is important that QuickSmart Instructors put in place an attendance process that records how

many lessons students attend (and how many lessons are offered). Attendance data may provide

some insight into the potential lack of improvement shown by some students compared to their

peers who are regular attendees.

Continuing to offer a QuickSmart place to a poor attendee may be a waste of resources that might

be better directed to another student who would benefit from the program. On the other hand, it

might be that QuickSmart, over time, can bring about a major positive change in attendance. This

is a tension when selecting students. Working with the student’s family or carers to improve

attendance could provide a solution.

If the attendance issue lies with the student then two possibilities are:

• discussion with the student about his/her attitude to QuickSmart instruction and then

challenging the student to continue for a limited period, e.g., contracting for 3 more weeks of

QuickSmart instruction which will be reviewed at the end of this period could provide a

breakthrough in commitment by the student; and

• contacting and working with the student’s family or carers to improve attendance.

Ideas for Dealing with Student Absences

Some ideas on how to maximise QuickSmart instructional time if QuickSmart students are absent

from school are to:

• work with the remaining student on his/her own. Concentrate on the student’s weaknesses

and complete two sets of Flash Cards, more OZCAAS tests, etc.;

• add students who have been away on other occasions to provide a catch-up lesson (This can

be challenging if the students are too different in their progress.);

• have backup students who can attend if a student is away; and

• allow the student to choose a friend to attend as a guest participant. This would need to be

negotiated with the classroom teacher. If this happens, it saves time to have a visitor file set

up on the OZCAAS.

IMPORTANT: Do not include QuickSmart Comparison Students as

participants because this will compromise your data. QuickSmart

Comparison Students are average-achieving students who have not

participated in QuickSmart lessons.


36

Chapter 11

Conclusion of the QuickSmart Numeracy Program

Students Exiting QuickSmart

The philosophy underpinning QuickSmart is that all Australian children should be able to at least

reach minimal standards in basic Mathematics. For the great majority of students in primary and

secondary school, QuickSmart is a thirty-week exit program. This means that most students will

attend as close as possible to 90 QuickSmart lessons. However, you may find that some students

require less than thirty weeks. These students should be retested on the OZCAAS and on the

standardised test when they reach the end of the program. After their exit, new students can take

their place and commence QuickSmart lessons.

Final Testing of Students

When the instructional phase of the QuickSmart Program is complete in the school, it is important

to retest both the group of QuickSmart Students and the group of Comparison Students on both

the standardised tests (PAT Mathematics) and the bank of OZCAAS assessment tests used at the

pre-test stage of the QuickSmart Program. At post-test, extra OZCAAS tests can be added if the

QuickSmart Student has mastered more numeracy skills during the instructional phase. This final

round of testing provides the data that will demonstrate whether the QuickSmart Program has

assisted in closing the achievement gap for QuickSmart Students compared to their average-

achieving peers.

Graduating QuickSmart Students

Conclusion of QuickSmart Program – Celebration of Success

At the conclusion of the QuickSmart program, it is suggested that some form of celebration be

held to acknowledge the success of the QuickSmart Students. There is a certificate proforma

included in the QuickSmart Numeracy Resources and Organisation Manual (Section 9: Essential

features), that can be copied and presented, along with the student’s QuickSmart Folder, at such a

celebration or at a school assembly. An electronic editable copy of the certificate is also available

on the QuickSmart website.

During the QuickSmart Instructional Phase

Occasionally, students chosen for the QuickSmart program make rapid progress in achieving

automaticity in their basic number facts for all four operations. When this happens it is valuable to

move them on, as soon as possible, to the problem-solving aspects of the program.

If students can then demonstrate that they are able to apply this new knowledge and skills to the

higher-order thinking tasks of problem solving then the school can contemplate graduating these

students out of the QuickSmart program and taking on other students that could benefit from

QuickSmart instruction.

Take care in making such decisions and ensure all program criteria have been met. Withdrawal

from QuickSmart instruction before consolidation of the skills of automatic recall of basic number

facts is established can undo the improvement that has been achieved. It is important to ensure

that students have retained automaticity and understanding of all four operations prior to any

departure.


37

Sharing / Recording Data

IMPORTANT: Data collection at your school is of critical importance to the future of the

QuickSmart program. Sharing your data with SiMERR allows us to prepare and send to you a

school report based on your school’s data. (Remember you need permission from the student’s

parent/carer to share data with SiMERR.) We will also compile an Annual Numeracy Program Report

(based on all schools each year) to which you will have access. Schools use these documents for a

variety of important purposes, including:

• confirming the learning gains of participating students in comparison to the scores of their

average achieving peers and sharing this information with members of the school community;

• justifying funding expenditure for grants;

• comparing the learning gains of participating QuickSmart Students from one year to the next;

• gaining insights about the successful implementation of the program over time; and

• promoting the school and its programs in local media.

The Data Upload Tool and further related information are located on the QuickSmart website. Use

your QuickSmart licence username and password to enter the website.

Transition to Secondary Setting

If QuickSmart Students are continuing on to secondary school in the year after completing the

QuickSmart program, it is important that information about their participation and achievement is

communicated to the appropriate secondary school. There is value in holding a transition meeting

to share information towards the end of the school year, especially if a number of QuickSmart

Schools are graduating students into the same secondary setting.

Alternative School Placement

Sometimes QuickSmart Students transfer to another school during their participation in the

QuickSmart Program. It is important to ensure that the receiving school is aware of the students’

involvement in QuickSmart and that any results and comments are sent on to that school.

IMPORTANT– Sharing Results: Placing a completed copy of the Individual

Student Data Sheet in each student file guarantees that participation in the

QuickSmart Program and the results obtained travel with that student

throughout his/her school life.


38

Appendix I

Pre- and Post-intervention Testing for QuickSmart Numeracy

The table below shows the assessments to be completed by each QuickSmart and Comparison

Student.

Pre-intervention Tests Post-intervention Tests

1. PAT Maths – no calculators to be used. 1. PAT Maths – no calculators to be used.

2. OZCAAS

Number Naming

Addition AND/OR Basic Addition

Subtraction AND/OR Basic Subtraction

Multiplication AND/OR Basic

Multiplication

Division AND/OR Basic Division

2. OZCAAS

Number Naming

Addition AND/OR Basic Addition

Subtraction AND/OR Basic Subtraction

Multiplication AND/OR Basic

Multiplication

Division AND/OR Basic Division on

Please note:

You should test each student on at least five assessment tasks; at least Number Naming

and one from each operation group.

The use of the Addition or Basic Addition etc. assessments is dependent on the skill level

of the student. All students should attempt Addition and if they find it too difficult, change

to the Basic Addition assessment. Continue this process for the other operations.

Where possible, the Comparison Students should complete the same assessments as the

QuickSmart Students.

It is important at the end of the program, that you test each student on EXACTLY the

same level of assessments as they did at the beginning.

Conditions for both sets of testing are to be EXACTLY THE SAME.

If you are using a “report” rather than a “graph” to collect data for pre- and post-

intervention test results, you need to use the results displayed in the “all” row.

If students find any of the testing too difficult and are becoming stressed, abandon the

testing.


39

Appendix II

Numeracy Lesson Format

1. Focus Facts – Knowledge / Understanding Check (5 minutes)

The lesson focuses on a targeted set of Focus Facts for either addition and subtraction or

multiplication and division. This encourages and directs the student’s attention to a limited and

controlled amount of learning and understanding.

Review and discuss the current set of Focus Number Facts.

Review errors and consolidate understanding. Examine patterns in the number facts and

how these make sense.

Encourage students to demonstrate their understandings of the processes. Focus on

accurate and efficient strategy use including developing understanding of number

patterns/number sense.

Provide explicit instruction and explanations targeting the facts that are difficult for

students to master.

2. Flash Cards - Automatic Recall of Focus Number Facts (5 minutes)

Continue to develop the automatic recall of the focus number facts through the use of the Flash

Cards.

Use a pack of Flash Cards of current Focus Number Facts to challenge each student

to see how many number facts they can get correct in one minute.

Graph the results in each student’s folder and discuss improvements and errors.

Initially, use a pack that focuses on a single operation and number fact e.g., +4. Follow this by

moving to another set of Flash Cards in addition.

3. Speed Sheet Challenge (5 minutes)

The Speed Sheet begins to expand the confidence of the students to use their basic number

knowledge to incorporate larger numbers and more complex representations of the same number

facts.

Students work as fast and accurately as they can to complete Speed Sheets of the

current set of Focus Number Facts in two minutes.

Correct completed work, give feedback on errors and record results.

4. OZCAAS Assessment (5 minutes: one Student)

The OZCAAS task tests the facts that are currently the focus of attention, facts that are already

well known plus facts that will be the focus of attention in subsequent QuickSmart lessons.

Individual students complete an OZCAAS assessment task.

The student views and discusses the graphs of their response time and accuracy

results with the Instructor and sets goals for the next session.


40

5. Independent Worksheet (5 minutes – Student not doing OZCAAS task)

The independent worksheet requires students to use pen and paper to complete worksheets that

include the current number facts and extensions, or worksheets that relate the basic number facts

to other aspects of mathematics.

Students are expected to work quickly and efficiently on their own (without disruption) for

five minutes on an independent worksheet.

Correct and give appropriate feedback.

Students swap between activities 4 and 5 so each student completes both activities.

(5+5=10 minutes)

6. Games (5 minutes)

Play some mathematics games to help students become quick and accurate at automatically

recalling Number Facts.

Games include Three-in-a-Row, Same Sums, Double O, QuickSmart Bingo or QuickSmart

Dominoes.

These games provide opportunities for using extension facts, approximations and the

application of number facts to real life situations.


41

Appendix III

Numeracy Glossary of Terms

1. Automaticity

This is the ability to perform a skill fluently with minimal conscious effort. According to some

researchers, the ability to succeed in higher-order skills appears to be directly related to the

efficiency with which lower-order processes are executed. The purpose of automaticity is to free

up as much working memory as possible to allow for higher-order thinking. The use of some

relevant strategies may be quite quick, but they are still slower than automatic recall, and thus

they will still use some of the working memory space unnecessarily.

The lack of automaticity in recalling basic number facts can result in a reduced ability to solve

problems and understand mathematical concepts. Even small decreases in the time taken to

process information in working memory during basic problem solving situations can be

significant.

2. Working Memory

Working memory refers to the ability to hold information in the memory (or brain) while working

on or processing it. Working memory capacity places specific constraints on the amount of

information that can be processed at any one time. As such, there is a strong theoretical basis

upon which to expect that improving the speed of recall of basic facts frees up working memory

capacity, which is then available for the cognitive processing of higher-order tasks.

We only have so much working memory. The difference between a QuickSmart Numeracy Student

and a non-QuickSmart student is between a child who has to count on their fingers vs one who

can add 5 and 7 automatically. In literacy, it’s the difference between effortful decoding of a series

of words in a sentence (thereby losing its sense of meaning), and the automatic recognition of the

words allowing for the processing of the meaning of the text.

Working memory as a concept is in everything we do. QuickSmart is about increasing students’

fluency with basic academic facts. Working memory’s efficiency is important because it determines

what is actively paid attention to, remembered and processed into long-term memory.

An example is when you are working in someone else’s kitchen on a recipe you know well.

Because the kitchen is unfamiliar, you have difficulty coping with interruptions and can’t also deal

with guests and their conversations while finishing off the meal. In your own kitchen with a

familiar recipe, all this is possible. The difference is explained by the concept of how much

working memory you need to use in each situation.

Another example might be if you got a phone call from your child’s school saying you need to

come in immediately because of an accident. The worry this causes uses up too much of your

working memory and you forget things like locking the door, turning off the iron and so on.

Driving is another common example. Experienced drivers are automatic with many processes. Do

you remember driving to work today? Why or why not?

3. Cognitive Load

This is the level of effort associated with thinking and reasoning. Short term memory is limited in

the number of elements it can operate on simultaneously. The structure of long term memory is

more complex but it permits us to perceive, think and solve problems.


42

Information contained in instructional material must first be processed by working memory. The

lighter the load placed on working memory, the more changes in long-term memory are facilitated.

4. Neural Pathways

In Numeracy, for example, the question we need to ask is, why do students in Year 7 to Year 9 still

use their fingers to calculate? The answer lies in the concept of neural pathways: once children

learn to use their fingers, the neural pathways for finger counting have been established. The only

way forward is to create new neural pathways that don’t include finger counting. Neural pathways

are strengthened by use: ‘use it or lose it’!

The development of neural pathways is like building a bridge – the structure is progressing, but

the bridge can’t be used until the last piece of the structure is in place. It seems to take 10-12

weeks to get neural pathways started and then another 20 or so weeks to see them firmly

established. ‘Neurons that fire together, wire together’!

Consider the analogy of the Old Pacific Highway out of Sydney vs the New Pacific Highway (i.e. the

freeway). The Old Pacific Highway represents slow and inefficient strategies like finger counting. If

you want to attend an appointment in Newcastle, you’d use the New Pacific Highway (the freeway)

which is faster and uses less fuel.

Sometimes it seems that the new neural pathways happen suddenly. Why might this be the case?

Perhaps it’s because it takes a lot of separate pieces of information that need to be put together

for automaticity to happen and maybe it’s not until the last thing is in place that it does happen. It

looks like it’s sudden, but perhaps it’s the last piece of the jigsaw falling into place.

The concept of neural pathways is also relevant in teaching: for example, it is difficult to effect

change in Instructors and Co-ordinators after just one Professional Development session. In

QuickSmart, the 6 days of training represent a developmental approach to learning. The model is

2 days of training – 15 weeks of practice – 2 days of training – 15 weeks of practice – 2 days of

training. This model is supported by the concepts of neural pathways – it takes 12+ weeks to

establish new behaviours in the Instructors and Coordinators as well as in the students.

5. QuickSmart - a Phase IV Intervention:

Phase 1: the teacher teaches

Phase 2: the teacher uses differentiated learning activities to overcome learning obstacles

Phase 3: the teacher is supported by an in-class aide, a Learning Support Teacher, or a

special learning program

Phase 4: Students are withdrawn from the large class for targeted support via an intervention

such as QuickSmart.


43

6. Class-wise

‘Class-wise’ applies to students who have learned to survive in the classroom (compare with

‘streetwise’). These students build up protective walls around themselves because they have failed

too often. The following anecdote of a young girl in the UK illustrates this:

At the beginning of the lesson, the teacher puts 10 questions on the board. The girl fiddles –

she rules a margin, she writes the date, she rummages in her bag – everything she can, she

does, to avoid having to start the task. The teacher doesn’t notice, and starts marking the

questions. The little girl copies down the right answer for most questions, and ticks those

answers. Occasionally she makes a deliberate mistake because she knows it would be far too

suspicious if she got everything correct. At the end, she proudly puts up her hand when the

teacher asks who got 10, who got 9, who got 8, … at the appropriate time to get the sought-

after smile of approval from the teacher.

Students with learning difficulties may act out or be passive in class to cover their lack of fluency

with basic academic tasks.

7. On-task Time

The QuickSmart lesson structure is set up to maximise on-task time in a structured but flexible

lesson format. Students move quickly through each component of the lesson with minimal

opportunities for distraction and maximum engagement with the learning and practice tasks.

8. Deliberate Practice

Deliberate practice is not just about working harder, and nor is it just a ‘practice makes perfect’

approach. Deliberate practice targets individual students’ areas of weakness and devises strategies

to help overcome those weaknesses. In QuickSmart, weaknesses in basic number facts or literacy

skills are targeted, and success is measured in terms of speed and accuracy. The targeted skills

are practised in the Focus Facts part of the QuickSmart lesson.

9. Formative Assessment

Formative assessment informs teaching and learning. It is assessment during a lesson. Formative

assessment records how students are learning and gives information that teachers use to adjust

their teaching. Teachers who use formative assessment have classes that do better. QuickSmart

uses formative assessment that helps Instructors to track progress and teach students according

to their specific learning needs. By contrast, another type of assessment is summative. Summative

assessment happens at the end of the assessment cycle when there is a summation of

performance on a number of tasks completed along the way.

10. Quantitative Data

Pre- and post-intervention data are collected by Instructors for QuickSmart and Comparison

Students using two forms of assessment: OZCAAS tests and independent state-wide or

standardised achievement tests (usually PATMaths).

11. Qualitative Data

These data consist mainly of interviews, teacher observations, and evaluations carried out at the

end of the intervention. QuickSmart provides a range of survey forms for students, QuickSmart

Instructors, QuickSmart School Co-ordinators, classroom teachers, Principals and parents to

complete at the end of the QuickSmart program.


44

12. Effect Size

Effect Size is a measure of the size of the academic gains made by a group of students over time.

If the Effect Size = 1, there is an improvement of 1 standard deviation. According to Hattie, an

Effect Size of 0.3 is the average growth you can expect from students in a year.

Effect Size Comment

0 – 0.2 This is the effect size of normal development with little or no schooling

0.2 – 0.4 The typical effect size from being in a classroom with a teacher

0.4 – 0.6 Something important is happening

0.6 – 0.8 Some major improvements

0.8 – 1 Too much to expect

13. Cluster

A group of schools in geographical proximity are linked together for the purposes of attending

professional development workshops. Schools in a cluster may also be part of a system – e.g. DEC

schools, CSO schools, Independent schools.

14. QuickSmart Students

These are children who are selected to participate in QuickSmart lessons. These students typically:

• experience persistent difficulty in either literacy or numeracy or sometimes both;

• display a good attitude to working in small groups;

• have average cognitive potential without major attention difficulties;

• are performing at or below national minimum standards;

• attend school regularly.

15. Comparison Students

These students:

• are in the same grades as the QuickSmart Students;

• are average (e.g., stanine 4 on PATMaths) achievers;

• complete the OZCAAS testing and the standardised tests at the beginning and end of the

intervention; and

• do not participate in QuickSmart lessons.


45

16. QuickSmart Sayings

• A fast game is a good game!

• Trust your head!

• My neural pathways made me do it!

• Have a go!

Often QuickSmart Students are used to being wrong, so they revert to effortful strategies such as

finger counting in order to be right. One of the reasons for preferring to start with those tasks that

are easy for these students is to give them the chance to be successful again and to feel what it’s

like to be quick. Some students take a while to be able to ‘trust their heads’.

17. Key QuickSmart Numeracy Lesson Components

i. Focus Facts

• Instructor-led discussion and dialogue about the relationship between number facts

and strategies. Revisit any incorrect number facts from previous lessons and any

persistent errors.

ii. Flash Cards

• Students should get 30-40 correct answers in 1 minute on 2 or 3 occasions.

iii. Speed Sheets

• These contain the focus facts and numerous extension examples in both addition and

subtraction, or multiplication and division.

iv. Independent Worksheets

• The content of this component can vary, but it should be written work requiring

minimal input from the Instructor.

v. OZCAAS

• The Cognitive Aptitude Assessment System is a software program developed at the

Laboratory for the Assessment and Training of Academic Skills (LATAS) at the

University of Massachusetts. It enables precise measurements of students’ accuracy

and information retrieval times. During OZCAAS assessments, students aim to increase

their accuracy and decrease their response times on a particular operation as a means

of demonstrating increased automaticity. The students’ OZCAAS assessment results

are automatically summarised by the software and made available in either a graph or

a report form that is easily interpretable by both students and teachers.

vi. Games

• Play one of the QuickSmart games from the kit or the Resources and Organisation

Manual, or one that you have sourced yourself.

• Make sure that the games include mental computation practice.

• Use the ‘6S Strategy for Problem Solving’ sheet found in the Numeracy Resource and

Organisation Folder.


46

18. The ‘6S’ Strategy for Problem Solving

This refers to the page in the Numeracy Resource and Organisation Folder. The 6 S’s are: search,

sort, see, select, solve, sense. Look in the User Guide for more details.

19. ‘Narrowing the Gap’ for Educationally Disadvantaged Students

The achievement gap between students who struggle with literacy and numeracy and those who

achieve national benchmarks increases unless steps are taken to address the underachievement of

the bottom 30% of students.

Low achieving students can be:

• 18 months behind in Year 3;

• 3 years behind in Year 5;

• 5 years behind in Year 7.

This means that what is being done in the classroom isn’t necessarily working for these students.

QuickSmart is about narrowing the achievement gap. We need to talk about growth for these

children in terms of catching up years. QuickSmart narrows the gap by facilitating growth of up to

2 or 3 years in a 30-week timeframe.

20. SiMERR: The National Centre of Science, information and Communications

Technology and mathematics Education for Rural and Regional Australia

The SiMERR National Centre is based at University of New England within the School of Education.

SiMERR has affiliates at universities in every state and territory in Australia. QuickSmart is one of

140 SiMERR projects.

21. The Numeracy Resource Package

The kit contains:

• User Guide

• Resource and Organisation Folder

• The QuickSmart perspex box including Flash Cards, stopwatch, timer, dice.

• QuickSmart Games

• Sample Student Folder

• OZCAAS software

• Access to the Speed Sheet Generator via the QuickSmart website.


47

22. Standardised Tests

PATM (Progressive Achievement Tests in Mathematics)

These are standardised achievement tests developed by ACER (the Australian Council for

Educational Research). In the 3rd edition, there are 8 different levels of test. The recommendation

is to use PATM Test 3 (3rd edition) for Primary students, and PATM Test 4 (3rd edition) for

Secondary students. Marking is normally carried out at the school. SiMERR provides each school

with a Teacher Manual, some test scripts at the appropriate level, and some answer sheets. Further

answer sheets need to be purchased from ACER as required. Test booklets can be reused. Results

are given in stanines, and the suggestion is that you choose your QuickSmart Students from those

scoring in stanines 2 and 3. Students with scores in stanine 1 may be included in QuickSmart but

these students may have other significant learning problems contributing to their low scores.

23. NAPLAN

The National Assessment Program Literacy and Numeracy for years 3, 5, 7 and 9 began in 2008.

Results are given on a 10 band national scale. Testing is carried out in May each year and

students’ results are given in bands.

Year level National Minimum Standard Minimum possible Maximum possible

3 Band 2 Band 1 Band 6




24. Benchmarks vs Minimum Standards

Standards described by the ‘benchmarks’ for Years 3, 5, 7 and 9 represent increasingly demanding

levels of proficiency against which progress of students through school can be measured.

Benchmarks are based on actual descriptions of minimal skills. The superceded ‘benchmark’

report showed achievement of the national minimum standard as being above or below a single

score. NAPLAN reports show the national minimum standard as a full band on the scale. If a child’s

result is in the bottom band for the year level, he or she has not achieved the basic skills of

literacy and numeracy for that year, and needs focused intervention and additional support to help

achieve the skills required to fully participate in schooling.


48

25. SOLO

‘SOLO’ is an acronym for ‘Structure of Observed Learning Outcomes’. This taxonomy is a useful

way to characterise different levels of questions in examinations and the corresponding responses

expected from students. SOLO has applications in many areas. It originates from the work of Biggs

and Collis (1982). The different levels in SOLO are summarised in the following table.

Pre-structural • students are acquiring pieces of unconnected information

• no organisation

• no overall sense

Unistructural • students make simple and obvious connections

• the significance of the connections is not demonstrated

Multistructural • students make a number of connections

• the significance of the relationship between connections is

not demonstrated

Relational level • students demonstrate the relationship between connections

• students demonstrate the relationship between connections

and the whole

Extended abstract level • students make connections beyond the immediate subject

area

• students generalise and transfer the principles from the

specific to the abstract


49

Appendix IV

Why you can’t divide by zero

Think about what it means to divide, for example, 6 by 3. You are asking how many groups of 3 it

takes to make 6. Clearly, it takes 2 groups of 3 to make 6.

This might look like:

The diagram shows how if you put 6 crosses into groups of 3,

there are 2 groups.

Then if we ask you to divide 6 by 0, we are asking how many groups of 0 it takes to make 6. The

problem is that it wouldn’t matter how many groups of zero there were, you would only ever have

zero in total – you just cannot put groups of zero together to make 6 eventually. There is nothing

in each group so the total is always nothing.

Here we see groups of zero crosses. Clearly there

will never be 6 crosses no matter how many groups

of zero you draw.

An interesting case arises when you consider 0 ÷ 0. You could try asking yourself, ‘How many

zeros does it take to make zero?’ The problem here is that you could answer ‘6’, or ‘10’, or ‘3452’

or whatever, and there isn’t a unique answer. So again, you can’t get an answer to the question of

dividing by zero.

x x x x x x


50

Appendix V

Case Studies: QuickSmart Numeracy Students

The two brief case studies presented below represent useful and integrated ways of presenting the

general findings of the QuickSmart research. Overall, obstacles to learning include persistent use

of unsophisticated strategies, inability to understand and participate in classroom instruction, lack

of meaningful practice opportunities for basic number facts, low levels of confidence and trust in

one’s own ability, anxiety, and poor motivation for involvement in Mathematics activities.

More specifically, our systematic observations suggest that students may be prevented from

achieving acceptable standards of numeracy due to:

inefficient strategy use, e.g., use of fingers to count;

poor recall of previously ‘known’ knowledge;

failure to transfer learning, i.e., students often demonstrate necessary understanding of the

conceptual base but frequently do not apply this knowledge to the task at hand;

poor motivation to practise, e.g., poor number thinkers who do not practise their times

tables;

generally negative beliefs about academic tasks and the self as a learner, e.g., “I hate Maths

’cos I’m dumb at it.”, “I can’t do these!”.

The following case studies use pseudonyms rather than the QuickSmart Students’ actual names.

Case 1

Eve has severe reading difficulties. In the past she had received support on a weekly basis from a

specialist teacher to improve her reading skills. As a participant in the Year 5 QuickSmart

Numeracy Program, Eve worked hard to improve her numeracy skills. She met with considerable

success over the course of the intervention.

On the initial CAAS assessment, Eve’s lack of strategy use was notable. For example, to work out

the answer to 15 – 15, Eve used her fingers and counted backwards from fifteen by ones to finally

arrive at zero. That a number minus itself always equals zero was one of the first understandings

we aimed to consolidate for Eve.

At the beginning of the QuickSmart program, Eve recorded average response speeds for addition,

subtraction, multiplication and division of 4.03 seconds, 3.61 seconds, 5.6 seconds and 4.56

seconds respectively. Her average achieving peers recorded average times of 2.69 seconds, 2.49

seconds, 3.03 seconds, and 3.75 seconds on the same operations. By the end of the intervention,

Eve’s times had improved to 2.38 seconds for addition, 1.31 seconds for subtraction, 1.89

seconds for multiplication and 1.84 seconds for division. All Eve’s CAAS times were recorded with

at least 80% accuracy. In contrast to this improvement, the average end of year scores of the Year

5’s who did not participate in the QuickSmart program were relatively stable at 2.05 seconds for

addition, 2.14 seconds for subtraction, 2.02 seconds for multiplication and 2.79 seconds for

NOTE: The CAAS was the original form of the OZCAAS Assessment which is

now used.


51

division. The accuracy range for these scores ranged from 67% to 100%.

Eve regularly recorded the fastest response times on CAAS assessments of any of the year 5

students in the QuickSmart Numeracy Program. To celebrate her success, she challenged her

Principal to a number fact contest. She also recorded good improvement on the standardised test

of Mathematics and problem solving. Eve’s score on Form A of this test before the intervention

placed her at the 5th percentile. Following the QuickSmart program, Eve scored at the 68th

percentile on Form B. Her scores represent an impressive improvement of 63 percentile points.

Case 2

The CAAS assessment system administered at the beginning of the intervention indicated that

Kathie, a year 7 student, had not mastered her addition, subtraction, multiplication, and division

facts.

Kathie applied herself to the practice opportunities available during QuickSmart lessons and

improved her performance. At the beginning of the intervention her average CAAS times for

addition, subtraction, multiplication, and division were 4.225 seconds (89.5%), 3.694 seconds

(94.7 %), 3.8 seconds (80%) and 4.79 seconds (89.5%). Kathie’s accuracy rates are provided in

brackets alongside her response speed values.

After participating keenly and working well with her partner in QuickSmart lessons, Kathie

improved both her speed and accuracy scores. At the end of the intervention, Kathie’s scores were

2.79 seconds (94.1%) for addition, 1.583 seconds (94.7%) for subtraction, 2.79 seconds (89.5%) for

multiplication; and 2.8 seconds (94.7%) for division. These scores compared favourably to those of

a Comparison Mathematics Student nominated by his teachers as a student of average ability i.e.,

2.43 seconds (73.7%), 2.48 seconds (89.5%), 1.72 seconds (94.7%), and 2.78 seconds (84.2%).

Notably, Kathie regularly reported that she used the academic skills she was reviewing during

QuickSmart lessons in other classes and in real life situations such as shopping. On one occasion,

she recounted how she surprised and pleased her parents by automatically knowing how much

change to expect after buying an item from a local store. Her father’s comment was that,

“Whatever you are doing in that program at school, you keep doing it!”

These descriptions of student performance couched in case-study descriptions are potentially

interesting and useful to QuickSmart Instructors for identification, assessment, and programming

purposes.

numeracy program for middle school students

Documents