Bruce Williams.

Creating Real Mathematicians is redefining mathematics in the classroom.

Mathematics is meant to be fun, engaging and accessible for ALL students.

Our philosophies are based on the latest scientific research on how students learn.

Let us show how to make all your students real mathematicians who can think, problem-solve, reason and even know their times tables!

Bruce is a Melbourne based numeracy consultant who is able to come to your school run interactive hands-on workshops on many mathematical topics that will enhance teaching and learning for students and teachers in all educational settings. Bruce will create real mathematicians of your teachers and students and teach them all how to think like a real mathematician. 

Contact Us

Bruces LinkedIn Page

Success story

PicturesNumbersWords. Using Multiple Representations for student thinking.

An engaging, proven, student-friendly approach to Problem Solving in Mathematics

Why students struggle with traditional algorithms.

Watch this video and see if you understand why each of these algorithms is wrong? Most students don't either. That's why we teach students how to perform addition, subtraction, multiplication and division (plus fractions, decimals and percents) as real mathematicians can, both in your head and on paper. What's more, students understand what they are doing and all can be learned in a fraction of the time it takes to learn the traditional algorithms for these operations.

We teach students, parents and teachers the strategies real mathematicians use for the four operations including fractions, decimals and percents.

What is teaching mathematics really about?

"What he's saying is that enough time is wasted in math classes on JUST calculation, that often the underlying concept is lost anyway." TremorX, YouTube

The problem with teaching from the textbook.

How to teach Authentic Mathematics through Differentiated Open Problem Solving. 


Do kids really need teachers?

Sugata Mitra's "Hole in the Wall" experiments have shown that, in the absence of supervision or formal teaching, children can teach themselves and each other, if they're motivated by curiosity and peer interest. If this then is the case, how can teachers best enhance students learning experience?

Ken Robinson: How schools kill creativity.

Sir Ken Robinson makes an entertaining and profoundly moving case for creating an education system that nurtures (rather than undermines) creativity.

The Developmental Continuum for Teaching Mathematical Understanding.

How Counting leads to Addition, Subtraction, Multiplication, then Division and finally Fractions (and Decimals and Percents).

Teaching Fractions Developmentally

Teaching Addition Developmentally

Numeracy Sequence of Teaching P-6 (Number)

What needs to be taught at each year level. 

The Learning Framework in Number. Count Me In Too.

The Learning Framework in Number draws on a range of theories from research projects conducted over the last fifteen years. The framework outlines how students move from using naive strategies to increasingly sophisticated strategies in order to solve number problems. It can be used to sequence instruction.

Assessment for common misunderstandings

Fishing Addition

Who Sank the Boat?

Bears in the house

234 Lollies. A place value activity

Skip Counting Frogs


Counting with Binary Numbers

Series of Open Problems with VELS Rubrics for Moderation.

Division Rubric: Sharing $12 with my friends with VELS rubric (VELS levels 0.5 to 4.0)

Addition and Subtraction Rubric: I had $20 to spend on new toys. How much did each toy cost? How much change did I get? (VELS levels 0.5 to 4.0)

Number Rubric: Teddies Coffee Time with VELS rubric (VELS levels 0.5 to 2.75)

Fractions/Decimals/Percents with VELS rubric. (VELS levels 3.0 to 6.0)

Division: Sharing $100 with my friends with VELS rubric. (VELS levels 3.0 to 6.0)

Sharing Pizza Fractions/Decimals/Percents with rubric. (VELS levels 3.0 to 4.5)

Multiplication Rubric: Doughnuts  (VELS levels 1.25 to 4.0)

Multiplication Rubric: Dads Money (VELS levels 1.25 to 4.0)

Lets Go Fishing (VELS levels 3.0 to 6.0)

Game Show Spinner

Area and Perimeter with VELS rubric (VELS levels 2.0 to 6.0)

Fruit Salad (VELS levels 1.0 to 4.0)

The 6D Maths Question

VELS Indicators of Progress

Mathematics Developmental Continuum: Mapping the ‘Indicators of progress’

Link from this page through "Related Progression Points" to find the relevant Progression Points for all units of work in numeracy.

Year Level Planners aligned to VELS

Year 1/2 Planner

Year 3/4 Planner

Year 5/6 Planner

Sample Lesson Plans for developing understanding of the four operations with VELS Progression Points (Year 2 examples).





AUSVELS Scope & Sequence

AUSVels Scope & Sequence link

Comparing AUSVELS with VELS. Whats changed?

AUSVELS Scope and Sequence

AUSVELS Annotated Work Samples

Learning Intentions

Mathematics Classroom Checklist

Asking The Right Questions

Rich Open Problems for Mathematical Problem Solving

Weekly Problem Solving for Grades 1-5 and why and how to make your own Rich Open Problems

ABC Splash

A great link for video and questions relating to a variety of interesting maths topics. (For Teachers and Parents).

Aligned Australian Curriculum Resources (Mathematics)

Scootle is an online repository, managed by Education Services Australia (ESA). Currently, it has over 10,000 digital resources, with a range of these resources being progressively aligned to the relevant learning area of the Australian Curriculum.

The Australian Association of Mathematics Teachers (AAMT):  

AAMT is the Australian mathematics teacher professional association, affiliated with state and territory associations such as the MAV, and provides teachers with mathematics curriculum, assessment and pedagogical resources; professional development activities.

Mathematics of Planet Earth, a source of classroom resources and activities that use mathematics and statistics to understand the challenges facing the world in fun and accessible ways, whilst providing teachers with related support materials, links and contacts.

MathWorld is Wolfram Research’s free on-line digital mathematics encyclopedia resource and is linked to the free on-line computational engine Wolfram Alpha. Together these provide teachers and students with access to mathematical knowledge and examples through on-line queries in natural language, and also a means of carrying out related numerical, graphical, statistical and symbolic computations on-line.

Lemon Pie A Measurement Story

Counting Wizard

Students learn Multiplication Facts through learning patterns in Skip Counting.

Mathematics Classroom Environment & Structure Evaluation Checklist

New York State Test Prep for Mathematics

Activities for developing Mathematical Understanding of Mathematics Performance Indicators.

Lesson Design

Australian Mathematical Sciences Institute Teacher Modules

These modules are prepared by AMSI as part of The Improving Mathematics Education in Schools (TIMES) Project.

The modules are organised under the strand titles of the Australian Curriculum.

The modules are written for teachers.

Each module contains a discussion of a component of the mathematics curriculum up to the end of Year 10.

Web Resources

National Library of Virtual Manipulatives

Jenny Eather Maths Dictionary for Kids & Classroom Displays

Jenny Eather's Maths Charts and Children's Maths Dictionary

Primary School Maths Teacher Resources

Lessons to help teachers bring maths instruction to life in their classrooms. Maths Solutions.

Times Tables Generator

Linear Calendar

Van de Walle "Teaching Student-Centered Mathematics"  Black Line Masters

K-3 Teacher Resources

Tarsia Puzzles

A Mathematicians Lament.

What is wrong with the way we teach mathematics?

"What do teachers make?" Taylor Mali(Video)

The Knights Tour

Bruce Williams



Contact Us