Thinking mathematically and using mathematical reasoning is an important part of maths.

The research shows that we need students to think mathematically not just follow processes with no understanding of the maths underpinning them.

Each lesson of the number sense intervention program starts with a thinking problem, a maths reasoning activity.

These are designed to get the student talking and thinking mathematically, using mathematical language and building concepts.

Subitizing is the ability to look at a group of objects and to know immediately how many there are without counting.

Think about a dice - you don't count the dots once you know the patterns.

Subitizing is a foundation skill in Maths which helps students move beyond counting in ones.

For students to progress in maths the research shows that they must move beyond counting in ones. The Mathtastic number sense intervention program provides multiple opportunities to develop this skill.

Counting is a key skills in maths in the early stages as knowing number order is a critical skill.

The development of an internal number line is key to developing number sense.

Through supported counting activities students learn to count forwards and backwards in increasing lengths. Initially to 5 and back, then 10 and back.

This progressively increases as you work through each level of the number sense intervention program with lots of opportunities to practice.

There are 3 core reasons why we need to understand number sense to support learning in maths:

1. Students need to use procedures in a flexible manner e.g. knows to switch the addends
2. Students need to use benchmark numbers – 10, 100, to support calculations and reasoning
3. Students need to understand the magnitude of numbers e.g which is bigger/ smaller.

The Mathtastic number sense intervention program is built on the 8 number sense strategies which spiral up through increasingly large numbers.

Using these number sense strategies students can become mathematicians with a deep understanding not just procedure followers:

There is extensive research that the playing of games supports in learning Maths.

Every lesson of the number sense intervention program includes games designed to practice the skills and concepts whilst keeping anxiety to a minimum.

Games can be played multiple times to reinforce and practice skills to fluency.

Developing fluency so that some number facts can be pulled automatically from long term memory frees up cognitive load and the working memory can be used for other components of the mathematical task.

Many of the games have variations to extend or simplify. Often the same game cards can be used for a number of different game e.g. you can use the same cards for Go Fish, Snap, Memory game and the Stealing game – my favourite game.

Every module in the number sense intervention program includes word problems based on the 11 different types of problem to ensure students are able to apply their math to real life situations.

It is important that students can apply their maths to real life as this is where maths is used.

As adults we do not sit with addition and subtraction problem pages to solve, we solve these problems but in real life problems.

There are 11 different ways problems can be presented where different information is provided and different parts of the problem need to be solved.

For example, Tracy has some apples and Mark gives her 3 more. Now there are 6 apples. How many apples did Tracy have?

Number problems support the student to solve numerical problems. Students need practice to develop their fluency calculating with numbers.

The Mathtastic number sense intervention program offers fluency practice through games, number problems and work problems.

These number problems are organised to ensure regular retrieval practice of previous concepts as well as current work through interleaving and spaced practice – each module has practice of the skills from that lesson concept and also questions which draw on previous learning to keep practicing these skills to automaticity.

Fluency and automaticity reduces cognitive load for students so they can focus on other components of maths. If you have 1+9 in your long term memory as a fact for automatic retrieval you can use your working memory for other parts of the mathematical task.