Using the Numeracy Continuum to Support all Students

Kate McKay Improving Literacy & Numeracy National Partnerships,

Uralla CS & Sandon PS

4th September, 2013

(with recognition of the work of Brian Tickle & Peter Gould)

Comments from teachers about how the Numeracy Continuum K-10 assists them in their classrooms. . .

“It gives me a guide to show where students are at, where they’re coming from and going to. I can then use the DEC support materials like DENS 1 and DENS 2 to move students forward . . “ AP, Stage 3

“You know exactly where they are on the continuum and then you can develop appropriate activities to take them to the next level . . “ Class Teacher, Stage 2

“I think it provides you with a bigger picture . . “ AP, Stage 2/3

Comments from teachers about how the Numeracy Continuum K-10 assists them in their classrooms. . .

“I’ve learnt how to differentiate worthwhile activities to cater for all of my students. I have students at Emergent through to Facile and some are already learning about tens and ones on the Place Value aspect. I also have students with behaviour problems as well as students who have not been to preschool and I have found that benchmarking my students has surprised me in many ways. Some students knew a lot more than I gave them credit for. . . “ Class Teacher, Kindergarten “I have such a range of ability levels in my class from very low to very high so it helps me target each individual student . . “ Class Teacher, Autism IO Class

Comments from teachers about how the Numeracy Continuum K-10 assists them in their classrooms. . .

“It pinpoints where students are and you can then target for success by building the confidence of students in small steps. You can then start to reduce all sorts of behaviour issues and address disengagement. . . “ LaST, Primary and Secondary “Firstly, the links to the new syllabus will be very helpful for teachers. Secondly, the continuum really supports Assessment for Learning. It allows teachers to be very clear about where students are and where they need to take them next. It also allows teachers to set learning goals and provide clear, constructive feedback. . . “ Principal, P4

Overview

!  Introduction and background to the Numeracy continuum K-10

!  A brief exploration of the philosophy that underpins the continuum with links to the new NSW syllabus for the Australian curriculum

!  A focus on Aspect 5: Multiplication & Division

!   Practical resources for you!

Introduction & background

!  Derived from the Learning Framework in Number and 20 years of research

!  Based on a progression of strategies and concepts.

!  Helps in moving students from naïve strategies to more sophisticated strategies

!  7 aspects (interconnected)

Introduction & background !   Counting sequences looks at the role of numerals and

students’ knowledge of counting sequences. !   Early arithmetical strategies describes the

transition from using count-by-one strategies to grouping strategies to solve addition and subtraction problems.

!   Pattern & number structure includes using knowledge of number combinations to solve problems.

!   This is elaborated within the Place value aspect with a focus on counting by tens and hundreds.

Introduction & background !   Multiplication & division involves creating, working

with and counting equal groups. !   Fraction units deals with understanding the relative

size of fractions, forming partitions and relating the part to the whole.

!   Unit structure of length, area and volume describes the progression from direct comparison to using units to measure and understand a row-column- layer structure.

Introduction & background

Why is it important?

!  Helps teachers understand how students develop key concepts

!  Assists in programming

!  Assists with planning next steps in learning

!  Assists with monitoring students’ progress

!  Encourages creativity and deeper thinking

Philosophy underpinning the continuum - with links to the new NSW syllabuses for

the Australian curriculum

Conceptual understanding vs

Procedural knowledge . . .

. . . with an emphasis on mental computation & number sense

The Indispensable Calvin and Hobbes, Bill Watterson, Universal Press Syndicate, Kansas City, 1992

What do we mean by mental computation?

!   Not the same as mental arithmetic

!   Emphasises the mental processes used to achieve the answer

!   We can encourage students to EXPLAIN how they worked out their answers

!   We can encourage students to compare their strategies with those of other students

How did you work it out?

39 + 25

4 x 199

What do we mean by number sense?

!   Understanding of number concepts, operations & applications of numbers & operations

!   Ability to use this understanding in flexible ways to make maths judgements

!   Develop useful strategies for handling numbers & operations

!   HENCE: mental computation is closely linked to the development of number sense

Types of calculations used in everyday life

(Northcote & McIntosh, 1999, APMC, 4(1), 19-21)

!   84.6% of all calculations involved some form of

mental mathematics !   11% written mathematics !   6.8% calculator use !   19.6% use of other physical objects

!   HOW MUCH TIME DO WE SPEND TEACHING ALGORITHMS?

Sledge hammers to crack nuts!!! (Brian Tickle, 2004)

1002 - 4

Mathematics K-10 Syllabus

Early Stage 1 – Addition & Subtraction

Stage 1 – Addition & Subtraction

Mathematics K-10 Syllabus

Stage 2 – Addition & Subtraction

Stage 1 – Addition & Subtraction

Mathematics K-10 Syllabus Stage 3 – Addition and Subtraction

Stage 4 – Computation with Integers

So what does this mean for students with: learning difficulties; disabilities;

behaviour challenges; all students?

!   We need to use the Numeracy continuum to benchmark students and design teaching and learning activities to move them to the next level or stage

!   We need to make their thinking visible (see examples in notebook in resources folder)

!   We need to use open-ended activities to cater for a wide range of ability levels – students can respond at their level

!   Knowing your students makes a difference to both you and them!

Aspect 5: Multiplication and division

A great resource in your package that will help move students along the Mult & Div continuum. Developed by Brian Tickle when he was a District Mathematics Consultant for the NSW DEC.

Activities for students working at a range of levels on the continuum

Multiplication & Division Activities

Ø Hoops for groups – vary the recording process, vary the concrete materials

Ø Tables Races – vary according to each student or group’s knowledge

Ø Multiplication Games – as per Tables Races

Resources for you! (Electronic folders)

DEC resources DENS S; DENS 2; Teaching Measurement ES1-S1; Teaching Measurement S2-S3; Teaching Space & Geometry K-6; Counting On Activities (PV & Mult/Div); Talking about Patterns & Algebra K-6; Teaching Angles Stage 2; Fractions, Pikelets & Lamingtons K-6; and Teaching Multiplication & Division by Brian Tickle

Making Thinking Visible Two articles by Brian Tickle plus a notebook illustrating how to make strategies visible for students

Resources for you!

Structured Observation Grids To be completed but so far you have: EAS, Place Value, Multiplication & Division Multiplication and Division Activities Includes 2 notebooks plus recording sheets From State Office •  Frequently asked questions about the Literacy and Numeracy continuums •  An overview of the Numeracy continuum K-10 (where to find the

interactive version) •  Poster of the continuum

For further information. . .

You are welcome to contact me on:

katie.mckay@det.nsw.edu.au

if you have any queries or questions.

With kind regards,

Kate.