1. Mathematics Differentiation using First Steps in Mathematics: Number
Presenter: Kelly Stevens

2. Contents First Steps in Mathematics: Number The Resources
The Planning Cycle
Diagnostic Maps
Diagnostic Tasks
Mathematics Planning
Differentiation using Key Understandings

3. First Steps in Mathematics
The Course and Resources were developed through extensive research conducted by Sue Willis at Murdoch University and a team from the Department of Education and Training in Western Australia.
Developed in the early 1990’s
Response to outcomes focused curriculum- still relevant to Australian Curriculum
 Western Australian Minister for Education: 2007

4. First Steps in Mathematics Resource Books
Overview
1 Understand Numbers Whole and Decimal Numbers / Fractions
2 Understand Operations / Calculate / Reason about Number Pattern
Number
1 Direct Measure / Understand Units
2 Estimate / Indirect Measure
Measurement
There is also a book online now for all of the diagnostic tests that can be used.
Represent Location / Represent Shape / Represent Transformation/ Reason Geometrically
Space
Chance & Data
Understand Chance / Collect and Organise Data / Summarise and Represent Data/ Interpret Data
 Western Australian Minister for Education: 2007

5. Accessing First Steps Resources
1. Go to ‘Resources’ in your Portal 2. Go to ‘Connect Resources’

6. Accessing First Steps Resources
3. Search ‘First Steps’ 4. Select the first result

7. Accessing First Steps Resources
5. Electronic resources for First Steps are available

8. Accessing First Steps Resources
Google ‘First Steps Maths’

9. Structure of First Steps Resources
Diagnostic Maps
Key Understandings
- Sample Learning Activities (Beginning, middle and later)
- Sample Lessons
- ‘Did you know?’ sections
Show Number Book 1
Diagnostic maps
Key understandings (these are the big mathematical ideas/ concepts that students need to know
Overview
Sample learning activities
Beginning (K-3), Middle (3-5), End (5-7)
Sample Lessons
an example of a sample activity as a lesson plan
‘Did you know?’ section
highlight common understandings and misunderstandings that students have, diagnostic activities

10. Planning Cycle Mathematics Pedagogy Professional judgment Students
Decide on the
mathematics needed to move
students on
Pedagogy
Decide on
learning activities
and focus
questions
Professional
judgment
knowledge
experience
evidence
Students
Observe students
and interpret
what they do
and say
Mathematics- What needs to be taught? Link back to the Australian Curriculum and Key Understandings
Students- What do they need to learn? Diagnostic testing.
Pedagogy- How will you teach it? This relates to the learning activities section of the resource and is where teachers can make adjustments to meet students needs by differentiating the activities
p 32
 Western Australian Minister for Education: 2007

11. What is the Diagnostic Map for Number?
Recognising these common patterns of thinking will help teachers to:
interpret children’s responses to activities,
to understand why they seem to be able to do some things and not others,
and also why some children may be having difficulty in achieving certain outcomes while others are not.
It should also help you to provide the challenges children need to move their thinking forward, to refine their half formed ideas, to overcome any misconceptions they might have and hence to achieve the outcomes.
Students section of the planning cycle- What do students need to know?
Describes characteristic phases in the development of student thinking in maths
Indicate the areas that need development to move thinking forward
Supports teachers to make judgements about student level of understanding and contribute to planning by clearly showing what needs to be taught next
The diagnostic maps assist teachers to plan for mathematics teaching and learning. Knowing where students are at and the major conceptual shifts in each phase will allow them to make choices about what KU should be focused on.
Show map:
6 phases
Approximate ages linked to levels
During section describes students major preoccupations during this phase, what they are focused on
At the end shows what students know
As students move section shows learning challenges and misconceptions that may occur, this part is important because sometimes it is difficult to know why students are struggling.
David Tripp quote- “Students do misunderstand, but it is seldom because they cannot understand, most often it is because they understand something else.”
 Western Australian Minister for Education: 2007

12. Diagnostic Tasks 34 First Steps Number Diagnostic Tasks
Used to see where students sit on the diagnostic map and to show misconceptions
Examples provided today
- KU1: Counting principles, Get me task, Ice Cream Task
- KU2: Hide the Jelly Beans
- KU4/5: Up to and over 100
Number: 34 diagnostic tasks at a range of levels across the diagnostic map
Diagnostic tasks (other mathematics strands): Measurement- 22, Space-7, Chance and Data-13.
Show book for Number.
Use the diagnostic test to identify understanding and misconceptions.
It is important to test until students get things wrong. If they are getting it all right, you know what they know but not what they need to know.
Will show some of the diagnostic tasks now so that you can see them in action. The tasks are targeted at an early childhood level and involve counting, partitioning and place value.

13. Diagnostic Tasks
Video Examples
See other notes

14. Diagnostic Tasks Want to show:
- That some of the tasks can be done as a class group
Show an upper primary activity as well
Purpose: Counting (and beginnings of place value)- to see if children know the pattern in the way we say and write numbers (KU4/5)
May need to ask clarifying questions to understand why a student has got the question wrong. This will inform planning.

15. Con (Year 5, Age 10)
Give me a tick when you have identified the problem.
Discussion
Test indicates that Con knows the counting up to 100 and requires more support with higher numbers. Might be good to ask him to orally count to make sure the misconception is clear.
I would predict: Needs to work on KU4 (Saying the numbers rather than writing the number)
Would want to give the student opportunities to use larger numbers.

16. Lucy (Year 2, Age 7)
Give me a tick when you have identified the problem.
Discussion
Test indicates that Lucy can count the numbers but is writing them how they are said phonetically.
Needs to work on KU5 (Writing the numbers rather than saying the number)

17. Ben (Year 6, Age 11)
Give me a tick when you have identified the problem.
Discussion
Test indicates that Ben knows the counting up to 100 and requires more support with higher numbers. Might be good to ask him to orally count to make sure the misconception is clear.
I would predict: Needs to work on KU5 (Writing the numbers rather than saying the number)

18. Maddison (Year 4, age 9)
Discussion
Test indicates that Maddison knows the counting up to 500 and requires more support with higher numbers
Needs to work on KU4 (Saying the numbers rather than writing the number)
Would want to give the student opportunities to use larger numbers.

19. Planning Cycle Mathematics Pedagogy Professional judgment Students
Decide on the
mathematics needed to move
students on
Pedagogy
Decide on
learning activities
and focus
questions
Professional
judgment
knowledge
experience
evidence
Students
Observe students
and interpret
what they do
and say
Diagnostic tests show us what the student needs to know. We can identify what they need to move on.
Next step is to identify what learning activities will be implemented as a result.
p 32
 Western Australian Minister for Education: 2007

20. Identify the key understanding to teach in your class based on diagnostic testing.
Once you have identified the Key Understanding that will be taught (either from diagnostic testing or from your Australian Curriculum), activity planning can be completed.
This is where differentiation can take place in the classroom.

21. Differentiation using Key Understandings
Planning using Key Understandings allows for easy differentiation
Allows for beginning, middle and later levels
Some of the activities for levels are the same
Lesson structure
- Introduction activity (based on KU) done as a class group
- Students complete activities based on level/phase of learning
- Summary activity/reflection as a group

22. Differentiation using Key Understandings

23. Any Questions?