Secondary Numeracy Project Introductory Workshop Pip Arnold.

Secondary Numeracy Project

Introductory Workshop

Pip Arnold

Startling Statements

Performance of SNP students on the number framework. Tagg and Thomas, 2006

1. What percentage of Year 9 students were diagnosed at being at Level 1-2 in the curriculum (Stage 0-5) at the beginning of the year in 2006?

1. What percentage of Year 9 students were diagnosed at being at Level 1-2 in the curriculum (Stage 0-5) at the beginning of the year in 2006?

• Additive domain 59%• Multiplicative domain

44%• Proportional domain

49%

0

10

20

30

40

50

60

Additive Multiplicative Proportional

CL 1-2CL 3CL 4-5

2. What percentage of Year 9 students were diagnosed at being at Level 4 or above in the curriculum (Stage 7-8) at the beginning of

the year in 2006?

2. What percentage of Year 9 students were diagnosed at being at Level 4 or above in the curriculum (Stage 7-8) at the beginning of

the year in 2006?



34%

0

10

20

30

40

50

60


CL 1-2CL 3CL 4-5

3. What percentage of Year 9 students were diagnosed at being at Level 4 or above in the curriculum (Stage 7-8) at the end of the year in 2006?




50%

0

5

10

15

20

25

30

35

40

45

50


CL 1-2CL 3CL 4-5





50%

05

1015

2025

3035

40

4550


CL 1-2

CL 3

CL 4-5

5. What percentage of Year 9 students in low decile schools were diagnosed at being at Level 1-2 in the curriculum (Stage 0-5) at the beginning of the year in 2006?

5. What percentage of Year 9 students in low decile schools were diagnosed at being at Level 1-2 in the curriculum (Stage 0-5) at the beginning of the year in 2006?



65%

0

10

20

30

40

50

60

70

80


CL 1-2

CL 3

CL 4-5

6. What percentage of Year 9 students in high decile schools were diagnosed at being at Level 1-2 in the curriculum (Stage 0-5) at the beginning of the year in 2006?

6. What percentage of Year 9 students in high decile schools were diagnosed at being at Level 1-2 in the curriculum (Stage 0-5) at the beginning of the year in 2006?



36%

0

10

20

30

40

50

60


CL 1-2

CL 3

CL 4-5

7. What percentage of Year 9 Maori students were diagnosed at being at Level 1-2 in the curriculum (Stage 0-5) at the beginning of the year in 2006?

7. What percentage of Year 9 Maori students were diagnosed at being at Level 1-2 in the curriculum (Stage 0-5) at the beginning of the year in 2006?



60%

0

10

20

30

40

50

60

70


CL 1-2

CL 3

CL 4-5

8. What percentage of Year 9 Pasifika students were diagnosed at being at Level 1-2 in the curriculum (Stage 0-5) at the beginning of the year in 2006?

8. What percentage of Year 9 Pasifika students were diagnosed at being at Level 1-2 in the curriculum (Stage 0-5) at the beginning of the year in 2006?



75%

0

10

20

30

40

50

60

70

80


CL 1-2

CL 3

CL 4-5

9. What percentage of Year 9 Maori students were diagnosed at being at Level 4 or above in the curriculum (Stage 7-8) at the beginning of the year in 2006?

9. What percentage of Year 9 Maori students were diagnosed at being at Level 4 or above in the curriculum (Stage 7-8) at the beginning of the year in 2006?



23%

0

10

20

30

40

50

60

70


CL 1-2

CL 3

CL 4-5

10. What percentage of Year 9 Pasifika students were diagnosed at being at Level 4 or above in the curriculum (Stage 7-8) at the beginning of the year in 2006?

10. What percentage of Year 9 Pasifika students were diagnosed at being at Level 4 or above in the curriculum (Stage 7-8) at the beginning of the year in 2006?



13%

0

10

20

30

40

50

60

70

80


CL 1-2

CL 3

CL 4-5

Numerate• To be numerate. What

does this mean to you?

• Discuss in your group.• Pick one key idea.

• Feedback.

MOE Definition

•To be numerate is to have the ability and the inclination to use mathematics effectively

- at home, at work and in the community.

Historical Background

1992 Mathematics in the New Zealand Curriculum

1994/5 Third International Maths & Science Study

1997 Maths & Science Task Force

1998 Numeracy Goal

1999 NAG Revision

1999 Count Me In - Pilot

2000 Numeracy Development Projects started

2005 Secondary Numeracy Project starts

1995 Results

NCEA Results 2003

Not achieved

Achieved MeritExcellen

ce

50.1% 32.8% 12.7% 4.4%

Level 1 Algebra: Use straightforward algebraic methods to solve problems.

What is the focus of SNP?

• The learning focus is Number and Algebra - students’ number sense and algebraic thinking skills.

• The teaching focus is to target teaching at the students’ diagnosed stage of learning for Number and Algebra.

What does the Numeracy project mean for Maths teachers?

• A professional development programme aimed at– “Increased student performance in Mathematics

through improving the professional capacity of teachers”

• Teaching tools– A strategy teaching model– A framework of increasing sophistication for

strategic reasoning– A diagnostic interview administered orally by

the teacher to every student in their class

What else does this mean for teachers?• Understanding how students develop number

concepts.• Understanding how students develop and use

mental strategies.• Recognising the stage of development of

each student and responding to their needs.

• Increasing confidence in teaching numeracy.

• Improving questioning techniques.• In-depth rather than coverage.

So the aims of SNP are:

• Identify gaps in student knowledge and understanding of Mathematics and to assist them in filling those gaps.

• Provide the students with the opportunity for success in Mathematics at an earlier stage in their [secondary] schooling rather than waiting for alternative courses at Year 11.

So the aims of SNP are:

• Encourage an interest and willingness to be actively involved in the learning of mathematics at a higher level than would otherwise be achievable.

• Raise the students confidence in Mathematics than would otherwise be achievable and in doing so enhance self esteem.

• Enable the student to better cope with the literacy associated with mathematics.

counting

Part whole

Advanced proportional

Advanced multiplicative

Advanced additive

Early additive

Advanced counting

Counting from one by imaging

Counting from one on materials

One to one counting

Emergent

Numeracy Stages

Getting started• Testing using the NumPA strategy test and the knowledge test.• The combination of these two give a profile of the students and the

class. • The knowledge test is useful for identifying knowledge hot spots.• The NumPA strategy test identifies which of the strategy stages the

student is at for addition/subtraction, multiplication/division and ratios and proportions.

***reminder about number framework and the knowledge framework***

Do the knowledge test, look at a couple of video clips.

Knowledge vs strategies

• Knowledge = those things that students need to recall automatically eg 8+8 =16 as a basic knowledge fact is used to find 8 + 9

• Book 4 Teaching Number Knowledge contains knowledge activities

• Books 5, 6 and 7, 8 and 9 contain activities to develop mental strategies.

• Learning to strategise is much more complex.

Strategy teaching model

Start by:• Using materials and/or diagrams to

illustrate and solve the problemProgress to:• Developing mental images to help solve

the problemExtend to:• Working abstractly with the number

property

Lesson formats

• Lessons can have many formats.• Initially whole class knowledge is a good way

to start. see p.4 in “Getting Started “ booklet

• Or use knowledge activities as a warm up to other strand teaching.

• As the you progress you can include some strategy teaching (from just some of the students to the whole class.)see page 4/5 in “Getting Started “ booklet

Differentiated learning

• Students have different needs.• Stage 4 students are still solving problems by

counting with their fingers. They need to be made to think using part-whole strategies. They are working at about Level 1-2 in the curriculum.

• Stage 6 students have a range of strategies to work with and need to be extended to using multiplicative strategies. These students are working at Level 3-4 in the curriculum.

• The needs of just these two groups of students is very different. What about the stage 5 students?

• This will mean that there will need to be different activities for different groups of students within the class.

SNP is about

• A strategy teaching model• A framework of increasing sophistication for

strategic reasoning• A diagnostic interview to be administered by the

class teacher• Observation and feedback• Changing pedagogy• Mathematical thinking• Differentiated learning• Mental strategies• Algebra - but that is for another day

• The start of a new journey• Small steps• Keep it all in perspective• Share, grow and support• How did you get that? - asking questions

Where to from here??

Secondary Numeracy Project Introductory Workshop Pip Arnold.

Documents

percentage of year

multiplicative domain

curriculum stage

additive domain

proportional domain

maori students

pasifika students

low decile schools