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?
• Additive domain 8%• Multiplicative domain
24%• Proportional domain
34%
0
10
20
30
40
50
60
Additive Multiplicative Proportional
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?
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?
• Additive domain 22%• Multiplicative domain
43%• Proportional domain
50%
05
101520253035404550
Additive Multiplicative Proportional
CL 1-2CL 3CL 4-5
4. What percentage of Year 10 students were diagnosed at being at Level 4 or above in the curriculum (Stage 7-8) at the end of the year in 2006?
4. What percentage of Year 10 students were diagnosed at being at Level 4 or above in the curriculum (Stage 7-8) at the end of the year in 2006?
• Additive domain 29%• Multiplicative domain
49%• Proportional domain
50%
05
101520253035404550
Additive Multiplicative Proportional
CL 1-2CL 3CL 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?
• Additive domain 74%• Multiplicative domain
62%• Proportional domain
65%
01020304050607080
Additive Multiplicative Proportional
CL 1-2CL 3CL 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?
• Additive domain 51%• Multiplicative domain
32%• Proportional domain
36%
0
10
20
30
40
50
60
Additive Multiplicative Proportional
CL 1-2CL 3CL 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?
• Additive domain 66%• Multiplicative domain
50%• Proportional domain
60%
0
10
20
30
40
50
60
70
Additive Multiplicative Proportional
CL 1-2CL 3CL 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?
• Additive domain 79%• Multiplicative domain
72%• Proportional domain
75%
01020304050607080
Additive Multiplicative Proportional
CL 1-2CL 3CL 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?
• Additive domain 4%• Multiplicative domain
18%• Proportional domain
23%
0
10
20
30
40
50
60
70
Additive Multiplicative Proportional
CL 1-2CL 3CL 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?
• Additive domain 1%• Multiplicative domain
8%• Proportional domain
13%
01020304050607080
Additive Multiplicative Proportional
CL 1-2CL 3CL 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 Background1992 Mathematics in the New Zealand
Curriculum1994/5 Third International Maths & Science
Study1997 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 Merit Excellen
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??