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?

Additive domain 59% Multiplicative domain 44% Proportional domain 49%

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%

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%

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%

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%

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%

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%

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%

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%

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%

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 1992Mathematics in the New Zealand Curriculum 1994/5Third International Maths & Science Study 1997Maths & Science Task Force 1998Numeracy Goal 1999NAG Revision 1999Count Me In - Pilot 2000Numeracy Development Projects started 2005Secondary Numeracy Project starts

1995 Results

NCEA Results 2003 Not achieved AchievedMeritExcellence 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 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 problem Progress to: Developing mental images to help solve the problem Extend 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??