Numeracy+explained

Hi kids and parents, you may have heard some things about the "numeracy project". In a nutshell it is an attempt to foster genuine mathematical understanding in our kids. It is used with varying intensity depending on the class, and is not uniformly administered - you will get a different opinion on it's usefulness from every person who has used it. At Hill School, we have jumped in boots and all, and our maths programme is entirely constructed around numeracy principles. Below, I have copied some bits outlining the ideas so that you know where we are coming from. I'll also attempt to explain "strategy stages" as they appear in all the kids' reports. Just quickly though, for kids in Room 19 (year 4) they should be at stage 4 at the start of the year, and transitioning to and working in stage 5 by the end. If a year 4 student is at stage 6, they are doing very well indeed, stage 7 exceptional. Thanks for your interest, Mr Moran. toc

For a more complete picture go to the comprehensive [|nzmaths] website.



Philosophy behind the numeracy projects
[|(copied directly from TKI)] The underlying philosophy behind the Ministry of Education's Numeracy Development Projects is that teachers are key figures in changing the way in which mathematics is taught and learned in schools. Their subject matter and pedagogical knowledge are critical factors in the teaching of mathematics for understanding. The effective teacher of mathematics has a thorough and deep understanding of the subject matter to be taught, how students are likely to learn it, and the difficulties and misunderstandings they are likely to encounter. The focus of the Numeracy Development Projects is to improve student performance in mathematics through improving the professional capability of teachers. It is intended that by 2005 most teachers of year 1 to 3 students, the majority of the teachers of year 4 to 6 students, and many of the teachers of year 7 and 8 students will have had the opportunity to participate in the numeracy projects. A key feature of the projects is their dynamic and evolutionary approach to implementation. This ensures that the projects can be informed by developing understandings about mathematics learning and effective professional development and that flexibility in approach and sector involvement is maximised. The projects build on the findings and experience associated with the numeracy professional development projects that operated in 2000 and 2001. These projects have made an important contribution to what we know about: Such findings continue to inform the modification and further development of the projects. National coordinators and facilitators from each region provide ongoing feedback about aspects of the projects. See [|map for details.] 
 * children's learning and thinking strategies in early mathematics;
 * effective identification of, and response to, children's learning needs;
 * the characteristics of professional development programmes that change teaching practice; and
 * effective facilitation.

Early Numeracy Project (ENP)
The Early Numeracy Project (ENP) professional development programme encourages teachers to analyse the mental strategies that students use to solve number problems, as opposed to simply checking that students have the correct solutions. The instruction is then targeted to the specific learning needs of each student. This programme reflects the principles behind the mathematics curriculum statement. It was piloted nationally during 2000, under the name of Count Me In Too, to inform the development of the numeracy policy. 

Advanced Numeracy Project (ANP)
The Advanced Numeracy Project (ANP) is the name given in 2001 to the pilot professional development project known previously as the Year 4–6 Numeracy Exploratory Study (NEST). In 2000, the Ministry of Education offered New Zealand schools the Year 4–6 Numeracy Exploratory Study, to improve the teaching and learning of number concepts and skills. The Numeracy Exploratory Study presented teachers with a framework of broad stages in students' mathematical thinking in which the different stages are characterised by the range of strategies that students use to solve problems. This number framework relates to most of the achievement aims and objectives at levels 1–4 of the Number strand of the mathematics curriculum. The overall aim of the Numeracy Exploratory Study was to develop the teachers' knowledge of number concepts, student strategies, and instructional practice in order to improve student achievement in years 4 to 6.

Strategy Stages
[|Numeracy Stages] (links to nzmaths site_
 * Emergent
 * 1 - One to One Counting
 * 2 - Count from one on Materials
 * 3 - Count from one by Imaging
 * 4 - Advanced Counting
 * 5 - Early Additive Part-Whole
 * 6 - Advanced Additive Part-Whole
 * 7 - Advanced Multiplicative
 * 8 - Advanced Proportional

What the stages look like in students: (remember, these are only very small examples)

Emergent  1,2,3,5,8...? //Can you get me 7 counters from the pile please?// The child can not consistently count a collection of objects. 

One to One Counting 1,2,3,4,5,6,7,8. //Can you get me 7 counters from the pile please?// The child can count a set of objects up to ten but can’t join and separate sets like 4 + 3 = 

Count From One on Materials 1,2,3,4,5,6,7. //There are 4 counters and another 3 counters. How many are there altogether?// The child solves the problem by using their fingers or other materials and counts from one. 

<span style="font-size: 200%; font-family: 'Comic Sans MS',cursive">Count From One By Imaging <span style="font-size: 200%; font-family: 'Comic Sans MS',cursive">Counts in head 1,2,3,4,5,6,7,8. <span style="font-size: 200%; font-family: 'Comic Sans MS',cursive">//There are 4 counters and another 3 counters. How many are there altogether?//

<span style="font-size: 200%; font-family: 'Comic Sans MS',cursive">The child counts all the objects from one by imaging visual patterns of the objects in their mind. <span style="font-size: 200%; font-family: 'Comic Sans MS',cursive">

<span style="font-size: 200%; font-family: 'Comic Sans MS',cursive">Advanced Counting <span style="font-size: 200%; font-family: 'Comic Sans MS',cursive">Counts on 9, 10, 11, 12, 13. <span style="font-size: 200%; font-family: 'Comic Sans MS',cursive">//There are 9 counters under there and another 4 counters under there. How many are there altogether?//

<span style="font-size: 200%; font-family: 'Comic Sans MS',cursive">The child counts on from the largest number <span style="font-size: 200%; font-family: 'Comic Sans MS',cursive">

<span style="font-size: 200%; font-family: 'Comic Sans MS',cursive">Early Part-Whole <span style="font-size: 200%; font-family: 'Comic Sans MS',cursive">“I know that <span style="font-size: 200%; font-family: 'Comic Sans MS',cursive">If I take one off the 6 and put it on the 9 it =10. 10 + 5 = 15” <span style="font-size: 200%; font-family: 'Comic Sans MS',cursive">//There are 9 counters under there and another 6 counters under there. How many are there altogether?//

<span style="font-size: 200%; font-family: 'Comic Sans MS',cursive">The child uses simple strategies to solve addition and subtraction problems mentally <span style="font-size: 200%; font-family: 'Comic Sans MS',cursive">

<span style="font-size: 200%; font-family: 'Comic Sans MS',cursive">Advanced Part-Whole <span style="font-size: 200%; font-family: 'Comic Sans MS',cursive">I think tidy numbers would be smartest. <span style="font-size: 200%; font-family: 'Comic Sans MS',cursive">63 – 40 = 23 <span style="font-size: 200%; font-family: 'Comic Sans MS',cursive">23 + 1 = 24 <span style="font-size: 200%; font-family: 'Comic Sans MS',cursive">//63 people are on the bus and 39 people get off the bus. How many people are left on the bus?//

<span style="font-size: 200%; font-family: 'Comic Sans MS',cursive">The child can select from a wide range of strategies to solve various addition and subtraction problems mentally <span style="font-size: 200%; font-family: 'Comic Sans MS',cursive">

<span style="font-size: 200%; font-family: 'Comic Sans MS',cursive">Advanced Multiplicative <span style="font-size: 200%; font-family: 'Comic Sans MS',cursive">Tidy Numbers would be a smart **strategy**. 30 x 6 = 180 <span style="font-size: 200%; font-family: 'Comic Sans MS',cursive">180 – (2 x 6) = 168 <span style="font-size: 200%; font-family: 'Comic Sans MS',cursive">//There are 28 fruit trees in each aisle of the orchard. There are 6 aisles. How many trees are there altogether?// <span style="font-size: 200%; font-family: 'Comic Sans MS',cursive">The child can select from a wide range of strategies to solve various multiplication and division problems mentally. <span style="font-size: 200%; font-family: 'Comic Sans MS',cursive">

<span style="font-size: 200%; font-family: 'Comic Sans MS',cursive">Advanced Proportional <span style="font-size: 200%; font-family: 'Comic Sans MS',cursive">I can see that 9:15 are both multiples of 3. I can simplify by ÷3 and get a ratio of 3:5 ?:10 <span style="font-size: 200%; font-family: 'Comic Sans MS',cursive">= 6 <span style="font-size: 200%; font-family: 'Comic Sans MS',cursive">//You can make 9 mittens from 15 balls of wool. How many mittens can you make from 10 balls of wool?// <span style="font-size: 200%; font-family: 'Comic Sans MS',cursive">The child can select from a wide range of strategies to solve challenging problems involving, decimals, fraction percentages and ratios. <span style="font-size: 200%; font-family: 'Comic Sans MS',cursive">

<span style="font-size: 200%; font-family: 'Comic Sans MS',cursive">The NZ **Numeracy** Framework <span style="font-size: 200%; font-family: 'Comic Sans MS',cursive">
 * <span style="font-size: 200%; font-family: 'Comic Sans MS',cursive">Each **Numeracy** Stage highlights key knowledge and **strategy** that a child should know.
 * <span style="font-size: 200%; font-family: 'Comic Sans MS',cursive">Strong knowledge is essential for students to broaden their strategies across a full range of numbers.

<span style="font-size: 200%; font-family: 'Comic Sans MS',cursive">**Strategy** <span style="font-size: 200%; font-family: 'Comic Sans MS',cursive">Knowledge <span style="font-size: 200%; font-family: 'Comic Sans MS',cursive">Creates new knowledge through use <span style="font-size: 200%; font-family: 'Comic Sans MS',cursive">Provides the foundation for strategies <span style="font-size: 200%; font-family: 'Comic Sans MS',cursive"> <span style="font-size: 200%; font-family: 'Comic Sans MS',cursive">Knowledge and **Strategy** <span style="font-size: 200%; font-family: 'Comic Sans MS',cursive">
 * <span style="font-size: 200%; font-family: 'Comic Sans MS',cursive">Knowledge – Number Identification, Number sequence and order, Grouping and place value, basic facts
 * <span style="font-size: 200%; font-family: 'Comic Sans MS',cursive">**Strategy** – Addition and Subtraction, Multiplication and Division, Fraction and Proportions