Reviewing the Standards for Mathematics and Statistics

1. Reviewing the Standards forMathematics and Statistics A progress report September 2009 Presented by Rhona Lever at the NZAMT Conference, on behalf of the writing group for the alignment of the Mathematics and Statistics standards

2. What has happened since the consultation in June: • The level 1 standards have been edited • A start has been made on writing tasks • A group has been set up to meet in October and November to work on literacy and numeracy standards which will replace the lower level unit standards (NZQA is leading this) • A timeline has been published in QA News and in the Gazette: • Draft standards available on TKI as they are developed • Level 2 consultation in 2010 after some trialling in schools

3. What were the issues from the consultation? • Concern about the workload resulting from more internal assessment • Concern about the lack of detail and lack of examples of tasks to clarify the standards • Mixed messages about credit values, titles, practical work, mode of assessment, the numbering system and duplication. • We also had useful feedback from a task writing workshop and the moderators about the wording of the standards.

4. The principles, values and key competencies in the new curriculum are mandated from Years 1-13. The achievement objectives (AOs) in English, the Arts, Health and Physical Education, Mathematics and Statistics, Science, Social Sciences and Technology are mandated until the end of Year 10. The intention of the new curriculum for Years 11, 12 and 13, is to be ‘enabling’ and allow schools maximum flexibility in learning programmes within the mandated framework of the principles, values and competencies. The expectation is that there will be more specialisation in Years 11, 12 and 13 than at previous year levels. Quote from Ministry Guidelines 28th May

5. This means that schools need to regard the new list of Achievement Standards at Level 1 as a “menu” from which to choose appropriate assessments for their students. Some points to remember: You do not need to assess every topic you teach. Some topics may have been adequately covered in Years 9 and 10 and do not need to be retaught or assessed in Year 11. Try not to over assess (fewer than 24 credits is OK) The first example that follows is suitable for an “academic” course. The second is a more practical course and entirely internally assessed.

6. Example 1 Ext 1.3Investigate relationships using tables, equations or graphs4 Ext 1.6 Apply geometric reasoning4 Ext 1.10 Demonstrate understanding of chance and data4 CAT 1.2 Apply algebraic methods4 Int 1.1 Apply numeric reasoning when solving problems4 Int 1.10Investigate a given multivariate data set using the statistical enquiry cycle4 Total credits 24

7. Example 2 Int 1.1Apply numeric reasoning when solving problems4 Int 1.4Apply linear algebra3 Int 1.5Solve measurement problems3 Int 1.7Solve measurement problems involving right-angled triangles3 Int 1.9Apply transformation geometry3 Int 1.10Investigate a given multivariate data set using the statistical enquiry cycle4 Int 1.13Investigate a situation involving elements of chance2 Total credits 22

8. All of the standards have been drafted in a generic format Design issues have been addressed • Standards or achievement criteria with multiple requirements can lead to unfair results • Replacement evidence not available because Merit questions or Excellence questions address different outcomes from Achieved questions. • Specific content attached to grade levels encourages some students to only attempt to learn what is required for Achieved • Specific requirements constrain examiners or make assessments too predictable

9. Our guidelines: Only one criterion per grade level (without “ands”) and “Students need to demonstrate a better (higher quality) performance on the same outcome in order to achieve higher grades”

10. Our challenge: To describe the expected levels of thinking when solving problems at Achieved, Merit or Excellence in terms of quality of thinking, not in terms of more content or different content • Our aim: • to describe current practice • NOT to alter the expected level of performance

11. Achieved level performance Apply numeric reasoning must involve using a range of appropriate numeric methods when solving problems, demonstrating knowledge of number concepts and terms and communicating solutions which would usually require only one or two steps.

12. Merit level performance • Relational thinking must involve one or more of • selecting and carrying out a logical sequence of steps • connecting different concepts and representations • demonstrating understanding of concepts • forming and using a model • and relating findings to a context or communicating thinking using appropriate mathematical statements.

13. Excellence level performance • Extended abstract thinking must involve one or more of: • devising a strategy to investigate or solve a problem • demonstrating understanding of abstract concepts • developing a chain of logical reasoning, or proof • forming a generalisation • and using correct mathematical statements or communicating mathematical insight.

14. What about the statistics and probability standards? Merit: with justification Using the statistical enquiry cycle with justification involves linking aspects of the statistical enquiry cycle to the context and the populations. Justification also involves making supporting statements which refer to evidence such as summary statistics, data values, trends or features of visual displays.

15. Excellence: with statistical insight Using the statistical enquiry cycle with statistical insight means integrating the statistical and contextual information and knowledge to show a deeper understanding. This may involve using contextual knowledge, or may involve considering the effects of related variables, or reflecting about the process.

16. Where is the “content”? The mathematical content of each standard is signalled by the title, but the title is not enough to tell you what should be included in the teaching programme to prepare a student for this assessment. Each standard quotes learning outcomes from the curriculum. This is the only specification of the content in some standards, so it is now important to pay close attention to these curriculum quotes. (We are used to ignoring them!) If we thought that the curriculum was not clear enough, more detail has been included in Explanatory Note 3. There will also be further guidance about the nature of the assessment in the assessment guidelines that will be available for every internal standard.

17. The decision on the calculator issue The aligned standards will be implemented from 2011 under the following calculator rules: Internally assessed standards are open to all types of technology, including computers The L1 Algebra CAT is calculator free (no calculator at all) The external standards will be limited to an approved list of calculators up to and including graphic calculators, but not CAS.

18. The standards review has been initiated to: • improve programme and pathway coherence for learners • improve the design of all standards • align standards with the NZC • enhance support for assessors’ professional practice • improve the credibility of the NCEA and the National • Qualifications Framework (NQF)