Level 1

Mathematics and Statistics clarifications

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Level 1 Achievement Standards – Mathematics and Statistics

The notes for each standard should be read in conjunction with the achievement standard which is available from the NZQA website and the Conditions of Assessment document.

Mathematics Standards

The titles of all of the Mathematics standards are Apply xxx in solving problems

xxx comes from content specified in the New Zealand Curriculum that students need to apply in solving problems so students need to be given a problem to solve.  Problems need to allow for all levels of achievement.  Within the problem there may be sub tasks but evidence for any level of achievement needs to come from the solution of the overall problem.  This means there needs to be sufficient scope within the problem for the thinking that is needed.  Problems are situations that provide opportunities to apply knowledge or understanding of mathematical concepts and methods.  Situations should be set in a real-life or mathematical context.  Students should not be presented with a task in an unfamiliar context.  It is acceptable for students to know the context before the assessment.

The SOLO taxonomy has been used to describe the different levels of thinking in the standards.

The stages in the SOLO taxonomy are increasing in quantity and quality of thought.

Achieved level is the multistructural stage where students need to know or use more than one piece of given information, fact, or idea, but do not integrate their ideas.

Merit is relational thinking where students see the significance of how the various pieces of information relate to one another.  ‘Questions’ that provide evidence for relational thinking will require students to integrate more than one piece of given knowledge, information, fact or idea.

Excellence is extended abstract thinking where students can make connections beyond the scope of the problem or question, to generalise or transfer learning into a new situation.  Going beyond the given information, knowledge or ideas, or deducing a more general rule or proof that applies to all cases are examples of extended abstract thinking.

At Achieved level all of the standards include the wording ‘selecting and using a range of methods’.  The evidence for this aspect can not come from a situation where students are told what method to use to solve problems.  Problems need to be presented so there are no instructions about the method of solution.

For the ‘method’ to provide evidence for the standard it needs to be relevant to the solution of the problem and also at the appropriate curriculum level.

The ‘methods’ which provide evidence for each standard are listed in Explanatory Note 4 of the standard.

The appropriate curriculum level can be determined by looking at Explanatory Note 1 of the standard which lists the achievement objectives from The New Zealand Curriculum (NZC) which are covered by the standard.  There is further information about the achievement objectives at level 6 of the curriculum in the Teaching and Learning Guide.  This information can be found by selecting the relevant achievement objective from the TKI website.  There is further information about the achievement objectives on the NZ Maths website.

Statistics Standards

All of the statistics standards involve students using a specified ‘process’.  The process varies from standard to standard depending on what aspect of statistics is involved.  The ‘process’ is detailed in Explanatory Note 3 of the standard.

The wording of the Achievement Criteria in the Statistics Standards reflects the step up in the quality of the response that is required at the different levels.  Merit level is ‘with justification’ and Excellence is ‘with statistical insight’.

At Achieved level students need to provide evidence of using each component of the ‘process’.

At Merit students need to link components of the ‘process’ to the context.  The justification comes from providing supporting evidence for any comments.

At Excellence students need to integrate statistical and contextual knowledge throughout the ‘process’.  They need to have an understanding about the context and are expected to demonstrate they have thought about the ‘process’ they have undertaken and their findings.

Information about the statistics achievement objectives can be found in the Teaching and Learning Guide at the TKI website. Additional information is available on the Census at School website.

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