Outcome+description


 * Scholarship: Statistics and Modelling Performance Standard **

**Outcome description**
The student will demonstrate the ability to apply mathematical, statistical and probability knowledge and methods to complex problems in contexts which may be unfamiliar, interpret and, where appropriate, generalise results and clearly communicate concepts and findings.  **Outstanding Performance – Performance Descriptor 1** In addition to meeting performance descriptor 2, below, the student will: · demonstrate sophistication of thinking across a range of concepts in the solution of problems · in solutions display logical development, precision and clarity across a range of concepts · critically evaluate processes and solutions.  **Performance Descriptor 2** =The student will:= · demonstrate an advanced level of statistical thinking · apply probability theory and models to solve complex problems · apply techniques of mathematical modelling to solve complex problems. **Performance Descriptor 3** =The student will demonstrate at least two of:= · an advanced level of statistical thinking <span style="font-size: 12pt; font-family: Symbol; mso-fareast-font-family: Symbol; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: Symbol; msofareastfontfamily: Symbol; msobidifontsize: 10.0pt; msolist: Ignore; msobidifontfamily: Symbol;">· <span style="font-size: 12pt; font-family: Arial; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: 'Times New Roman';">application of probability theory and models to solve complex problems <span style="font-size: 12pt; font-family: Symbol; mso-fareast-font-family: Symbol; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: Symbol; msofareastfontfamily: Symbol; msobidifontsize: 10.0pt; msolist: Ignore; msobidifontfamily: Symbol;">· <span style="font-size: 12pt; font-family: Arial; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: 'Times New Roman';">application of techniques of mathematical modelling to solve complex problems. <span style="font-size: 12pt; font-family: Arial; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: 'Times New Roman';"> <span style="font-size: 12pt; font-family: Arial; mso-ansi-language: EN-GB; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: 'Times New Roman';"> <span style="font-size: 12pt; font-family: Arial; mso-fareast-font-family: Arial; mso-ansi-language: EN-GB; mso-bidi-font-size: 10.0pt; msofareastfontfamily: Arial; msobidifontsize: 10.0pt; msolist: Ignore; msoansilanguage: EN-GB;">1 <span style="font-size: 12pt; font-family: Arial; mso-ansi-language: EN-GB; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: 'Times New Roman';">The content covered by this standard is identical with that of achievement standards 3.1 to 3.7, and may draw on skills from lower level statistics and probability achievement standards, which are in turn derived from //<span style="font-size: 12pt; font-family: 'Arial Mäori'; mso-bidi-font-size: 10.0pt;">Mathematics in the New Zealand Curriculum //<span style="font-size: 12pt; font-family: 'Arial Mäori'; mso-bidi-font-size: 10.0pt;">, Learning Media, Ministry of Education, 1992, and //Mathematics in the New Zealand Curriculum//, //Addendum to Level 8//, Learning Media, Ministry of Education, 1995 <span style="font-size: 12pt; font-family: 'Arial Mäori'; mso-ansi-language: EN-GB; mso-bidi-font-size: 10.0pt;">. <span style="font-size: 12pt; font-family: Arial; mso-ansi-language: EN-GB; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: 'Times New Roman';">For scholarship the questions will require a higher level of processing and thinking. <span style="font-size: 12pt; font-family: Arial; mso-ansi-language: EN-GB; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: 'Times New Roman';"> <span style="font-size: 12pt; font-family: Arial; mso-fareast-font-family: Arial; mso-ansi-language: EN-GB; mso-bidi-font-size: 10.0pt; msofareastfontfamily: Arial; msobidifontsize: 10.0pt; msolist: Ignore; msoansilanguage: EN-GB;">2 <span style="font-size: 12pt; font-family: Arial; mso-ansi-language: EN-GB; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: 'Times New Roman';">Assessment will <span style="font-size: 12pt; font-family: Arial; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: 'Times New Roman';"> require integration of knowledge and processes from across these Level 3 achievement standards. <span style="font-size: 12pt; font-family: Arial; mso-ansi-language: EN-GB; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: 'Times New Roman';"> <span style="font-size: 12pt; font-family: Arial; mso-ansi-language: EN-GB; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: 'Times New Roman';"> <span style="font-size: 12pt; font-family: Arial; mso-fareast-font-family: Arial; mso-bidi-font-size: 10.0pt; msofareastfontfamily: Arial; msobidifontsize: 10.0pt; msolist: Ignore;">3 <span style="font-size: 12pt; font-family: Arial; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: 'Times New Roman';">For <span style="font-size: 12pt; font-family: Arial; mso-ansi-language: EN-GB; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: 'Times New Roman';">performance descriptor 1 <span style="font-size: 12pt; font-family: Arial; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: 'Times New Roman';"> assessment could include: <span style="font-size: 12pt; font-family: Symbol; mso-fareast-font-family: Symbol; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: Symbol; msofareastfontfamily: Symbol; msobidifontsize: 10.0pt; msolist: Ignore; msobidifontfamily: Symbol;">· <span style="font-size: 12pt; font-family: Arial; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: 'Times New Roman';">solutions that demonstrate imagination and creativity <span style="font-size: 12pt; font-family: Symbol; mso-fareast-font-family: Symbol; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: Symbol; msofareastfontfamily: Symbol; msobidifontsize: 10.0pt; msolist: Ignore; msobidifontfamily: Symbol;">· <span style="font-size: 12pt; font-family: Arial; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: 'Times New Roman';">critical analysis of the use of statistical, probability and mathematical models. <span style="font-size: 12pt; font-family: Arial; mso-fareast-font-family: Arial; mso-ansi-language: EN-GB; mso-bidi-font-size: 10.0pt; msofareastfontfamily: Arial; msobidifontsize: 10.0pt; msolist: Ignore; msoansilanguage: EN-GB;">4 <span style="font-size: 12pt; font-family: Arial; mso-ansi-language: EN-GB; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: 'Times New Roman';">Problems can be //complex// because of their context or because of the models they require and may involve: <span style="font-size: 12pt; font-family: Symbol; mso-fareast-font-family: Symbol; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: Symbol; msofareastfontfamily: Symbol; msobidifontsize: 10.0pt; msolist: Ignore; msobidifontfamily: Symbol;">· <span style="font-size: 12pt; font-family: Arial; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: 'Times New Roman';">mathematising practical situations <span style="font-size: 12pt; font-family: Symbol; mso-fareast-font-family: Symbol; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: Symbol; msofareastfontfamily: Symbol; msobidifontsize: 10.0pt; msolist: Ignore; msobidifontfamily: Symbol;">· <span style="font-size: 12pt; font-family: Arial; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: 'Times New Roman';">stating and evaluating assumptions or models <span style="font-size: 12pt; font-family: Symbol; mso-fareast-font-family: Symbol; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: Symbol; msofareastfontfamily: Symbol; msobidifontsize: 10.0pt; msolist: Ignore; msobidifontfamily: Symbol;">· <span style="font-size: 12pt; font-family: Arial; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: 'Times New Roman';">algebraic manipulation <span style="font-size: 12pt; font-family: Symbol; mso-fareast-font-family: Symbol; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: Symbol; msofareastfontfamily: Symbol; msobidifontsize: 10.0pt; msolist: Ignore; msobidifontfamily: Symbol;">· <span style="font-size: 12pt; font-family: Arial; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: 'Times New Roman';">drawing on skills from a range of areas of statistics and modelling <span style="font-size: 12pt; font-family: Symbol; mso-fareast-font-family: Symbol; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: Symbol; msofareastfontfamily: Symbol; msobidifontsize: 10.0pt; msolist: Ignore; msobidifontfamily: Symbol;">· <span style="font-size: 12pt; font-family: Arial; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: 'Times New Roman';">critically evaluating the appropriateness and usefulness of the solutions. <span style="font-size: 12pt; font-family: Arial; mso-ansi-language: EN-GB; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: 'Times New Roman';"> <span style="font-size: 12pt; font-family: Arial; mso-fareast-font-family: Arial; mso-ansi-language: EN-GB; mso-bidi-font-size: 10.0pt; msofareastfontfamily: Arial; msobidifontsize: 10.0pt; msolist: Ignore; msoansilanguage: EN-GB;">5 //<span style="font-size: 12pt; font-family: Arial; mso-ansi-language: EN-GB; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: 'Times New Roman';">Statistical thinking //<span style="font-size: 12pt; font-family: Arial; mso-ansi-language: EN-GB; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: 'Times New Roman';"> includes the following abilities. <span style="font-size: 12pt; font-family: Symbol; mso-fareast-font-family: Symbol; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: Symbol; msofareastfontfamily: Symbol; msobidifontsize: 10.0pt; msolist: Ignore; msobidifontfamily: Symbol;">· <span style="font-size: 12pt; font-family: Arial; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: 'Times New Roman';">Skills in dealing with variability including an understanding that any variable will vary within its range of possible values
 * <span style="font-size: 12pt; font-family: Arial; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: 'Times New Roman';">Explanatory notes **<span style="font-size: 12pt; font-family: Arial; mso-ansi-language: EN-GB; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: 'Times New Roman';">

The skills also include the abilities to
<span style="font-size: 12pt; mso-ansi-language: EN-GB; mso-bidi-font-size: 10.0pt; msobidifontsize: 10.0pt; msolist: Ignore; msoansilanguage: EN-GB;"> -  <span style="font-size: 12pt; font-family: Arial; mso-ansi-language: EN-GB; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: 'Times New Roman';">describe the distribution of this variation, <span style="font-size: 12pt; mso-ansi-language: EN-GB; mso-bidi-font-size: 10.0pt; msobidifontsize: 10.0pt; msolist: Ignore; msoansilanguage: EN-GB;"> -  <span style="font-size: 12pt; font-family: Arial; mso-ansi-language: EN-GB; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: 'Times New Roman';">measure its size, <span style="font-size: 12pt; mso-ansi-language: EN-GB; mso-bidi-font-size: 10.0pt; msobidifontsize: 10.0pt; msolist: Ignore; msoansilanguage: EN-GB;"> -  <span style="font-size: 12pt; font-family: Arial; mso-ansi-language: EN-GB; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: 'Times New Roman';">relate this variation to other variables, <span style="font-size: 12pt; mso-ansi-language: EN-GB; mso-bidi-font-size: 10.0pt; msobidifontsize: 10.0pt; msolist: Ignore; msoansilanguage: EN-GB;"> -  <span style="font-size: 12pt; font-family: Arial; mso-ansi-language: EN-GB; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: 'Times New Roman';">suggest why it is varying <span style="font-size: 12pt; mso-ansi-language: EN-GB; mso-bidi-font-size: 10.0pt; msobidifontsize: 10.0pt; msolist: Ignore; msoansilanguage: EN-GB;"> -  <span style="font-size: 12pt; font-family: Arial; mso-ansi-language: EN-GB; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: 'Times New Roman';">suggest how the variation can be controlled and used. Variability arises with time series, sampling and confidence intervals, investigations, probability and probability distributions and aspects of mathematical modelling. <span style="font-size: 12pt; font-family: Symbol; mso-fareast-font-family: Symbol; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: Symbol; msofareastfontfamily: Symbol; msobidifontsize: 10.0pt; msolist: Ignore; msobidifontfamily: Symbol;">· <span style="font-size: 12pt; font-family: Arial; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: 'Times New Roman';">Skills in applying mathematical and statistical methods to contexts. <span style="font-size: 12pt; font-family: Symbol; mso-fareast-font-family: Symbol; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: Symbol; msofareastfontfamily: Symbol; msobidifontsize: 10.0pt; msolist: Ignore; msobidifontfamily: Symbol;">· <span style="font-size: 12pt; font-family: Arial; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: 'Times New Roman';">Combining of mathematical and contextual knowledge can arise in every part of the standard's content. <span style="font-size: 12pt; font-family: Symbol; mso-fareast-font-family: Symbol; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: Symbol; msofareastfontfamily: Symbol; msobidifontsize: 10.0pt; msolist: Ignore; msobidifontfamily: Symbol;">· <span style="font-size: 12pt; font-family: Arial; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: 'Times New Roman';">An inclination to learn about how a process works, so as to make improvements. <span style="font-size: 12pt; font-family: Symbol; mso-fareast-font-family: Symbol; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: Symbol; msofareastfontfamily: Symbol; msobidifontsize: 10.0pt; msolist: Ignore; msobidifontfamily: Symbol;">· <span style="font-size: 12pt; font-family: Arial; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: 'Times New Roman';">Abilities to deal with the stages of the investigative cycle: plan, find data, explore and analyse, act, criticise, plan. <span style="font-size: 12pt; font-family: Symbol; mso-fareast-font-family: Symbol; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: Symbol; msofareastfontfamily: Symbol; msobidifontsize: 10.0pt; msolist: Ignore; msobidifontfamily: Symbol;">· <span style="font-size: 12pt; font-family: Arial; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: 'Times New Roman';">Skills in exploring data, and looking for patterns and departures from patterns. <span style="font-size: 12pt; font-family: Symbol; mso-fareast-font-family: Symbol; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: Symbol; msofareastfontfamily: Symbol; msobidifontsize: 10.0pt; msolist: Ignore; msobidifontfamily: Symbol;">· <span style="font-size: 12pt; font-family: Arial; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: 'Times New Roman';">Skills in stating assumptions about a context, assessing whether they hold, and dealing with departures from assumptions. <span style="font-size: 12pt; font-family: Symbol; mso-fareast-font-family: Symbol; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: Symbol; msofareastfontfamily: Symbol; msobidifontsize: 10.0pt; msolist: Ignore; msobidifontfamily: Symbol;">· <span style="font-size: 12pt; font-family: Arial; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: 'Times New Roman';">Critical thinking about all methods, models and conclusions. <span style="font-size: 12pt; font-family: Symbol; mso-fareast-font-family: Symbol; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: Symbol; msofareastfontfamily: Symbol; msobidifontsize: 10.0pt; msolist: Ignore; msobidifontfamily: Symbol;">· <span style="font-size: 12pt; font-family: Arial; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: 'Times New Roman';">Thinking that is commonsense, lateral, graphical, creative, imaginative and prepared for the unexpected. <span style="font-size: 12pt; font-family: Arial; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: 'Times New Roman';">Assessment <span style="font-size: 12pt; font-family: Arial; mso-ansi-language: EN-GB; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: 'Times New Roman';">may require the student to demonstrate the learning they have gained from the practical experiences of designing and carrying out experiments and investigations. <span style="font-size: 12pt; font-family: Arial; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: 'Times New Roman';"> <span style="font-size: 12pt; font-family: Arial; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: 'Times New Roman';">Assessment could include requiring the student to: <span style="font-size: 12pt; font-family: Symbol; mso-fareast-font-family: Symbol; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: Symbol; msofareastfontfamily: Symbol; msobidifontsize: 10.0pt; msolist: Ignore; msobidifontfamily: Symbol;">· <span style="font-size: 12pt; font-family: Arial; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: 'Times New Roman';">plan an investigation which may include experimental design or sampling methods <span style="font-size: 12pt; font-family: Symbol; mso-fareast-font-family: Symbol; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: Symbol; msofareastfontfamily: Symbol; msobidifontsize: 10.0pt; msolist: Ignore; msobidifontfamily: Symbol;">· <span style="font-size: 12pt; font-family: Arial; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: 'Times New Roman';">interpret data <span style="font-size: 12pt; font-family: Symbol; mso-fareast-font-family: Symbol; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: Symbol; msofareastfontfamily: Symbol; msobidifontsize: 10.0pt; msolist: Ignore; msobidifontfamily: Symbol;">· <span style="font-size: 12pt; font-family: Arial; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: 'Times New Roman';">make inferences <span style="font-size: 12pt; font-family: Symbol; mso-fareast-font-family: Symbol; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: Symbol; msofareastfontfamily: Symbol; msobidifontsize: 10.0pt; msolist: Ignore; msobidifontfamily: Symbol;">· <span style="font-size: 12pt; font-family: Arial; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: 'Times New Roman';">provide recommendations for action based on the findings of an investigation. <span style="font-size: 12pt; font-family: Arial; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: 'Times New Roman';">Alternatively assessment may require the student to analyse /critique a description of an investigation. <span style="font-size: 12pt; font-family: Arial; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: 'Times New Roman';"> <span style="font-size: 12pt; font-family: Arial; mso-fareast-font-family: Arial; mso-bidi-font-size: 10.0pt; msofareastfontfamily: Arial; msobidifontsize: 10.0pt; msolist: Ignore;">6 <span style="font-size: 12pt; font-family: Arial; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: 'Times New Roman';">Assessment <span style="font-size: 12pt; font-family: Arial; mso-ansi-language: EN-GB; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: 'Times New Roman';">may require the student to d <span style="font-size: 12pt; font-family: Arial; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: 'Times New Roman';">emonstrate a high level of usage of probability and <span style="font-size: 12pt; font-family: Arial; mso-ansi-language: EN-GB; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: 'Times New Roman';">mathematical <span style="font-size: 12pt; font-family: Arial; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: 'Times New Roman';"> problem solving techniques.