Each mathematics standard is for a designated point in a student’s first eight years at school. Recognising that students begin school at different times in the year, the first three standards are described in terms of the time a student has spent at school, that is, 'After one year at school', 'After two years at school', and 'After three years at school'. From year 4, the standards are described in terms of the school year the student is in, that is, 'By the end of year 4', 'By the end of year 5', and so on.
The standards for mathematics build directly on the strands and levels of the mathematics and statistics learning area in The New Zealand Curriculum. Like the curriculum, they place a strong emphasis on students’ ability to solve problems and model situations in a range of meaningful contexts by selecting and applying appropriate knowledge, skills, and strategies.
Many learning outcomes from The New Zealand Curriculum are implicit in the standards but not explicitly stated. This is particularly true of basic knowledge across the three strands, including number facts. While knowledge is critically important for mathematical understanding, its primary role is to facilitate the student’s solving of problems and modelling of situations. Just demonstrating knowledge – for example, by recalling basic facts – is not sufficient to meet a standard. Rather, the student must use knowledge to think mathematically when solving problems or modelling situations.
Taken as a whole, the standards show how students progress in their learning in mathematics and statistics. This means that the 'next step' for a student meeting a particular standard is broadly described by the standard for the next year. Similarly, if a student is not able to meet a standard, their current achievement is likely to be described by a previous standard. Examples of problems and descriptions of students’ thinking in response to the problems accompany each standard. Together, these illustrate and clarify the standard and exemplify the kinds of tasks students should engage with in their learning in mathematics and statistics.
Meeting a standard depends on the nature of a student’s responses to given problems, not just their ability to solve the problems. For this reason, the examples give a range of responses to illustrate the types of responses that meet the expectation. In many cases, the examples include responses above and below the expectation in order to show the progression in a student’s understanding.
The examples of problems and students’ responses are not a definitive collection for use in assessing achievement in relation to the standards. They are illustrative, and they represent only a small sample of possible problems and responses that teachers might draw on in determining whether a student is meeting the standard.
Published on: 13 Oct 2009
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