• the characteristics of today's important mathematics lead to a broader view of curricular relevance.

CONTENT OF TASKS

Because mathematics has been stereotyped as cut and dried, some assessment designers have assumed that creating high-quality mathematics tasks is simple and straightforward. That assumption is false. Because mathematics relies on precise reasoning, errors easily creep into the words, figures, and symbols in which assessment tasks are expressed.

Open-ended tasks can be especially difficult to design and administer because there are so many ways in which they can misrepresent what students know and can do with mathematics.6 Students may give a minimal response that is correct but that fails to show the depth of their mathematical knowledge. They may be confused about what constitutes an adequate answer, or they may simply be reluctant to produce more than a single answer when multiple answers are called for. In an internal assessment constructed by a teacher, the administration and scoring can be adapted to take account of misunderstanding and confusion. In an external assessment, such adjustments are more difficult to make. The contexts in which assessment tasks are administered and the interpretations students are making of them are critical in judging the significance of the content.

The Ironing Board

The diagram shows the side of an ironing board.

The two legs cross at x°

  1. Use the information in the diagram to calculate the angle x°. Give your answer to the nearest degree.

  2. Calculate the value of l.

Difficulties arise when attempts are made to put mathematics into realistic settings. The setting may be so unfamiliar that students cannot see mathematics in it. Or, the designer of the task may have strained too hard to make the mathematics applicable, ending up with an artificial reality, as in the example above.7 As a practical matter, the angle between



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