In simplest terms, tasks are what students do in classrooms every day when they come to school. Tasks are the vehicles by which standards are achieved.
The NCTM Professional Teaching Standards for Mathematics defines tasks this way:
If the word science were substituted for the word mathematics, science teachers would agree that the previous paragraph describes their most important responsibilities. The first two science teaching standards speak directly to the teacher's role in task identification, creation, and execution. In addition, the emerging science teaching standards support inquiry, which is defined in three ways that are consistent with a classroom filled with worthwhile instructional tasks:
Task-oriented teaching is more than activity. Good tasks are defined as ones that "do not separate . . . thinking from . . . concepts or skills, that capture students' curiosity and that invite them to speculate and pursue their hunches. Many such tasks can be approached in more than one interesting and legitimate way; some have more than one reasonable solution."
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Tasks selected should be evaluated for their ability to accurately sample important concepts and processes of science and mathematics and to provide opportunities to practice skills in context. They have to be suitable for the students and based on their experiences. The tasks should be based on what the students know and can do, what they are or can be interested in, what they need to work on, and how they are challenged.
Good classrooms are not ones in which the primary activity is the teacher transmitting information that the children listen to, practice, and repeat.
The traditional approach to curricula, which is still dominant in most schools, assumed students came to school with the same experiences, progressed at the same rate and learned in the same way. Built to standards of efficiency, lessons were simple, standardized and easy to man age. The movement of the 1960s and 1970s was toward small, isolated behavioral objectives that stated what children will be able to do; this encouraged activities designed around these specific behaviors and separate testing of the objectives to see if they had been learned. This view of the curriculum fit common notions of how to educate large numbers of children efficiently.
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The desire to cover the material efficiently led to having curriculum emphasize basic skills and facts. Consequently, the curriculum tended to be repetitive and decontextualized and offer little integration of skills.
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While assessment will be discussed later, it is important to note now that as teaching becomes multidimensional in nature, so must assessment.
Assessment is systematic evaluation of the evidence (or documentation) of thinking and doing (see "Keeping Track"). Assessment is central to instruction; assessment must be a part of instruction.
The mathematics tasks in which students engage - projects, problems, constructions, applications, exercises, and so on - and the materials with which they work, frame and focus students' opportunities for learning mathematics in school. Tasks provide the stimulus for students to think about particular concepts and procedures, their connections with other mathematical ideas and their applications to real world contexts. Good tasks can help students to develop skills in the context of their usefulness. Tasks also convey messages about what mathematics is and what doing mathematics entails. Tasks that require students to reason and to communicate mathematically are more likely to promote their ability to solve problems and to make connections. Such tasks can illuminate mathematics as an intriguing and worthwhile domain of inquiry. A central responsibility of teachers is to select and develop worthwhile tasks and materials that create opportunities for students to develop these kinds of mathematical understandings, competence, interests and dispositions.
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