Everybody Counts A Report to the Nation on the Future of Mathematics Education (1989) / Chapter Skim
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TEACHING
TEACHING
Pages 57-72
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From page 57... ...
Lacking freedom to establish fully either ends or means, teachers rarely have the opportunity to exercise truly professional responsibilities. What emerges, often, are foreshortened ideals and shattered dreams.
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From page 58... ...
Effective teachers are those who can stimulate students to learn mathematics. Educational research offers compelling evidence that students learn mathematics well only when they construct their own mathematical understanding.
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From page 59... ...
Insights from contemporary cognitive science help confirm these earlier observations by establishing a theoretical framework based on evidence from many fields of study. Engaging Students No teaching can be effective if it does not respond to students' prior ideas.
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From page 60... ...
Just as chiloren need the opportunity to learn from mistakes, so students need an environment for learning mathematics that provides generous room for trial and error. In the long run, it is not the memorization of mathematical skills that is particularly important without constant use, skills fade rapidly but the confidence that one knows how to find and use mathematical tools whenever they become necessary.
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From page 61... ...
People believe that calculators will prevent children from mastering arithmetic, an important burden which their parents remember bearing with courage and pride. Computers, on the other hand, are not perceived as shortcuts to undermine school traditions, but as new tools necessary to society that children who understand mathematics must learn to use.
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From page 62... ...
It is true, as many say, that we are not sure how best to teach mathematics with computers. Nevertheless, despite risks of venturing into unfamiliar territory, society has much to gain from the increasing role of calculators and computers in mathematics education: · School mathematics can become more like the mathematics people actually use, both on the job and in scientific applications.
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From page 63... ...
Innovative instruction based on a new symbiosis of machine calculation and human thinking can shift the balance of learning toward understanding, insight, and mathematical intuition.
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From page 64... ...
Such experiences leave many elementary teachers totally unprepared to inspire children with confidence in their own mathematical abilities. What is worse, experienced elementary teachers often move up to middle grades (because of imbalance in enrolIments)
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From page 65... ...
To encourage more widespread adoption of diverse patterns for mathematics specialists, states must alter certification requirements to encourage these new models. Then universities must implement new courses with open constructive instructors so that prospective school teachers can grow in confidence as a result of their university study of mathematics.
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From page 66... ...
All students, and especially prospective teachers, should learn mathematics as a process of constructing and interpreting patterns, of discovering strategies for solving problems, and of exploring the beauty and applications of mathematics. Above all, courses taken by prospective teachers must create in these teachers confidence in their own abilities to help students discover richness and excitement in mathematics.
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From page 67... ...
How can texts and software act as incentives rather than as brakes for the newly emerging standards for school mathematics? Even while educators work to reduce the dominance of text-based learning in mathematics classrooms, publishers and teachers need to explore new modes of publication that will enable good innovative ideas to enter expeditiously into typical classroom practice.
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From page 68... ...
Tests designed for diagnostic purposes are often used for evaluating programs; scores from self-selected populations (for example, takers of Scholastic Aptitude Tests) are used to compare districts and states; and commonly used achievement tests stress simple skills rather than sophisticated tasks, not because such skills are more important, but because they are easier to measure.
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From page 69... ...
Similar problems arise when detailed learner outcomes rather than teacher judgments define the objectives of courses. Like items on objective tests, specific learner outcomes bias teacher effort and constrain student learning.
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From page 70... ...
out how to get their kids into our program. 70 To assess development of a student's mathematical power, a teacher needs to use a mixture of means: essays, homework, projects, short answers, quizzes, blackboard work, journals, oral interviews, and group projects.
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