We are not
yet sure whether this may be a part of our category of
knowledge of content and teaching or whether it may run
across the several categories or be a category in its own
right. We also provisionally include a third category
within subject matter knowledge, what we call “horizon
knowledge” (Ball, 1993). Horizon knowledge is an
awareness of how mathematical topics are related over
the span of mathematics included in the curriculum. Firstgrade
teachers, for example, may need to know how the
mathematics they teach is related to the mathematics
students will learn in third grade to be able to set the
mathematical foundation for what will come later. It also
includes the vision useful in seeing connections to much
later mathematical ideas. Having this sort of knowledge
of the mathematical horizon can help in making decisions
about how, for example, to talk about the number line.
Likewise third graders appreciate that the number line
they know will soon “fill in” with more and more
numbers? And might it matter how a teacher’s choices
anticipate or distort that later development? Again we are
not sure whether this category is part of subject matter
knowledge or whether it may run across the other categories.
We hope to explore these ideas theoretically,
empirically, and also pragmatically as the ideas are used
in teacher education or in the development of curriculum
materials for use in professional development.
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We are notyet sure whether this may be a part of our category ofknowledge of content and teaching or whether it may runacross the several categories or be a category in its ownright. We also provisionally include a third categorywithin subject matter knowledge, what we call “horizonknowledge” (Ball, 1993). Horizon knowledge is anawareness of how mathematical topics are related overthe span of mathematics included in the curriculum. Firstgradeteachers, for example, may need to know how themathematics they teach is related to the mathematicsstudents will learn in third grade to be able to set themathematical foundation for what will come later. It alsoincludes the vision useful in seeing connections to muchlater mathematical ideas. Having this sort of knowledgeof the mathematical horizon can help in making decisionsabout how, for example, to talk about the number line.Likewise third graders appreciate that the number linethey know will soon “fill in” with more and morenumbers? And might it matter how a teacher’s choicesanticipate or distort that later development? Again we arenot sure whether this category is part of subject matterknowledge or whether it may run across the other categories.We hope to explore these ideas theoretically,empirically, and also pragmatically as the ideas are usedin teacher education or in the development of curriculummaterials for use in professional development.
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