 Mathematics: From Concrete to Conceptual During the years from kindergarten to eighth grade, students must
repeatedly extend their conception of number. At first, “number” means
“counting number”: 1, 2, 3, … Soon after that, 0 is used to represent
“none” and the whole numbers are formed by the counting numbers together
with zero. The next extension is fractions. At first, fractions are
barely numbers and tied strongly to pictorial representations. Yet by
the time students understand division of fractions, they have a strong
concept of fractions as numbers and have connected them, via their
decimal representations, with the base-ten system used to represent the
whole numbers. During middle school, fractions are augmented by negative
fractions to form the rational numbers. In Grade 8, students extend
this system once more, augmenting the rational numbers with the
irrational numbers to form the real numbers. In high school, students
will be exposed to yet another extension of number, when the real
numbers are augmented by the imaginary numbers to form the complex
numbers.Please click on the links below to access unit plans and YAG's. |
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