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There are lots of ways. Each time patterns are investigated and the child is able to make a generalization is higher-order thinking. When children take an idea (pattern) and apply it to something, you have higher-order thinking. When they sort buttons by type, deciding on the discriminating factors is higher order - size, shape; the more intricate their rule, the higher the thinking. You should check out THE ARITHMETIC TEACHER published by NCTM for some great ideas. You can also go to the Eisenhower Clearinghouse at http://www.enc.org to look up ideal math lessons for grades K-2.
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