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Karp, Karen S.; Bush, Sarah B.; Dougherty, Barbara J. – Mathematics Teaching in the Middle School, 2015
Many rules taught in mathematics classrooms "expire" when students develop knowledge that is more sophisticated, such as using new number systems. For example, in elementary grades, students are sometimes taught that "addition makes bigger" or "subtraction makes smaller" when learning to compute with whole numbers,…
Descriptors: Mathematics Instruction, Secondary School Mathematics, Middle School Students, Standards
Dougherty, Barbara J.; Slovin, Hannah – International Group for the Psychology of Mathematics Education, 2004
Measure Up is a research and development project that uses findings from Davydov (1975) and others to introduce mathematics through measurement and algebra in grades 1-3. This paper illustrates the use of generalized diagrams and symbols in solving word problems for a group of 10 children selected from a grade 3 Measure Up classroom. Students use…
Descriptors: Symbols (Mathematics), Grade 3, Educational Research, Word Problems (Mathematics)

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