Making Sense of Equivalent Equations and Expressions - Mathematics for Teaching

Here are some questions your students have been wanting to ask you in your algebra class. Daniel Chazan and Michal Yerushalmy in their article On Appreciating the Cognitive Complexity of School Alg...

Here are some questions your students have been wanting to ask you in your algebra class. Daniel Chazan and Michal Yerushalmy in their article On Appreciating the Cognitive Complexity of School Algebra posed these questions about equivalence of equations , solving equations, and equivalence of expressions for us teachers to ponder upon. How often do we give students the opportunities to think about these questions? Questions: If one can add x to both sides of an equation in one variable—and if multiplication is repeated addition—why cannot one always multiply each side of an equation by x?…

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