The kind of task we ask our learners to engage in algebra communicates particular notions of algebra and with it particular use of variable. There are at least four conceptions of algebra embedded in the curriculum. These are reflected in the tasks in textbooks and in our lessons. Zalman Usiskin proposed the following conceptions of...

Original by Erlina Ronda

]]>Think twice before you even say “a variable is a letter … or a variable is a symbol that stands for numbers ….” Zalman Usiskin reminds us that a variable need not only stand for numbers. It could stand for a point (in Geometry), a proposition (in Logic), a function (in Analysis), a matrix or...

Original by Erlina Ronda

]]>I propose here ideas teachers need to know and pay attention to when teaching mathematical proofs and how to prove. A. What is a (mathematical) proof? I define proof as a relational network of claims (propositions and conclusions), substantiation (established knowledge that makes the claim legitimate) and appropriate connectives so sequenced to justify why the conclusion is a...

Original by Erlina Ronda

]]>Whether a mathematical notation is a variable, parameter, or constant depends on what you mean by it. If you intend to represent the value of a quantity whose measure varies within a situation, then you are using that notation as a variable. If you intend to represent the value of a quantity whose measure is the...

Original by Erlina Ronda

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