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Do your students think that the vertical line test is indispensable and foolproof for determining whether a relationship is a function? Do they believe that every function can be modeled by an equation? Do they interpret the graph of a function as the function itself? What tasks can you offer - what questions can you ask - to determine what they know or don't know - and move them forward in their thinking? This book focuses on the specialized pedagogical content knowledge that you need to teach functions effectively in grades 9-12. The authors demonstrate how to use this multifaceted...

Like algebra at any level, early algebra is a way to explore, analyse, represent and generalise mathematical ideas and relationships. This book shows that children can and do engage in generalising about numbers and operations as their mathematical experiences expand. The authors identify and examine five big ideas and associated essential understandings for developing algebraic thinking in grades 3-5. The big ideas relate to the fundamental properties of number and operations, the use of the equals sign to represent equivalence, variables as efficient tools for representing mathematical...

Do your students suppose that if the perimeter of a shape increases, the area also increases? Do they think that area is the product of base and height, without understanding that this applies only to parallelograms? Do they believe that a transformation happens only on or to a particular object and not the entire plane? What tasks can you offer-what questions can you ask-to determine what they know or don't know-and move them forward in their thinking? This book focuses on the specialized pedagogical content knowledge that you need to teach geometry effectively in grades 6-8. The...