1. Signature Pedagogies Potent teaching approaches that warrant common application Potent teaching approaches that warrant common application Global to local, although individual teaching practices acknowledged and valued Global to local, although individual teaching practices acknowledged and valued Phrase borrowed and idea adapted from Shulman (2005) Phrase borrowed and idea adapted from Shulman (2005)

2. Signature Pedagogies: Global Examples Investigative Approach (re: Baroody 2003) Investigative Approach (re: Baroody 2003) Teaching through problem solving (re: Schoen 2003, Kilpatrick 2001, Grouws 2000) Teaching through problem solving (re: Schoen 2003, Kilpatrick 2001, Grouws 2000) Teaching focused on reasoning and sense making (re: NCTM 2009, Focus in High School Mathematics) Teaching focused on reasoning and sense making (re: NCTM 2009, Focus in High School Mathematics) Teaching focused on a connected and coherent approach to content Teaching focused on a connected and coherent approach to content Mathematics in context Mathematics in context Multiple connected representations Multiple connected representations

3. Signature Pedagogies: Strand Examples Algebra Algebra  Functions approach to teaching algebra Geometry Geometry  Conjecturing approach to teaching geometry (re: Polya: “First believe it, then prove it.”) Statistics and Probability Statistics and Probability  Focus on the big idea of variability  Simulation  Real data

4. Signature Pedagogies: Topic Examples Functions Functions  Include a recursive view of functions Recursion Recursion  Include use of pedagogically powerful informal notation, like NEXT and NOW Vertex-Edge Graphs Vertex-Edge Graphs  Modeling with graphs

5. Signature Pedagogies: Topic Examples Counting Counting  Counting as sense-making before and while counting with formulas  Explicitly clarify and concretely represent what is being counted Logarithms Logarithms  Begin teaching earlier, gently, when teaching exponents  A logarithm is an exponent  Logarithms help us understand very large scales  Logarithms undo exponentiation (inverse functions)