Facilitator's Guide to Ways to Think about MathematicsFacilitating mathematical investigations with teachers will help improve their teaching! National and state standards suggest that mathematical investigation, problem solving, and exploratory learning should play a central role in mathematics lessons. It is therefore necessary for teachers to experience mathematical explorations as learners themselves. This Facilitator Guide and accompanying CDROM provides resources for planning and implementing courses and workshops using Ways to Think About Mathematics by containing:

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Contents
Dissections and Area  16 
Linearity and Proportional Reasoning  42 
Pythagoras and Cousins  72 
Combinatorial Algebra  101 
Common terms and phrases
15 minutes algebra algorithm angle answer asks participants binomial theorem circle coefficients coin flips compute the area conjecture connection consecutive sums consider context create derive determine diagonals dice discussion dissection egg function Encourage participants entries equal equation example fact figure Further Exploration CD Further Exploration materials give given Goal graph horizontal hypotenuse idea integer interpolation investigate k cars Law of Cosines linear combinations linear mapping linearly dependent look mathematical method mixture multiple notation number of paths number of trains parallelogram Pascal's Triangle pattern polygons polynomial possible previous problem Problem 11 Problem 9 Problems presented Proofs without words proportional reasoning prove Pythagorean Theorem Pythagorean triangles Pythagorean triples quadrilateral rectangle result right triangle session shear side lengths solution solve squares strategies subsets sums problem taxicab teachers text Problem there's trains of length trapezoid vectors vertex vertical