This brochure highlights key concepts of the American Federation of Teachers (AFT) "Thinking Mathematics" courses. Citing adherence to No Child left Behind Act (NCLB) mandates, these courses are: (1) based on scientific research about how children learn mathematics; (2) designed to increase teacher mathematical knowledge; (3) provide a sustained, intensive and classroom-focused experience; (4) improve classroom management skills; and (5) provide experiences to help students meet high standards. "Thinking Mathematics" is aimed primarily at topics addressed in pre-K through grade 6, stressing: (1) situational context, understanding and problem-solving; (2) problem representation; (3) balance of conceptual and procedural learning; (4) mathematical justification; (5) moving from concrete to abstract; and (6) commutative and distributive properties that lay groundwork for higher level math. "Thinking Mathematics" can also be used in training offered by NCLB Mathematics/Science Partnerships.