We report on findings from two one-on-one teaching experiments with prospective middle school teachers (PTs). The focus of each teaching experiment was on identifying and explicating the mental processes and types of intermediate, supporting reasoning that each PT used in their development of combinatorial reasoning. The teaching experiments were…

One of the most challenging daily experiences of teaching young adolescents is helping them transition from Piaget's concrete to the formal operational stage of cognitive development during the middle school years. Students who have reached formal operations can design and test hypotheses, engage in deductive reasoning, use flexible thinking,…

Examined is the relationship between junior high school students' directional reasoning about rates and numerical reasoning on proportion-related word problems. The relationship between the ability to solve context-free fraction exercises and the ability to solve mathematically similar word problems is discussed. (KR)

One of three related documents produced in response to a need for direct instruction in thinking skills, this program for middle school or junior high school students bases its approach on involvement of students in direct experiences. The book contains four units. Focusing on perception, Unit 1: "Experiencing the Arts" begins with ways sensory…