We interviewed 40 students each in grades 7 and 11 to investigate their integer-related reasoning. In one task, the students were asked to write and interpret equations related to a story problem about borrowing money from a friend. All the students solved the story problem correctly. However, they reasoned about the problem in different ways.…

FIFTEEN DAILY DRILLS EMPHASIZING MASTERY OF BASIC NUMBER FACTS, SUCH AS ARITHMETIC OPERATIONS AND UNITS OF MEASUREMENT WERE CONSTRUCTED TO ENCOMPASS 7 PREVIOUSLY REPORTED ATTRIBUTES OF AN EFFECTIVE DRILL. ATTRIBUTES ARE MIXED DRILL, TIME LIMIT, INCREASINGLY DIFFICULT EXAMPLES, THOROUGH COVERAGE, FREQUENT AND SMALL AMOUNTS, VERBAL PROBLEMS,…

FOUR SELF-INSTRUCTIONAL PROGRAMS WERE STUDIED AND REVISED BY USE OF TUTORING TECHNIQUES WITH INDIVIDUAL STUDENTS TO CREATE MODIFIED PROGRAMS SUPERIOR TO THE ORIGINAL ONES. THE PROGRAMS USED IN THE STUDY WERE FIRST-GRADE READING, FIRST-GRADE ARITHMETIC, JUNIOR HIGH SCHOOL SPANISH, AND SENIOR HIGH SCHOOL GEOMETRY. PROGRAMS THAT LED TO IMPROVED…