Research findings indicate that certain teaching strategies and methods are worth careful consideration as teachers strive to improve their mathematics teaching practices. The extent of the students' opportunity to learn mathematics content bears directly and decisively on student mathematics achievement. Strong correlations were found between OTL scores and mean student achievement scores, with high OTL scores associated with high achievement. Focusing instruction on the meaningful development of important mathematical ideas increases the level of student learning. Investigations have consistently shown that an emphasis on teaching for meaning has positive effects on student learning, including better initial learning, greater retention and an increased likelihood that the ideas will be used in new situations.
Students can learn both concepts and skills by solving problems.
Research suggests that students who develop conceptual understanding early perform best on procedural knowledge later. Students with good conceptual understanding are able to perform successfully on near-transfer tasks and to develop procedures and skills they have not been taught. Students with low levels of conceptual understanding need more practice in order to acquire procedural knowledge. Giving students both an opportunity to discover and invent new knowledge and an opportunity to practice what they have learned improves student achievement. Virtually no time is spent inventing new procedures and analyzing unfamiliar situations.