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Improving Student Achievement in Mathematics
註釋The ideas presented here are based on the idea that, in order to succeed, efforts to improve instruction must focus on the existing knowledge base in respect of effective teaching and learning. The practises proposed to increase the effectiveness of teaching and learning are -the extent of the students' opportunity to learn mathematics content bears directly and decisively on student mathematics achievement -focusing instruction on the meaningful development of important mathematical ideas increases the level of student learning -students can learn both concepts and skills by solving problems -giving students both an opportunity to discover and invent new knowledge and an opportunity to practise what they have learned improves student achievement -teaching that incorporates students intuitive solution methods can increase student learning, especially when combined with opportunities for student interaction and discussion -using small groups of students to work on activities, problems and assignments can increase student mathematics achievement -whole-class discussion following individual and group work improves student achievement -teaching mathematics with a focus on number sense encourages students to become problem solvers in a wide variety of situations and to view mathematics as a discipline in which thinking is important -long-term use of concrete materials is positively related to increases in student mathematics achievement and improved attitudes towards mathematics -using calculators in the learning of mathematics can result in increased achievement and improved student attitudes.