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Students have agonized over mathematics for decades, yet teachers continue to write twoexample problems on the board and assign a set of similar ones for students to practice hopingthat this strategy will somehow breed deep understanding and appreciation of mathematics. Withthis teaching technique present in schools across the nation, it is not difficult to reason why theUnited States was so poorly represented in the Third International Mathematics and ScienceStudy (Goldsmith and Mark, 1999). Recognizing this detrimental trend, the National Council ofTeachers of Mathematics (NCTM) developed and revised a set of standards and curriculum in1989, 1991, and 1995 called standards-based mathematics (Phillips, Lappan, and Grant, 2006).The goal of standards-based mathematics is to remedy students’ fear, aversion, andmisunderstanding of mathematics by providing instruction which instills lasting comprehensionof concepts and processes; enhances students’ ability to make connections within the content,other disciplines, and to everyday experiences; and finally generates students’ capability ofcommunicating mathematical ideas (Phillips et al. 2006)
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