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Abstract This study examined relationships among first-grade teachers' pedagogical content beliefs, teachers' pedagogical content knowledge, and students' achievement in mathematics. Teachers (N = 39) completed structured questionnaires and interviews on their beliefs and knowledge about instruction, children's learning, and the mathematics content in addition and subtraction. Results indicated significant positive relationships among teachers' beliefs, teachers' knowledge, and students' problem-solving achievement. Compared to teachers with a less cognitively based perspective (LCB teachers), teachers with a more cognitively based perspective (CB teachers) made extensive use of word problems in introducing and teaching addition and subtraction. They also spent time developing children's counting strategies before teaching number facts. CB teachers had greater knowledge of word problem types and greater knowledge of their children's problem-solving strategies than did LCB teachers. Furthermore, CB teachers obtained this latter knowledge by observing their children in problem situations rather than by relying on tests or formal assessments. Children with CB teachers scored higher on word problem-solving achievement than did children with LCB teachers, but children from both types of classes did equally well on addition/subtraction number facts.
Peterson et al. (Wed,) studied this question.