Understanding signed quantities and its arithmetic is one of the challenging topics of middle school mathematics. Thespecia'/> Teachers’ construction of meanings of signed quantities and integer operation
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Teachers’ construction of meanings of signed quantities and integer operation

机译：教师签署数量和整数运作的含义构建

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AbstractUnderstanding signed quantities and its arithmetic is one of the challenging topics of middle school mathematics. Thespecialized content knowledge(SCK) for teaching integers includes understanding of a variety of representations that may be used while teaching. In this study, we argue that meanings of integers and integer operations form the foundation for the construction of SCK about representations used to teach integers. We report that teachers’ concerns about teaching the topic of integers implicate issues of meaning, although this may not always be explicitly acknowledged by teachers. We develop a framework of integer meanings synthesizing previous research, and describe how the framework allowed teachers to investigate a wide range of representations including contexts and thereby construct SCK in a professional development setting. Teachers constructed SCK by connecting various meanings of integers with one another and with representations including contexts. Teachers made two important shifts, from exclusively using the state meaning of integers to including the application of change meaning to representations and from exclusive use of formal models to including contexts to teach integer addition and subtraction. An implication of the study is that frameworks of meaning for key mathematical topics could be an important component of pre- and in-service teacher education.]]>
机译：Abstract理解符号量及其算术是中学数学中具有挑战性的课题之一。专业内容知识（SCK）对于教学整数来说，包括理解教学中可能用到的各种表示法。在这项研究中，我们认为，整数和整数运算的含义形成的基础上建立SCK关于表示教整数的表示。我们报告说，教师对整数主题教学的关注涉及到意义问题，尽管教师可能并不总是明确承认这一点。我们综合之前的研究开发了一个整数意义框架，并描述了该框架如何允许教师调查广泛的表征，包括上下文，从而在专业发展环境中构建SCK。教师通过将整数的各种含义相互联系起来，并通过包括上下文在内的表示来构建SCK。教师们做出了两个重要的转变，从只使用整数的状态意义转变为将变化意义应用到表示，从只使用形式模型转变为包含上下文来教授整数加减法。这项研究的一个含义是，关键数学主题的意义框架可能是职前和在职教师教育的重要组成部分]>

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