Exploring the link between task features and generalisation
Exploring the link between task features and generalisation
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探索任务特征和泛化之间的联系
DOI：
10.1080/14794800902732233
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发表时间：
2009
影响因子：
1.3
通讯作者：
Chua B
中科院分区：
文献类型：
--
作者：
Chua B
关于学生在模式概括问题中的概括性表达的研究广泛地记录了他们在用文字或代数符号表达和表示函数规则方面的困难（Hoyles和Küchemann 2001）。但最近的研究似乎将困难主要归因于这些问题中模式的描述方式（Stalo et al. 2006; Lannin，Barker and汤森2006）。除了这些发现之外，关于问题的其他特征可能会影响学生表达概括性的能力以及如何影响学生表达概括性的能力，人们知之甚少。在这项研究中，我们推测学生在模式概括问题中的表现可能会受到以下五个任务特征的影响。(i)图案显示的格式。有两种类型的模式概括问题：数字或图形。数值概括型问题将模式列为一系列数字或方程，而图形类型则使用图表来描述模式。这个任务的特点是关注的模式是否被列为一系列的数字，方程或图表，或简单地作为一个单一的图表。(ii)函数的类型。一般化问题中的模式可以表示为显示两个变量之间关系的规则。此任务功能考虑规则描述的是线性关系还是非线性关系。(iii)涉及的独立变量的数量。在大多数文献中报道的模式概括问题的规则保持简单的线性函数的形式N 0an 'b，其中N表示第n项。这样的规则只包含一个自变量n，它通常是表示术语或图在模式中的位置的序数。然而，一些问题涉及包括一个以上自变量的规则。一个恰当的例子是池塘瓷砖任务，要求学生确定用瓷砖层包围任何给定尺寸的矩形池塘所需的单位正方形瓷砖的数量。在这个任务中，所需的瓷砖数量取决于两个独立变量：池塘的长度和宽度。我们想强调的是，在确定函数的类型和所涉及的自变量的数量时，应该考虑规则的简化形式。(iv)对生成器的引用。在一些一般化的问题中，特别是图形类型，自变量可以连接到某个
Research on students’ expression of generality in pattern-generalising problems has widely documented their difficulties in articulating and representing the functional rule in words or in algebraic notation (Hoyles and Küchemann 2001). But recent studies seem to attribute the difficulties mainly to the way the patterns are depicted in such problems (Stalo et al. 2006; Lannin, Barker and Townsend 2006). Apart from these findings, little else is known about what and how other features of the problems might affect students’ abilities to express generality. In this study, we speculate that students’ performance in pattern-generalising problems might be influenced by the five task features described below.(i) The format of pattern display. There are two types of pattern-generalising problems: numerical or figural. Numerical generalising problems list the pattern as a sequence of numbers or equations while the figural type uses diagrams to depict the pattern. This task feature is concerned with whether the pattern is listed as a sequence of numbers, equations or diagrammatic figures, or simply as a single diagram.(ii) The type of functions. The pattern in a generalising problem can be represented as a rule showing the relationship between two variables. This task feature considers whether the rule describes a linear or non-linear relationship.(iii) The number of independent variables involved. The rules in most of the pattern-generalising problems reported in the literature are kept simple to linear functions of the form N0an'b, where N denotes the nth term. Such rules contain only one independent variable, n, which is normally the ordinal number indicating the position of the term or the diagram in the pattern. However, some problems involve rules comprising more than one independent variable. A case in point is the pond-tiling task where students are asked to determine the number of unit square tiles needed to surround a rectangular pond of any given dimensions with a layer of tiles. In this task, the number of tiles required depends on two independent variables: the length and width of the pond. We like to emphasise that the simplified form of the rule should be considered when determining both the type of functions and the number of independent variables involved.(iv) The reference to the generator. In some generalising problems, in particular the figural type, the independent variable can be connected to a certain
对多种表示形式的模式的理解水平
DOI：
--
发表时间：
2006
期刊：
影响因子：
--
作者：
S. Michael;I. Elia;A. Gagatsis;A. Theoklitou;A. Savva
通讯作者：
A. Savva