Mathematical tasks form the basic unit in instruction and learning in K-12 classrooms. Research indicates that different math tasks elicit different levels and types of student thinking. Because this variety is viewed as a plus, curriculum designers have made efforts to develop different kinds of task. One kind of task, called for by researchers and evident in “Common Core” mathematical curricula, is the contextual task, which is designed to get students to connect disciplinary knowledge to real world contexts. Researchers have debated the effectiveness of contextual tasks, often because the problematic contextual tasks and teachers have difficulty in realizing the instructional intent of these tasks. The purpose of this study is to examine this issue. Specifically, it addresses two questions: What do mathematics tasks look like as written in textbooks? What’s the relationship between the context feature and the cognitive demand of contextual math tasks? It draws on a representative sample of math tasks across three different curriculum materials (i.e., textbooks) at three intermediate grade levels--sixth, seventh, and eighth to address these questions. The study focuses on two important categories of written math tasks: the first called “context,” the second “cognitive demand.”, the third “structure”, and the forth “representation”. The “context” category, in my analysis, are further divided into three sub-categories. The set of variables, for context, are labelled “mathematization,” “realism,” and “necessity.” As reported in the text, I found considerable variation across the three curriculum materials in the way math tasks were written. Although the majority of the math tasks in all three curriculum materials were presented as contextual tasks, the importance of the role that context played in supporting the mathematical knowledge differed in two ways: In the first approach, the task was less complex, and thus afforded students less opportunity to think about the mathematics of the situation (e.g., a shopper adding up items he or she wants to buy). In the second, the context was more complex and thus increased the likelihood that students would connect the mathematics to the context (e.g., shopping with a limited budget). The correlation results suggested that the likelihood to mathematize and the necessity degree of the context are significantly correlated to the cognitive level of the task. The realism, however, is not significantly correlated to the cognitive level of the task.
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