ABSTRACT

Researching students’ responses to tasks at different year levels and in varied curriculum contexts can provide insights that relate their understandings to prior learning experiences and teaching approaches. In this article, we discuss evidence of students from three curriculum contexts (English, Australian, and Israeli) (n = 350) ways of attending to the functional relationship between two variables at different levels of secondary school in their responses to two linear functions tasks. We found that the students from an English national curriculum context were more likely than the other cohorts to focus only on the dependent variable when presented with a table of values. With a figural pattern generalization task, no examples of invalid proportional reasoning were found among student responses from the Israeli curriculum context, unlike those in the English and Australian curriculum contexts. A high percentage of the Year seven-eighths responses from the Israeli curriculum context evidenced symbolic generalization whereas several responses from the Australian curriculum indicated explicit descriptive, but not symbolic, generalization. Twenty teachers also participated in the study. Analysis of national curriculum content and task examples from each context, along with the teachers’ expectations of their students’ responses to the tasks and described teaching approaches for linear functions, led to our exploration of possible reasons for differences and similarities found among the responses. We suggest possible implications for teaching and learning linear functions and avenues for further research.

摘要

研究学生在不同年级和不同课程背景下对任务的反应可以提供将他们的理解与先前的学习经历和教学方法联系起来的见解。在本文中，我们讨论了来自三种课程环境（英语，澳大利亚和以色列）（n = 350）的学生在应对两个线性函数任务时如何关注中学不同水平上两个变量之间的函数关系的证据。我们发现，来自英语国家课程环境的学生在显示值表时，比其他同类人群更有可能只关注因变量。通过图形化模式概括任务，在来自以色列课程环境的学生回应中，没有发现无效的比例推理的例子，不同于英语和澳大利亚课程环境中的课程。在以色列八年级的八年级学生中，有很高比例的回答表明是象征性的概括，而澳大利亚课程的几项回答则表明了明确的描述性而非象征性的概括。二十名老师也参加了这项研究。分析来自各个上下文的国家课程内容和任务示例，以及教师对学生对任务的反应的期望以及所描述的线性函数的教学方法，促使我们探索了在响应中发现差异和相似之处的可能原因。我们建议对教与学线性函数和进一步研究的途径可能产生的影响。在以色列八年级的八年级学生中，有很高比例的回答表明是象征性的概括，而澳大利亚课程的几项回答则表明了明确的描述性而非象征性的概括。二十名老师也参加了这项研究。分析来自各个上下文的国家课程内容和任务示例，以及教师对学生对任务的反应的期望以及所描述的线性函数的教学方法，促使我们探索了在响应中发现差异和相似之处的可能原因。我们建议对教与学线性函数和进一步研究的途径可能产生的影响。在以色列八年级的八年级学生中，有很高比例的回答表明是象征性的概括，而澳大利亚课程的几项回答则表明了明确的描述性而非象征性的概括。二十名老师也参加了这项研究。分析来自各个上下文的国家课程内容和任务示例，以及教师对学生对任务的反应的期望以及所描述的线性函数的教学方法，促使我们探索了在响应中发现差异和相似之处的可能原因。我们建议对教与学线性函数和进一步研究的途径可能产生的影响。