Ulrich Catherine, Wilkins Jesse L M
1School of Education, Virginia Tech, War Memorial Hall, RM 306, 370 Drillfield Drive, Blacksburg, VA 24061 USA.
2School of Education, Virginia Tech, War Memorial Hall, RM 300C, 370 Drillfield Drive, Blacksburg, VA 24061 USA.
Int J STEM Educ. 2017;4(1):23. doi: 10.1186/s40594-017-0085-0. Epub 2017 Oct 24.
Students' ability to construct and coordinate units has been found to have far-reaching implications for their ability to develop sophisticated understandings of key middle-grade mathematical topics such as fractions, ratios, proportions, and algebra, topics that form the base of understanding for most STEM-related fields. Most of the related research on unit coordination relies on time-intensive clinical interviews and teaching experiments. In this study, we investigate the work of 93 sixth-grade students on a written assessment containing whole number and fraction contexts using both continuous and discrete quantities, and how this work can be used to assess stages in students' construction and coordination of units. Our investigation is guided by the following general research questions: (1) What forms of written work evidence the construction of and operation on composite units (units made up of other units)? (2) How does the categorization of students based on responses from a written assessment compare to written performance on a set of tasks conveying a continuous whole number multiplicative context?
We documented the different ways students represented composite units in their written work. In particular, student written work on tasks that included figurative unit items provided the greatest variety of evidence regarding students' construction of and operation on composite units. However, written evidence from partitioning tasks did not seem as promising for distinguishing student stages. Students' performance on decontextualized bar tasks involving continuous quantities was found to be consistent with students' level of unit coordination based on written work providing evidence for the validity of stage categorizations.
Our findings shed light on the affordances and constraints associated with particular stages in unit construction and coordination that a student brings to bear on tasks provided in a formal, written assessment. These findings provide promising evidence for scaling up the assessment of students construction and coordination of units through the use of written assessments instead of time-intensive clinical interviews.
研究发现，学生构建和协调单位的能力对他们深入理解关键的初中数学主题有着深远影响，这些主题包括分数、比率、比例和代数，它们是大多数与STEM相关领域理解的基础。大多数关于单位协调的相关研究依赖于耗时的临床访谈和教学实验。在本研究中，我们调查了93名六年级学生在一份包含整数和分数情境（使用连续和离散量）的书面评估中的表现，以及这项工作如何用于评估学生在单位构建和协调方面的阶段。我们的调查以以下一般研究问题为指导：（1）书面作业的哪些形式证明了复合单位（由其他单位组成的单位）的构建和运算？（2）根据书面评估的回答对学生进行分类，与在一组传达连续整数乘法情境的任务中的书面表现相比如何？
我们记录了学生在书面作业中表示复合单位的不同方式。特别是，学生在包含具象单位项目的任务上的书面作业提供了关于学生对复合单位的构建和运算的最多样化的证据。然而，来自分割任务的书面证据在区分学生阶段方面似乎不太有前景。发现学生在涉及连续量的去情境化条形任务上的表现与基于书面作业的单位协调水平一致，这为阶段分类的有效性提供了证据。
我们的研究结果揭示了与单位构建和协调的特定阶段相关的优势和限制，学生在正式的书面评估中应对任务时会体现这些优势和限制。这些发现为通过使用书面评估而非耗时的临床访谈来扩大对学生单位构建和协调的评估提供了有前景的证据。
