In the basic understanding of measurement, students are expected to be able to subdivide a given whole into a unit and then change the position of that unit along the entire length of the whole. These basic operations of subdivision and change of position are related to the more formal operations of partitioning and iterating. In the context of fractions, partitioning and iterating play a fundamental role in understanding fractions as measures, where students are expected to partition a whole into an iterable unit. In the context of angle measurement, students are expected to measure angles as a fractional amount of a full rotation or a circle, by partitioning the circle into a unit angle and then iterating that unit angle to find the measure of the given angle. Despite this link between measurement, fractions, and angles, research suggests that there is a disconnect between students' concepts of measurement and geometry concepts, including angle and angle measurement. Therefore, one area of study that might help us understand this disconnection would be to investigate the relationship between students' concepts of measurement and their concepts of angle measurement.
This current study documents sixth, seventh, and eighth grade students' measurement schemes for fractions and their quantifications of angularity, and then investigates the relationship between them. This research is guided by the following question: What is the relationship between middle school students' measurement schemes for fractions and their quantifications of angularity? Results indicate that the majority of students involved in this study do not possess a measurement concept of fractions nor a measurement concept of angularity. However, these results demonstrate that there is a relationship between students' measurement schemes for fractions and their quantifications of angularity. It is concluded that students who construct more sophisticated fraction schemes tend to construct more sophisticated quantifications of angularity.
Doctor of Philosophy
Although the concepts of measurement, fractions, and angle measurement are related, research suggests that there is a disconnect between students' concepts of measurement and geometry concepts, including angle and angle measurement. Therefore, one area of study that might help us understand this disconnection would be to investigate the relationship between students' concepts of measurement and their concepts of angle measurement. This current study documents sixth, seventh, and eighth grade students' understandings of measurement, as indicated by their fraction schemes, and angle measurement, as indicated by how they quantify angularity or the openness of an angle. This study then investigates the relationship between them. This research is guided by the following question: What is the relationship between middle school students' measurement schemes for fractions and their quantifications of angularity? Results indicate that the majority of students involved in this study do not possess a measurement concept of fractions nor a measurement concept of angularity. However, these results demonstrate that there is a relationship between students' measurement schemes for fractions and their quantifications of angularity. It is concluded that students who construct more sophisticated fraction schemes tend to construct more sophisticated quantifications of angularity.