Applying Cognition-Based Assessment to Elementary School Students' Development of Understanding of Area and Volume Measurement

A Learning Progression for Geometrical Measurement in One, Two, and Three Dimensions

“…The idea of using a larger unit instead of a smaller unit in measurement is referred to as the concept of composite units, an iterable set of individual, single units (Reynolds & Wheatley, 1996; see also Battista, 2004;Battista & Clements, 1996;Stephan & Clements, 2003). In their study on elementary-school students' strategies and errors in counting the number of unit cubes in rectangular prisms built from the unit cubes, Battista and Clements (1996) found that students conceptualized a column or row of cubes and a horizontal or vertical layer of cubes as iterable composites.…”

“…Here we briefly introduce the LP of Barrett et al (2006) for perimeter in terms of one-dimensional length measurement and the LPs of Battista (2004) for area and volume measurement as the most recent ones drawn from their own empirical research on students' developmental sequence of geometrical measurement understandings within each dimension. Barrett et al (2006) examined 38 second through 10th graders' development of levels of measurement understanding observed during two fixed-perimeter measurement tasks (one for a rectangle and the other for a triangle), asking students to find all possible cases of a rectangle/triangle with a perimeter of 24 units.…”

“…• including particular content in a certain level, such as adding the idea of space filling and measurement estimation with inconsistent/incorrect units to Level 2, or proportional reasoning related to unit conversion to Level 5; • presenting the idea of correct unit iteration and use of composite units as two sublevels of Level 3, such as Level 3 in which correct iteration of measurement units appears and Level 3.5 in which composite unit iteration appears; and • for Level 4, reframing the meaning of efficient composite unit for linear measurement in comparing to the concept of maximal composite units for area and volume measurement (i.e., for area, rows or columns of squares; for volume, layers of cubes, Battista, 2004). …”

“…This level may be related to Clements and Battista's (1992) van Hiele Level 0 for measurement: pre-recognition and Mason's (1998) Clements and Battista's (1992) van Hiele Level 0 for measurement: pre-recognition, Mason's (1998) (2) Has insufficient unit conception (i.e., partitioning with inconsistent units) and is not using a fixed (equal-sized) volume unit (Battista, 2004;Battista & Clements, 1996).…”

The impact of Google SketchUp on spatial ability and 3D geometric thinking of 7th grade students in volume measurement of solid figures

“…즉, 기하 문제를 해결하는 과정에서 사용하는 모 든 수학적 지식과 3차원의 도형을 상상하고 조작하는 능 력을 이용하여 해결해 가는 모든 활동을 의미한다. Pittalis & Christou(2010) (Battista et al, 1996) [ Table 1] Students' reasoning patterns in spatial structuring (Battista et al, 1996) 4) 측정 3차원 공간 기하적 사고 중의 '측정' 사고는 입체도형 의 겉넓이 또는 부피를 계산하는 활동을 의미한다 (Pittalis & Christou, 2010 Battista, 2004) [ Table 2] Levels of sophistication in students' understanding of volume measurement (Battista, 2004) 3. 공간능력과 공간 기하적 사고의 관계 Pittalis et al(2010) The purpose of the study is to examine how effects of activities using Google SketchUp on students' spatial ability and 3D geometric thinking in measuring the volume of solid figures.…”