Children’s unit concepts in measurement: a teaching experiment spanning grades 2 through 5

Abstract

We examined ways of improving students' unit concepts across spatial measurement situations. We report data from our teaching experiment during a six-semester longitudinal study from grade 2 through grade 5. Data include instructional task sequences designed to help children (a) integrate multiple representations of unit, (b) coordinate and group units into higher-order units, and (c) recognize the arbitrary nature of unit in comparison contexts and student's responses to tasks. Our results suggest reflection on multiplicative relations among quantities prompted a more fully-developed unit concept. This research extends prior work addressing the growth of unit concepts in the contexts of length, area, and volume by demonstrating the viability of level-specific instructional actions as a means for promoting an informal theory of measurement.

Children’s Conceptions of Area Measurement and Their Strategies for Solving Area Measurement Problems

“…Moreover, instructors must give careful attention to the non-formula-users' understanding of multiplication concepts, unit concepts for spatial measurement, and knowledge of 2-D geometry (e.g., Barrett, Cullen, Sarama, Clements, Klanderman, Miller, & Rumsey, 2011). When children have acquired the concept of the structure of rectangular arrays, instructors may remove the grids from the given figures to stimulate children to adopt other strategies instead of the counting-and-addition approach.…”

Measurement in Primary School Mathematics and Science Textbooks

“…Most research on measurement in mathematics education focuses on length [16,17] and area [18], with very few studies dealing with teaching and learning mass or volume. In one prominent article on mass, Clarke et al [19] put forward a theoretical structure describing the developmental progression of related skills: perception of and use of language to describe mass; comparing, sorting and matching objects by their mass; precisely quantifying object mass using units and measurement principles; choosing and using of units to estimate and precisely measure mass; and solving problems involving key skills and concepts relating to mass.…”

Movement and Song Idiom Traditional to Enhance Early Mathematical Skills: Gelantram Audio-visual Learning Media

“…Direct participation in measuring objects in class allows children to make their understanding of length measurements, and relates classroom learning to their own experiences in meaningful ways (Macdonald & Lowrie, 2011). Teacher instructional actions at a specific level can be a means of promoting informal measurement theory (Barrett et al, 2011). It takes a special learning environment design to teach children about measurement, which is the development of flexible strategies and adaptive, depending on the use of mathematical structures.…”