Young children's unit understanding in length measurement : structure, cognitive underpinnings, and relation to spatial measurement

Abstract

Measurement is an important domain of mathematics. Traditional measurement curriculum and instruction emphasize teaching children how to use measurement tools (e.g., rulers) while ignoring their conceptual knowledge about measurement. As a result, many children cannot understand what their measurement results exactly mean and are not able to respond flexibly to unfamiliar measurement problems that cannot be solved through the application of procedural skills. There is emerging research suggesting that children’s understanding of unit concepts in measurement lays a critical foundation for their future measurement achievement. The focus of the present research is on young children’s unit understanding in length measurement (UULM). Three studies were conducted to address the following research gaps: (1) the unclear structure of young children’s UULM and the lack of appropriate instruments to validate its structure, (2) the few studies that examine the cognitive-linguistic antecedents of UULM, and (3) the understudied relations between UULM and young children’s achievement in spatial measurement of length, area, and volume. Study 1 aimed to develop a test of young children’s UULM and validate its structure. Participants were 333 Chinese children, including 88 in the pilot study and 245 in the main study (age: M ± SD = 75.01 ± 5.86 months). The results showed that the newly developed UULM test was a reliable and valid instrument for young children who attended pre-primary programs. They also provided support for a five-dimensional structure of UULM that included partitioning, unit iteration, identical unit, accumulation of distance, and the relation between unit size and unit number. Study 2 examined how fundamental cognitive-linguistic skills were related to children’s early acquisition of UULM. A total of 208 Chinese preprimary children (age: M ± SD = 67.26 ± 5.15 months) participated. It was found that early cognitive-linguistic skills (i.e., visual-spatial skills, executive function, and receptive vocabulary) were associated with young children’s later acquisition of UULM, even after controlling for their prior performance in UULM, age, sex, and family socioeconomic status. Study 3 investigated the reciprocal relations between young children’s UULM and their achievement in spatial measurement of length, area, and volume, based on the same participants as those in Study 2. The results showed reciprocal longitudinal relations between children’s UULM and spatial measurement achievement even after controlling for their cognitive-linguistic skills and demographics. The present research makes significant contributions to the existing body of knowledge. First, it represents the first endeavor to develop a test of UULM and validate its structure. The test will be useful for researchers and educators who are interested in assessing young children's UULM. Second, the research clarifies the role of cognitive-linguistic skills in young children’s UULM and suggests that early cognitive-linguistic skills provide a basis for children’s development of UULM. Third, the present research is the first of its kind to examine the reciprocal relations between children’s UULM and achievement in spatial measurement. The findings highlight the importance of UULM as the building block of children’s spatial measurement achievement while simultaneously suggesting that UULM may be refined as children acquire more measurement experiences. (500 words)