Understanding place value and early math achievement

In a recent study of Chinese first-graders, researchers Connie Suk-Han Ho and Fanny Sim-Fong Cheng, Chinese University of Hong Kong, examined whether specific training in place-value concepts would improve arithmetic achievement. The effectiveness of the training was deter-mined by testing the children’s understanding of place-value concepts and arithmetic performance before and after training.

Sixty-nine first-graders were assessed on intelligence, place-value understanding and addition and subtraction skills. Children were divided into above- and below-average achievers and matched for age, IQ and gender. Half of the below-average students received training in place-value concepts while the rest served as a control group.

Five weekly one-hour training sessions were given to the low-achieving experimental group. Each session involved direct instruction, demonstrations, games, classwork and homework. Beginning sessions stressed counting orally and with objects and bundling objects in groups of 10.

Significant impact on low achievers

Follow-up testing after training revealed that differences between the experimental and control groups in addition, subtraction and place-value understanding were significant, even after controlling for IQ. The low-achieving children who received training showed the greatest growth in place-value understanding and addition skills. Gains were smaller for subtraction. After five weeks, the trained group of low achievers had caught up with the high-achieving group in place-value understanding, but not in addition or subtraction.

These results show that place-value understanding aids the development of arithmetic skills. Just five sessions of training in place-value concepts significantly improved the arithmetic performance of poor achievers at the first-grade level. These researchers offer the following guiding principles for instruction in place-value concepts: Children must understand the connections between how quantities are represented in the physical world and how these physical representations are related to the ways in which we speak and write numbers.

Physical manipulatives are effective in helping to develop understanding. Bundling in units of 10, 100 and 1000 (10 straws tied together, 10 bundles in a glass, 10 glasses on a tray) encourage multi-unit rather than unitary representation.

After the teacher has established a connection between physical and oral representations, this must be linked to the written format children learn at school. Written numerals can be placed next to the physical manipulatives.

When trading objects between groups, it is important to emphasize the reversibility of the trading process.

International differences and language

The short duration of the training period may have been the reason that these low achievers only caught up to the good math students in their understanding of place-value concepts but not in their addition and subtraction skills. Five hours is probably not sufficient time to assimilate newly acquired place-value concepts and apply them to arithmetic problems. Given more time, the arithmetic skills of these below-average students are expected to continue to improve relative to the skills of above-average students. Further research is needed to demonstrate this.

International math tests show significant variations in mathematical skills between countries. Asian students outperform students in most western countries, including the United States. Differences in curricula are often cited as one reason for this inequality. However, when examining the performance of the youngest school children, we still see higher achievement among Asian students. Young Asian students perform better on counting, number representation, addition and subtraction tasks. These differences are not easily explained on the basis of curricula, since children have been in school a relatively short time.

Previous studies have found that number words in a language can affect memory for numbers, and that the regularity of a number-naming system can affect the cognitive representation of numbers and understanding of place-value concepts. For example, the number 12 corresponds directly to the base-10 system when it is spoken in Chinese (and other Asian languages) as “ten-two” but not when spoken as “twelve” in English. In Asian countries, early instruction (at home and at school) supports this understanding by emphasizing the number 10 as a counting unit and using 10 as a base unit in addition and subtraction.

If this makes it easier for most Asian children to understand place-value concepts in the primary grades, it may be one factor that gives them a strong start in arithmetic. If western students don’t have this language advantage, and if, as this study shows, students’ arithmetic skill depends upon adequate understanding of place-value concepts, then effective instruction in place-value concepts is particularly important.

“Training in Place-Value Concepts Improves Children’s Addition Skills” Contemporary Educational Psychology ,Volume 22, October 1997 pp. 495-506.

Published in ERN April 1998 Volume 11 Number 4

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