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Which Type of Rational Numbers Should Students Learn First?

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Abstract

Many children and adults have difficulty gaining a comprehensive understanding of rational numbers. Although fractions are taught before decimals and percentages in many countries, including the USA, a number of researchers have argued that decimals are easier to learn than fractions and therefore teaching them first might mitigate children’s difficulty with rational numbers in general. We evaluate this proposal by discussing evidence regarding whether decimals are in fact easier to understand than fractions and whether teaching decimals before fractions leads to superior learning. Our review indicates that decimals are not generally easier to understand than fractions, though they are easier on some tasks. Learners have similar difficulty in understanding fraction and decimal magnitudes, arithmetic, and density, as well as with converting from either notation to the other. There was too little research on knowledge of percentages to include them in the comparisons or to establish the ideal order of instruction of the three types of rational numbers. Although existing research is insufficient to determine the best sequence for teaching the three rational number formats, we recommend several types of research that could help in addressing the issue in the future.

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Acknowledgements

The research reported here was supported in part by the Institute of Education Sciences, US Department of Education, through Grants R305A150262 and R324C100004:84.324C, Subaward 23149 to Carnegie Mellon University, in addition to the Teresa Heinz Chair at Carnegie Mellon University and the Siegler Center for Innovative Learning and Advanced Technology Center, Beijing Normal University. The opinions expressed are those of the authors and do not represent views of the Institute or the US Department of Education.

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  1. Department of Psychology, Carnegie Mellon University, Baker Hall, 5000 Forbes Ave, Pittsburgh, PA, 15213, USA

    Jing Tian & Robert S. Siegler

  2. Siegler Center for Innovative Learning and Advanced Technology Center, Beijing Normal University, Beijing, 100875, China

    Jing Tian & Robert S. Siegler

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Tian, J., Siegler, R.S. Which Type of Rational Numbers Should Students Learn First?. Educ Psychol Rev 30, 351–372 (2018). https://doi.org/10.1007/s10648-017-9417-3

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