Dr. Bailey and Dr. Zhou, Spring, 2013.

**Research Programs**

**1. National, developmental, and individual differences in fraction knowledge.**

**Researchers: Drew Bailey, David Braithwaite, Jiaxin Cui, Ruizhe Liu, Jing Tian, Yunqi Wang, Yiyun Zhang, Xinlin Zhou, and Robert Siegler.**

**Synopsis: **In Western samples, earlier knowledge of fractions uniquely predicts later mathematical achievement and algebraic proficiency. The SCIL is currently conducting studies in China that parallel those conducted in Western countries and is assessing how Chinese and American children learn about fractions.

The goals of these projects are to identify the strengths and weaknesses of Chinese and American students’ fraction knowledge, to compare methods for teaching fractions in the two countries, and to use this information to develop interventions to improve fraction knowledge among students in China and the U.S.

In order to gain a deeper understanding into these issues, in 2016, David Braithwaite analyzed the distribution of fraction arithmetic problems in Chinese and American mathematics textbooks. Both countries’ textbooks revealed similar “spurious associations” between arithmetic operations and mathematically-irrelevant features of operands. In an experiment conducted by David in Pittsburgh and Beijing (in cooperation with Dr. Zhou and other SCIL members), both U.S. and Chinese middle school students’ associations between operations and operands paralleled those found in the textbooks.

However, these spurious associations appear to have a greater negative impact on U.S. than on Chinese students’ problem solving. Future research will explore the reasons for this difference.

Some more general issues about rational numbers are why there are three rational number notations (i.e., fractions, decimals, and percentages) and when people prefer to use each of them. To address these issues, in 2016, Jing Tian conducted parallel experiments in Pittsburgh and in Beijing with the help from SCIL members on college students’ preference of using each rational number notation for ratio relations.

These experiments suggest that percentages are the preferred notation for representing ratios whose exact values are difficult to determine (e.g., ratios in continuous quantities or in discrete sets involving a large number of elements). In contrast, fractions are the preferred notations for representing exact ratios (e.g., in discrete sets involving a small number of elements). Importantly, U.S. and Chinese students exhibited similar preference despite their different educational and cultural background.

During the spring of 2013, Drew Bailey visited SCIL and was hosted by SCIL members at Beijing Normal University. While on site, Drew and other researchers worked together collecting data for the study, and were able to discuss and exchange ideas about how best to increase fraction understanding in children from all cultures.

This ongoing cross-cultural research project promises to bring to light different ways in which educators can assist all children to understand frations in a meaninful way, and to positively contribute to their mathematical development.

**2. Neural correlates of fraction and whole number.**

**Researchers: Jiaxin Cui, Xiaodan Yu, Xinlin Zhou, and Robert Siegler**

**Synopsis:** This project explores neural correlates of understanding and processing of fraction and whole number magnitudes. We hypothesized greater activation in the parietal and prefrontal cortex for processing fraction than whole number magnitudes because of the greater complexity of estimating fraction magnitudes and the greater number of strategies that could be used with fractions.

**3. Linear number board games for low-income preschoolers of China.**

**Researchers: Fang Wang, Hui Zhao, Xinlin Zhou, and Robert Siegler**

**Synopsis:** SCIL is running a project examining the effects of playing linear number board games on the mathematics understanding of low-income preschoolers of China. This intervention study has three main goals: to examine the effects of the linear number game on Chinese children, to explore whether playing the linear number board game has larger or smaller effects on Chinese than American preschoolers, and to explore whether kinesthetic manipulations of the tokens during the game influence the amount of learning.