Cognitive Development Research
My research in this area is on children’s development of numerical concepts, focusing primarily on children’s early concepts of ratios.- Spatial Configuration Effects on Ratio Reasoning in Young Children
- Young Children Solve Numerical Ratio Problems with an Intervention Based on Intuitive Knowledge
Spatial Configuration Effects on Ratio Reasoning in Young Children
Previous research indicated that children could solve spatial ratio problems earlier than they could solve numerical ratio problems. In this study I examined whether young children could solve numerical ratio problems if they were presented with spatial cues (DeLong & Sophian, 2001). I presented young children (5- and 7-years-old) with numerical ratio problems with and without spatial cues in two studies. In the first study, children were given missing value proportional reasoning problems in which they were given three parts of the ratio and had to generate the fourth part (e.g., 1:2 = 2:x, 1:3 = 2:x). The children were told the stimuli were plates of food for two teddy bears and their task was to give the second bear the same mix of red and blue food pieces that the first bear had on his plate (food of one color was already on the second bear’s plate). The children could solve the numerical ratio problems with the benefit of spatial cues (but not without spatial cues).
I conducted a second experiment in which the presentation method changed from one in which the children had to generate the answer to a match-to-sample task, and the result was the same. The idea that spatial relations facilitate numerical proportional reasoning has important implications for both developmental theory and mathematics instruction. Children’s ability to perform well on proportional reasoning problems that employ spatial stimuli or spatial cues provides support for theory that children have an intuitive sense of the ratio concept that seems to originate in the perception of spatial relations between and within objects. Ratio knowledge may be similar to knowledge about counting or addition and subtraction in that there are precursors to numerical development.
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| 7-year-old solving a series of match-to-sample ratio problems |
Young Children Solve Numerical Ratio Problems with an Intervention Based on Intuitive Knowledge
I conducted a study that tested the possibility that young children could be taught to solve numerical ratio problems given an intervention designed to evoke protoquantitative (spatial) ratio knowledge (DeLong & Sophian, 2003). I used children’s understanding of spatial ratios to teach them how to solve numerical ratio problems. I tested 5- and 7-year-olds and a comparison group of 11-year-olds. The training method involved eliciting spatial ratio reasoning, and then showing the children a simple numerical method to achieve the same answer. Both the 5- and 7-year-olds were able to solve numerical ratio problems without spatial support by the end of the study, and the 7-year-olds performed as well as the 11-year-olds who received no training. The results of my research suggest it is possible to facilitate children’s proportional reasoning at an early age. This line of work may result in a new and effective teaching tool for educators. 
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| 7-year-old receiving
training to solve numerical ratio problems |