As adults, we represent and think about number, space, and time in at least two ways: our intuitive—but imprecise—perceptual representations, and the slowly learned—but precise—number words. With development, these representational formats interface, allowing us to use precise number words to estimate imprecise perceptual experiences.
In the study, 'Children dynamically update and extend the interface between number words and perceptual magnitudes', researchers Denitza Dramkin, PhD Student in the department Psychology at UBC, and Dr. Darko Odic, Assistant Professor in the department of Psychology at UBC, examine the extent to which children can use and deploy the logic of structure mapping across different perceptual magnitudes: Number, Length, and Area.
In this Q&A with Language Sciences, Denitza Dramkin touches on how we use perceptual representations of number, space and time, defines structure mapping, explores perceptual magnitudes and more!
Can you explain the differences between reasoning about number, space and time through the perceptual system, compared to using number words?
Our perceptual representations of number, space, and time are present from birth, are species- and culturally-universal, and are imprecise. For example, while it would be really easy to distinguish between a plate of 100 versus 200 cookies), it would be nearly impossible to visually tell apart 100 versus 101. On the other hand, number words are slowly learned, culturally-specific, and precise. With these tools, we could count and determine exactly which plate has "one-hundred" versus "one-hundred-and-one" on it using number words. This is one of the reasons why the interface between perceptual magnitudes and number words is so interesting! It's essentially a question of how do we link universal and readily available perceptual representations to culturally-specific tools?
How do people learn the generative link between language and perception?
This is something that a number of our projects have been working to explore! But one popular theory is that this link is initially based on forming item-by-item associations. For example, children might hear "three" and also see 3 items. After repeated experience, these become linked; children come to associate the number word "three" with a perceptual representation of 3 things. Eventually, with even more experience, children might realize that both number words and their perceptual experiences of number share some common structure (e.g., increases in one format lead to increases in another), and then use this to extend number words across their perceptual representations. For example, if they realize that the difference between "one" and "two" is the same as the difference between "two" and "four", then they could extend this logic to other experiences (e.g., "ten" and "twenty", "one-thousand" and "two-thousand", etc.).
Why are experiential long-term associative links not required for children to achieve a logical interface between number words and perceptual magnitudes?
While associative links might be important during the initial process of mapping number words to number perception, our data suggests that once children have formed a broader analogical link between number words to their perception of number, they can rely on this logic to attach number words to any perceptual experience. This includes other perceptual magnitudes (e.g., length, area). In our work, we found that once children learned what counted as "one" unit in any magnitude, they could readily estimate (e.g., guessing that a line is "five" units long), even if they had not learned how to measure length in school).
How are children able to apply novel mappings to established dimensions through structure mapping?
Structure mapping, in and of itself, is a process of creating analogical links between formats. Once children have formed this structural link between number words and perceptual magnitudes, it's just a matter of applying it to different contexts. In our study, children were introduced to a novel unit for number (i.e., 3 dots corresponded to "one toma"). Despite years of experience with the number word "one" being a single item, when children were shown a display with 15 dots, rather than responding with the brute number of dots on the screen (i.e., "fifteen"), they readily estimated using the novel unit provided (i.e., judging that there were "five tomas" rather than 15 dots). We think that the ease with which children could do this is because of structure mapping. Children formed a logical interface (i.e., structure mapping) between number words and number perception, and they relied on this logic even when the novel units conflicted with prior experiences. Once they understood that 3 dots is 1 toma, they understood that 15 dots is 5, 24 is 8, and so on.
Can you explain how children are able to readily estimate Length and Area, despite their difficulties understanding measurement units?
One reason why we think children could estimate in length and area in our task is because it allowed them to capitalize on the same logic as their interface between number words and number perception. When learning units of measurement, the process is often taught in a way that abstracts away from that logic. Children are taught to measure by segmenting and then counting the segments (e.g., 1 foot is made up of 12 inches). However, children often struggle with sequential and equal segmentation. For example, when children are given a line and asked to draw out one inch segments beneath it to determine its length, it's very common for them to draw segments varying in size and even stack segments on top of each other. At the same time, a large body of research suggests that children can reason about ratios and proportions early on in development, long before they're taught these concepts in school. Our task could have easily lent itself to making ratio-based judgements. For example, once children learned what "one" unit of length looked like, and they saw something that appeared 5 times as long, they just needed to respond with "five". By capitalizing on children's intuitions and abilities that children already possess, including the ability to reason about ratios, even the youngest children in our sample were able to readily estimate length and area.
Click here to access the full study.
Written by Kelsea Franzke