This paper reflects the research and thoughts of a student at the time the paper was written for a course at Bryn Mawr College. Like other materials on Serendip, it is not intended to be "authoritative" but rather to help others further develop their own explorations. Web links were active as of the time the paper was posted but are not updated.
2002 Third Paper
There are many theories about the nature of intelligence. The formal definition of intelligence is "the capacity to acquire and apply knowledge." One aspect or kind of intelligence, according Dr. Howard Gardner, founder of the multiple intelligence theory, is spatial intelligence(1). Spatial intelligence is one amongst eight kinds of intelligence. The most common description of spatial intelligence is the ability to be able to recreate one's visual experience and reasoning about shape, measurement, depiction and navigation.
Spatial intelligence might be one of less familiar kind of intelligence, however it has wide implications in many academic and professional disciplines. It is extremely important in disciplines such as mathematics and computer science. Spatial Intelligence also accounts for the thinking process of engineers, architects, designers, sculptors and inventors. This paper is an over all comprehension of spatial reasoning and why it is important in learning and problem solving, it is an investigation into what spatial reasoning is and its role in learning and cognition. This paper will also address the neurobiology of spatial reasoning and discuss the specific areas and organization of the brain that accounts for spatial intelligence.
There are many theories and models attempting to define spatial reasoning. The first model is called the MV/PD model. According to this model, spatial representation consist of two parts. The first is a metric diagram, which includes quantitative information and provides a substrate, which can support perceptual-like processing. The second part of the model is termed place vocabulary, which makes explicit qualitative distinction in shape and space relevant to the current task (2). Therefore, spatial reasoning is not just visualization of objects and space but also the ability to take qualitative information and then transformation them to spatial representations so that it can be better understood.
Spatial reasoning is useful in physics, math and computer science and can be applied to different industries. Engineers use graphs to express complex relationships, such as temperature-entropy or pressure volume plots, Often these graphs are sketches, intended to convey qualitative information about the shapes of curves and relative magnitudes rather than precise numerical values(2). Therefore, spatial reasoning is an essential part of the thinking process of scientist and engineers because they need to understand and interpret qualitative information in graphs and models in order to gain critical understanding of the problems at hand.
What exactly is the process through which humans use spatial reasoning to solve problems?
Another theory addressing spatial intelligence is called the mental model theory,
developed by Johnson-Laird and Byrne. According to the mental model theory, first, the person constructs a mental model of the premises of the problem. Second, the person draws a conclusion from the model that is informative. The model helps to extract information that is not directly asserted by the premises. Third, the participant tries to construct another alternative model to try and contradict the initial one, if they cannot construct an alternative model, then they take the first one to be correct(3). According to the mental model theory, reasoning is guided by a 'search for counter –examples procedure." However, if the search of counter examples takes too much working memory capacity, then the process of searching for counter examples to get the right answers will come to a halt. Also, the mental model theory predicts that problem difficulty increases as the number of different possible mental models increases.
To illustrate how mental models can be used to solve a problem and why the problem difficulty increases as the number of different possible model increases, consider these two problems.
1. A is on the right of B
2. C is on the left of B
3. D is in front of C
4. E is in front of B.
What is the relationship between D and E?
1. B is on the right of A.
2. C is on the left of B.
3. D is in front of C.
4. E is in front of B.
What is the relationship between D and E?
Both of the problem is expressed in the same number of expressions however, there is only one model for the first problem which looks like this. C B A
However, for the second problem there are two models: C B A and A C B
D E D E
For the second problem the answer is the same, D is on the left of E regardless of the models. However, according to the result from studies on subjects trying to solve both problems, 70% of participants get the first one right where as only 46% get the second right. This result is consistent with the mental model theory and its prediction that the problem gets more difficult if there the number of possible model increases.
According to the last two paragraphs, spatial intelligence is an essential part of how we absorb and process problems. If this is true, then would it make sense to say that spatial reasoning has an overall effect on intelligence or IQ? IQ, or intelligence quotient is found to have a direct correlation with RT, which is the decision time. The equation for RT is RT=mx+c. This equation is called Hick's law, according to equation, IQ is proportional to the slope m, which is a representation of the processing speed; m is lower in individuals with higher IQ(4). A challenge to this idea is that slope relates only weakly to IQ and that the absolute RT correlates better to IQ. This implies that IQ correlates better with choice RT or the c intercept. Studies had also shown that when the choices or stimulus is increased in complexity and spatial representations of the choices, the Hick's equation can produce the same correlation of IQ to RT without having to focus on just m, the processing speed. Therefore, it is reasonable to conclude that spatial effect added to the experience has a significant influence on RT and in turn also on IQ and that "effects of spatial attention requirements on choice RT may provide a better measure of intelligence than just measuring the processing speed (4)."
Now we know that spatial reasoning is significant to the way we learn and has a direct relationship in reference to intelligence, it is also important to look into the brain and the specific region of the brain that accounts for spatial intelligence. In order to detect the area of the brain that is responsible for spatial awareness scientists conduct studies on individuals who are deficient in spatial detection. When four individual with left lesion and another four with right lesion were asked to replicate a model of a house. Drawings of the right-lesion individuals show spatial disorganization, left hemisphere neglect and lack of perspective(5). This study indicates that spatial awareness is probably a function of the right hemisphere of the brain.
A recent article in nature confirms this presumption. According to the article, at first the area of the brain though to be responsible for spatial awareness is the posterior parietal lobe. However, by studying individuals with "pure" spatial defection rather than spatial defection along with deficiencies in other areas indicates that spatial awareness is " largely confined to the right superior temporal cortex, a location topographically reminiscent that of language on the left (6)
Since the brain needs to process problems involving space and dimension, it is not absurd to say that the functional brain structure can be described in geometric terms. In the book Brain Theory: Spatio-temporal aspects of brain function, the author argues that the brain exist primarily in space and the function of the brain, especially in the "front end" or visual system, can be viewed and understood geometrically(7). This notion of the brain as a geometry engine demonstrates that the way information is processed in the brain adheres to the structure of the brain. The brain is not purely logical and linear, therefore, when data or information is passed through it, it does not solved the problem in linear steps, it makes more sense to perceive the brain as an organ that naturally stores the information in different areas and then constructs models from the data and correlates different data according to the models in order to derive an answer or solution.
So far we've discuss spatial intelligence and its role in cognition and problem solving, we also discuss the neurobiological aspects of spatial reasoning and found out what areas of the brain accounts of spatial awareness. At the beginning of the paper, spatial intelligence is only one kind of intelligence, however, as I found out more about the topic, I am convinced that spatial reasoning is not separate from other kind of intelligence but is a part of many thinking processes. No matter what the problem at hand is, it always helps to use spatial representation such as pictures, graphs models and metaphors, if not written physically, than envisioned mentally to better understand the problem and come to a valid conclusion. As I finish this paper, I begin to view the multiple intelligence theory in a different light, instead of perceiving spatial intelligence or any other kind of intelligence as completely different entities unrelated to each other, I start to ponder the possibility that intelligence is consisting of all kinds of thinking processes that are interrelated and interactive to prompt the individual to absorb and process information in the most efficient way.