Mathematics and Psychology

Psychology is the scientific study of the relationships between mental processes, emotions, and behavior. Mathematics and psychology are linked in three major ways. First, psychologists study mathematical cognition, i.e., the brain's development, acquisition, and application of mathematical skills. Second, psychologists investigate people's feelings and attitudes regarding mathematics. Third, psychologists use mathematics, particularly statistics, as a professional tool to quantify and analyze their scientific findings.

Psychologists working in the field of mathematical cognition study how humans process information, interpret mathematical symbols, and develop and use strategies to solve mathematical problems. For example, these skills are particularly important for so-called "word" problems, where written descriptions must be translated into equations. Most students consider "word" problems more difficult to solve than other types of math problems. This is because "word" problems require a variety of skills from the brain, including the ability to read and comprehend the meaning and context of the words, the ability to perceive and define the mathematical problem, the ability to assign mathematical symbols to unknown variables, and finally, the ability to apply problem-solving strategies and calculate the correct answer.

Mathematical cognition is a very important field in psychology. It benefits scientists and doctors studying the brain, and it helps educators develop better teaching methods for mathematics. In addition, its study is crucial to the development of "smart" computers, neural networks, fuzzy logic, robots, and artificial intelligence.

Psychologists also study how people feel about mathematics, because a person's feelings about a subject influence their willingness to learn and use it. For example, cultural and gender differences in attitudes about mathematics affect test scores. Another area receiving a lot of attention is called math phobia or math anxiety. Math phobia is a fear of mathematics. People with math phobia become so uncomfortable and anxious when confronted with mathematical tasks that they can experience physical symptoms including increased heart rate, nervous stomach, and breathing difficulties that prevent them from concentrating and learning. These feelings have been traced to a variety of sources, including negative experiences in the class room, poor self-image, lack of appreciation for the application of mathematics to "real life," and shyness that prevents asking questions.

The third major link between psychology and mathematics is that psychologists use mathematical and statistical tools to quantify and analyze their research findings. This use is called psychometrics and arises from the application of the scientific method in psychology, i.e., a systematic method of data collection, hypothesis development, and experimental testing that can be duplicated and verified by other scientists.

One example of psychometrics is the Intelligence Quotient (IQ) test, a standardized test that measures a person's relative intelligence. An IQ score is a relative measurement; it is compared to a reference IQ of 100 for the average score. IQ scores for a large population are an example of a statistical function called the normal distribution. Normal curves or Gaussian curves are the familiar bell-shaped curves in which measurements are graphed along the x-axis and frequency is graphed along the y-axis. The majority of IQ scores fall in the wide part of the curve near the mean value of 100. As scores deviate negatively or positively from 100, they decrease in frequency.

Q methodology is a type of analysis used in psychology to measure and quantify the feelings of a group of people regarding a particular subject. For example, a large group of students could be asked the following question: "How do you feel about your school?" A wide variety of answers would be collected ranging from "I hate it" to "I love it" with many opinions in between pointing out good and bad qualities of the school. This entire opinion set is called the concourse. From it, a limited number of opinions (the Q sample) would be selected that represent the spectrum of responses. During the next interview, the students would read the Q sample and rank their level of agreement with each opinion using a scale of -4 to +4, where -4 indicates strong disagreement and +4 indicates strong agreement with the opinion. This process is called Q sorting. The resulting numerical data can be analyzed using statistical functions to provide a mathematical description of student opinions about their school.

Common statistical concepts and tools studied and used by psychologists include correlation, regression, sampling distributions, probability density functions, and factor analysis.