Maths and people: how is mathematical psychology useful to people?

15 November 2023

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Mathematical psychology focuses on the use of mathematical and computational models to accurately explain and predict human behaviour, including cognitive processes, social behaviour, personality, personal development, and mental health. This branch of psychology can be useful to people in many areas such as education, marketing, and mental health.


How is mathematical psychology used in education?

Mathematical psychology has contributed to education through the development of effective educational programs enabling learning through the use of interactive digital tools. Mathematical models of learning are able to formulate computational learning programs specifically tailored to each student’s individual needs and ability. An example is the Personalised System of Instruction (PSI), also known as the Keller Plan, developed in the mid-1960s by Fred S. Keller with J. Gilmour Sherman, Carolina Bori, and Rodolpho Azzian. The PSI is an individualised learning system using mathematical models of student aptitude to track statistical progress and provide additional support where necessary, mainly in higher education but also in primary and upper school. Its key elements are based on mathematical psychology, such as unit mastery, which requires students to learn a small quantity of information and pass a test with a certain percentage. If they do not pass the test, they must restudy the information and continue taking the test until they are deemed to have mastered the material. The PSI, and other similar systems, use mathematical psychology to design tests that are effective in measuring student mastery of units, and analyse data from the tests to identify areas where students need more support, and factors essential to student success, which can help improve the software and the progress made by students.

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How is mathematical psychology used in marketing?

Mathematical psychology uses mathematical models in marketing to help professionals predict how consumers will react to the release of products. Data analysis and mathematical-based research suggests that people are slower to make choices when they are faced with a greater number of options, and researchers can quantify this difference in reaction time to develop more effective ad campaigns. In addition, mathematical psychology aids marketing professionals in evaluating these ad campaigns with mathematical models of consumer behaviour. For example, Florida Atlantic University and collaborators developed and introduced a new mathematical innovation model generating qualitative and quantitative predictions of adoption trends of new products to improve their success rate upon release. Researchers labelled consumers as 1 of 4 different psychological profiles: the innovator (thought to make independent purchase decisions), early adopter, majority, or laggard, and assigned particular preferences for adoption trends based on these profiles to predict the sales data of 200 supermarket chain products across 4 years. The study suggests that different types of consumers seek different properties of adoption trends to inform their purchasing decisions, which can be formulated mathematically with provable predictions. Findings indicate evidence of these 4 different types of consumer behaviour, and, crucially, illustrate the usefulness in quantifying psychological behaviour in social contexts, combining maths with psychology.

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How is mathematical psychology used in mental health?

Mathematical psychologists study the way that mental health problems affect people’s behaviour and use maths to model methods used for prevention, diagnosis, and treatment. Mathematical models have been used to devise treatment interventions, evaluate treatments, predict patient outcomes, improve the design of clinical trials, personalise mental health care, and develop diagnostic tools for mental health disorders. For example, mathematical psychology was used to develop the Beck Depression Inventory (BDI), a multiple choice 21-item self-report questionnaire measuring characteristic attitudes and symptoms of depression. He employed mathematical methods when formulating the inventory, such as factor analysis for item selection, which identified the underlying dimensions of depression as affective, cognitive, motivational, and somatic symptoms, validation of the BDI, and scaling. As a quantitative assessment of depression, the BDI has a numerical scoring scale from 1 to 63 as a total score for people to compare their own against and assign a level to. Still widely used today, it has helped people recognise their depression, provided many with a sense of perspective about their condition, and has also enhanced healthcare professionals’ understanding of depression as a disorder significantly impacted by patients’ own thoughts and cognitions. This, and other diagnostic tools using mathematical models and methods, allow for better diagnosis of mental health disorders and provide the opportunity for differentiated treatment.

To conclude, mathematical psychology is a vital discipline beneficial to people in a wide range of fields. Its study of the human mind, patterns of behaviour, statistical analysis, and mathematical models makes it a useful branch of psychology applicable to education, marketing, and mental health, whether it be through the development of interactive educational online tools, forecasts of retail sales, or the diagnosis of mental health disorders. Hopefully, as it continues to evolve and develop, in the future, many more people will be able to benefit from the inventions of this invaluable marriage of psychology, and maths.

By Amber, NLCS Student

This article was taken from the latest edition of Tangents which you can read here.


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