School design

Summary: Principles of geometry affect school design and mathematical models of risk may help identify safety issues.

When people think of mathematics in schools, most probably envision the teaching and learning of mathematics that occurs inside classrooms. However, there are many aspects of twenty-first century schools that depend on mathematics. For example, the transition of school design from one-room schoolhouses that were common in the nineteenth century, through the often rectangular and symmetric classroom buildings of the latter nineteenth and early twentieth centuries, to the open-plan schools initiated in the 1950s, to twenty-first century schools that consider contemporary concerns about renewable energy, technology, accessibility, and safety. Changes in teaching philosophies over time, such as loop education and emphasis on science, technology, engineering, and mathematics (STEM) education principles in the lower grades, led to some of these changes, as did studies on tragedies like the 1999 shootings at Columbine High School and other deadly school shootings throughout the first decades of the twenty-first century. Mathematics principles can be used to map the flow of students to and from classes, optimize locker placement and access, build accommodations and accessibility for students with disabilities, and plan for athletic facilities and other non-classroom spaces. These applications are increasingly important as schools seek to educate students to live and work within the rapidly changing economies, technologies, and environments of the twenty-first-century global society. Other studies may determine whether to retrofit old buildings or construct new facilities using mathematical methods like cost-benefit analysis. There are many organizations and publications devoted to discussing the mathematics, engineering, and technical aspects of school design and construction.

Optimizing School Design

The notion of what constitutes “optimal school design” has markedly changed over time. There are some who consider the classic one-room schoolhouse to be the original open-plan design, since the teacher accommodated all students in all grades in a single space, dividing class time among the various grades. Famed Boston architect Gridley J. F. Bryant, who also studied engineering, is credited with revolutionizing the design of many public buildings. His Quincy School, which opened in 1847, was among the first multi-classroom schools. The school was three stories tall, with four identical and symmetrically arranged classrooms on each floor. This model was used for schools throughout the late nineteenth and early twentieth centuries and would be further evolved with movable desks and tables to allow for some flexibility within the “box in a box” construction, as it was called by some. This design led to other considerations such as optimal selection and placement of furniture such as desks, tables, chairs, and later computers, as well as features such as lockers and storage spaces, all of which must be fit into a limited amount of space yet be accessible and functional for a varying student body. Proper placements rely on mathematical concepts such as volume and are related to mathematical packing problems.

Detractors often likened Bryant’s school configuration to prisons, which he also designed. The evolution of open-plan schools of the latter twentieth century was motivated by cost and changes in teaching philosophies, derived in part from research in mathematics education. There was and continues to be controversy regarding the efficacy and desirability of open plan schools. Mathematicians, architects, facilities planners, and others continue to research effective strategies for design and construction. For example, architect Prakash Nair was internationally recognized as a leader in school design, and has been cited for using educational research as a basis for designs that optimize teaching and learning. He helped develop a “pattern language” that draws on geometric ideas and uses a modular set of design patterns, sub-patterns, and groupings to match school designs to goals and needs. It can be used to develop new schools and assess existing structures. Other education professionals like C. Kenneth Tanner, whose background included work in design, mathematics, statistics, and operations research, also used a combination of data-based research with mathematical techniques and tools to address a broad spectrum of school planning issues, such as technology integration. Organizations like the School Design and Planning Laboratory at the University of Georgia used data-driven methods and models for assessing school design and forecasting student populations and demographics, which may impact design, use, and sustainability.

In 1990 Congress passed the Americans with Disabilities Act (ADA), a civil rights law which prohibits discrimination based on disability. The ADA also mandated that facilities and services used by the public had to provide a reasonable level of accommodation to ensure people with disabilities could access and take advantage of these services. In the decades after the ADA, school designers in the US worked to ensure new school buildings provided equal access for people with disabilities; many of these designers drew on the principle of universal design, which advocates designing and building spaces which can be used by a wide range of people. However, since many US school buildings built in earlier decades remained in use, school officials and designers also faced the challenge of retrofitting old buildings to improve accessibility.

Safety

The safety of children in US schools has become a growing concern for parents, teachers, and society in general. The 1999 shootings at Columbine High School focused national attention on issues of school security, safety, and patterns of police response to such incidents. Even more debate occurred after the 2007 shootings at Virginia Tech and continued to intensify in subsequent decades as the US experienced other deadly school shootings, including the attacks at Sandy Hook Elementary in Newtown, Connecticut, in 2011; Marjorie Stoneman Douglas High School in Parkland, Florida, in 2018; and Robb Elementary School in Uvalde, Texas, in 2022. The Secret Service, the Department of Education, and the Federal Bureau of Investigation (FBI) have all conducted broad studies into the causes and prevention of school violence. While much of the dialogue focused on gun control, mental health in teenagers, and other issues considered central to the issue of school shootings, some school designers also sought ways to design schools and classrooms in ways that could mitigate these types of dangers and improve safety during a crisis.

Another mathematically based strategy schools may employ for risk assessment is actuarial methods. Actuarial models for school risk statistically combine empirically chosen threat factors to produce probabilities for particular outcomes or behaviors, and sometimes they may be standardized for specific student populations. In some cases where there are sufficient data and the models can be validated, they have often performed better at identifying in-school threats than subjective human judgments. However, other model-based assessments of risk that are based on sparse data or with a short window for prediction have not been shown to be as reliable. Some researchers have tried to develop expert systems for school threat assessment and decision making, which are automated or semi-automated tools that use artificial intelligence and algorithms developed from data, achieving mixed success. Both actuarial models and expert systems for schools may be revised to incorporate new data as it is identified, making them flexible mathematical modeling tools.

Bibliography

Institute for the Development of Educational Activities, Inc. “The Open School Plan; Report of a National Seminar” (1970). http://archone.tamu.edu/CRS/engine/archive‗files/efl/6000.0205.pdf.

Marquardt, Virginia E. "Inclusive Schools: Designing for Disability in Classrooms." HMC Architects, 12 June 2020, hmcarchitects.com/news/inclusive-schools-designing-for-disability-in-classrooms/. Accessed 17 Oct. 2023.

Nair, Prakash, and Randall Fielding. The Language of School Design: Design Patterns for 21st Century Schools. 2nd ed. Minneapolis, MN: Designshare, Inc. 2005.

Reddy, Marissa, Randy Borum, John Berglund, Bryan Vossekuil, Robert Fein, and William Modzeleski. “Evaluating Risk for Targeted Violence in Schools: Comparing Risk Assessment, Threat Assessment, and Other Approaches.” Psychology in the Schools 38, no. 2 (2001). http://www.secretservice.gov/ntac/ntac‗threat‗postpress.pdf.

Seshadri, Mallika. "With Gun Control far from Sight, Schools Redesign for Student Safety." NPR, 17 Mar. 2023, www.npr.org/2023/03/17/1163551356/with-gun-control-far-from-sight-schools-redesign-for-student-safety. Accessed 17 Oct. 2023.

Tanner, C. Kenneth, and Jeff Lackney. Educational Facilities Planning: Leadership, Architecture, and Management. Boston: Allyn and Bacon, 2006.