Constructing Architectural Theory: A pedagogical framework for engaging the logic of precedents with shape rules

Introduction

Theory and practice are essential to architecture as a discipline, and thus to architectural education. Architectural theorists since Vitruvius have reminded us of the fundamental relationship between practice, theoretical reasoning, and architectural pedagogy, ¹ suggesting an active, applied notion of theory as a practice that is discursive, material, and in continual revision. ² Still, the teaching of architectural theory in the undergraduate curriculum tends to be positioned in a peripheral role that neglects theory’s essential function in the everyday conversations and practices of architecture. ³ Rather than emphasizing theory as a construct designed through ongoing speculation and reflection, these courses typically facilitate an introduction to canonical ideas or texts in architecture that are difficult for students to grasp in their early design education. The recursive nature of theory and practice is understudied in this scenario, missing the opportunity to relate theory-making to the analytic and synthetic core of design (and design computing). With the onslaught of emerging technologies and advanced workflows in the discipline, revisiting architectural theory in the undergraduate curriculum in search of creative and parsimonious pedagogies that can reckon with the evolution of architectural principles, practices, and procedures in the context of computation opens a broad inquiry.

From this perspective, the shape grammar formalism offers a powerful framework for recalibrating architectural theory coursework to develop fundamental reasoning in design education.^4,5 The logical study of precedents and how they embody theories of practice can subsequently inform a constructive understanding of architectural theory to enliven design thinking and pedagogies. More specifically, the study of spatial systems in architecture and their formalization provides a link – and even a feedback loop – between architectural ideas, how they are embedded in precedents, and how they can be critically transformed with specific operations and rules. This requires creative interpretations to unpack design principles (analysis) and critical transformations through design practices or procedures to modify or change that logic (synthesis). An introductory theory course offered to students during the second year of their undergraduate architectural education, which combines formal methods, rule-based design, and curatorial practice, is presented here to speculate on the power and potential of this approach.

Constructing Architectural Theory

The constructive program developed in the Architectural Theory I course presented here is part of a larger effort to rework a three-semester curriculum that spans the second and third years of a five-year undergraduate architectural education (Figure 1). These three semesters are initiated by the Constructing Architectural Theory (CAT) course in the fall semester of the second year and followed by back-to-back architectural design studios, Design 4 (D4) and Design 5 (D5), taught in the two subsequent semesters. The overall aim of the sequence is to introduce students to rule-based design incrementally and iteratively to develop a curricular link between the fundamentals of computational design thinking engaged in the foundations curriculum and more advanced computational approaches to architectural design developed in the core studio agendas of the professional curriculum. More specifically, to develop a blend of architectural thinking and computational design thinking, the three-semester sequence is recalibrated through the lens of shape computation, which defines design as a geometric, spatial, and perceptual calculation with the capacity to bridge form and meaning procedurally.^5–7

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Figure 1.

Overview of the five-year, ten-semester course curriculum where the constructing architectural theory (CAT) course and subsequent rule-based architectural design studios, D4 and D5, serve as a bridge from foundations to professional coursework.

The connection between form, meaning, and procedure in architectural thought is the pedagogical focus of the CAT course that initiates the three-semester sequence. This introductory course is a core elective that has traditionally focused on the analysis and understanding of architectural ideas manifest in architectural form, space, and elements. While the redevelopment of the course over the last two academic years (during the fall semesters of 2023 and 2024) shares this emphasis, previous versions of the elective introduced architectural theory primarily through text-based readings, discussions, and exams. The current evolution of the course aims to integrate textual and visual learning modalities through the formal and rule-based study of precedents to emphasize architectural theory as a constructed and malleable project curated by the discipline. By formalizing architectural theory in this way, precedents become a powerful resource for interpreting design reasoning and reformulating it algorithmically to foster a critical dialogue between analysis and synthesis in design theory.^8–10 Moreover, this allows students to be introduced to analog computation as a way of thinking about architectural ideas slowly, deliberately, and intuitively with their eyes and hands. ¹¹

This approach aims to address two concerns confronting rule-based pedagogies in architectural curricula. The first challenge is developing computational design thinking and related skills to support generative design within an already packed core curriculum of a professional degree program. The high learning curves of design and research studios that engage computational design in the upper years of undergraduate curricula are often limited by underdeveloped skillsets – both conceptual and technical – that are critiqued as opportunities for additional pedagogical refinement.^12,13 In response to this need, beginning design courses are emerging as sites for developing a foundation that engages computational thinking and making to learn logical and systematic approaches to design and craft, often through analog, iterative, and rule-based means.^14–16 On the other hand, an alternative curricular solution involves choreographed parallel courses, where an architectural design studio steeped in formal methods and a complementary digital representation course are synchronized to reinforce criticality, creativity, and computation, achieving greater impact within a single semester. ¹⁷

Beyond the computational design thinking and skill-building challenges, a second issue is the growing interest and opportunity for recalibrating architectural education in the context of recent technological advances, especially in generative artificial intelligence (AI). Perhaps counterintuitively, these advancements are enlivening a reevaluation of formalist methodologies, including the analysis and synthesis of precedents, which offer parallels and insights into machine learning processes. ¹⁸ The pedagogical value of these insights is only beginning to be explored in experimental workshops and studios, for example, by reviving forms of analog design production and representation, like collage-making, with state-of-the-art AI-driven tools and techniques. ¹⁹ In the architectural design studio, computational precedent-based instruction ²⁰ offers an extension of precedent-based learning ²¹ that integrates technology, specifically parametric Building Information Modeling, to offer a rigorous formal method for teaching systematic design reasoning at the undergraduate level. Other examples of this approach can be found in pedagogies that emphasize the formal analysis of precedents to jumpstart generative design processes in the context of specific design problems, including building envelope design generation with multimodal large language models in an elective ²² or the additive manufacturing of precast facades in a design studio. ²³

These examples offer constructive models for incorporating rule-based design into architectural studios and electives, promoting computational design thinking and/or design processes that reengage formalist approaches in the context of current advancements in AI, often reliant on precedent analysis. However, rule-based curricula for core coursework in architectural theory remain underdeveloped in contemporary pedagogies. This is especially true for the initial years of undergraduate architectural education, where an effort to understand the fundamentals of relationships between design, design reasoning, critical argumentation, and architectural representation is essential. While the ongoing dialogue between shape computation and architectural theory is elaborated in recent scholarship, ²⁴ the potential for the shape grammar formalism to transform architectural theory pedagogies today remains an open area of inquiry. The hypothesis here is that shape rules and their visual computations can aid students in understanding: (1) architectural principles and how they are manifest in the spatial relationships of building precedents; (2) design practices of critical observation and creative speculation that develop design reasoning skills; and (3) rule-based procedures that simulate and transform design concepts into operative theoretical projections.

To test this, an introduction to architectural theory course was developed for second-year undergraduate students, focusing on a specific corpus of architectural precedents studied for the full semester. The corpus includes a selection of house designs from Paul Rudolph’s early career in Florida (Figure 2). These designs are chosen for several reasons. First, the house designs demonstrate the progression from Rudolph’s early work in collaboration with Ralph Twitchell, shown in the first three rows from Figure 2(a)–(i), to independent work starting in 1952, shown in the last two rows from Figure 2(j)–(o), and thus illustrate the evolution of a design language through changing influences and practices. Second, the modernist language of the houses enables the course to focus primarily on organization in plan, which limits the scope and complexity of the studies to a reasonable level for an undergraduate in their third semester of architecture studies. Third, despite the planimetric design focus of the course, the houses represent Rudolph’s early interest in regionalism, ²⁵ elucidated in several features, details, and materials used in the houses that are richly complex in articulating how a design language responds to the outdoor lifestyles and extremes of the Florida climate. These complexities allow students to discover intriguing details as they get into the depth of their studies, while also introducing design solutions that respond to dynamic climatic factors from heat to hurricanes. Fourth, there are enough designs in the corpus to keep it interesting for a class of fifty or more students. Students choose one house precedent on the first day of the course, with up to four students having the same design. This is viewed as a positive because the students can help each other to understand and research their precedents. Lastly, documentation of these projects is readily available through publication ²⁶ and the online archive of the Paul Rudolph Institute for Modern Architecture. ²⁷ For these reasons and more, the houses have provided a generous scaffold for investigating a constructive approach to architectural theory over the first 2 years of the course.

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Figure 2.

Precedent floor plans: (a) Denman residence, 1946–47 (redrawn by N Moubarak); (b) Roberta Finney guest house, 1947 (redrawn by K Saravia); (c) Miller residence, 1947 (redrawn by K Leonard); (d) Revere quality house, 1948 (redrawn by J Schvarzberg); (e) Healy guest house/Cocoon house, 1948–49 (redrawn by J Schwanz); (f) Siegrist residence, 1948–49 (redrawn by J Moreno); (g) Wheelan cottages, 1951 (redrawn by K Levasseur); (h) Walker residence, 1951 (redrawn by E Soucy); (i) Knott residence, 1951–52 (redrawn by E Morales); (j) Hook guest house, 1952–53 (redrawn by R Burgess); (k) Walker guest house, 1952–53 (redrawn by A Niketic); (l) Davidson residence, 1953 (redrawn by T Dareau); (m) Hiss residence/Umbrella house, 1953–54 (redrawn by V Garcia); (n) Cohen residence, 1953–55 (redrawn by I Lictaoa); and (o) Milam residence, 1959–62 (redrawn by K Shkurko).

Once a house precedent is chosen, the course is structured around a sequence of four individual studies that aim to lead students through an iterative process of theory-making involving stages of decoding, transforming, blending, and curating their work (Figure 3). The studies are complemented by weekly lectures, in-class workshops to practice the formal methods introduced, and multiple informal pin-up sessions where progress work is discussed with the instructor and teaching assistants. The first study, decoding, emphasizes formal analysis as a process for understanding the architectural principles embedded in the spatial relationships of a precedent design and representing them graphically. The second study, transforming, introduces shape rules as mechanisms for modifying the composition of a design based on a personal critique. The third study, blending, prompts students to select a second house precedent and develop a new design language by fusing compositional principles and related elements from their first and second houses. The final study, curating, invites students to represent their work of the entire semester in an interactive micro-exhibit. The goal of each exercise is to experiment with theory-making through understanding, changing, remixing, and displaying the studies of the Rudolph houses. These efforts are all framed through the lectures to emphasize rule-based design and computation as a lens for describing, interpreting, and evaluating architecture, with a focus on analog shape computations achieved by drawing and physical or digital modeling.

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Figure 3.

Diagrammatic workflow of the four main exercises of the CAT course, from left to right: the decoding and transforming exercises are developed in the first half of the semester through the study of precedent one; the blending exercise adds the consideration of precedent 2 to initiate the second half of the semester; and the final curating exercise reconsiders and reformats all previous exercises into a culminating micro-exhibit (student work by A Niketic).

Decoding

The initial study of the course is geared toward formal analysis and representation of design principles within each precedent design. The discussion begins with an introduction to Rudolph’s larger body of work, writings, and lectures. More specifically, a lecture Paul Rudolph gave at the Southern California Institute of Architecture (SCI-Arc) called “The DNA of Architecture” provides six specific design considerations for us to decode as principles within each precedent. ²⁸ Rudolph categorizes these as: (1) site; (2) space; (3) scale; (4) structure; (5) function; and (6) spirit. In the lecture, Rudolph explains each of these considerations with reference to representative projects. However, these categories are not hard and fixed, resulting in debate and discussion in the course on how to define, distinguish, and represent each as a basis for design reasoning in Rudolph’s architecture. If Rudolph uses this language to describe his own work, can we see it articulated in the precedents? For example, what is spirit, architecturally speaking? How is it exhibited in a design? Can you draw or model the spirit of a building? The decoding assignment engages these questions through graphic representation.

The assignment consists of three parts. The first is to redraw the plan of the precedent and research the house to learn more about its site, client, materials, etc. Even if a house consists of more than one floor, students are asked to study the primary or main entry level floor plan for simplicity and ease of comparison between the precedents. Even redrawing the plan could be met with some challenges since we are working with an archive of hand-drawn plans of differing levels of detail and types of architectural notation. This allows us to address some basic conventions of architectural representation that need review in the second year, especially about line types, for example. The second part of the assignment involves participating in an in-class visual analysis workshop to start developing a series of diagrams, one for each of the first five design principles. Each diagram is focused on the single plan selected for the study. In the workshop, we use tracing paper to highlight different features in the plan and to emphasize how each diagram category gave us an opportunity to critically analyze the spatial relationships of the houses through a different lens.

Figure 4 depicts five decoding studies organized in columns and rows. Each column is a separate study by an individual student (Figure 4(a)–(e)). The top row includes the redrawn plan of each precedent, organized chronologically from left to right. Rows two through six isolate the separate principles in the following order: site, space, scale, structure, and function. In the second row, the site diagrams emphasize context, orientation, and the relationship between the massing and outdoor spaces. Then, in the third row, the space diagrams focus on the definition of rooms, boundaries, and volumes. The fourth row presents scale diagrams, which aim to capture dimensions, proportions, or compositional relationships, for example, of symmetry or asymmetry in the designs. Next, the fifth row depicts diagrams that isolate the structure, defined as the fixed load-bearing system, aiming to understand its cadence. Lastly, the sixth row illustrates functional organization in terms of circulation, use, furnishings, or divisions of public and private zones. Together, the diagrams provide an opportunity to discuss each ordering principle as a separate layer of unique spatial relationships and then to consider how they are integrated to complement or contrast each other in the overall design composition.

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Figure 4.

Decoding | Analysis diagrams: (a) Denman residence, 1946–47 (analysis by N Moubarak); (b) Roberta Finney guest house, 1947 (analysis by K Saravia); (c) Wheelan cottages, 1951 (analysis by K Levasseur); (d) Hook guest house, 1952–53 (analysis by J Wheeler); and (e) Cohen residence, 1953–55 (analysis by J Elias).

The third part of the assignment addresses the sixth principle, spirit. For this, we developed a working definition of spirit as the spatial qualities of the design that couldn’t be appreciated in the floor plan alone. We looked at architectural drawings readily available in the online archives of the Canadian Centre for Architecture, ²⁹ Drawing Matter, ³⁰ and the US Modernist Architecture Media Library ³¹ to study how spatial qualities are represented in architectural drawings throughout the recent past. Students were asked to develop a spirit study for their precedent that aimed to adopt the representational style of one of these drawings and to reinterpret their house precedent through that same representational approach. The medium and size of the study are not limited, resulting in a wide variety of expressions, from digital drawings to mixed-media collages to paintings on canvas. Figure 5 includes nine spirit studies of Rudolph’s Florida houses in representational styles that may be recognizable to readers. For example, Figure 5(d) depicts the Hook Guest House in the “situated objects” graphic style of Stan Allen; Figure 5(h) studies the Davidson Residence through the lens of Aldo Rossi’s Modena Cemetery as drawn by Jesse Reiser; and Figure 5(i) develops a drawing of the Denman Residence based on John Hejduk’s rendering of Bye House.

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Figure 5.

Decoding | Spirit studies: (a) Hook guest house, 1952–53 (study by A Buchanan); (b) Healy guest house/Cocoon house, 1948–49 (study by T Mascioletti); (c) Milam residence, 1959–62 (study by K Shkurko); (d) Hook guest house, 1952–53 (study by R Burgess); (e) Wheelan cottages, 1951 (study by K Levasseur); (f) Wheelan cottages, 1951 (study by M Noriega); (g) Knott residence, 1951–52 (study by A Flores); (h) Davidson residence, 1953 (study by T Dareau); and (i) Denman residence, 1946–47 (study by N Moubarak).

The decoding assignment culminates with a final pinup of the work and a class discussion on the variety of interpretations achieved in the studies. Students review each other’s work, especially those with the same precedent, to discuss how they interpret and represent things differently, which is emphasized as a strength and challenge of both visual representation and theoretical work. We also discuss architectural theory as an ongoing effort to articulate the ideas motivating the discipline constructively, which resonates with students who are beginning to understand how their designs in studio will also be analyzed and decoded to account for their reasoning and the ways that they present their work. This lays the groundwork for moving into studies that emphasize criticality and design synthesis.

Transforming

The second study of the course is introduced as a theoretical project characterized by the speculative transformation of a precedent design. Shape grammars are presented as a formalism for specifying spatial relationships and geometric transformations through the mechanisms of shape rules and their generous visual computations.^5,7 Students are introduced to geometric rules as a method for encoding a design action from an existing condition on the left-hand side (LHS) of the rule to its transformation as a revised condition on the right-hand side (RHS). The emphasis is on rulemaking and rule-play for design exploration, inspired by each student’s individual perception of their precedent. The development and application of rules are presented as a type of practice, similar to drawing or sketching, where design ideas can be explored freely, intuitively, and iteratively. The lectures introducing this assignment focus on the translation from analysis to synthesis: how can the spatial relationships and ordering systems identified in the diagrams of the decoding study inform the encoding of modifications to generate changes within the same language of the precedent designs? Could surgical transformations be made that are so true to the original designs that they are challenging to detect to the untrained eye? The transforming assignment addresses these questions through rule-based design, aiming to generate imitative variations that suggest families of designs based on each precedent house.

The assignment consists of three parts. The first is to critique each precedent by imagining that a client has purchased the house and is interested in renovations that preserve the integrity of the original design. Students are asked to speculate on how they would add, subtract, or modify their precedent to create an improved living environment for their client, while still adhering to the logic of the precedent. For example, Figure 6(a) includes a critique of the Walker Guest House (Figure 2(k)), where a student highlights the kitchen, circulation, and limited outdoor porch space as opportunities for transforming the design to better reflect contemporary living patterns. The second part of the assignment includes an in-class visual synthesis workshop to start working with shape rules to encode modifications to the original designs based on each student’s critique and initial sketches. Students are limited to six shape rules for the assignment and are expected to draw, test, and refine them in the context of their design goals. To overcome any initial awkwardness or intimidation about designing with rules, shape rules are introduced as basic drawing mechanisms. Several “cheater’s rules” are presented in the workshop, including simple rules for drawing operations commonly encoded in software applications. Rules are also proposed as “reversible” when using a diamond between the LHS and RHS rather than the conventional arrow. The goal is not to perfect the rules, but rather to become familiar with using geometric rules strategically and to work within their constraints to produce design variations economically. Figure 6(b) illustrates six shape rules developed to transform the Walker Guest House. These rules specify erasing, drawing, scaling, moving, mirroring, and extending actions that operate on the lines of the redrawn plan of the precedent to develop variations.

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Figure 6.

Transforming | The Walker guest house (1952–53): (a) critique of kitchen, circulation, and limited porch area; and (b) shape rules for modifications, including cheater’s rules and reversible ones (study by A Niketic).

The third part of the assignment involves using the shape rules to produce a catalog of four design options. These designs are not constrained by any program requirements or specifications other than those articulated in the student’s design critique of the precedent. Of the required four variations, one must be explained through the graphic depiction of the rule application in three steps, as the derivation in Figure 7 shows. Between each step, color is used to identify the changes made when rules are applied. The family of transformed designs produced following this method is given in Figure 8. The first variation of the Walker Guest House (Figure 2(k)) in Figure 8(a) includes an L-shaped exterior porch with an elongated kitchen on the interior. Figure 8(b) depicts a second variation with front and back porches and an entry kitchen. A third variation is given in Figure 8(c) with public and private corner porches (one at the entry and the other at the bedroom) with an elongated kitchen. Lastly, the fourth variation shown in Figure 8(d) features front and corner porches with an enlarged entry kitchen.

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Figure 7.

Transforming | The Walker guest house: rule application process (derivation) to generate the first variation featuring an L-porch with elongated kitchen (study by A Niketic).

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Figure 8.

Transforming | Four variations of the Walker guest house: (a) L-porch variation with elongated kitchen; (b) entry kitchen with front and back porches; (c) public and private corner porches with extended kitchen; and (d) entry kitchen with front and corner porches (study by A Niketic).

Like the previous assignment, the final submission of this study includes a pinup and a class discussion, where we review the notion of the rule and its relation to design intent by looking at the details of peer-selected projects. Figure 9 illustrates two additional examples of transformed precedents produced in this assignment, for example. The first shown in Figure 9(a) is based on revising the Denman House (Figure 2(a)) to include expanded kitchen, dining, and living room areas. The second variation illustrated in Figure 9(b) is based on the Healy Guest House, also known as the Cocoon House (Figure 2(e)), and explores enlarging the house with two additional bays to allow for a carport, waterside dining porch, and revised entry porch. The examples given here foreground the subtlety and playfulness of this initial synthesis exercise. Within this assignment, rule design and application are positioned as computational devices for design exploration and theory-making from a personal perspective. These specifications are then tested in a design context through the iterative study of multiple design variations that each play on solutions from the same critique. This builds constructive muscle and progresses the course toward more expressive studies with rules that emphasize creativity and design synthesis.

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Figure 9.

Transforming | Additional examples: (a) variation of the Denman house (study by N Moubarak); and (b) variation of the Healy guest house/Cocoon house (study by J Schwanz).

Blending

The third study of the course challenges students to combine or remix the languages of two precedent designs. The intent of the assignment is to develop a unique language by creating hybrid designs that fuse the two precedents in a precise and rigorous way. The second precedent is chosen from the selection of designs already studied in the course (Figure 2) so that students can rely on the research and work by their peers in the previous assignments to understand their second precedent. The lectures and workshops for this study delve further into formal synthesis and composition by presenting a variety of architectural organization types ³² and mathematical definitions of symmetry groups, mappings, and transformations. ³³ In addition, the shape rule is more rigorously defined through an in-depth study of shape grammars in architectural research. For example, the shape rules of the Palladian grammar express the Renaissance ideals of symmetry articulated in Palladio’s theoretical writings ³⁴ ; rules elaborating Wright’s commitment to organizing domestic spaces around the centrality of the hearth are defined in the prairie house grammar ³⁵ – and even more, this is accomplished in a playful manner inspired by Wright’s formal education with Froëbel’s gifts ⁴ ; the logic of Portman’s grid of major and minor spaces allows for order, variety, and volumetric surprise specified in the rules of the Entelechy I grammar ³⁶ ; and a commitment to the study of the transformation of forms at multiple scales with wood framing is manifest in the rules of the grammar of Anne Tyng’s domestic space structures. ³⁷ Even closer to the blending assignment, the rule-based interpretation of Portman’s hotels allows for the automated production of hybrids that share the design concepts and tropes of the atrium. ³⁸ These examples allow us to reconsider rulemaking as a type of theory-making, where variations produced with the rules validate and express a theoretical argument visually.

Rather than emphasizing critique, this assignment foregrounds the creative aspects of working constructively with shape rules. The rules represent the formalization of a design intuition: how can new formal organizations be introduced in the design exercise to fuse the language of the two precedents? Or, alternatively, can a rhythm be found between the logic of the two precedents to define a hybrid language like a musical remix? This exercise also allows us to question if and how these methods relate to the state-of-the-art of generative design in architecture, for example, can our analog processes help us understand techniques of style transfer in generative AI? The blending assignment aims to answer these queries by revisiting shape rules and their computations with increased design intent.

The assignment consists of three parts. The first step is to select a second precedent and develop a collage that blends select parts of the first and second houses into a third design. Students may create their collage manually or digitally; an example of each is given in Figure 10. Figure 10(a) depicts a manual collage that develops a symmetrical remix of the Hiss Residence or Umbrella House (Figure 2(m)) and the Cohen Residence (Figure 2(n)). The collage in Figure 10(b) takes a different approach by reworking the rhythms of the structural bays of the Miller Residence (Figure 2(c)) and the Siegrist Residence (Figure 2(f)) to develop an L-shaped blend of the two precedents. Once the collaged design is created following an intuitive mode of design exploration, the second part of the assignment is to reflect on the collaged design to identify the design actions and organizational modes engaged to produce this initial hybrid variation more explicitly. From this reflection, students develop a series of ten shape rules that aim to represent their approach to blending the two precedent designs.

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Figure 10.

Blending | Collages of two precedents: (a) symmetrical remix of the Hiss residence/Umbrella house and the Cohen residence (study by H Adamson); and (b) a L-shaped remix of the Miller residence and the Siegrist residence (study by K Leonard).

The third part of the assignment asks students to develop and refine their rules by testing them and producing another series of design variations based on their concepts for blending precedents. An additional requirement of these variations is the consideration of a residential program. Two programs must be achieved: (a) a four-bedroom, three-and-a-half-bathroom configuration; and (b) a three-bedroom, two-and-a-half-bathroom configuration. Figure 11 depicts an example of results from the blending exercise based on the initial collage of Figure 10(b), which blends the Miller Residence (Figure 2(c)) and the Siegrist Residence (Figure 2(f)). The ten shape rules in Figure 11(a) illustrate the evolution from the drawing rules of the transforming study (Figure 6(b)) to more elaborate rules for modifying specific spatial relationships to create hybrid designs. Figure 11(b) illustrates the rule application process for producing one of the variations. This process mirrors the collage process in how the student starts with a collection of parts from both houses at the top of the derivation and applies the rules to organize and extend those parts to achieve the hybrid design. Lastly, Figure 11(c) includes two variations, one for each program, generated with these rules. The upper design is organized around a central pool courtyard, defined by two L-shaped masses, to create a variation that satisfies the three-bedroom, two-and-a-half-bathroom program. The lower design features a single H-shaped mass, also organized around a pool, with wall extensions that define separate patio areas around the perimeter of the house to create a four-bedroom, three-and-a-half-bathroom variation. Both variations exploit the L-shapes, grids, patios, and linear massing of the original precedents.

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Figure 11.

Blending | Combining the Miller residence and the Siegrist residence: (a) shape rules for modifications; (b) rule application process (derivation); and (c) two remixed variations generated with the shape rules (study by K Leonard).

To conclude this assignment, a final pinup and discussion are organized, where we revisit the rule as a mechanism for design reasoning and theoretical exploration. By blending two precedents, looking for opportunities to engage existing organizations or add to them based on their own preferences, the students gain more design agency with rules than in the previous exercises and start to reflect on the creative potential of generative design. We discuss the strengths of certain rules and their procedural outcomes based on peer-selected examples to structure this discussion. In addition, we consider how the hybrid designs produced in this exercise relate to other modes of computational design, where algorithms inform design processes in various ways. Due to the iterative nature of this study, especially in relation to the previous transforming study, the notion of rule-based variation and its relation to design intent and agency comes forward with additional resonance, suggesting a reflective opportunity to revisit and assess the outcomes of the course.

Curating

The final study of the course is focused on reviewing the work of the semester and designing an interactive display of the results for exhibition. The emphasis is on curation and refinement of previous assignments to convey the semester’s work as a cumulative project. Each student is provided with a 12" square wooden box, which is the “site” for their individual “cabinet of curiosities.” The lectures and course activities supporting this study are focused on the architectural exhibition as a place of display, debate, and, more importantly, as a context for projecting theoretical work to advance the discipline. We look at examples from various years and themes of the Venice Biennale to frame conversations on curation and to question the contributions and challenges of exhibition work. For example, we studied the Emotional Heritage project by Flores & Prats Architects, ³⁹ especially, which deploys a series of models, drawings, and studies to explore themes common to our own iterative work between theory and practice. Several of these studies are housed in crates and containers for traveling that are like the wooden boxes adopted for our exhibit. This final assignment emphasizes analysis and synthesis together as a practice of organizing and presenting a project: How can the entire work of the semester be contained in a single exhibit? What should be foregrounded in the display? What should be in a secondary or background role? How can a display attract engagement to unpack the different layers of the coursework?

The assignment consists of two parts. The first is to develop a concept sketch for a “cabinet of curiosities” based on the lectures and examples presented in the course. Each student’s exhibit is required to include their work from the previous three studies of the semester. In addition, one of their design configurations generated in the third assignment, blending, must be presented three-dimensionally with a physical model housed within each wooden box. Students are encouraged to consider how to design their display with engaging booklets, models, or even interactive pieces so that viewers can reconfigure or simulate some of the rule-based design processes developed in the coursework. After a preliminary discussion of display concepts in a pinup with the instructor and teaching assistants, the second part of the assignment consists of creating the micro-exhibit and displaying it at our final course exhibition.

Nine “cabinets of curiosities” are included in Figure 12, each representing the work of one student. Some of the boxes are more subtle in their curation, for example, those in Figure 12(a), (b) and (h). Each of these uses the back of the box as a pin-up area and the front bed as a model display. In these three displays, any interactive parts are minimized as smaller elements to open or flip through, while the models are foregrounded. A second group, as shown in Figure 12(c), (d) and (i), employs a similar approach, but with enlarged folded and expanding booklets that invite the viewer to more thoroughly investigate all the studies contained within the box. The last group introduces additional mechanisms of display to engage interaction, including cable-suspended booklets in Figure 12(e), expanding drawers built into the box in Figure 12(f), and playful magnet parts that can be used to reconstruct design variations in Figure 12(g).

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Figure 12.

Curating | Cabinets of curiosities: (a) Milam residence (study by C Burt); (b) Hook guest house (study by A Buchanan) (c) Milam residence (study by K Shkurko); (d) Cohen residence (study by I Lictaoa); (e) Knott residence (study by E Morales); (f) Roberta Finney guest house (study by K Magin); (g) Hiss residence/Umbrella house (study by V Garcia); (h) Knott residence (study by A Florez); and (i) Denman residence (study by N Moubarak).

The resulting exhibition featured fifty of these boxes, one for each student of the course. At the opening of the exhibition, a brief presentation introducing the constructive approach and exercises of the course was given to invited reviewers. This was followed by an informal, gallery-style review, where each student presented their micro-exhibits to our guests and received their feedback. This culminating assignment reiterated the analysis-synthesis feedback loops modeled throughout the semester’s studies. However, in this case, the students were critiquing and revisiting their own work instead of their initial precedents designed by Paul Rudolph. The intent is to thoughtfully review and reframe the outcomes of the course through practices of self-reflection to develop habits of critical and logical reasoning. Subsequently, each box represents an individual student’s perspective on what was learned in the semester, with different hierarchies given to various exercises and methodologies, providing insight into what each student identified as important throughout these processes. The exercise thus concludes the course with the micro-exhibit as a site of theory-making.

Discussion

The work presented here demonstrates how an architectural theory course is informed by a constructive approach to enliven an understanding of precedents through the lens of principles, practices, and procedures at the undergraduate level. The first study, decoding, engaged formal analysis and representational studies to unpack how architectural principles can be extracted from precedents to emphasize the study of buildings themselves as sites of architectural reasoning and argumentation (Figures 4 and 5). The second and third studies, transforming and blending, proposed rule-based design with shape grammars as a procedural mechanism for theory-making, based first on subtle critique deployed with surgical modifications (Figures 6–9) and second on more creative speculations to imagine new languages of designs (Figures 10 and 11). Both studies emphasize design reasoning through the iterative study of variations. Lastly, the final study, curating, focuses on self-reflection and display (Figure 12) to conclude the course with another round of analysis and synthesis from a personal perspective to highlight theory as a construct for individual articulation and identity.

The students enrolled in the course completed a survey at the end of the semester to provide their comments on the class and how to improve it. Much of the feedback emphasized the constructive basis of the course. For example, one student commented, “The interactive nature of the course helped me stay more engaged.” In addition, multiple students described the course and assignments as “interesting,” “fun,” and “creative.” Some students commented on the “challenging” nature of the exercises, summarizing the course as “a bit difficult, but the studies encouraged me to think about architecture in new ways.” One student emphasized the simplicity of the course as a strength: “I liked that it was very focused on a single thing: floorplans,” while another student felt that the assignments were “too repetitive.” A third student assessed that the assignments were “too complicated and should be simplified.” Students also disagreed on the way feedback was given in the course through the pinup presentations and discussions with the instructors and teaching assistants. Some felt that not enough feedback was given to be beneficial during these sessions and that other methods should be developed, which will be explored in the next iteration of the class. Still, the overall tone of the reviews suggests the successful delivery of the course, with one student summarizing, “I liked learning about theory because of its significance in one’s architectural identity … this class helped me learn more about developing that identity by learning from the works of others.”

Conclusion

The ‘Constructing Architectural Theory’ course aims to foreground a recursive and ongoing dialogue between theory and practice through the lens of visual computations and analysis-synthesis feedback loops. These methods are derived from shape computation, a discourse that emphasizes spatial relationships and their systems to understand form and meaning both in architecture and throughout the history and logic of design, more broadly speaking.^5–7,40 The goal of developing these constructive processes in the course is to first learn to decompose architectural precedents with a critical eye. And second, to respond to this initial understanding creatively to generate new designs that challenge, change, and combine the relationships observed in the precedents. The entire process is framed as one of theory-making, where interpretations, designs, and displays are produced to visually convey design ideation, conceptual positioning, and self-assessment as a habitual practice. Similar analytic-synthetic processes can be applied to other architectural precedents or typologies, and that is something we build on in subsequent design studios to advance this agenda, since a single introductory course is not enough for developing these skills.

The theory course outlined here commences a three-semester sequence, where shape grammars are expanded upon in two design studios in the second and third years of the undergraduate curriculum (Figure 1). Both studios aim to introduce students to the power of precedents as a basis for interpretation and analysis that can produce the seeds of a new project. Even more, they aim to model a process that foregrounds formal actions specified with shape rules, rule schemata, and design machines to help students understand the power of description, interpretation, and evaluation in design and computation. We do all this primarily by drawing and modeling a generative system with slow, analog computations. ¹¹ This analog mode aims to simulate the more experimental and computationally intensive processes, such as environmental design simulation, machine learning, structural optimization, and more, that students will take on in more advanced courses and design studios in our curriculum. This foundation in formal analysis and rule-based synthesis provides students with a basis for understanding these processes, software, and workflows fundamentally.

Paul Rudolph, who was not only interested in excellence in architecture but also in excellence in architectural education, summarizes the question of architectural quality as a pursuit of understanding: “What was the architect trying to do in the first place?” He follows this question by discussing architectural education, stating:

The schools approach architecture as a creative art, but this, as creativity, cannot be taught. However, an atmosphere and approach can be nurtured, whereby the problems are defined, and the student can commence the endless journey to find himself. ⁴¹

If precedent is the data of architecture, and the return of precedent, formal analysis, imitation, and style are nigh in the face of advancements in generative AI, ¹⁸ then perhaps shape grammars are more relevant than ever for nurturing such an “atmosphere and approach” of architectural thinking and self-discovery. The processes of decoding, transforming, blending, and curating outlined here are rich visual analogues that correlate to the mathematical calculations behind today’s most advanced emerging technologies and generative AI systems. ⁴² The procedural, visual, and constructive nature of shape rules and their computations provides a context for bridging between analog and digital formalisms to build a strong foundation in design thinking that can evolve our disciplinary traditions and speculative futures. As a context for architectural theory, this advances criticality and creativity in building theories and practices for ourselves, and for educating the machine, too.