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1. Reasoning Patterns in Galileo’s Analysis of Machines and in Expert Protocols: Roles for Analogy, Imagery, and Mental Simulation

   Clement, John (March 2018, Topoi)

   Abstract: Reasoning patterns found in Galileo’s treatise on machines, On Mechanics, are compared with patterns identified in case studies of scientifically trained experts thinking aloud, and many similarities are found. At one level the primary patterns identified are ordered analogy sequences and special diagrammatic techniques to support them. At a deeper level I develop constructs to describe patterns that can support embodied, imagistic, mental simulations as a central underlying process. Additionally, a larger hypothesized pattern of ‘progressive imagistic generalization’—Galileo’s development of a model or mechanism that becomes more and more general with each machine while still being imagistically projectable into many machines—provides a way to think about his progress toward a modern explanatory model of torque. By unpacking his arguments, we gain an appreciation of his skillful ability to foster imagistic processes underlying scientific thinking. 

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2. Four Levels of Scientific Modeling Practices in Expert Learning

   Clement, John (June 2017, NARST)

   Abstract This paper describes model construction practices used by scientifically trained experts. Our work on science experts has involved analyzing data from videotaped protocols of experts thinking aloud about unfamiliar explanation problems. These studies document the value of nonformal heuristic reasoning processes such as analogies, identification of new variables, Gedanken experiments, and the construction and running of visualizable explanatory models. Although theses processes are less formal than formal deduction or induction or statistical inference procedures, the case study analyzed here shows that they can lead to real insights and conceptual change. At a larger time scale, the subject went through model evolution cycles of model generation, evaluation, and modification that utilized the heuristic reasoning processes above. In addition, the prevalence of imagistic simulation as an underlying foundation in these episodes suggests that it may be important to pay greater attention to an imagistic level of processing in the analysis of expert thinking. Larger time scale modes of model evolution and model competition were also evidenced. The analysis leads to four levels of processes or practices: IV. An overarching set of Model Construction Modes, primarily alternating between Model Evolution, in which a model is improved, and Model Competition, in which two or more models compete. III. Modeling (GEM) Cycle process of Model Generation, Evaluation, and Modification at a Macro level, as shown in Figure 10. II. Nonformal Reasoning Processes at a Micro level: e.g. analogy, running a model, identifying a new variable, and conducting a Gedanken experiment. I. Underlying Imagistic process including Imagistic Simulation that may have been occurring within all of the above processes. To our knowledge these four levels of processes have not been analyzed together in the past. They complement empirical processes of discovery, experimentation, and evaluative argumentation documented by others. Diagrams of how the above processes interact may give us some new ways to picture the roles of nonformal reasoning and imagistic processes during qualitative model construction. We call the set of processes at all four levels a 'Modeling Practices Framework'. Processes at a lower level serve as subprocesses for the level above it in this framework. Each level has multiple "things to try" to achieve tasks at the level above it. Thus the framework is an organized but flexible structure of heuristic processes. This lies between and contrasts with those who would describe theory making in science as either 'anarchistic', with no method structure, or 'algorithmic', with fairly standardized procedures. 

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3. Identifying Multiple Levels of Heuristic Reasoning Used in Scientific Model Construction: A Framework Grounded in Imagistic Processing

   https://doi.org/10.1007/978-3-031-94709-4_8  

   Clement, John J (August 2025, Springer Nature Switzerland)

   Ippoliti, E; Sterpetti, F (Ed.)

   This chapter first consolidates a set of important heuristic strategies used for constructing innovative scientific models from three books, including studies in the history of genetics and electromagnetism, and an expert think-aloud study in mechanics. Twenty-four strategies are identified, most of which are field-general. Patterns in their use suggest a partially organized hierarchy of interconnected strategies and substrategies, contrary to the view that heuristics are simply tried in random order. Strategies at four different size and time scale levels are described, including larger Modeling Cycle Phases of model generation, evaluation, and modification, each of which can utilize many smaller Tactical Heuristics as substrategies, e.g., analogy, or testing predictions from the model. These in turn can utilize Grounded Imagistic Processes, such as imagistic mental simulation, an important alternative to deduction for evaluating a model by running it. The framework links higher level, serially organized processes with lower level, imagery-based processes. Its intermediate degree of organization is neither anarchistic, nor fully algorithmic. Possible benefits of organization are narrowing the search space involved and balancing sources of model construction and criticism for productive creativity. Unorganized, spontaneous processes are also discussed, along with their possible benefits. 

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4. IDENTIFYING TEACHING STRATEGIES THAT SUPPORT THINKING WITH IMAGERY DURING MODEL-BASED DISCUSSIONS

   Stephens, L; Clement, J; Price, N; Nunez-Oviedo, M (April 2017, NARST)

   Abstract: This study investigates strategies teachers use to support mental imagery during modelbased science class discussions. A microanalysis of videos of classroom discussions was conducted in order to (1) identify and describe teaching strategies for supporting imagery; and (2) identify evidence that the students were engaging in the use of imagery as they constructed models and reasoned about competing models. This study starts from prior work on experts’ use of imagery, as well as from prior analyses of imagistic characteristics of concrete exemplars used successfully in a curriculum. Sixteen teacher support strategies for imagery are identified, along with thirteen student imagery process indicators. As the list of descriptors stabilizes, we are also identifying larger categories of descriptors—that is, structured categories of imagistic practices and categories of support. We present examples from a case study based on a transcript of a middle school discussion that served as one of the sources for our new organized set of imagery descriptors. 

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5. Geoclidean: Few-Shot Generalization in Euclidean Geometry

   Joy Hsu; Jiajun Wu; Noah D. Goodman (January 2023, NeurIPS 2022 Datasets and Benchmarks)

   Euclidean geometry is among the earliest forms of mathematical thinking. While the geometric primitives underlying its constructions, such as perfect lines and circles, do not often occur in the natural world, humans rarely struggle to perceive and reason with them. Will computer vision models trained on natural images show the same sensitivity to Euclidean geometry? Here we explore these questions by studying few-shot generalization in the universe of Euclidean geometry constructions. We introduce Geoclidean, a domain-specific language for Euclidean geometry, and use it to generate two datasets of geometric concept learning tasks for benchmarking generalization judgements of humans and machines. We find that humans are indeed sensitive to Euclidean geometry and generalize strongly from a few visual examples of a geometric concept. In contrast, low-level and high-level visual features from standard computer vision models pretrained on natural images do not support correct generalization. Thus Geoclidean represents a novel few-shot generalization benchmark for geometric concept learning, where the performance of humans and of AI models diverge. The Geoclidean framework and dataset are publicly available for download. 

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