Introducing Complex Systems Analysis in High School Mathematics Using System Dynamics Modeling: A Potential Game-Changer for Mathematics Instruction

Regional complex system simulation optimization through linking governance and environment performance: A case study of water environmental carrying capacity based on the SDES model

The complexity of problems facing society continues to grow, and decision-makers and problem-solvers are finding many of today's emerging problems to be beyond their capability to adequately address. There is agreement in the literature that problems of this nature are complex system problems, inextricably linked to some highly complex system of systems. Establishing a clear understanding of the specific complex system context is fundamental to the process of understanding and analyzing complex systems and complex system problems across all of the different systems-based disciplines. While complex system context is widely referred to in systems literature, there is no clear characterization of exactly what system context is, making this foundational system concept ambiguous. This research addressed this gap in the systems body of knowledge by providing the needed detail and clarity to the concept of complex system context. A rigorous research methodology, employing the grounded theory method, was used to analyze data collected through a series of semi-structured interviews conducted with individuals reflecting a wide range of systems education and practical experience. Two research questions were identified as integral to increasing the understanding of context within complex systems. (1) What are the constituent elements of complex system context, and what attributes and dimensions characterize these elements? (2) What systems-based framework can be developed for constructing and articulating complex system context? Using the grounded theory method, a theory of system context was constructed, adding to the systems body of knowledge and substantiating a comprehensive and unambiguous theoretical construct for system context within complex systems. Then, based on this theory, a conceptual model to articulate and capture system-specific complex system context was developed---the Complex System Contextual Framework (CSCF). The CSCF shows significant promise for contribution to systems practitioners by supporting the future development of tools to help practitioners capture system context as a part of complex system problem formulation. The research also made a contribution in the area of research methodologies by furthering the use of the grounded theory method in the engineering management and systems engineering domain, an area where its application has been very limited.

This paper describes a multi-level system dynamics (SD) / discrete event simulation (DES) approach for assessing planning and scheduling problems within an aviation training continuum. The aviation training continuum is a complex system, consisting of multiple aviation schools interacting through interschool student and instructor flows that are affected by external triggers such as resource availability and the weather. SD was used to model the overall training continuum at a macro level to ascertain relationships between system entities. SD also assisted in developing a shared understanding of the training continuum, which involves constructing the definitions of the training requirements, resources and policy objectives. An end-to-end model of the continuum is easy to relate to, while dynamic visualisation of system behaviour provides a method for exploration of the model. DES was used for micro level exploration of an individual school within the training continuum to capture the physical aspects of the system including resource capacity requirements, bottlenecks and student waiting times. It was also used to model stochastic events such as weather and student availability. DES has the advantage of being able to represent system variability and accurately reflect the limitations imposed on a system by resource constraints. Through sharing results between the models, we demonstrate a multi-level approach to the analysis of the overall continuum. The SD model provides the school’s targeted demand to the DES model. The detailed DES model is able to assess schedules in the presence of resource constraints and variability and provide the expected capacity of a school to the high level SD model, subjected to constraints such as instructor availability or budgeted number of training systems. The SD model allows stakeholders to assess how policy and planning affect the continuum, both in the short and the long term. The development of this approach permits moving the analysis of the continuum between SD and DES models as appropriate for given system entities, scales and tasks. The resultant model outcomes are propagated between the continuum and the detailed DES model, iteratively generating an assessment of the entire set of plans and schedule across the continuum. Combining data and information between SD and DES models and techniques assures relevance to the stakeholder needs and effective problem scoping and scaling that can also evolve with dynamic architecture and policy requirements. An example case study shows the combined use of the two models and how they are used to evaluate a typical scenario where increased demand is placed on the training continuum. The multi-level approach provides a high level indication of training requirements to the model of the new training school, where the detailed model indicates the resources required to achieve those particular student levels.

168 Impact of Connecticut’s Good Samaritan Laws in Preventing Opioid Overdose Deaths – An Applied System Dynamics Approach

Complex sociotechnical systems with multiple competing objectives and nonlinear dynamics pose significant challenges for policy optimization. Traditional simulation-based methods often struggle with high-dimensional policy spaces. This study addresses these challenges by combining genetic algorithms (GAs) with system dynamics (SD) modeling to optimize policy configurations in complex environments. Our approach merges SD’s capacity to simulate intricate system behaviors with GA’s prowess in multi-objective optimization. The SD model uses predefined decision variables to simulate system behavior, while GA iteratively adjusts these variables to find optimal policy configurations. We apply this hybrid approach to a media industry case study, focusing on balancing profit, competitiveness, and audience satisfaction. The research methodology integrates SD’s ability to capture complex system behaviors with GA’s strength in optimizing multiple objectives. An SD model simulates system behavior based on predefined decision variables representing key policy levers. GA then iteratively adjusts these variables based on fitness objectives derived from the SD model. This process evaluates performance and identifies the globally optimal policy configurations. The results show that the hybrid SD–GA framework significantly improves policy solutions compared to conventional methods. Sensitivity analysis confirms the optimized policies’ robustness and comparative assessments highlight our approach’s advantages in navigating complex policy spaces. This study introduces a new SD–GA framework that improves data-driven policy formulation in complex systems. It combines policy informatics and evolutionary algorithms to offer a comprehensive approach to multi-criteria decision-making. Future research could include long-term validation of this approach in the broadcasting industry to further refine and apply this methodology across various domains.

BackgroundMathematical modelling has been a vital research tool for exploring complex systems, most recently to aid understanding of health system functioning and optimisation. System dynamics models (SDM) and agent-based models (ABM) are two popular complementary methods, used to simulate macro- and micro-level health system behaviour. This systematic review aims to collate, compare and summarise the application of both methods in this field and to identify common healthcare settings and problems that have been modelled using SDM and ABM.MethodsWe searched MEDLINE, EMBASE, Cochrane Library, MathSciNet, ACM Digital Library, HMIC, Econlit and Global Health databases to identify literature for this review. We described papers meeting the inclusion criteria using descriptive statistics and narrative synthesis, and made comparisons between the identified SDM and ABM literature.ResultsWe identified 28 papers using SDM methods and 11 papers using ABM methods, one of which used hybrid SDM-ABM to simulate health system behaviour. The majority of SDM, ABM and hybrid modelling papers simulated health systems based in high income countries. Emergency and acute care, and elderly care and long-term care services were the most frequently simulated health system settings, modelling the impact of health policies and interventions such as those targeting stretched and under resourced healthcare services, patient length of stay in healthcare facilities and undesirable patient outcomes.ConclusionsFuture work should now turn to modelling health systems in low- and middle-income countries to aid our understanding of health system functioning in these settings and allow stakeholders and researchers to assess the impact of policies or interventions before implementation. Hybrid modelling of health systems is still relatively novel but with increasing software developments and a growing demand to account for both complex system feedback and heterogeneous behaviour exhibited by those who access or deliver healthcare, we expect a boost in their use to model health systems.

Implementation of the Common Core State Standards in Mathematics has provided teacher educators a great opportunity to reexamine whether teacher preparation programs adequately provide the experiences to develop the base of knowledge and 21st century skills necessary to be effective teachers. The Mathematics TPACK Framework provides a roadmap for a series of pathways to integrate three knowledge components that are essential in teacher development: content knowledge, pedagogical knowledge, and technological knowledge. In this chapter, the authors examine how a teacher preparation program has evolved to integrate meaningful uses of digital technologies in content and pedagogy that are relevant to the teaching and learning of mathematics through the lens of implementing the Common Core State Standards.

The purpose of our paper entitled Hierarchical Diagnostic Classification Models: A Family of Models for Estimating and Testing Attribute Hierarchies (Templin & Bradshaw, 2014) was two-fold: to create a psychometric model and framework that would enable attribute hierarchies to be parameterized as dependent binary latent traits, and to formulate an empirically driven hypothesis test for the purpose of falsifying proposed attribute hierarchies. The methodological contributions of this paper were motivated by a curious result in the analysis of a real data set using the log-linear cognitive diagnosis model, or LCDM (Henson, Templin, & Willse, 2009). In the analysis of the Examination for Certification of Proficiency in English (ECPE; Templin & Hoffman, 2013), results indicated that few, if any, examinees were classified into four of the possible eight attribute profiles that are hypothesized in the LCDM for a test of three binary latent attributes. Further, when considering the four profiles lacking examinees, it appeared that some attributes must be mastered before others, suggesting what is commonly called an attribute hierarchy (e.g., Leighton, Gierl, & Hunka, 2004). Although the data analysis alerted us to the notion that such a data structure might be present, we lacked the methodological tools to falsify the presence of such an attribute hierarchy. As such, we developed the Hierarchical Diagnostic Classification Model, or HDCM, in an attempt to fill the need for such tools. We note that the driving force behind the HDCM is one of seeking a simpler, or more parsimonious, solution when model data misfit is either evident from LCDM results or implied by the hypothesized theories underlying the assessed constructs. As a consequence of the ECPE data results, we worked to develop a more broadly defined set of models that would allow for empirical evaluation of hypothesized attribute hierarchies. We felt our work was timely, as a number of methods, both new and old, are now using implied attribute hierarchies to assess examinees in many large scale analyses—from so-called intelligent tutoring systems (e.g., Cen, Koedinger, & Junker, 2006) to large scale state assessment systems for alternative assessments using instructionally imbedded items (e.g. the Dynamic Learning Maps Alternate Assessment System Consortium Grant, 2010–2015). Moreover, such large scale analyses are based on tremendously large data sets, many of which simply cannot fit with the types of (mainly unidimensional) models often used in current large scale testing situations. Furthermore, newly developed standards in education have incorporated ideas of learning progressions which indirectly imply the existence of hierarchically structured attributes (e.g., Progressions for the Common Core State Standards in Mathematics, Common Core State Standards Writing Team, 2012). In short, the current and

In this work, we explored the relationship of the Common Core State Standards in Mathematics (CCSSM) to student achievement. Building on techniques developed for the Third International Mathematics and Science Study (TIMSS), we found a very high degree of similarity between CCSSM and the standards of the highest-achieving nations on the 1995 TIMSS. A similar analysis revealed wide variation in the proximity of state standards in effect in 2009 to the CCSSM. Finally, we used regression and analysis of covariance techniques to assess the relationship between the proximity of a state’s standards to the CCSSM and performance on the 2009 National Assessment of Educational Progress (NAEP). After adjusting for cut-points on state assessments and controlling for state demographics related to socioeconomic status and poverty, we found that states with standards more like the CCSSM, on average, had higher NAEP scores.

In this paper, a learning progression for geometric transformations is developed based on research that demonstrates the importance of viewing transformations as functions of the plane. The 5 levels of the progression reflect a student's evolving understanding of transformations as functions and their evolving understanding of the domain of these transformation as functions. The learning progression developed here is designed to be in alignment with the Common Core State Standards in Mathematics (CCSSM), in that a student who is placed at a particular level in the learning progression would have mastered the Common Core standards at the corresponding grade level. The description of the learning progression also includes sample tasks at each level that are intended to target that level of the progression.

Dynamic hybrid modelling: Switching between AB and SD designs of a predator-prey model

There has been a long histroy of the System Dynamics developed by J.Forrester and its analysis of complex system behaviors. It is necessary to know the detailed system structure and a large amount statistical data to build the flow diagram when using this method. However, our quantitative analysis show that the integrated model can be seen as a combination of many abstracting grey system modeles which may be decomposed from complex system. In this way, the integrated model can be simulated on a computer. The approach of combining quantitative analysis with simulation has the following features, (1) A continuous differential model is established using grey generating numbers. (2) The integrated model can be run on a computer to simulate the system behavior using DYNAMO language. In this paper, the approach of modelling the available abstracting grey dynamic systems and of simulating the integrated systems is described. The system analysis of experimental example show that grey system modelling is very useful in System Dynamics model.

Transport is a vast and complex socio-technical system, and despite a clear need to reduce dependence on fossil fuels due to undesirable environmental impacts, it is largely locked into business-as-usual. Systems approaches are a useful way to help make sense of multiple competing influences which may be simultaneously driving change and supporting the status quo. This paper applies qualitative system dynamics modelling to help interpret the results of a Delphi study into global transport transitions, involving 22 international experts in various aspects of transport. The main contribution of the paper is its exploration of the use of system dynamics (SD) modelling to interpret the Delphi findings. SD modelling was used to reveal and elucidate the causal arguments put forward by the expert panel about the factors driving business-as-usual, the factors creating barriers to more sustainable transport systems, and the drivers of change. The SD model is used to explore and expose the key causal patterns at play, and how these interact to both support and hinder change. The resulting model shows the complex, interdependent dynamics involved in supporting the status quo. Even at the relatively high level of analysis reported here, the model is useful in revealing interdependencies between parts of the system, where change in one part may well have knock-on effects elsewhere in the system. In particular the model reveals the strong reinforcing loops that act to minimise the impact of change drivers and thus retain the dominance of automobility. The result is a system that is highly dependent on the continued existence of key reinforcements such as policies that subsidise fossil fuels. From a methodological perspective, the outcomes of the Delphi study provided a rich source of qualitative material which was highly suitable for developing a system dynamics model.

Many problematic outcomes in agricultural and food systems have important dynamic dimensions and arise due to underlying system structure. Thus, understanding the linkages between system structure and dynamic behavior often is important for the design and implementation of interventions to achieve sustained improvements. System Dynamics (SD) modeling represents system structure using stock-flow-feedback structures expressed as systems of differential equations solved by numerical integration methods. SD methods also encompass a broader methodological approach that emphasizes model structural development and data inputs to replicate one of a limited number of problematic behavioral modes, anticipates dynamic complexity and focuses on feedback processes arising from endogenous system elements. A variety of data sources may be used in SD model development, and parametric sensitivity analysis with SD models can determine priority information needs in feedback-rich systems when data are lacking. Although numerous applications of SD modeling to agriculture exist, the approach is underutilized as a useful tool for research, instruction and programmatic development. This presentation highlights key elements of SD modeling using two examples from animal agriculture at different scales. A dynamic version of the Cornell Net Carbohydrate and Protein System (CNCPS) that represents outcomes for an individual dairy cow is formulated as an SD model, and illustrates the benefits of the SD approach in animal nutrition research and for farm-level nutritional management decisions. At a very different scale, an SD model of the Brazilian dairy supply chain (farms, processing and consumers) illustrates the country-level impacts of efforts to improve cow productivity and how impacts differ if productivity improvement occurs on small farms rather than large farms. The presentation concludes with recommendations to increase awareness and training is SD methods to enhance its appropriate use in research and instruction.

The high selectivities of liquid chromatography and mass spectrometry make liquid chromatography-mass spectrometry one of the most popular tools for quantitative analysis in complex chemical, biological, and environmental systems, while the potential mathematical selectivity of liquid chromatography-mass spectrometry is rarely investigated. This work discussed the mathematical selectivity of liquid chromatography-mass spectrometry by three-way calibration based on the trilinear model, with an application to quantitative analysis of coeluting aromatic amino acids in human plasma. By the trilinear decomposition of the constructed liquid chromatography-mass spectrometry-sample trilinear model and individual regression of the decomposed relative intensity versus concentration, the proposed three-way calibration method successfully achieved quantitative analysis of coeluting aromatic amino acids in human plasma, even in the presence of uncalibrated interferent(s) and a varying background. This analytical method can ease the requirements for sample preparation and complete chromatographic separation of components, reduce the use of organic solvents, decrease the time of chromatographic separation, and increase the peak capacity of liquid chromatography-mass spectrometry. As a "green analytical method", the liquid chromatography-mass spectrometry three-way calibration method can provide a promising tool for direct and fast quantitative analysis in complex systems containing uncalibrated spectral interferents, especially for the situation where the coelution problem is difficult to overcome.