IntroductionIn this paper I show, using a nested sequence of simple examples increasing in complexity, why math teachers need not rely solely on the current symbolic representation (closed form equation) for studying dynamic problems in algebra.Mathematizing story problems into closed form has, historically, been difficult for students (Schwartz & Yerashalmy, 1995). However, new technologies can provide alternate and more visual representations of many functions studied in algebra, making algebraic concepts accessible to more students. While the closed form representation of problems has served us well in the past, many of the problems our students will face, as adults, will require the ability to understand and make decisions about complex systems (Lesh, 2006). The goal of this paper is to support an evolution in teaching strategy and the content employed so as to make the study of complex systems accessible to algebra students.Change is accelerating, and as the of the systems in which we live grows, so do the unanticipated side effects of human actions, further increasing complexity (Sterman, 1994). Our nation and the global community face serious problems such as global warming, soaring national debt, unsustainable consumption of natural resources, daunting health costs for families, rising numbers of children in poverty, environmental impacts on health, and more. How will our children be able to successfully address these problems if teachers do not have strategies that are designed to help students build understanding of dynamic systemic problems?Using technology, specifically Stella, it is possible to have students represent and analyze problems that would typically have been out of their mathematical reach using traditional closed form equation approaches (Blume & Heid 2008; Fisher, 2011a; Pea, 1987). In what follows, I first describe Stella's visual interface and present a series of models using that software. Based on this presentation, I argue how the use of the software extends the range of possibilities for modeling, and in so doing reorganizes algebraic thinking. Finally, I consider some extensions beyond the scope of this paper, reflecting on the unchanging nature of the mathematics curriculum in the light of the need to understand dynamic systems, and the new possibilities offered by technology.A Graduated Series of Stella ModelsStella IconsThe Stella SD software uses four main icons. One icon operates as an accumulator of stuff' over time. This stuff' can be physical, like the number of cars in a city, or abstract, like concern about child homelessness. The accumulator is identified as a shown as a rectangular icon. The stock depicts an important variable of interest and represents an aspect of the state of the system. See Figure 1.As will become clear in the examples that follow, Stella models situations dynamically through updating repeatedly how the state of the system repeats over time (similar to recursive equations). The time step is changeable, with precision increasing as it is made smaller; calculus represents the limiting case as the time step approaches zero).A icon represents a rate of change in a stock. If the flow arrowhead is pointing toward/away from the stock, a positive value (within the icon) represents the rate of increase/decrease of the stock value.Another icon called a converter could represent either a parameter value or a non-stock variable whose value is computed using a formula.Finally, there are icons called connectors that link converters to flows, converters to other converters, stocks to flows, or stocks to converters. They act like telephone lines, communicating numeric information between components so formulas can be updated each time step (calculation interval).A series of simple finance scenarios will be used to show how it is possible to think about a problem using different symbolic representations, and will show some of the advantages of each representation. …