When great events happen in isolation from the larger system within which they operate, we fall short of what might be possible otherwise.... Articulation and collaboration are important tools for making lasting systemic change. When educators fail to take advantage of these tools, students ... miss opportunities to connect mathematical ideas. [Emphasis added.] (p. 171) A Metaphor of Change
The complexity of an educational ecosystem is difficult to understand from outside the system. Consider the tranquility of watching fish swimming in an aquarium. At first glance, the aquarium may be thought of as a single simple system where one need only add water, a filtering system, and fish, and then hours of enjoyment for the owner ensue. Aquarium owners, however, understand that the complexity of a healthy aquarium requires careful thought about the quality of the water, types of fish, appropriate food, filtering systems, and lighting.
Once one makes a decision regarding the water type--saltwater or freshwater--water quality is a key factor to a healthy aquarium. Water must first be tested, treated, and then retested. Appropriate plants, coral or rocks, and other underwater furnishings are added. After a few days, while still monitoring the water, one may slowly add fish to the tank. The keeper of the aquarium must give careful thought to the collection of fish, as not all fish get along together. Certain fish will hover near the bottom to keep things clean, while others school together in spiral patterns all over the tank. Some fish must be purchased in pairs, yet others are solitary and prefer to have no one else like them in the aquarium. All fish must be slowly introduced to their new home; otherwise, they will suffer shock and die.
Each aquarium has a fish population it can manage. A limit exists for how many fish, coral, snails, and flora can be added before changes must occur. Overcrowding the water causes pollution beyond what a filter is able to clear, and continually adding new additives to the water will not correct the quality. Regular and consistent maintenance of the tank requires removing and replacing a quantity of water. However, if toxins build up for too long, no amount of filtering or water replacement can purify the tank so the fish can thrive. Fish must be removed, water siphoned, tank scrubbed, and the process restarted. Although viewers from the outside see only the aquarium's beauty, the keeper understands the vast complexity of the aquarium's ecosystem.
Just as different aquariums require varying amounts of effort, so too do different schools require varying levels of engagement to bring about change. The filtering system in a school can be thought of as its communication network, constantly assuring toxins are not building up. The larger the school, the more complex the need for creative communication options becomes. For example, a complex population--novice teachers, veteran teachers, administrators--all at different levels of education and experience, will not perceive digital communication equally. Thus, a simple e-mail request of "Come to my office to discuss this!" can create unwarranted panic for some, while others totally ignore the message. The diverse population has dissimilar mindsets and goals and not all will work well together. Just as in the aquarium, one must consider the population of the school when adding new hires. Will the Clownfish fit in with the Anemone? Will this Damselfish interact well with the Yellow Tang? Sometimes when one determines a new fish might be a bad fit for the aquarium, it is not added. Nonetheless, when a new fish is highly desirable, then fish perceived to react badly with the new one are often removed from the tank. Maintaining the aquarium is a complex endeavor.
A similar complexity exists with changes to the curriculum and pedagogy in schools. As in an aquarium, where one cannot change the fish without considering the environment, likewise, when one considers the complexity in education one cannot change what happens in elementary schools without considering what happens at other educational levels. Changing curriculum at one level causes ripples throughout the system. Although a specific change may make it easier for the teachers and/or administrators at one level, it may not be best for the students, or vice versa. The change has to be systemic and universal; the process should consider the needs of all levels, all students, and all teachers. Everyone in the system must be engaged in the change process. Research suggests that to truly change the way elementary students learn mathematics, for example, one must first change the way elementary teachers are taught mathematics at the university level (e.g. Association of Mathematics Teacher Educators, 2017; Conference Board of the Mathematical Sciences, 2001, 2012; Ma, 2010).
Reticence to Change
Evolution is a slow, arduous process because Nature is innately reticent to change. Mountains, rivers, streams, and even great canyons have remained in the same location for centuries. Their alterations have only occurred through Nature's extreme events--earth-moving forces in the form of melting glaciers, volcanoes, rushing rivers, and meteors. Sir Isaac Newton expressed this in his First Law: "Every body continues in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed upon it" (Newton, 1934/1952, p. 14). Other scientists, such as Max Planck and Albert Einstein, imagined less fixed notions in the realm of physics (Hayles, 1991), lending substance for a more chaotic state of the coming and continuance of the cosmos. History and research seem to indicate, however, that Human nature tends to avoid chaos and be more comfortable with Newton's Law of stasis.
People--and the systems they create--resist change, and most systems are not fond of chaos. People carve out comfortable niches for them selves and find contentment in familiarity and the status quo. Change, whether in location, occupation, social status, or political leadership, creates conflict inside comfort zones, and conflict often creates chaos. Systems, as well as organizations, experience this chaos with regularity as people move in and out and up and down, thus disrupting the flow of status quo. Nonetheless, disrupting the flow is necessary for growth in any system. Waldrop (1992) suggested "species evolve for better survival in a changing environment ... complex systems are more spontaneous, more disorderly, more alive," than static objects and somehow have managed to find a niche at "the edge of chaos" where the components of the systems "never quite lock into place, and yet never quite dissolve into turbulence" (Waldrop, 1992, pp. 11-12). Organisms in systems at the edge of chaos do not indicate or even create the hopefulness they will be willing to change. Achieving lasting systemic change in people may require similar interactive forces basic to Newton's Laws of Motion.
Searching for mechanisms to achieve lasting systemic change in education leads researchers away from physical science toward biological science--psychology. Changing people is a markedly different process than changing the location of a hill, perhaps because people tend to have more to say about what happens to them. Should a highway department decide to move a hill to make a new road more conducive to travel, no concern is given to the will of the hill. Rather, with a few well-placed explosives, the hill has been moved and road construction begins. However, should a more willful organism, such as a school district, decide to restructure its curriculum or staff, a few well-placed explosives will not have the desired effect. Chaos will ensue and, undoubtedly, change will happen, but not in any controlled manner. Change within systems involving people requires careful study, intentional consistency, engagement in the process at all levels, and knowledgeable leadership.
The works of Whitehead, Piaget, and Bandura have contributed to theories of change and are all familiar to educators. Other change theorists, such as Lewin, Lippitt, Prochaska, and DiClemente, are perhaps more familiar to medical professionals. Each of these theorists added worthy knowledge to the field of change, often building on the work of one another. However, Bandura's work remains the most relevant if one seeks to create lasting systemic change. His cardinal defining properties of a genuine change stage theory include "qualitative transformations across stages, invariant sequence of change, and nonreversibility" (Bandura, 1997, p. 412), and describe the traits required for lasting systemic change.
Developing a Stance for Change
Research on change theories began to emerge shortly after the end of World War II. In the late 1940s, both Whitehead and Lewin published their views on how change should occur; however, their foci were quite different (Lewin, 1947; Whitehead, 1949). While Whitehead focused his views of change on the development of children, Lewin examined societal changes. Both views are crucial to how change occurs in education. Lewin's three step process for permanent change--unfreeze, move, and refreeze - sounds simplistic in nature, but because the process is forced change, it can cause considerable disruption to the system it is forced upon. For example, even something as innocent as rearranging the teachers in a building by grade instead of subject can be unwarranted change for the teachers. In the unfreezing step, Lewin advised that problems can arise in different cases--including the removal of prejudices, complacency, and self-righteousness--in order to "bring about deliberately an emotional stir-up" (p. 35). Regarding such cases, Lewin cautioned, "since any level is...