If visualization is to be democratized, we need to provide a means for non-experts to create visualizations that allow them to engage with datasets. We present constructive visualization as a new paradigm for the simple creation of flexible, dynamic visualizations. Constructive visualization is simple---that skills required to build and manipulate the visualizations are akin to kindergarten play; it is expressive---one can build within the constraints of the chosen environment, and it also supports dynamics as these visualizations can be rebuilt and adjusted. We describe the conceptual components and processes underlying constructive visualization, and describe real-world examples to illustrate the utility of this approach. The constructive visualization approach builds on our inherent understanding and experience with physical building blocks, the model enables non-experts to create entirely novel visualizations, and to engage with datasets in a manner that would not have otherwise been possible.