The popularity and influence of digital interaction in museum design has greatly increased along with developments of society and technology. Science museums and natural history museums treat digital interactions, such as multi-touch displays, as important tools in exhibition design that improve the interactivity of visitor experience through open-ended activities. Art museums, however, which mostly focus on displaying art collections and lack hands-on activities in exhibits, have yet to embrace this type of interactivity. The visitor experience in art museums is still relatively passive: their digital interactions are limited to catalogs of art history, which offer few opportunities for personal input. Furthermore, modern art is especially difficult for visitors to interpret and engage. This study is an attempt to address this gap in usage of interactive displays in art museums by introducing open-ended interactions as a way to engage visitors about modern art. It culminates in the design of a multi-touch application, What Inspires You?, to demonstrate possible approaches that can be used to enrich the visitor experience in art museums through educative perspectives. Museum education literature shows that constructivism is an effective theory for guiding interaction design to personalize visitors' learning experiences at museums. The conceptual prototype developed in this study is informed by constructivism and a way for art museums to help visitors bridge modern art and personal experience by engaging them with the inspirations that affect art creation and then allowing them to experiment with artistic expression themselves. The prototype combines concepts of museum interactivity, pedagogies of museum education, and multi-touch interface design to enhance dynamic experience so visitors can create their own unique learning experience. This prototype is a new potential approach that can help art museums to engage their visitors more effectively through open-ended interactivity.