When teachers provide students with every opportunity to visually understand a mathematical concept, process, definition, or notation, they allow them to construct and manipulate relevant and useful images in their minds. Visual understanding has a dynamic character that they do not easily develop with alphanumeric symbols alone despite the advantage of seeing and verbally manipulating the explicit symbolic forms. Also, visual understanding comes with, or in the absence of, external tools such as manipulatives and graphing technologies. In this article, the author shares work that has been done in class when the author redesigned and implemented significant portions of the state-mandated algebra curriculum from a visual perspective. The author shares with readers how the class of 7th- and 8th-grade students individually, and in joint activity with one another, successfully constructed their algebraic notions by tapping onto their natural phenomenal capacity to see, think, and reason with the mind's eye. The experiences the author shares in this article reflect the rigour of both the visual forms and visualisation strategies that students developed that consequently enabled them to see the significance and necessity of the corresponding algebraic notions in alphanumeric form. (Contains 11 figures.)