“…Many of these incorporate the use of multiple representations of a functional relationship -diagrams of a growing pattern with item numbers, verbal and worded descriptions, symbolic expressions and equations, tables of values, and graphs (e.g., Confrey & Smith, 1994, Kaput, 1999MacGregor & Stacey, 1995). A number of studies advocated the use of concrete materials in constructing growing patterns so that students are able to notice the changes between items and the structure within an item (Markworth, 2010;Moss, Beatty, Barkin, & Shillolo, 2008;Warren & Cooper, 2008). Friel and Markworth (2009) provided examples of several types of geometric patterns of increasing levels of complexity which give students multiple opportunities to experience the process of noticing the structure of the items -answering the question, "What is it that all these instances have in common?"…”