Students need models that provide (1) countable, visually distinct model for each number, (2) can be organized in obvious and predictable ways, and (3) provide a clearly defined context of ten.
Ten-frame tiles give students the visual model to make the connection between each number name and the quantity it represents. It also shows the “unique configuration” for each number quantity from 0 – 10 – giving the students a “shape” of the quantity to recognize. The dots show the “completeness” of each ten easily without students needing to recount each group to confirm that there are ten.
Ten-frames do not require students to internalize the concept of tens and ones and that one unit can more than one countable unit such as a base-10 rod. These models also do not provide students with manipulatives in which they can “build” things and “play.”
Ten-frames also provide students with a visually distinct, instantly recognizable picture of the number – which leads to subtizing (instantly recognizing a number of things without counting each individual piece). This step is missing if teachers skip using ten-frames and jump right to using tens-rods.
When computing, these frameworks give students a model that “invites number composition and decomposition as part of visualizing a quantity.” So, this is evident when viewing the example “figure 4” in the literature. Two ten-frames show a 5 and an 8. If we wanted to add these two numbers together, it is easy to SEE that two of the units can easily move to the 8 frame to complete it, becoming a 10-frame, leaving 3 on the 5 frame; 10 + 3 = 13. It is easy to see this and visually make that understanding while working with the oral and written number as well.