Models are important for fractional understanding. The variety of models and the context in which they are used is key. I have concerns with misusing tools/objects, as in the case of “popsicle stick fractions”, when they are used as a model for fraction notation (i.e. being represented as 2 popsicle sticks placed over a horizontal line and 3 popsicle sticks under the horizontal line).
The popsicle sticks themselves can be a powerful tool for teaching fractions of a set if used in a way that allows students to see fractions as numbers. Placing two popsicle sticks over three popsicle sticks does little to help a student see "two-thirds" as a number, and understand it lies between 0 and 1.
Other tools (manipulatives), such as fraction circles are great, but add in other representations like modeling fractions on number lines, rulers, fraction bars, and real objects – even paper folding – because they work well.