I'll talk about just one idea: quantitative reasoning is extremely important for mathematical modeling. This may seem obvious to some, especially to science educators, but I rarely hear mathematics educators discussing quantitative reasoning and the related literature, even though modeling is becoming an increasingly popular conversation topic.
In a 2022 article, "A bridging study analyzing mathematical model construction through a quantities-oriented lens," Czocher et al. describe various modeling competencies that align well with your description of modelling. "Modelling competencies include forming an understanding of a real-world scenario, simplifying, mathematizing (producing a representation), solving, interpreting, and validating."
In their introduction, Czocher et al. mention that the "simplifying" and "mathematizing" competencies are known to be particularly challenging for students. A goal of the study was to analyze the relationship between these competencies and students' quantitative reasoning abilities. The authors concluded that "with regard to mathematizing, the data support Thompson’s (2011) position that quantitative reasoning should be the basis of mathematical modelling."
In Thompson's (2011) article "Quantitative Reasoning and Mathematical Modeling," he describes a theoretical framework for quantitative reasoning, and there are several implications for teaching modeling that I've taken away. One is that I need to intentionally support students to conceive of quantities in productive or desired ways.
The point that quantities are mental constructions, and that their creation is often effortful, is central to mathematics education. Too often quantities, such as area and volume, are taken as obvious, and hence there is no attention given to student’s construction of quantity through the dialectic object-attribute-quantification. Instead, textbook writers and teachers just use them to teach. (Thompson, 2011, p. 34)
Lobato and Siebert (2002), in "Quantitative reasoning in a reconceived view of transfer," describe a teaching experiment in which students who had previously learned about slope were taught again with a focus on quantitative reasoning. They present the case of a student who, at the start of the experiment, explicitly rejected the use of the slope formula on a task involving the steepness of a ramp. According to the researchers, after "a lengthy process of reconstructing his understanding of the quantitative relationships involved," the student was able to employ proportional reasoning on the same task.
Another implication for teaching modeling that I've taken from the quantitative reasoning literature is that I need to attend closely to students' conceptions of "variation." In the same article, Thompson describes two students' differing perspectives on how quantities vary, a "chunky" perspective and a "continuous" perspective, from a teaching experiment by Castillo-Garsow.
In Tiffany’s thinking, the account’s earned interest did not pass through the 1/4-year amount on its way to the one-year amount. Rather, the 1/4-year amount was an amount to be computed ad hoc. Derek, who thought of time passing continuously and thought of an account having a value at each moment in time, thought more in terms of the account changing at the rate of a number of dollars per year for some number of years, and the number of years needn’t be a whole number. Earned interest accrued continuously. Tiffany could not see that the account's rate of change with respect to time was proportional to the account’s value. Derek saw this relationship intuitively. (p. 49)
There are other important ideas about teaching mathematical modeling in the literature, and Czocher et al. acknowledge several of them in their article. But I find the link to quantitative reasoning to be the most compelling, based on my personal experience with students' difficulties with modeling.