There's a lot of fallacious concept's in the article, and the OP. It's necessary to have them clear for a proper answer.
While Logic is the FORMAL set of rules that govern reason, Mathematics is a type of knowledge consisting of an abstract description of the world. As such, Mathematics is an individual (rather than social) asset. This is how it develops:
Following Kant, you need to know the form of an apple -a sphere-, in order to know an actual apple and vice-versa: you need to know an apple in order to know the sphere. This is essentially how a priori knowledge (Mathematics) is developed: simultaneously to a posteriori knowledge (empirical knowledge, objects of the world). The apple is a PHYSICAL object, and the sphere is a METAPHYSICAL object that correspondiente to it.
Please remark that in the Kantian jargon, a priori does not mean "before", but instead "necessary for". The key contribution of Kant lies here: metaphysical truth (e.g. Mathematics) is possible, exists, and it develops simultaneously to empirical truth (e.g. physical objects).
From the moment you know the object, you start to develop your own mathematical knowledge: more than one apple is two apples (addition), dividing such system provides two groups of a single apple (division, subtraction, etc.). Check Kant's discussion about the Transcendental Analytic a priori knowledge: Kant's categories.
Mathematical truth, in this context, is just the logical CONSISTENCY between the facts of the world (apples, as perceived by our senses) and mathematical knowledge (spheres, Kantian categories).
Now, mathematics has the following functional structure:
- Mathematics is a TOOL that helps knowing the world and predicting the future (what has been described, for example, if I go get an apple, I can predict that I will have more than what I have now, and if I have 1, I can add what comes: 1+1=2).
- Mathematics is a LANGUAGE, which allows communicating mathematical ideas. Here, it becomes SOCIAL. In this context, mathematical truth is not only CONSISTENCY, but also AGREEMENT. I use the word "seven" or the symbol "7" to describe something, that MUST have the same meaning for the rest of my social group (agreement). In other words, mathematics, as a LANGUAGE is an OBJECTIVE (not only SUBJECTIVE) agreement about its CONTENTS (objective essentially means shared subjectivity). So, mathematical truth is the shared-subjective (OBJECTIVE) agreement about the CONSISTENCY between the PHYSICAL facts of the world, their METAPHYSICAL representation (Mathematical)
Now, if you want to address the Mathematics social process (the social process of the development of Mathematics), the previous concepts must be crystal clear. Eugenia Cheng's article, -in form and content- is poor in concepts. Perhaps it is Ok for a TV audience, but not to make philosophy,
MORALS is a set of RULES that help social coexistence. For example, if the final, shared goal of the group is to exist, and grow, instead of dissipating, Morals is the set of rules that determine how to socially interact in order to survive.
Chang's definition of mathematical morality is this:
Mathematical morality is about how mathematics should behave, not just that this is right, this is wrong.
If so, Chang should have used "mathematical behaviorism" (behaviorism is understood as "way of thinking" when its subject is passive, unable to behave).
Well, Mathematics don't "behave", because TOOLS or LANGUAGES (which are ultimately communication TOOLS) don't behave. Tools are just resources for survival.
In any case, Chang's poor definition of mathematical morality is derived from social morality, regarding an absolute imperative "how X should behave", which has no sense. Morals are subjective, RELATIVE to each society, they are not ABSOLUTE, for all humanity; as said, the moral rules of group A, which has the goal of survival, might be radically different than those of group B, which has the goal of making war. Moral rules are relative. So, no mathematical morality.
There might be few or none sociological concerns regarding Mathematics, simply because, as said, Mathematics is a TOOL, and tools are far from presenting sociological considerations (commonly, guns are considered a social problem, but in final terms, the concern is never about guns; guns as such are just extensions of our fingers, if you stick a needle to your hand, you need to avoid scratching your eyes, the problem is not needles). There are no sociological considerations regarding tools (what are the sociological considerations of a Phillips screwdriver? What are the sociological considerations of integer addition?)
On the contrary, there might be sociological considerations related to the risks or impact of disciplines sustained by Mathematics, but this the same as the risks or impact of discipline X. Mathematics is not part of the problem. For example, https://en.m.wikipedia.org/wiki/Social_constructionism, which might raise the conflicts between social goals and the origin and application of the tool.