With the rising emphasis on computer science (CS) education, many states, school districts, and schools have grappled with how to address computing in the K-12 curriculum. While some approaches dedicate classroom time to specific CS topics, others are attempting to infuse computing curriculum into other subjects like math and science. Preparing educators without prior CS experience to teach this integrated content is challenging. In this paper, we share programming-integrated mathematics learning (PML) modules that we developed to support teachers in learning to use programming in mathematics classrooms through argumentation. To test the effectiveness of the modules, we implemented them in a mathematics content course for elementary education majors and a mathematics pathway course for non-STEM majors. This paper focuses on student-written reflections as data to investigate how education and non-STEM majors describe their learning through the PML modules. Our analysis shows that the PML modules helped study participants understand mathematical concepts better because it allows for both the illustration of the concepts in new ways as well as the ability to perform trial and error experimentation. They also described the value of learning programming in mathematics classrooms through argumentation, such as learning different perspectives and helping each other understand. Future study is needed to explore what knowledge about mathematics and programming study participants develop through the PML modules and in what ways to increase students’ and teachers’ self-efficacy concerning programming in the context of CS-and-mathematics-integrated classrooms.