Creating a culture of argumentation in the science classroom requires adequate argumentation competence among future teachers. This study analyzes the impact of instruction based on a validated learning progression on the argumentation competence of preservice elementary science teachers. The focus for the instructional module was the socioscientific issue of breastfeeding. Participants were 106 students from year 3 of a 4-year Bachelor’s in Elementary Education offered by The University of Malaga, who for the purposes of the study were divided into two groups: experimental (those who received the instructional module) and control. The impact of instruction on students’ argumentation competence was examined using a pre-test/post-test assessment tool comprising two tasks: one related to the topic of breastfeeding and which required scientific knowledge to construct or critique arguments, and another, focused on a school lunch program that did not necessitate domain-specific knowledge. Students’ responses were analyzed using rubrics that linked the assessment questions to different learning progression levels, with various performance levels being established for each question. At pretest, students in both groups achieved only intermediate or low performance levels on all the learning progression levels, with the exception of constructing a claim. Following instruction, students in the experimental group showed a significant improvement in performance in relation to all the learning progression levels analyzed, with the exception of providing a counter-critique. We believe that the instructional module and assessment tool described here could usefully be applied to other contexts of argumentation.