Prospective K-8 teachers’ noticing of student justifications and generalizations in the context of analyzing written artifacts and video-records

Abstract Background This paper contributes to current discussions about supporting prospective teachers (PSTs) in developing skills of noticing students’ mathematical thinking. We draw attention PSTs’ initial (prior instruction focused on noticing) as PSTs engage analyzing written artifacts student work and video-records. examined compared they analyzed how students reason about, generalize, justify generalizations figural patterns given video records. identified aspects thinking justifications, which addressed interpreted. also respond analyze or video-records small group discussions, we the foci responding practice. Results Our data revealed that justifications differed while accounting for ways was externalized (written video-records). attending- -interpreting their practices were mathematically significant a greater extent context While work, demonstrated patterns, generalization strategies, linked an understanding pattern structure, captured via videos. Conclusion results document without providing any intentional support skills, are more deliberate focus believe analysis might demand from be analytical. examining representations, have reconstruct reasoning. Unlike videos where tell use gestures express thinking, provides fewer clues Thus, demands deeper level engagement strive understand study extends research by documenting differences relation nature analyze. adds prior characterizing specific address students.