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This research article contributes to the growing literature highlighting the potential for innovation in mathematics education through design cycles that involve creative risk-taking and failure-based learning. Specifically, we explore how “failed” cycles of StoryCircles—a practice-based professional development approach that centers on teacher collaboration—have been productive in fostering innovations within the program. Our focus is on the challenges that arose in our efforts to enable feedback mechanisms within the StoryCircles system that support teachers’ interrogation of their own instructional practice, as they collaboratively develop lessons and expand their collective knowledge base for teaching mathematics. Through examples of three challenges, we illustrate how various lesson artifacts, including those constructed by teachers in anticipation of implementation and those extracted from actual implementations, failed to serve as the sole source of feedback for supporting teachers’ growth. 

Wolbachia is a widespread endosymbiont of insects and filarial nematodes that profoundly influences host biology. Wolbachia has also been reported in rhizosphere hosts, where its diversity and function remain poorly characterized. The discovery that plant-parasitic nematodes (PPNs) host Wolbachia strains with unknown roles is of interest evolutionarily, ecologically, and for agriculture as a potential target for developing new biological controls. The goal of this study was to screen communities for PPN endosymbionts and analyze genes and genomic patterns that might indicate their role. Genome assemblies revealed 1 out of 16 sampled sites had nematode communities hosting a Wolbachia strain, designated w Tex, that has highly diverged as one of the early supergroup L strains. Genome features, gene repertoires, and absence of known genes for cytoplasmic incompatibility, riboflavin, biotin, and other biosynthetic functions placed w Tex between mutualist C + D strains and reproductive parasite A + B strains. Functional terms enriched in group L included protoporphyrinogen IX, thiamine, lysine, fatty acid, and cellular amino acid biosynthesis, while dN/dS analysis suggested the strongest purifying selection on arginine and lysine metabolism, and vitamin B6, heme, and zinc ion binding, suggesting these as candidate roles in PPN Wolbachia . Higher dN/dS pathways between group L, w Pni from aphids, w Fol from springtails, and w CfeT from cat fleas suggested distinct functional changes characterizing these early Wolbachia host transitions. PPN Wolbachia had several putative horizontally transferred genes, including a lysine biosynthesis operon like that of the mitochondrial symbiont Midichloria , a spirochete-like thiamine synthesis operon shared only with w CfeT, an ATP/ADP carrier important in Rickettsia , and a eukaryote-like gene that may mediate plant systemic acquired resistance through the lysine-to-pipecolic acid system. The Discovery of group L-like variants from global rhizosphere databases suggests diverse PPN Wolbachia strains remain to be discovered. These findings support the hypothesis of plant-specialization as key to shaping early Wolbachia evolution and present new functional hypotheses, demonstrating promise for future genomics-based rhizosphere screens.