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This study analyzed geometry problems in four middle-grade mathematics textbook series from Taiwan, Singapore, Finland, and the United States, while exploring the expectations for students' learning experiences with these problems. An analytical framework developed for mathematics textbook problem analysis had three dimensions: representation forms, contextual features, and response types. The results showed that the Taiwanese and Singaporean textbooks contained more problems in combined form, whereas the Finnish and American textbooks contained more problems in verbal and visual forms. The problem distribution across various representation forms was more balanced in the Finnish and Singaporean textbooks than in the Taiwanese and American textbooks. Most problems were non-application and close-ended problems compared to other application and openended problems. The Taiwanese textbooks contained the lowest proportion of real-world problems, whereas the American textbooks contained the highest proportion of openended problems. Implications of this study's findings for textbook developers and future research directions are discussed.

BackgroundPrevious studies in Saccharomyces cerevisiae showed that ALA1 (encoding alanyl-tRNA synthetase) and GRS1 (encoding glycyl-tRNA synthetase) respectively use ACG and TTG as their alternative translation initiator codons. To explore if any other non-ATG triplets can act as initiator codons in yeast, ALA1 was used as a reporter for screening.ResultsWe show herein that except for AAG and AGG, all triplets that differ from ATG by a single nucleotide were able to serve as initiator codons in ALA1. Among these initiator codons, TTG, CTG, ACG, and ATT had ~50% initiating activities relative to that of ATG, while GTG, ATA, and ATC had ~20% initiating activities relative to that of ATG. Unexpectedly, these non-AUG initiator codons exhibited different preferences toward various sequence contexts. In particular, GTG was one of the most efficient non-ATG initiator codons, while ATA was essentially inactive in the context of GRS1.ConclusionThis finding indicates that a sequence context that is favorable for a given non-ATG initiator codon might not be as favorable for another.

Two oligomeric types of glycyl-tRNA synthetase (GlyRS) are found in nature: a α2 type and a α2β2 type. The former has been identified in all three kingdoms of life and often pairs with tRNAGly that carries an A73 discriminator base, while the latter is found only in bacteria and chloroplasts and is almost always coupled with tRNAGly that contains U73. In the yeast Saccharomyces cerevisiae, a single GlyRS gene, GRS1, provides both the cytoplasmic and mitochondrial functions, and tRNAGly isoacceptors in both compartments possess A73. We showed herein that Homo sapiens and Arabidopsis thaliana cytoplasmic GlyRSs (both α2-type enzymes) can rescue both the cytoplasmic and mitochondrial defects of a yeast grs1 - strain, while Escherichia coli GlyRS (a α2β2-type enzyme) and A. thaliana organellar GlyRS (a (αβ)2-type enzyme) failed to rescue either defect of the yeast mull allele. However, a head-to-tail αβ fusion of E. coli GlyRS effectively supported the mitochondrial function. Our study suggests that a α2-type eukaryotic GlyRS may be functionally substituted with a α2β2-type bacterial cognate enzyme despite their remote evolutionary relationships.

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