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Development of fraction number line estimation was assessed longitudinally over 5 time points between 4th and 6th grades. Although students showed positive linear growth overall, latent class growth analyses revealed 3 distinct growth trajectory classes: Students who were highly accurate from the start and became even more accurate (n = 154); students who started inaccurate but showed steep growth (n = 121); and students who started inaccurate and showed minimal growth (n = 197). Younger and minimal growth students typically estimated both proper and improper fractions as being less than 1, failing to base estimates on the relation between the numerator and denominator. Class membership was highly predictive of performance on a statewide-standardized mathematics test as well as on a general fraction knowledge measure at the end of 6th grade, even after controlling for mathematic-specific abilities, domain-general cognitive abilities, and demographic variables. Multiplication fluency, classroom attention, and whole number line estimation acuity at the start of the study predicted class membership. The findings reveal that fraction magnitude understanding is central to mathematical development. (PsycINFO Database Record

The goal of the present article is to synthesize findings to date from the Delaware Longitudinal Study of Fraction Learning. The study followed a large cohort of children ( N = 536) between Grades 3 and 6. The findings showed that many students, especially those with diagnosed learning disabilities, made minimal growth in fraction knowledge and that some showed only a basic grasp of the meaning of a fraction even after several years of instruction. Children with low growth in fraction knowledge during the intermediate grades were much more likely to fail to meet state standards on a broad mathematics measure at the end of Grade 6. Although a range of general and mathematics-specific competencies predicted fraction outcomes, the ability to estimate numerical magnitudes on a number line was a uniquely important marker of fraction success. Many children with mathematics difficulties have deep-seated problems related to whole number magnitude representations that are complicated by the introduction of fractions into the curriculum. Implications for helping students with mathematics difficulties are discussed.

Palmitoylation is the post-translational addition of a palmitate moiety to a cysteine residue through a covalent thioester bond. The addition and removal of this modification is controlled by both palmitoyl acyl-transferases and thioesterases. Using bioinformatic analysis, we identified 22 DHHC family palmitoyl acyl-transferase homologs in the Drosophila genome. We used in situ hybridization, RT-PCR, and published FlyAtlas microarray data to characterize the expression patterns of all 22 fly homologs. Our results indicate that all are expressed genes, but several, including CG1407, CG4676, CG5620, CG6017/dHIP14, CG6618, CG6627, and CG17257 appear to be enriched in neural tissues suggesting that they are important for neural function. Furthermore, we have found that several may be expressed in a sex-specific manner with adult male-specific expression of CG4483 and CG17195. Using tagged versions of the DHHC genes, we demonstrate that fly DHHC proteins are primarily located in either the Golgi Apparatus or Endoplasmic Reticulum in S2 cells, except for CG1407, which was found on the plasma membrane. We also characterized the subcellular localization and expression of the three known thioesterases: Palmitoyl-protein Thioesterase 1 (Ppt1), Palmitoyl-protein Thioesterase 2 (Ppt2), and Acyl-protein Thioesterase 1 (APT1). Our results indicate that Ppt1 and Ppt2 are the major lysosomal thioesterases while APT1 is the likely cytoplasmic thioesterase. Finally, in vivo rescue experiments show that Ppt2 expression cannot rescue the neural inclusion phenotypes associated with loss of Ppt1, further supporting distinct functions and substrates for these two thioesterases. These results will serve as the basis for a more complete understanding of the protein palmitoylome's normal cellular functions in the fly and will lead to further insights into the molecular etiology of diseases associated with the mis-regulation of palmitoylation.