Inferentialism as an alternative to socioconstructivism in mathematics education

The purpose of this article is to draw the attention of mathematics education researchers to a relatively new semantic theory called inferentialism, as developed by the philosopher Robert Brandom. Inferentialism is a semantic theory which explains concept formation in terms of the inferences individuals make in the context of an intersubjective practice of acknowledging, attributing, and challenging one another’s commitments. The article argues that inferentialism can help to overcome certain problems that have plagued the various forms of constructivism, and socioconstructivism in particular. Despite the range of socioconstructivist positions on offer, there is reason to think that versions of these problems will continue to haunt socioconstructivism. The problems are that socioconstructivists (i) have not come to a satisfactory resolution of the social-individual dichotomy, (ii) are still threatened by relativism, and (iii) have been vague in their characterization of what construction is. We first present these problems; then we introduce inferentialism, and finally we show how inferentialism can help to overcome the problems. We argue that inferentialism (i) contains a powerful conception of norms that can overcome the social-individual dichotomy, (ii) draws attention to the reality that constrains our inferences, and (iii) develops a clearer conception of learning in terms of the mastering of webs of reasons. Inferentialism therefore represents a powerful alternative theoretical framework to socioconstructivism

Supplementing High-Density SNP Microarrays for Additional Coverage of Disease-Related Genes: Addiction as a Paradigm

Commercial SNP microarrays now provide comprehensive and affordable coverage of the human genome. However, some diseases have biologically relevant genomic regions that may require additional coverage. Addiction, for example, is thought to be influenced by complex interactions among many relevant genes and pathways. We have assembled a list of 486 biologically relevant genes nominated by a panel of experts on addiction. We then added 424 genes that showed evidence of association with addiction phenotypes through mouse QTL mappings and gene co-expression analysis. We demonstrate that there are a substantial number of SNPs in these genes that are not well represented by commercial SNP platforms. We address this problem by introducing a publicly available SNP database for addiction. The database is annotated using numeric prioritization scores indicating the extent of biological relevance. The scores incorporate a number of factors such as SNP/gene functional properties (including synonymy and promoter regions), data from mouse systems genetics and measures of human/mouse evolutionary conservation. We then used HapMap genotyping data to determine if a SNP is tagged by a commercial microarray through linkage disequilibrium. This combination of biological prioritization scores and LD tagging annotation will enable addiction researchers to supplement commercial SNP microarrays to ensure comprehensive coverage of biologically relevant regions

Genome-Wide and Candidate Gene Association Study of Cigarette Smoking Behaviors

The contribution of common genetic variation to one or more established smoking behaviors was investigated in a joint analysis of two genome wide association studies (GWAS) performed as part of the Cancer Genetic Markers of Susceptibility (CGEMS) project in 2,329 men from the Prostate, Lung, Colon and Ovarian (PLCO) Trial, and 2,282 women from the Nurses' Health Study (NHS). We analyzed seven measures of smoking behavior, four continuous (cigarettes per day [CPD], age at initiation of smoking, duration of smoking, and pack years), and three binary (ever versus never smoking, ≤10 versus >10 cigarettes per day [CPDBI], and current versus former smoking). Association testing for each single nucleotide polymorphism (SNP) was conducted by study and adjusted for age, cohabitation/marital status, education, site, and principal components of population substructure. None of the SNPs achieved genome-wide significance (p<10−7) in any combined analysis pooling evidence for association across the two studies; we observed between two and seven SNPs with p<10−5 for each of the seven measures. In the chr15q25.1 region spanning the nicotinic receptors CHRNA3 and CHRNA5, we identified multiple SNPs associated with CPD (p<10−3), including rs1051730, which has been associated with nicotine dependence, smoking intensity and lung cancer risk. In parallel, we selected 11,199 SNPs drawn from 359 a priori candidate genes and performed individual-gene and gene-group analyses. After adjusting for multiple tests conducted within each gene, we identified between two and five genes associated with each measure of smoking behavior. Besides CHRNA3 and CHRNA5, MAOA was associated with CPDBI (gene-level p<5.4×10−5), our analysis provides independent replication of the association between the chr15q25.1 region and smoking intensity and data for multiple other loci associated with smoking behavior that merit further follow-up

Genome-Wide and Candidate Gene Association Study of Cigarette Smoking Behaviors

The contribution of common genetic variation to one or more established smoking behaviors was investigated in a joint analysis of two genome wide association studies (GWAS) performed as part of the Cancer Genetic Markers of Susceptibility (CGEMS) project in 2,329 men from the Prostate, Lung, Colon and Ovarian (PLCO) Trial, and 2,282 women from the Nurses' Health Study (NHS). We analyzed seven measures of smoking behavior, four continuous (cigarettes per day [CPD], age at initiation of smoking, duration of smoking, and pack years), and three binary (ever versus never smoking, ≤10 versus >10 cigarettes per day [CPDBI], and current versus former smoking). Association testing for each single nucleotide polymorphism (SNP) was conducted by study and adjusted for age, cohabitation/marital status, education, site, and principal components of population substructure. None of the SNPs achieved genome-wide significance (p<10−7) in any combined analysis pooling evidence for association across the two studies; we observed between two and seven SNPs with p<10−5 for each of the seven measures. In the chr15q25.1 region spanning the nicotinic receptors CHRNA3 and CHRNA5, we identified multiple SNPs associated with CPD (p<10−3), including rs1051730, which has been associated with nicotine dependence, smoking intensity and lung cancer risk. In parallel, we selected 11,199 SNPs drawn from 359 a priori candidate genes and performed individual-gene and gene-group analyses. After adjusting for multiple tests conducted within each gene, we identified between two and five genes associated with each measure of smoking behavior. Besides CHRNA3 and CHRNA5, MAOA was associated with CPDBI (gene-level p<5.4×10−5), our analysis provides independent replication of the association between the chr15q25.1 region and smoking intensity and data for multiple other loci associated with smoking behavior that merit further follow-up

Associations of Variants in CHRNA5/A3/B4 Gene Cluster with Smoking Behaviors in a Korean Population

Multiple genome-wide and targeted association studies reveal a significant association of variants in the CHRNA5-CHRNA3-CHRNB4 (CHRNA5/A3/B4) gene cluster on chromosome 15 with nicotine dependence. The subjects examined in most of these studies had a European origin. However, considering the distinct linkage disequilibrium patterns in European and other ethnic populations, it would be of tremendous interest to determine whether such associations could be replicated in populations of other ethnicities, such as Asians. In this study, we performed comprehensive association and interaction analyses for 32 single-nucleotide polymorphisms (SNPs) in CHRNA5/A3/B4 with smoking initiation (SI), smoking quantity (SQ), and smoking cessation (SC) in a Korean sample (N = 8,842). We found nominally significant associations of 7 SNPs with at least one smoking-related phenotype in the total sample (SI: P = 0.015∼0.023; SQ: P = 0.008∼0.028; SC: P = 0.018∼0.047) and the male sample (SI: P = 0.001∼0.023; SQ: P = 0.001∼0.046; SC: P = 0.01). A spectrum of haplotypes formed by three consecutive SNPs located between rs16969948 in CHRNA5 and rs6495316 in the intergenic region downstream from the 5′ end of CHRNB4 was associated with these three smoking-related phenotypes in both the total and the male sample. Notably, associations of these variants and haplotypes with SC appear to be much weaker than those with SI and SQ. In addition, we performed an interaction analysis of SNPs within the cluster using the generalized multifactor dimensionality reduction method and found a significant interaction of SNPs rs7163730 in LOC123688, rs6495308 in CHRNA3, and rs7166158, rs8043123, and rs11072793 in the intergenic region downstream from the 5′ end of CHRNB4 to be influencing SI in the male sample. Considering that fewer than 5% of the female participants were smokers, we did not perform any analysis on female subjects specifically. Together, our detected associations of variants in the CHRNA5/A3/B4 cluster with SI, SQ, and SC in the Korean smoker samples provide strong evidence for the contribution of this cluster to the etiology of SI, ND, and SC in this Asian population

The 3′ Splice Site of Influenza A Segment 7 mRNA Can Exist in Two Conformations: A Pseudoknot and a Hairpin

The 3′ splice site of influenza A segment 7 is used to produce mRNA for the M2 ion-channel protein, which is critical to the formation of viable influenza virions. Native gel analysis, enzymatic/chemical structure probing, and oligonucleotide binding studies of a 63 nt fragment, containing the 3′ splice site, key residues of an SF2/ASF splicing factor binding site, and a polypyrimidine tract, provide evidence for an equilibrium between pseudoknot and hairpin structures. This equilibrium is sensitive to multivalent cations, and can be forced towards the pseudoknot by addition of 5 mM cobalt hexammine. In the two conformations, the splice site and other functional elements exist in very different structural environments. In particular, the splice site is sequestered in the middle of a double helix in the pseudoknot conformation, while in the hairpin it resides in a two-by-two nucleotide internal loop. The results suggest that segment 7 mRNA splicing can be controlled by a conformational switch that exposes or hides the splice site