Challenges in mathematical cognition: a collaboratively-derived research agenda

This paper reports on a collaborative exercise designed to generate a coherent agenda for research on mathematical cognition. Following an established method, the exercise brought together 16 mathematical cognition researchers from across the fields of mathematics education, psychology and neuroscience. These participants engaged in a process in which they generated an initial list of research questions with the potential to significantly advance understanding of mathematical cognition, winnowed this list to a smaller set of priority questions, and refined the eventual questions to meet criteria related to clarity, specificity and practicability. The resulting list comprises 26 questions divided into six broad topic areas: elucidating the nature of mathematical thinking, mapping predictors and processes of competence development, charting developmental trajectories and their interactions, fostering conceptual understanding and procedural skill, designing effective interventions, and developing valid and reliable measures. In presenting these questions in this paper, we intend to support greater coherence in both investigation and reporting, to build a stronger base of information for consideration by policymakers, and to encourage researchers to take a consilient approach to addressing important challenges in mathematical cognition

Factors associated with children’s understanding of mathematical equivalence: An investigation across six countries

Many primary school students have difficulties understanding mathematical equivalence with considerably poorer performance in some countries than in others. However, students’ formal understanding of equivalence has significant and long-lasting effects as it predicts arithmetic and algebra achievement throughout school years. Currently, little is known about the factors influencing students’ understanding of mathematical equivalence particularly across different countries. We have conducted the first large-scale study to explore the factors associated with primary school students’ understanding of mathematical equivalence across six countries (China, England, New Zealand, South Korea, Turkey, and the US). Participants were 2760 primary school students and their teachers (N = 108). Using multilevel structural equation modelling, we found that students’ knowledge of definitions of the equals sign relates to their equation-solving performance. We also found that while teachers’ knowledge of students’ relational strategies does relate to students’ understanding of equivalence, teachers’ knowledge of students’ operational strategies, and the format of arithmetic practice presented in the students’ current year textbooks do not. Using England as the reference country, we found that this pattern was similar across the samples from all the participating countries. Taken together, our findings have important theoretical and practical implications, providing a more complete picture of the individual and classroom-level factors associated with students’ understanding of equivalence

Novel near-diploid ovarian cancer cell line derived from a highly aneuploid metastatic ovarian tumor

<div><p>A new ovarian near-diploid cell line, OVDM1, was derived from a highly aneuploid serous ovarian metastatic adenocarcinoma. A metastatic tumor was obtained from a 47-year-old Ashkenazi Jewish patient three years after the first surgery removed the primary tumor, both ovaries, and the remaining reproductive organs. OVDM1 was characterized by cell morphology, genotyping, tumorigenic assay, mycoplasma testing, spectral karyotyping (SKY), and molecular profiling of the whole genome by aCGH and gene expression microarray. Targeted sequencing of a panel of cancer-related genes was also performed. Hierarchical clustering of gene expression data clearly confirmed the ovarian origin of the cell line. OVDM1 has a near-diploid karyotype with a low-level aneuploidy, but samples of the original metastatic tumor were grossly aneuploid. A number of single nucleotide variations (SNVs)/mutations were detected in OVDM1 and the metastatic tumor samples. Some of them were cancer-related according to COSMIC and HGMD databases (no founder mutations in <i>BRCA1</i> and <i>BRCA2</i> have been found). A large number of focal copy number alterations (FCNAs) were detected, including homozygous deletions (HDs) targeting <i>WWOX</i> and <i>GATA4</i>. Progression of OVDM1 from early to late passages was accompanied by preservation of the near-diploid status, acquisition of only few additional large chromosomal rearrangements and more than 100 new small FCNAs. Most of newly acquired FCNAs seem to be related to localized but massive DNA fragmentation (chromothripsis-like rearrangements). Newly developed near-diploid OVDM1 cell line offers an opportunity to evaluate tumorigenesis pathways/events in a minor clone of metastatic ovarian adenocarcinoma as well as mechanisms of chromothripsis.</p></div

Chromosome 18 CNA profiles showing acquisition of chromothripsis-like rearrangements on 18p during cell culturing of OVDM1.

<p>Blue lines–gains, red–losses.</p

Whole chromosome gains and losses and number of FCNAs in tumor sample MT1 and OVDM1 cell line (early, intermediate, and late passages).

<p>Whole chromosome gains and losses and number of FCNAs in tumor sample MT1 and OVDM1 cell line (early, intermediate, and late passages).</p

Summary of sequence variants (SV) found in 197 cancer-related genes in tumor sample MT1 and OVDM1 cell line.

<p>Summary of sequence variants (SV) found in 197 cancer-related genes in tumor sample MT1 and OVDM1 cell line.</p

OVDM1 early passage karyotype: 42–47, XX, der(4)t(4;22)(p11;q11),-16, der(22)t(20;22)(q11?,q13).

<p>Upper panel shows a metaphase spread of OVDM1-P3: (A) chromosomes in display colors, (B) G-banding-like DAPI converted image, (C) chromosomes in classification colors. Lower panel shows SKY karyotype: (D) classified chromosomes from the same metaphase in display colors.</p

Whole genome view of CNAs in an ovarian metastatic tumor sample and the newly established OVDM1 ovarian cancer cell line, derived from the same tumor.

<p>(A) Whole genome CNA profiles of MT1 sample and OVDM1 cell line. (B) Frequency of CNAs considering MT1 and early, middle and late passages of OVDM1. Blue lines–gains, red–losses.</p

OVDM1 ovarian cancer cell line derived from an ovarian metastatic tumor after immortalization with SV40 large-T antigen and hTERT.

<p>(A) Primary culture of the ovarian metastatic tumor prior to immortalization. (B) Early passage of OVDM1 after immortalization. (C) Late passage of OVDM1 after immortalization.</p