Proofs produced by secondary school students learning geometry in a dynamic computer environment

As a key objective, secondary school mathematics teachers seek to improve the proof skills of students. In this paper we present an analytic framework to describe and analyze students' answers to proof problems. We employ this framework to investigate ways in which dynamic geometry software can be used to improve students' understanding of the nature of mathematical proof and to improve their proof skills. We present the results of two case studies where secondary school students worked with Cabri-Géeomèetre to solve geometry problems structured in a teaching unit. The teaching unit had theaims of: i) Teaching geometric concepts and properties, and ii) helping students to improve their conception of the nature of mathematical proof and to improve their proof skills. By applying the framework defined here, we analyze students' answers to proof problems, observe the types of justifications produced, and verify the usefulness of learning in dynamicgeometry computer environments to improve students' proof skills.     

Effects of purposeful soccer heading on circulating small extracellular vesicle concentration and cargo

BackgroundConsidering the potential cumulative effects of repetitive head impact (HI) exposure, we need sensitive biomarkers to track short- and long-term effects. Circulating small extracellular vesicles (sEVs) (<200 nm) traffic biological molecules throughout the body and may have diagnostic value as biomarkers for disease. The purpose of this study was to identify the microRNA (miRNA) profile in circulating sEVs derived from human plasma following repetitive HI exposure.MethodsHealthy adult (aged 18–35 years) soccer players were randomly assigned to one of 3 groups: the HI group performed 10 standing headers, the leg impact group performed 10 soccer ball trapping maneuvers over 10 min, and the control group did not participate in any soccer drills. Plasma was collected before testing and 24 h afterward, and sEVs were isolated and characterized via nanoparticle tracking analysis. Next-generation sequencing was utilized to identify candidate miRNAs isolated from sEVs, and candidate microRNAs were analyzed via quantitative polymerase chain reaction. In silico target prediction was performed using TargetScan (Version 7.0; targetscan.org) and miRWalk (http://mirwalk.umm.uni-heidelberg.de/) programs, and target validation was performed using luciferase reporter vectors with a miR-7844-5p mimic in human embryonic kidney (HEK) 293T/17 cells.ResultsPlasma sEV concentration and size were not affected across time and group following repetitive HI exposure. After 24 h, the HI read count from next-generation sequencing showed a 4-fold or greater increase in miR-92b-5p, miR-423-5p, and miR-24-3p and a 3-fold or greater decrease in miR-7844-5p, miR-144-5p, miR-221-5p, and miR-22-3p. Analysis of quantitative polymerase chain reaction revealed that leg impact did not alter the candidate miRNA levels. To our knowledge, miR-7844-5p is a previously unknown miRNA. We identified 8 miR-7844-5p mRNA targets: protein phosphatase 1 regulatory inhibitor subunit 1B (PPP1R1B), LIM and senescent cell antigen-like domains 1 (LIMS1), autophagy-related 12 (ATG12), microtubule-associated protein 1 light chain 3 beta (MAP1LC3B), integrin subunit alpha-1 (ITGA1), mitogen-activated protein kinase 1 (MAPK1), glycogen synthase kinase 3β (GSK3β), and mitogen-activated protein kinase 8 (MAPK8).ConclusionCollectively, these data indicate repetitive HI exposure alters plasma sEV miRNA content, but not sEV size or number. Furthermore, for the first time we demonstrate that previously unknown miR-7844-5p targets mRNAs known to be involved in mitochondrial apoptosis, autophagy regulation, mood disorders, and neurodegenerative disease.