Developing mathematical thinking in the primary classroom: liberating students and teachers as learners of mathematics

This paper reports on a research study conducted with a group of practising primary school teachers (n = 24) in North East Scotland during 2011–2012. The teachers were all participants in a newly developed Masters course that had been designed with the aim of promoting the development of mathematical thinking in the primary classroom as part of project supported by the Scottish Government. The paper presents the background for this initiative within the context of the Scottish Curriculum for Excellence reform. Particular attention is given to the epistemological positioning of the researchers as this influenced both the curriculum design process and also the theoretical framing of the research study which are both described. The project was set up within a design research framework, which aimed to promote classroom-based action research on the part of participants through the course and also research by the university researchers into the process of curriculum development. The research questions focused on the teachers’ confidence, competence, attitudes and beliefs in relation to mathematics and their expectations and experiences of the impact on pupil learning arising from this course. Empirical data were drawn from pre- and post-course surveys, interviews and observations of the discussion forums in the online environment. Findings from this study highlight the way the course had a transformational and emancipatory impact on these teachers. They also highlight ways in which the ‘framing’ of particular aspects of the curriculum had an oppressive impact on learners in the ways that suppressed creativity and limited the exercise of learner autonomy. Furthermore, they highlight the ways in which a number of these teachers had experienced mathematics as a school subject in very negative ways, involving high levels of ‘symbolic violence’ and of being ‘labelled’.     

Rhetoric and poetry

To win in 1972 the Democrats needed a unified rhetoric. Their strategy was to emphasize persona. The breaking news of Senator Eagleton's mental health, coming at a strategic time, created a fantasy that chained through the electorate and presented the McGovern persona as inconsistent, inept, and untrustworthy.     

Human affection exchange: V. Attributes of the highly affectionate

The present study examines differences in the individual‐and social‐level characteristics of high‐affection and low‐affection communicators. One hundred nine adults completed extensive questionnaires about their happiness, attachment patterns, susceptibility to depression and stress, mental health, social activity, relationship satisfaction, and other variables. Results revealed that highly affectionate people are advantaged in numerous psychological, mental, emotional, social, and relational characteristics, relative to those who communicate little affection to others.     

OBE: Some Answers for the Uninitiated

In this article, leaders of the North Carolina Writing Project explore whether students of teachers who attended Writing Project summer institutes out-performed other teachers' students on state writing tests. The authors accordingly developed a test to compare the writing of those students with the writing of students of non-writing project teachers. The test, however, produced no significant difference in the writing of the two groups. Seventeen years later, the authors compared the longevity of writing project teachers with that of comparable non-writing project teachers to see if the institutes infused a spirit of professionalism and self-efficacy in participants that other teachers did not possess. This comparison affirmed the authors' beliefs: writing project teachers had greater staying power than comparable teachers.     

Using Case Study Analysis and Case Writing to Structure Clinical Experiences in a Teacher Education Program

This study reports on the design and results of a two-semester study on the use of case study analysis and case writing in clinical experiences in an undergraduate teacher education program. Findings indicated that structured experiences with case studies and case writing increase preservice teachers' informed decision making on educational issues.     

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.     

A comparison of cognitive skills between completes and dropouts in a college physics course

Separate tests of mathematics skills, proportions and translations between words, and mathematical expression given the first week of class were correlated with performance for students who completed a college physics course (completes) and students who dropped the course (drops). None of the measures used discriminated between completes and drops as groups. However, the correlations between score on the test of math skills and on both of the measures involving mathematical reasoning (proportions, and translations) were dramatically different for the two groups. For the completes, these correlations were slightly negative, but not significant. For the drops, the correlation was positive and signficant at the p < 0.01 level. This suggests the possibility that the students who complete the course tend to have independent cognitive skills for the “mechanical” mathematical operations and for questions requiring some degree of reasoning, while, in contrast, the same skills for students at high risk for dropping overlap significantly. The study also found that when students are given the results of mathematics skills tests in a diagnostic mode, with feedback on specific areas of weakness and time to remediate with self study, the correlation between mathematics and physics is lower than previously reported values.     

An Examination of a Small‐Group Decoding Intervention for Struggling Readers: Comparing Accuracy and Automaticity Criteria

In this study, we compared methods to improve the decoding and reading fluency of struggling readers. Second‐grade poor readers were randomly assigned to one of the two practice conditions within a repeated reading intervention. Both interventions were in small groups, were 20–28 min long, took place 2–4 days per week, and consisted of phonemic awareness training, letter sound practice, and practice in word families. Students in the accuracy condition (n= 27) practiced each page until they reached 98 percent accuracy while students in the accuracy + automaticity condition (n= 29) practiced until they reached rate (30–90 cwpm) and accuracy criteria. Hierarchical linear modeling revealed no differences between practice conditions in decoding accuracy, reading comprehension, and grade‐level text reading fluency. Significant differences favoring the accuracy + automaticity group were found in measures of decoding automaticity.     

Teaching Students with Moderate Intellectual Disability Who Are Emergent Readers to Comprehend Passages of Text

A modified system of least intrusive prompting was used to teach middle school students with moderate intellectual disability who were emergent readers to comprehend short passages of text. Text passages were summaries of the chapters of age-appropriate novels rewritten for a beginning reading level. Time delay was used to teach the participants to pair WH words to their definition. A modified system of least intrusive prompting was used to teach strategies for answering comprehension questions. All participants improved the number of correct responses for both rules definitions and comprehension responses from baseline to intervention. Additionally, probes collected during the session prior to the introduction of a new book indicated comprehension skills generalized to new untaught books.