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In this paper, we propose an enriched and extended application of Harel and Sowder's proof schemes taxonomy that can be used as a diagnostic tool for characterizing secondary students' emergent learning of proof and proving. We illustrate this application in the analysis of data collected from 85 Year 9 (age 14-15) secondary students. We capture these students' first encounters with proof and proving in an educational context (mixed ability, state schools in Greece) where mathematical proof is explicitly present in algebra and geometry lessons and where proving skills are typically expected, and rewarded, in key national examinations. We analyze student written responses to six questions, soon after the students had been introduced to proof and we identify evidence of six of the seven proof schemes proposed by Harel and Sowder as well as a further eight combinations of the six. We observed these combinations often within the response of the same student and to the same item. Here, we illustrate the eight combinations and we claim that a dynamic use of the proof schemes taxonomy that encompasses sole and combined proof schemes is a potent theoretical and pedagogical tool for mapping students' multi-faceted and evolving competence in, and appreciation for, proof and proving.

Research often reports an overt discrepancy between theoretically/out-of context expressed teacher beliefs about mathematics and pedagogy and actual practice. In order to explore teacher knowledge in situation-specific contexts we have engaged mathematics teachers with classroom scenarios (Tasks) which: are hypothetical but grounded on learning and teaching issues that previous research and experience have highlighted as seminal; are likely to occur in actual practice; have purpose and utility; and, can be used both in (pre- and in-service) teacher education and research through generating access to teachers' views and intended practices. The Tasks have the following structure: reflecting upon the learning objectives within a mathematical problem (and solving it); examining a flawed (fictional) student solution; and, describing, in writing, feedback to the student. Here we draw on the written responses to one Task (which involved reflecting on solutions of [chi] + [chi]-1 = 0) of 53 Greek in-service mathematics teachers in order to demonstrate the range of teacher knowledge (mathematical, didactical and pedagogical) that engagement with these tasks allows us to explore.

Sinoxylon anale Lesne, 1897 and S. unidentatum (Fabricius, 1801) (Coleoptera, Bostrichidae), two almost cosmopolitan species most likely native of the Oriental Region, are recorded for the first time from Greece on the basis of several specimens intercepted in a consignment at the Piraeus harbor (Attica, Athens) in wood packaging material originating from China. The establishment of these species in Greece is briefly discussed, moreover, an updated list of their interceptions, countries of establishment and host plants, is provided. [ABSTRACT FROM AUTHOR]

Purpose of the study: To cross-culturally adapt and validate the Greek version of the Patient-Rated Tennis Elbow Evaluation (PRTEE-G) Questionnaire. Methods: Four bi-lingual translators were involved in the translation and cultural adaptation procedures. Eighty-two patients (61 women and 21 men) with Lateral Elbow Tendinopathy (LET) participated in the study. To establish test - retest reliability, the patients were asked to complete the PRTEE-G Questionnaire before and after the first physiotherapy treatment. Internal consistency of the translated instrument was measured using Cronbach ‘alpha’. An intraclass correlation coefficient was used to assess the test - retest reliability of the PRTEE-G Questionnaire. Concurrent validity was measured by correlating the PRTEE-G Questionnaire scores with the Greek version of the Disabilities of the Arm, Shoulder, and Hand Questionnaire (DASH) scores using Pearson's correlation coefficient. Results: The Greek PRTEE questionnaire has acceptable internal consistency (Cronbach 'alpha’ = 0.95), excellent test - retest reliability (ICC = 0.94) and demonstrates expected concurrent validity (r > 0.72). Conclusion: The Greek version of PRTEE Questionnaire is a reliable and valid measure when administered to patients with LET. [ABSTRACT FROM AUTHOR]