A teacher’s use of dynamic digital technology to address students’ misconception about additive strategies for geometric similarity

Research has well documented that students develop a significant misconception associated with the incorrect use of additive strategies when engaging with geometric similarity (GS) tasks. Since dynamic digital technology (DDT) has the potential to support students in addressing this misconception, teachers can exploit the affordances of DDT in the classroom to accomplish it. The aim of this paper is to explore how and why a secondary mathematics teacher uses DDT in the classroom to promote students’ understanding of why additive strategies are inappropriate to use for GS tasks. Drawing on the data collected, through classroom observations and post-lesson teacher interviews, the research findings indicate that the dynamic and visual nature of DDT can be used to help students realise the inappropriateness of the use of additive strategies for GS tasks

Interpolation function of the genocchi type polynomials

The main purpose of this paper is to construct not only generating functions of the new approach Genocchi type numbers and polynomials but also interpolation function of these numbers and polynomials which are related to a, b, c arbitrary positive real parameters. We prove multiplication theorem of these polynomials. Furthermore, we give some identities and applications associated with these numbers, polynomials and their interpolation functions.Comment: 14 page

Special Functions Related to Dedekind Type DC-Sums and their Applications

In this paper we construct trigonometric functions of the sum T_{p}(h,k), which is called Dedekind type DC-(Dahee and Changhee) sums. We establish analytic properties of this sum. We find trigonometric representations of this sum. We prove reciprocity theorem of this sums. Furthermore, we obtain relations between the Clausen functions, Polylogarithm function, Hurwitz zeta function, generalized Lambert series (G-series), Hardy-Berndt sums and the sum T_{p}(h,k). We also give some applications related to these sums and functions

Mitral regurgitation:when to intervene? A historical perspective

Although mitral regurgitation (MR) is the most common valvular heart disease, it should be regarded as a complex multifactorial disease that involves multiple entities. Optimal medical therapy alone does not hinder the progression of the disease, and in the 1980s it was already recognised that corrective surgery is indicated if MR is severe and patients are symptomatic (except for those with the most severe left ventricle dysfunction). Later on, asymptomatic patients with deterioration of the left ventricular ejection fraction were also operated on to avoid irreversible left ventricular dysfunction, heart failure and eventually death. However, a major drawback remains the fact that a significant group of patients is considered to have a high perioperative risk due to their advanced age or severe comorbidities. Since less invasive, percutaneous interventions have been developed and recently thoroughly investigated in the MITRA-FR and the COAPT studies, the type of intervention and also the timing have become more crucial. In this critical review of the literature, we describe what we should have learned from the past and which (haemodynamic) parameters can best predict the outcome in patients with MR

Reliability and validity of the Turkish translation of the beliefs about medicines questionnaire (BMQ-T) in patients with Behçet’s disease

OBJECTIVES: The aim of this study was to evaluate the reliability and validity of the Turkish translation of the Beliefs about Medicines Questionnaire (BMQ-T, ©Prof. Rob Horne) for patients with Behçet's disease. METHODS: This methodological study enrolled a sample of 125 patients. The scale was adapted to Turkish through a process including translation, comparison with versions in other languages, back translation, and pretesting. Construct validity was evaluated by factor analysis. Medication adherence evaluated as poor, moderate and good according to the Morisky Medication Adherence Scale (MMAS). BMQ-T scores compared along medication adherence status groups. RESULTS: In our study, as in the original scale, the factor analysis confirmed that the BMQ-T had a four-factor structure explaining 54.73% of the total variance. The BMQ-T had acceptable internal consistency (Cronbach's alpha coefficient: Specific Necessity=.812; Specific Concerns=.672; General Harm=.677; General Overuse=.656), adequate test-retest reliability (intraclass correlation coefficients: Specific Necessity=.715; Specific Concerns=.680; General Harm=.678; General Overuse=.327). Specific Necessity and Specific Concerns scores were significantly different between medication adherence status groups. CONCLUSIONS: The psychometric properties of the BMQ-T were consistent with those reported in the original study. The BMQ-T was found to be a valid and reliable tool for evaluating beliefs about medicines in patients with Behçet's disease

Spontaneous Coronary Artery Dissection as Presenting Feature of Vascular Ehlers-Danlos Syndrome

A spontaneous coronary artery dissection as the sole presenting feature of vascular Ehlers-Danlos syndrome is an uncommon finding. We present a 33-year-old woman with sudden onset chest pain caused by a spontaneous coronary artery dissection. Genetic testing revealed vascular Ehlers-Danlos syndrome as the underlying cause. Specifically, we show the value of genetic testing, which in some patients may be the only way of establishing a diagnosis

A note on q-Bernoulli numbers and polynomials

By using p-adic q-integrals, we study the q-Bernoulli numbers and polynomials of higher order.Comment: 8 page

A note on q-Euler numbers and polynomials

The purpose of this paper is to construct q-Euler numbers and polynomials by using p-adic q-integral equations on Zp. Finally, we will give some interesting formulae related to these q-Euler numbers and polynomials.Comment: 6 page