Matematik öğretmen adaylarının lineer cebir kavramlarını anlayışlarının düşünme yapıları ve uzamsal yetenekleri bağlamında incelenmesi

Lineer cebir dersinin öğrenciler tarafından kavramların anlaşılmasından ziyade dersi geçmek için problem çözme sürecinde çeşitli tekniklerin kullanıldığı ve işlemsel süreçlerin takip edildiği bir ders olarak görülmesi bulgusu, lineer cebir eğitimi üzerine yapılan araştırmaların artmasını sağlamıştır. Anlayarak lineer cebir öğretimi ve öğrenimi odağından yola çıkarak yürütülen bu araştırmada, matematik öğretmeni adaylarının lineer cebir kavramlarında sergiledikleri anlama boyutları performansları, uzamsal yetenekleri ve matematiksel düşünme yapıları bağlamında değerlendirilmiştir. Amacına uygun olarak, araştırma nitel-yorumlayıcı paradigmaya sahiptir. Araştırmada desen olarak iç içe geçmiş tek durum deseni kullanılmıştır. Araştırmanın durumunu lineer cebir kavramlarında sergilenen anlama boyutları; analiz birimlerini matematiksel düşünme yapıları, uzamsal yetenek ve lineer cebir performansı oluşturmaktadır. Araştırmada geçen lineer cebir kavramları ifadesi, vektör uzayları, alt vektör uzayları, lineer bileşim ve bağımsızlık, taban ve boyut kavramlarını kapsamaktadır. Katılımcılar, olasılıksız örnekleme yöntemlerinden amaçlı örnekleme tekniği ile belirlenmiş olup 2012-2013 eğitim-öğretim yılında, bir devlet üniversitesi eğitim fakültesi ortaöğretim matematik eğitimi lisans programına kayıtlı 41 lineer cebir öğrencisinden oluşmaktadır. Veri toplama aracı olarak araştırmacı tarafından geçerlik ve güvenirliği sağlanan Lineer Cebir Testi, Purdue Uzamsal Görselleştirme Testi ve Matematiksel Süreç Aracı kullanılmış olup katılımcıların bu testlerde sergiledikleri performanslara göre seçilen öğretmen adayları ile yarı-yapılandırılmış görüşmeler yapılmıştır. Elde edilen veriler, betimsel istatistik ve içerik analizi yöntemlerinden faydalanılarak analiz edilmiş ve yorumlanmıştır. Ayrıca öğretmen adaylarının kavram tanımlarında kullandıkları kelimelerin analizinde Wordaizer programı kullanılmıştır. Veri analizleri sonucunda, öğretmen adaylarının her bir lineer cebir kavramı için çeşitli imgeler kullandıkları ve bu imgelerin kavramlara göre farklılaştığı, ilişkili kavramların tanım ve tariflerinde kullanılan ortak kelime yüzdesinin yüksek olduğu görülmüştür. Öğretmen adaylarının lineer cebir kavramlarında sergiledikleri performanslar kavram bazı bazında farklılaştığı gibi bireysel farklılık olarak katılımcıların matematiksel düşünme yapılarına ve uzamsal yeteneklerine göre de farklılaşmaktadır. Öğretmen adaylarının sergiledikleri anlama boyutları kavram bazında farklılaştığı gibi genel olarak en yüksek yüzde ile beceri-algoritma anlama boyutunu ve en düşük yüzde ile temsil-metafor anlama boyutunu sergilemişlerdir. Sergilenen anlama boyutları, öğretmen adaylarının performanslarına, matematiksel düşünme yapılarına ve uzamsal yeteneklerine göre de farklılaşmaktadır. Çalışma kapsamında elde edilen diğer bulgular, ilgili literatür ışığında tartışılarak, öğretmen adaylarının lineer cebir kavramlarını anlamalarını geliştirecek ve bu gelişimi performanslarına yansıtacakları önerilerde bulunulmuştur. Anahtar Kelimeler: Lineer Cebir, Kavram, Anlama, Performans, Matematiksel Düşünme Yapıları, Uzamsal Yetenek. ABSTRACT The findings of the research on linear algebra, which is understood as a technique to solve the problems rather than having conceptual understanding and algorithm by students, provided to increase the research about linear algebra education. In this research whose main points are learning and teaching linear algebra with understanding, pre-service mathematics teachers' dimensions of understanding are investigated within the context of their performance, spatial abilities, and thinking modes. The research has a qualitative paradigm which is convenient for the purpose of the study. In the research, embedded single case study design is used as a research design. The units of research consist of mathematical thinking modes, spatial abilities and linear algebra performance and the case of research consist of dimensions of understanding linear algebra concepts. The linear algebra concepts which are used in the research consist of vector spaces, subspaces, linear combination and linear independence, basis, and dimension. The participants of this research were identified with purposeful sampling technique which is one of the improbable sampling methods. The participants are 41 linear algebra students who studied in the department of secondary mathematics education at a public university between 2012-2013. All the data were collected by Linear Algebra Test, Purdue Spatial Visualization Test and Mathematical Processing Instrument and semi-structured interviews were conducted with some of the students. All the data were analyzed with descriptive and content analysis methods. The pre-service mathematics teachers' definitions-descriptions of linear algebra concepts are analyzed by using Wordaizer Program. At the end of the analyses, it seems that pre-service mathematics teachers have various concept images of each linear algebra concept and those images changes by the concept. Also, it seems that the percentage of the words which are used to define related concept are very high. As pre-service mathematics teachers' performance on linear algebra is differentiated by concepts, it is differentiated by their spatial abilities and mathematical thinking modes. Generally, participants have performed the highest percentage in the dimension of skill-algorithm understanding and the lowest percentage in the dimension of representation-metaphor understanding. Pre-service mathematics teachers' dimensions of understanding are differentiated by their performance, spatial ability and mathematical thinking modes. The findings from the research are argued with the knowledge of literature and offers are suggested to improve linear algebra students' understanding of linear algebra concepts and their performance. Keywords: Linear Algebra, Concept, Understanding, Performance, Mathematical Thinking Modes, Spatial Ability

University Students’ Solution Processes in Systems of Linear Equation

AbstractThe focus of the study is system of linear equations which is one of the important topics of linear algebra. The aim is to investigate how university students’ skills in the process of solving systems of linear equations by focusing on how they perform operations with matrices. This study is a case study based on a non-positivist paradigm with interpretivist approach. Findings indicate that candidates face differing levels difficulties in conceptualizing and doing operations in their solutions

Trends in heart failure between 2016 and 2022 in Türkiye (TRends-HF): a nationwide retrospective cohort study of 85 million individuals across entire population of all ages

Background: Data on the burden of heart failure (HF) outside western countries are limited, but available data suggest it may present differently in other countries. The aim of this study was to examine the incidence, prevalence, and survival rates of HF in Türkiye, with a specific focus on how these rates vary according to age, sex, comorbidities, and socioeconomic status (SES). Methods: We harnessed the extensive National Electronic Database of the Turkish Ministry of Health, covering Turkey's entire population from January 1, 2016, to December 31, 2022, to identify 2,722,151 cases of HF and their associated comorbidities using ICD-10 codes. Analyzing the primary endpoint of all-cause mortality, our study utilized anonymized data to examine patient demographics, comorbidities, socioeconomic status, and survival patterns, employing statistical techniques to delve into relationships and trends. The data were segmented by gender, socioeconomic status, and age, involving cross-tabulations and statistical metrics to explore connections, odds ratios, and survival rates. Findings: The estimated prevalence of HF was 2.114% in Türkiye at the end of 2022, with an annual incidence ranging between 3.00 and 6.06 per 1000 person years. Females were older than males (69.8 ± 13.9 years vs. 66.8 ± 13.9 years, respectively). The most common comorbidities were congenital heart diseases and anemia under the age of 20, and hypertension and atherosclerotic cardiovascular disease in the adult population. Only 23.6% (643,159/2,722,151) of patients were treated with any triple guideline-directed medical therapy (GDMT) and 3.6% (96,751/2,722,151) of patients were on quadruple GDMT. The survival rates for patients with HF at 1, 5, and 7 years were 83.3% (95% CI: 83.2–83.3), 61.5% (95% CI: 61.4–61.6), and 57.7% (95% CI: 57.6–57.8) among females, and 82.1% (95% CI: 82.0–82.2), 58.2% (95% CI: 58.1–58.3), and 54.2% (95% CI: 54.0–54.3) among males. Despite a tendency for an increase from the highest to the lowest SES, the prevalence of HF and mortality were paradoxically lowest in the lowest SES region. Interpretation: The prevalence, incidence, and survival rates of HF in Türkiye were comparable to western countries, despite the notable difference of HF onset occurring 8–10 years earlier in the Turkish population. Drug usage statistics indicate there is a need for effective strategies to improve treatment with GDMT. Funding: None

2001 Research Honors Program Abstracts

Faculty in the College of Agriculture and Life Sciences at Cornell University mentor and guide undergraduate students who have chosen to pursue a research project and graduate with honors. These abstracts reflect the depth of their scholarship and intellectual ability. The research projects encompass work in animal science, biological science, entomology, natural resources, physical science, plant science, and social science

Comparative in vitro activity of plazomicin and older aminoglyosides against Enterobacterales isolates; prevalence of aminoglycoside modifying enzymes and 16S rRNA methyltransferases

Comparative in vitro activity of plazomicin and 4 older aminoglycosides was evaluated with broth microdilution in 714 blood isolates from 14 hospitals in Turkey