İlköğretim Matematik Öğretmenliği Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.11779/1932

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Citation - WoS: 28
Citation - Scopus: 41
An Analysis of Elementary School Children's Fractional Knowledge Depicted With Circle, Rectangle, and Number Line Representations
(Springer, 2015) Tunç-Pekkan, Zelha
It is now well known that fractions are difficult concepts to learn as well as to teach. Teachers usually use circular pies, rectangular shapes and number lines on the paper as teaching tools for fraction instruction. This article contributes to the field by investigating how the widely used three external graphical representations (i.e., circle, rectangle, number line) relate to students' fractional knowledge and vice versa. For understanding this situation, a test using three representations with the same fractional knowledge framed within Fractional Scheme Theory was developed. Six-hundred and fifty-six 4th and 5th grade US students took the test. A statistical analysis of six fractional Problem Types, each with three external graphical representations (a total of 18 problems) was conducted. The findings indicate that students showed similar performance in circle and rectangle items that required using part-whole fractional reasoning, but students' performance was significantly lower on the items with number line graphical representation across the Problem Types. In addition, regardless of the representation, their performance was lower on items requiring more advanced fractional thinking compared to part-whole reasoning. Possible reasons are discussed and suggestions for teaching fractions with graphical representations are presented. Copyright of Educational Studies in Mathematics is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.
Citation - WoS: 26
Citation - Scopus: 33
An Explanatory Sequential Mixed-Method Research on the Full-Scale Implementation of Flipped Learning in the First Years of the World's First Fully Flipped University: Departmental Differences
(Elsevier, 2021) Demir, Ömer; Birgili, Bengi
This study evaluates the first years of the full-scale flipped learning implementation process that began with an authority innovation-decision at the world's first fully flipped university in terms of departmental differences. The study employs an explanatory sequential mixed-method research. The primary respondents were 69 freshmen enrolled in the Faculty of Education at a private university in Istanbul, Turkey. In addition to student participants, five faculty members were recruited to the study. The primary data was collected through a Likert-type scale on flipped learning, including components on motivation, course structure, and interaction. Pre and post semi-structured interviews and a structured ranking form were also used to support the quantitative data. The findings of the study reveal that the students felt relatively unmotivated when instructed through flipped learning, although were satisfied with the course structure. In general, the students lacked student-student interaction. Due to the nature of the Guidance and Psychological Counseling department, the students faced some difficulties in engaging in all three types of interaction (student-student, student-educator, and student-content). Lengthy and poor-quality videos and students' lack of preparation for classes emerged as major problems in flipped learning. The faculty members complained about the amount of time required for pre-class preparation (i.e., recording flipped videos). This paper discusses how to foster motivation, collaboration, discussion, and interaction in flipped learning in higher education settings so as to guide prospective practitioners.
Citation - WoS: 4
Citation - Scopus: 6
An Online Laboratory School Research on Pre-Service Mathematics Teachers’ Experiences and Mathematics Teaching Anxiety
(Springer, 2022) Ölmez, İbrahim Burak; Taylan, Rukiye Didem; Pekkan, Tunç Zelha
During the COVID-19 pandemic, we founded an Online Laboratory School (OLS) under the roof of a university in Turkey to support students from public schools that were not technologically prepared for an online education and to provide an opportunity for our pre-service teachers (PSTs) to continue their internship by teaching online. The purpose of this research, consisting of two studies, was to examine experiences of 43 PSTs (first-, third- and fourth-years) during the OLS period of 8 weeks and how the OLS affected their mathematics teaching anxiety during Fall 2020. In the first study, we administered a survey to inquire into PSTs’ views on their experiences at the OLS, and in the second study we examined their mathematics teaching anxiety before and after the OLS experience using another survey. One main result was that the OLS experience served as an effective introduction to the profession for first-year PSTs and fourth- and third-year PSTs reported learning in-depth about online teaching in terms of the planning, teaching, and reflecting cycle. Another main result was that PSTs had mathematics teaching anxiety from “a little” to “a moderate amount” before the OLS and their teaching anxiety did not significantly change during the OLS period of 8 weeks. PSTs experienced highest mathematics teaching anxiety when they were observed and evaluated by supervisors during their teaching. The implications of these findings are discussed for teacher education programs.
Citation - WoS: 13
Citation - Scopus: 19
Characterizing a Highly Accomplished Teacher’s Noticing of Third-Grade Students’ Mathematical Thinking
(Springer, 2017) Taylan, Rukiye Didem
This study investigated a highly accomplished third-grade teacher’s noticing of students’ mathematical thinking as she taught multiplication and division. Through an innovative method, which allowed for documenting in-the-moment teacher noticing, the author was able to explore teacher noticing and reflective practices in the context of classroom teaching as opposed to professional development environments. Noticing was conceptualized as both attending to different elements of classroom instruction and making sense of classroom events. The teacher paid most attention to student thinking and was able to offer a variety of rich interpretations of student thinking which were presented in an emergent framework. The results also indicated how the teacher’s noticing might influence her instructional decisions. Implications for both research methods in studying noticing and teacher learning and practices are discussed.
Citation - Scopus: 5
Predicting Undergraduate Students' Mathematical Thinking About Derivative Concept: a Multilevel Analysis of Personal and Institutional Factors
(Elsevier BV, 2014) Ubuz, Behiye; Aydın, Utkun
This cross-sectional study examines the determinants of mathematical thinking aspects at two levels: within-classroom level and between-classroom level. We hypothesized that personal factors (gender, socioeconomic status (parents' educational attainment), current cumulative grade point average, prior mathematic achievement (high school mathematics achievement)) and institutional factors (faculty/school affiliation, grade level) have concomitant associations with students' mathematical thinking about the derivative. The sample consisted of 2424 undergraduates from 130 classrooms. Multilevel modeling showed that students' mathematical thinking about the derivative varied primarily as a function of their gender and cumulative grade point average (within-classroom level) and of their faculty affiliation (between-classroom level). Parents' educational attainment and high school mathematics achievement at the within-classroom level, and grade level at the between-classroom level were only moderately associated with different mathematical thinking aspects. Methodological and practical implications of the findings are further discussed. © 2014 Elsevier Inc.
Citation - WoS: 1
Citation - Scopus: 1
Preservice Teachers' Understandings of Division and Ratios in Forming Proportional Relationships
(Springer, 2022) Ölmez, İbrahim Burak
This study aimed at investigating how preservice teachers' understandings of division and reasoning about ratios support and constrain their formation of proportional relationships in terms of quantities. Six preservice teachers from a middle-grade preparation program in the USA were selected purposefully based on their mathematics performance in a previous course. An explanatory case study with multiple cases was used to make comparisons within and across cases. Two semi-structured interviews were conducted with each pair. The results revealed that preservice teachers who did not explicitly identify different meanings for division struggled to differentiate between the two perspectives on ratios. The results also showed that those teachers had difficulty forming proportional relationships while solving the proportion tasks. These results suggest that explicit identification of the meanings for both types of division is critical to keeping the two perspectives on ratios separate, which is a key aspect for a robust understanding of proportional relationships.
Citation - WoS: 7
Citation - Scopus: 8
Teachers' Attention To and Flexibility With Referent Units
(Springer, 2021) Ölmez, İbrahim Burak; Çopur-Genctürk, Yasemin
Attending to the whole unit that a number refers to in a mathematical problem situation and showing flexibility in coordinating different units are foundational for mathematical understanding. In this study, we explored teachers’ attention to and flexibility with referent units in situations involving fractions and fraction multiplication. Using data collected across the USA from 246 mathematics teachers in Grades 3–7 where fractions are taught, we found that teachers’ attention to and flexibility with referent units were related to each other as well as to teachers’ overall knowledge of fractions.
Citation - WoS: 1
Citation - Scopus: 2
The Mediating Role of Instructional Design and Video Length Between Grade Level and Pupil-Content Interaction in Instructional Mathematics Videos on Youtube
(Springer, 2024) Demir, Ömer; Birgili, Bengi
The use of instructional videos is rampant in education; however, their interaction is limited by weak instructional design. Gagne has never insisted on using his renowned 9 Events of Instruction slavishly in situations as a viable paradigm for utilization in video design. Connecting grade level, video length, and interaction, this study seeks to determine the relevance of Gagne's prescribed 9 event sequence in instructional mathematics videos. We scrutinized 50 instructional mathematics videos on YouTube geared towards middle school pupils ranging between 5th and 8th grades. We used quantitative media content analysis for video analysis. In data analysis, partial least squares were used. Bayesian estimation was also resorted to for cross checking. The data revealed that one-third of Gagne's instructional design steps were not always present: activating prior knowledge, eliciting performance, and finally providing feedback. A mediation analysis between grade level and video length revealed that 6 events fully mediated the association between the two. We also elicited the impact of these variables on affective and behavioral interactions in videos. This study assists in creating an idiosyncratic instructional design model, called Birgili's 8 steps for instructional video design, and in infusing this with a melange of four theories. In contrast with the status quo attesting that the literature abounds with scholarly works touting the shorter is the better mantra, the results substantiated that longer may be better in leveraging video interactions provided that the length is judiciously used to conform to instructional design principles.
Citation - WoS: 5
Citation - Scopus: 5
The Pisa Tasks: Unveiling Prospective Elementary Mathematics Teachers’ Difficulties With Contextual, Conceptual, and Procedural Knowledge
(Taylor & Francis, 2019) Özgeldi, Meriç; Aydın, Utkun
The aim of this mixed methods study was to investigate the difficulties prospective elementary mathematics teachers have in solving the Programme for International Student Assessment (PISA) 2012 released items. A mathematics test consisting of 26 PISA items was administered, followed by interviews. Multiple data were utilized to provide rich insights into the types of mathematical knowledge that a particular item requires and prospective teachers’ difficulties in using these knowledge types. A sample of 52 prospective teachers worked the mathematics test, and 12 of them were interviewed afterwards. The data-sets were complementary: the quantitative data showed that PISA items could be categorized under contextual, conceptual, and procedural knowledge and indicated the most frequent difficulties in the combined contextual, conceptual, and procedural knowledge items. The qualitative data revealed that few prospective teachers could give mathematical explanations for conceptual knowledge items, and that their contextual knowledge was fragmented. Educational implications were discussed.
Citation - WoS: 14
Citation - Scopus: 16
The Relationship Between Pre-Service Mathematics Teachers’ Focus on Student Thinking in Lesson Analysis and Lesson Planning Tasks
(Springer Verlag, 2018) Taylan, Rukiye Didem
This study explored whether pre-service teachers’ (PSTs’) lesson analysis skills during a teacher education course in the country of Turkey were related to their skills of lesson planning. PSTs’ lesson analysis skills during fieldwork were assessed by their attention to and interpretation of student thinking and learning, and how it is influenced by the teachers’ instructional decisions. The PSTs’ lesson analysis scores were significantly and positively correlated with scores in lesson planning task focusing on student thinking. The findings contribute to the literature on whether PSTs’ lesson analysis skills may be transferred to one of the core activities of teaching.
Citation - WoS: 6
Citation - Scopus: 9
The Thinking-About Test for Undergraduate Students: Development and Validation
(2015) Ubuz, Behiye; Aydın, Utkun
Two studies were conducted for the development and validation of a multidimensional test to assess undergraduate students' mathematical thinking about derivative. The first study involved two phases: question generation and refinement of the Thinking-about-Derivative Test (TDT). The second study included four phases as follows: test administration, generalizability analysis, confirmatory factor analysis, and subgroup validity analysis. Findings suggested that the 30-item multiple-choice TDT, which comprises 6 mathematical thinking aspects, enactive, iconic, algorithmic, algebraic, formal, and axiomatic thinking, demonstrates acceptable levels of reliability and validity. Followed by additional cross-validation studies, the TDT may be a useful tool for mathematics education researchers and mathematicians. Directions for future research and implications for educational practice are discussed.
Citation - WoS: 78
Citation - Scopus: 111
The Trends and Outcomes of Flipped Learning Research Between 2012 and 2018: a Descriptive Content Analysis
(Springer, 2021) Oğuz, Ebru; Seggie, Fatma Nevra; Birgili, Bengi
As an innovative active learning method, flipped learning provides students with several opportunities. This study was conducted to reveal the trends and outcomes in research into the flipped learning approach published between 2012 and 2018. Descriptive content analysis was used to review 316 research and conceptual articles published in academic journals included in five significant databases that ascribe to journals the highest impact factor. The results indicate that most of the studies are conducted with students as the most frequent study group and with a mixed-method research design in the subject areas of education and medicine. The flipped learning approach is mostly conducted in higher education. As a region, Asia has taken the lead in flipped learning studies. Finally, the outcomes of flipped learning indicate an increase in student performance and positive influence on cognitive, affective, and soft skills.
Validating Psychometric Classification of Teachers' Fraction Arithmetic Reasoning
(Springer, 2023) Ölmez, İbrahim Burak; Izsak, Andrew
In prior work, we fit the mixture Rasch model to item responses from a fractions survey administered to a nationwide sample of middle grades mathematics teachers in the United States. The mixture Rasch model located teachers on a continuous, unidimensional scale and fit best with 3 latent classes. We used item response data to generate initial interpretations of the reasoning characteristic of each latent class. Our results suggested increasing facility reasoning about fraction arithmetic from one class to the next. The present study contributes two further arguments for the validity of our initial interpretations. First, we administered the same survey to a new sample of future middle grades mathematics teachers before and after 20 weeks of instruction on multiplication, division, and fractions, and we found that from pretest to posttest future teachers transitioned from one latent class to another in ways consistent with increased proficiency in fraction arithmetic. Second, we interviewed 8 of the future teachers before and after the instruction and found that future teachers' reasoning during interviews was largely consistent with our original interpretation of the 3 latent classes. These results provide further support for our original interpretation of the mixture Rasch analysis, demonstrate the utility of our approach for capturing growth and change in future teachers' reasoning during teacher education coursework, and contribute innovative applications of psychometric models for surveying teachers' reasoning at scale.

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