Online Journal of Mathematics, Science and Technology Education

Volatility Modelling of Nigerian Bank Stocks: Evidence from Real and Simulated Data using GARCH and Machine Learning

Sandra C. Emenyonu, Bright O. Osu, Promise A. Azor — Tue, 30 Jun 2026 00:00:00 +0000

This study examines the volatility dynamics of selected Nigerian banking stocks us- ing both real and simulated share price data. Daily closing prices of five major Nige- rian banks Access Holdings Plc (ACCESSCORP), Guaranty Trust Holding Company Plc (GTCO), Fidelity Bank Plc (FIDELITYBK), FBN Holdings Plc (FBNH), and United Bank for Africa Plc (UBA) are analyzed over a common sample period from January 1, 2015, to December 17, 2025. Log-returns are computed and volatility is modelled using the GARCH (1,1), EGARCH (1,1), and TGARCH (1,1) models under Normal and Student-t er- ror distributions. To assess the robustness of volatility behaviour, simulated return series are generated from the empirical properties of the real data under a Gaussian assumption and analysed alongside the observed data. Furthermore, machine learning models includ- ing Random Forest regression, Long Short-Term Memory (LSTM) networks, and hybrid GARCH LSTM approaches are employed to enhance volatility forecasting performance. Results indicate that real data exhibits higher volatility persistence and thicker tails than simulated data across most banks. Among the GARCH-family models, EGARCH with Student-t innovations provides superior performance in capturing asymmetric effects and extreme market movements. Machine learning models further improve forecasting accu- racy, particularly during periods of financial stress. The findings offer important insights for investors, risk managers, and policymakers in emerging financial markets.

Effects of Virtual Laboratory Applications on Academic Achievement and Six-Month Retention of Learning in 4th Grade Science Education

Enis Abdiusta, Ahmet Ünal — Tue, 30 Jun 2026 00:00:00 +0000

This study investigated the effects of virtual laboratory applications on students' academic achievement and retention of learning in the Movements of the World unit taught in 4th grade Science education. The research adopted a pre-experimental, single-group pretest–posttest design. Instruction was delivered by the researcher using the EBA (Education Information Network) portal and the Mozaweb three-dimensional simulation platform. A 10-item achievement test developed by the researcher — encompassing all unit learning outcomes across three Bloom's Taxonomy cognitive levels (knowledge, comprehension, and application) and yielding a Cronbach's Alpha reliability coefficient of .727 — served as the primary measurement instrument. The study group comprised 65 fourth-grade students from three public primary schools in the Yakakent district of Samsun province, Turkey, selected through convenience sampling. The achievement test was administered as a pretest before instruction, as a posttest immediately after the unit, and — crucially — as a retention test six months later, a substantially longer retention interval than is typical in comparable studies (most of which employ two-to-four-week delays). Paired-samples t-tests and one-way ANOVA were conducted at α = .05. Findings indicated a statistically significant improvement from pretest (M = 6.41) to posttest (M = 8.25; t = −9.42, p < .001), demonstrating that virtual laboratory instruction enhanced academic achievement. Equally importantly, no significant decline was observed between posttest and six-month retention test scores (M = 8.11; t = 0.90, p = .37), indicating durable learning. These findings offer evidence — particularly valuable at the primary school level, where research on virtual laboratory applications is limited — that simulation-based science instruction can produce both immediate and long-lasting learning benefits.

Pre-service Teachers’ Tendencies Between Formal Definition and Procedural Orientation: The Polynomial as an Algebraic Object

Saliha Nur Öpaydın, Alper Cihan Konyalıoğlu — Tue, 30 Jun 2026 00:00:00 +0000

This study aims to examine pre-service mathematics teachers’ concept images of the polynomial concept. Conducted as a qualitative case study, the research involved 41 pre-service teachers. Data were collected through a concept test with open-ended questions and analyzed using content analysis. The findings indicate that participants predominantly approached polynomials in a procedural and template-based manner. A considerable number of participants defined polynomials as functions, neglecting their algebraic object nature. In addition, incorrect generalizations were observed in responses related to the zero polynomial and the classification of algebraic expressions. The results reveal a mismatch between concept image and concept definition, as well as an incomplete transition from process to object.

An Overview of Technology Use in Special Education

Seniha Kurtoğlu, Funda Ulugöl — Tue, 30 Jun 2026 00:00:00 +0000

Technological advancements provide significant opportunities to support the education, communication, and daily living skills of individuals with special needs. The aim of this review study is to classify the technologies used in special education, examine the contributions of these technologies to the independent lives of individuals with special needs through concrete examples and scenarios, and offer practical recommendations for the future.

In this study, technologies used in special education were examined under three main categories assistive technology, educational technology, and supportive/digital technology taking into account their purpose and function.

Scenarios and concrete examples are presented showing that assistive technologies play a significant role in increasing individuals’ functional competencies and independence; educational technologies support the quality and individualization of the learning process; and supportive/digital technologies play important roles in organizing learning processes and strengthening daily living skills.

Word'de ihtiyaç duyduğunuz yerlerde görüntülenen yeni düğmeler sayesinde zaman kazanın. Bir resmin belgenize sığma şeklini değiştirmek için resme tıklayın. Resmin yanında bir düzen seçenekleri düğmesi belirir. Bir tablo üzerinde çalışırken, bir satır veya sütun eklemek istediğiniz yere tıklayın ve ardından artı işaretine tıklayın.

In conclusion, the effective use of technology in special education is possible through selection based on individual needs, pedagogical integration, and informed implementation. This study offers a guiding framework for practitioners and researchers by approaching technology use not from a tool-centered perspective, but from a purpose- and function-oriented viewpoint.

STEM and Artificial Intelligence: A Bibliometric Analysis of Integrated Approaches in Education (2006–2025)

Çağrı Avan, Selçuk Açıkgöz — Tue, 30 Jun 2026 00:00:00 +0000

This study aims to analyze the academic literature produced at the intersection of STEM (Science, Technology, Engineering, and Mathematics) education and artificial intelligence (AI) technologies between 2006 and 2025 through a bibliometric approach. As personalized learning approaches and interdisciplinary integration become increasingly vital in education, the convergence of these two domains necessitates a comprehensive investigation. In this context, the study seeks to reveal publication trends, citation performance, conceptual structures, collaboration networks, and intellectual clusters within the STEM-AI literature.

The data were obtained from the Web of Science Core Collection on July 7, 2025, and include 449 peer-reviewed publications published between 2006 and 2025. Using the bibliometrix R package and its biblioshiny interface, analyses such as annual publication trends, citation distributions, co-citation networks, keyword co-occurrence, and thematic evolution maps were conducted.

The findings indicate an annual publication growth rate of 20.93%, with a notable increase in research output observed during 2021–2022. The most frequently used keywords include “STEM education,” “artificial intelligence,” “intelligent tutoring systems,” and “computational thinking.” Co-citation and conceptual structure analyses identified works by VanLehn, D’Mello, and Graesser as intellectual anchors within the field. Thematic evolution analysis highlights a recent shift toward user-centered and ethically oriented concepts such as “AI ethics,” “personalized learning,” and “chatbots.” This study demonstrates that the literature on STEM and AI has evolved not only technically but also pedagogically, theoretically, and ethically.

Bibliometric Analysis of Theses on Sets in the Field of Mathematics Education

Sebahattin Çetinkaya, Abdullah Çağrı Biber — Tue, 30 Jun 2026 00:00:00 +0000

The aim of this research is to determine the research trends of postgraduate theses on the topic of "Sets" in mathematics education in Turkey. To this end, 13 master's theses and 2 doctoral theses on sets completed in the field of mathematics education in the YOK (Council of Higher Education) database were examined using descriptive analysis. The studies were analyzed according to seven criteria: publication year, sample level, sample size, aims, methods and designs, data collection tools, and teaching methods preferred in the studies. The findings obtained from the studies were presented in tables using frequency and percentage values. Furthermore, the analysis of the theses was completed by three different researchers specializing in mathematics education according to specific criteria, and the reliability of the study was ensured by considering the agreement of the results obtained. The research revealed that the vast majority of theses were conducted in 2009 and later, and the studies were predominantly conducted at the middle school level, especially with 6th-grade students. It was observed that half of the theses examined in the research had experimental designs, and a significant portion of these studies investigated the effect of different teaching methods on academic achievement. The results show that postgraduate research on clusters tends to focus on specific themes, and methodological diversity remains limited. This suggests that future studies should incorporate different research designs and variables.

An examination of Libyan and Turkish Students' Thinking Skill Levels Through their Generalization in Quadratic Patterns according to SOLO Taxonomy

Awatef Elazzabi, Ahmet Kaçar — Tue, 30 Jun 2026 00:00:00 +0000

This study aimed to an examination of Libyan and Turkish students' thinking skill levels through generalization in quadratic patterns according to SOLO taxonomy. The study model was a hybrid design with predominantly qualitative design. In this study, the working group was consisted of 112 from Libyan students at three high school in the city of Tripoli in Libya and 129 Turkish students at three high school in the city of Kastamonu in Turkey. The study was undertaken in the 2018-2019 academic year. Overall, the results showed that most Turkish and Libyan students who participated in the study mostly their level on the Uni-structural level, the Multi structural level and the Relational structure level, However, some of them were able to reach successful in moving Advanced thinking levels. Despite of this, there Libyan and Turkish students left the problems blank and there were students at the pre-structural level. Obtaining ideas about students' thinking and knowledge levels about the patterns is rather important. So, recommend supporting students to develop their thinking skills by solving problems and getting them involved in different activities that are aimed at promoting their skills and improving their ability in thinking. This means, mathematics teachers should create opportunities for students to relate their mathematical ideas and concepts to enable the students to promote their ability in thinking especially algebraic thinking, as well support students' thinking skills in moving from a design-based learning environment that encourages "recalling facts" to one that encourages "analysis and synthesis". Thus, students will attain a higher level of thinking in understanding Generalization in Quadratic Patterns.