Danlami, Kazaik Benjamin
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Psychometric Validation of the Mathematics Attitude Questionnaire (MAQ): A Confirmatory Factor Analysis Approach Danlami, Kazaik Benjamin
International Journal of Mathematics and Mathematics Education (IJMME) Vol. 3 No. 3 (2025)
Publisher : EDUPEDIA Publisher

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.56855/ijmme.v3i3.1505

Abstract

Purpose – Mathematics underperformance remains a global challenge, especially in low-resource and conflict-affected contexts where students often face affective barriers such as anxiety, low enjoyment, and self-doubt. Although the Mathematics Attitude Questionnaire (MAQ) has been widely used internationally, its structural validity has rarely been examined in sub-Saharan Africa. This study aimed to validate the MAQ among Nigerian senior secondary school students. Methodology – A cross-sectional quantitative design under a post-positivist paradigm was employed. Using multistage sampling, 204 students (mean age = 16.8 years; 55% male) from three educational zones in Kaduna State completed a culturally adapted 31-item MAQ. Exploratory Factor Analysis (EFA) was first conducted to identify the underlying structure, followed by Confirmatory Factor Analysis (CFA) in Mplus to evaluate model fit. Reliability was assessed using coefficient omega, while validity was examined through Average Variance Extracted (AVE) and Heterotrait-Monotrait ratio (HTMT). Findings – EFA supported a two-factor structure: Enjoyment of Mathematics and Perception of Incompetence. CFA indicated suboptimal model fit (CFI = .831; TLI = .808; RMSEA = .141; SRMR = .100), though factor loadings (.49–.80) were significant. Reliability was strong (ω = .933; .872), AVE exceeded .58, and HTMT (.67) supported discriminant validity. The results affirm the relevance of the two constructs but highlight the need for theoretical refinement and cultural adaptation. Novelty – This is the first empirical validation of the MAQ using CFA in Nigeria, addressing a critical methodological gap in sub-Saharan mathematics education research. Significance – The validated MAQ provides educators, curriculum developers, and policymakers with a reliable diagnostic tool to assess and strengthen students’ affective engagement, guiding interventions to enhance enjoyment, self-efficacy, and mathematics performance.
Problem-Solving Pedagogy and Attitudinal Change in Mathematics: A Quasi-Experimental Study in Nigerian Secondary Schools Danlami, Kazaik Benjamin; Ayuba, Istafanus; Anas, Halliru; Ezumezuh, Gladys
Hexagon: Jurnal Ilmu dan Pendidikan Matematika Vol. 3 No. 2 (2025): October
Publisher : LPPM Universitas Terbuka

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.33830/hexagon.v3i2.13311.

Abstract

This study examined the effect of a Pólya-based problem-solving instructional strategy on senior secondary students’ attitudes toward mathematics in Kaduna State, Nigeria. Guided by constructivist learning theory, the study adopted a quasi-experimental pretest–posttest control group design involving 200 students purposively selected from public schools. The Mathematics Attitude Questionnaire (MAQ) was administered before and after a six-week intervention to measure enjoyment, anxiety, perceived competence, and perceived usefulness. The experimental group received instruction based on Pólya’s four-step model, while the control group received conventional teaching. Data was analyzed using descriptive statistics and analysis of covariance (ANCOVA) to control baseline attitudes. Results revealed that although the problem-solving group achieved higher mean post-test attitude scores, the difference was not statistically significant (p > .05). Pre-attitude scores were the strongest predictor of post-attitudes, indicating that existing dispositions largely determined outcomes. These findings suggest that short-term problem-solving interventions may foster slight positive trends but require longer and more sustained implementation to produce significant attitudinal change. The study recommends integrating structured problem-solving with effective support strategies to enhance students’ confidence and interest in mathematics.
On the Connectivity and Eulerian Properties of Cayley Digraphs in Transformation Monoids Danlami, Kazaik Benjamin; Eze, Chibueze; O., Olaiya O.
Mikailalsys Journal of Mathematics and Statistics Vol 3 No 3 (2025): Mikailalsys Journal of Mathematics and Statistics
Publisher : Darul Yasin Al Sys

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.58578/mjms.v3i3.6134

Abstract

This paper establishes fundamental connections between the graph-theoretic properties of Cayley digraphs and the algebraic structure of transformation monoids. Our main contributions include a complete characterization of strong connectivity in transformation monoids, proving that for a transformation monoid T acting on a finite set X, the Cayley digraph Cay(T, S) with respect to a generating set S ⊆ T is strongly connected if and only if T contains the full symmetric group S(X); and a classification of Eulerian properties in symmetric groups, demonstrating that for the symmetric group Sn with any generating set S, the Cayley digraph Cay(Sn, S) is Eulerian precisely when it is strongly connected. We provide concrete examples illustrating these theorems, including detailed Cayley graph constructions for S3 with explicit generating sets. Our results reveal deep connections between monoid theory and graph theory, showing how algebraic properties manifest in combinatorial structures. The proofs employ techniques from semigroup theory, algebraic graph theory, and finite group theory, offering new insights into the representation of transformation monoids through their generator-dependent digraphs. This work contributes to the broader understanding of how algebraic structures can be studied through their associated graphs.