Mathematics is required from primary (basic) through junior secondary and senior secondary levels of education in Nigeria. The position of mathematics within the curriculum is reflective of the significance of the subject to the expansion of scientific knowledge and technological capability. However, student performance in mathematics, particularly algebraic aspects, is a challenge for Nigerian secondary school students. The purpose of this study was to investigate the relationship between self-concept (SC), emotional intelligence (EI), and problem-solving skills (PSS) on students’ attitudes towards solving algebraic problems (ATSAP). The study aimed at developing a model based on students’ SC, EI, PSS, and ATSAP. A total of 377 students were proportionately and randomly selected to collect the quantitative data. Two instruments: (i) a questionnaire measuring SC, EI, and ATSAP, and (ii) a test measuring PSS developed by the researcher, were used in this study. The data was analyzed by using structural equation modelling (SEM) and partial least square (SEM-PLS3). The major findings of the study revealed that secondary school students’ PSS could be improved with due consideration of their SC and EI. However, the three hypotheses tested indicated that there was a significant but negative relationship between SC and the students’ ATSAP (t > ±1.96, α = 0.05) and also there was a significant positive relationship between PSS and their ATSAP; however, the relationship between EI and their ATSAP was not significant (t < ±1.96, α = 0.05). Therefore, a model was developed based on the study’s findings. This model has a practical implication for the federal and state governments, curriculum planners, students, teachers, and parents.