Problem-solving is the ability to understand issues and steps that will affect students’ mathematics learning results. The research goals are: describing students’ problem-solving understanding and mathematics learning results; testing the influence of gender and grade level on students’ problem-solving understanding and mathematics learning results; and testing the influence of students’ problem-solving understanding on mathematics learning results. The population is all students in the fourth through sixth grades at two primary schools (263 respondents). The sample consists of 244 respondents, with female and male respondents of 123 and 121, and low- and high-grade students of 74 and 170, respectively. The researchers calculated and converted scores into values. Statistical tests were carried out by means of analysis of linear regression and the t-test. The Me of students’ mathematics learning results and problem-solving understanding are 69.679 and 66.889. The female students’ problem-solving understanding Me is greater than male ones’, but male students’ mathematics learning results Me is greater than female ones. The low-grade students’ problem-solving understanding Me is greater than high-grade students, but high-grade students’ mathematics learning results Me is greater than low-grade students. Gender has no influence on students’ mathematics problem-solving understanding or learning results. The grade level has a significant influence on students’ problem-solving understanding but no significant influence on mathematics learning results. The students’ problem-solving understanding has a significant influence on mathematics learning results, with a p value of 0.000. The research findings and results have implications for and contribute to assisting students in processing information and building mathematical knowledge.
Self-efficacy is an integral part of personal factors that contributes substantially to students' success in mathematics. This review draws on previous intervention studies to identify, describe, and expose underlying mechanisms of interventions that foster mathematics self-efficacy. The findings show that effective mathematics self-efficacy interventions can be categorized into three categories using their underlying mechanisms: those that directly manipulate sources of self-efficacy to foster the construct, and those that either embed self-efficacy features in teaching methods or in learning strategies. Specific examples of interventions that fall in each of these three categories are described including their features and the underlying mechanisms that improve students' mathematics self-efficacy. I argue for the two “most effective” interventions that foster mathematics self-efficacy and their relevance to either pre-university or university students with implications for teaching and learning of mathematics.