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Abstract
This study developed a model of self-efficacy beliefs, engagement and triarchic intelligence on mathematics achievement of 1148 Grade 10 students in the Division of Davao del Norte who were enrolled in the school year 2017-2018. It investigated the relationship among variables and determined the variables that best predict mathematics achievement as well as the best fitting structural model on achievement. The study utilized a descriptive correlational and causal-comparative research design. Pearson-r, mean, standard deviation, and regression analysis are the statistical tools used in this study. Structural equation model (SEM) was shown to find the best fit model of the study. Modified survey questionnaires were used for self-efficacy scale, engagement scale and triarchic intelligences scale while Division Unified Test was used to measure the mathematics achievement. The findings of the study showed that students did not meet the expectation in mathematics achievement were lacked of knowledge and skills in terms of mastering the content area in the topic for the first quarter of the said school year. Self-efficacy beliefs, engagement and triarchic intelligences were at moderate level. Behavioral engagement and verbal persuasion of self – efficacy belief were the predictors of the achievement. Among the five structural models, only model 5 consistently indicate a very good fit model to the data, since both self-efficacy and engagement contributed much to the mathematics achievement with the total effects of 7% and 17% respectively. This model indicates that the mathematics achievement of the students is best anchored on their self-efficacy and engagement. Thus, the model suggests that the more engaged the students are, coupled with self-efficacy beliefs, the better and higher is the achievement of the students.
