Abstract: Values and character traits constitute essential components of mathematical core competencies. Investigating their conceptual definitions and classifications facilitates the targeted implementation of these competencies. Both values and character traits share the characteristics of being tacit, oriented toward goodness, and indirect. Distinctively, values demonstrate pervasiveness, subjectivity, and relative stability, while character traits exhibit formative nature, stability, and objectivity. Mathematical values and mathematical character traits represent the disciplinary manifestations of values and character traits. Mathematical values refer to correct values held and developed by learners through mathematics education, primarily classified into instrumental rationality and value internalization. Mathematical character traits denote outstanding learning qualities demonstrated in mathematical disciplines, mainly categorized as instrumental traits and cultural traits. Teachers may structure mathematics instruction around these classifications: by developing students’ mathematical values to enhance their affective engagement in mathematics learning, and by directing pedagogical practices toward cultivating mathematical character traits to foster students’ mathematical learning competencies.