Looking for invariance properties in variance and using invariance to cope with variance are essences of mathematical knowledge  and concept development. A mathematical concept is, in fact, an invariant. Thus, in acquiring mathematical knowledge, perceiving and understanding invariant amid variation are central epistemic goals. The variance-invariance concept in mathematics is not usually emphasized enough in mathematics learning and in research reports. The development of computerized possibilities enables dynamic learning demands nurturing motivation, of which self-efficacy is a major component. Instruction that is focused on variance and invariance in mathematics can supply information about the four sources, which are needed for the construction of efficacy beliefs. In this theoretical paper, we develop an argument for variance- and invariance-focused instruction in dynamic geometry environments, which can enhance students’ mathematics self-efficacy and performance. Thinking through variance and invariance extends across content strands in mathematics and in other fields of science. The implication that arises is that researchers and school practitioners should pay attention to students’ beliefs about their mathematics capabilities because they are critical features of classroom dynamics, instruction, and academic achievement.

variance and invariance, dynamic geometry environments, mathematics pedagogy, mathematics self-efficacy, self-efficacy sources, higher order thinking, creativity.