Students come to the classroom with theories that they have actively constructed from their everyday experiences. However, some of these theories are incomplete half-truths. Although such misconceptions interfere with new learning, students are often emotionally and intellectually attached to them. Some common mathematical misconceptions involve: (1) confusion between variables and labels, with failure to understand that variables stand for numerical expressions; (2) mistakes about the way that an original price and a sale price reflect one another; (3) misconceptions about the independent nature of chance events; and (4) reluctance to multiply fractions. Hispanic students display some unique mathematical error patterns resulting from differences in language or culture. In addition, linguistic difficulties increase the frequency with which Hispanic students commit the same errors as Anglo students. Since students will not easily give up their misconceptions, lecturing them on a particular topic has little effect. Instead, teachers must help students to dismantle their own misconceptions. One effective technique induces conflict by drawing out the contradictions in students' misconceptions. In the three steps of this technique, the teacher probes for qualitative, quantitative, and conceptual understanding, asking questions rather than telling students the right answer. In the process of resolving the conflicts that arise, students actively reconstruct the concept in question and truly overcome their misconceptions. This digest contains 10 references. (SV)