Four studies are reported that used a metacognitive evaluation procedure that can be group-administered and objectively scored. The procedure assesses the knowledge monitoring component of metacognition by evaluating the discrepancy between students' estimates of how well they are likely to perform on a task and their actual performance. The first study examined mathematics and mathematics anxiety in 51 fifth graders. Another study examined whether the metacognitive evaluation procedure was related to a more distant domain, such as learning in school. Participants were 139 college students (84 with complete data) taking a word knowledge test. The third study examined correlations of scores from the metacognitive evaluation procedure and prior learning in college for 115 students. The fourth study investigated the relationship between student estimation of words they would know and their estimates of performance on examinations for 77 college students. Results of the four studies confirm the importance of metacognitive monitoring on achievement in mathematics for elementary students and for college learning. Two tables and six figures present study findings. (Contains 43 references.) (SLD)