A test to assess student understanding of measurement and uncertainty has been developed and administered to more than 500 students at two large research universities. The aim is two-fold: 1) to assess what students learn in the first semester of introductory physics labs and 2) to uncover patterns in student reasoning and practice. The forty-minute, eleven item test focuses on direct measurement and student attitudes toward multiple measurements. The test was administered to students to three groups: students enrolled in traditional laboratory lab sections of first semester physics, students in an experimental (SCALE-UP) section of first semester physics, and students in first semester physics. The results were analyzed using a mixture of qualitative and quantitative methods. Test items were grouped into four main aspects of performance: "point/set" reasoning, meaning of spread, ruler reading and "stacking." Student performance on the pretest was examined to identify links between these aspects. Items within each aspect are correlated to one another, sometimes quite strongly, but items from different aspects rarely show statistically significant correlation. Taken together, these results suggest that student difficulties may not be linked to a single underlying cause. The study shows that current instruction techniques improve student understanding, but hat many students exit the introductory physics lab course without appreciation or coherent understanding for the concept of measurement uncertainty.