It may sound strange, but in today's mathematics classroom, teachers are encouraged to have students struggle. This struggle, however, is not what might come to mind upon first hearing the word. The struggle I refer to here is what researchers have termed "productive struggle," which is present when students must persevere in solving challenging problems for which solutions are not immediately apparent (Hiebert & Grouws, 2007). Opportunities to struggle productively are essential if students are to develop rich understandings of foundational mathematics concepts (Carpenter et al., 1989; Hiebert & Grouws, 2007; Kapur, 2010; Stein & Lane, 1996). Such opportunities, however, remain more the exception than the norm for many students (Carter, 2008; Stein et al., 1996; Stigler & Hiebert, 2004). While students increasingly have access to the kind of challenging problems necessary to elicit struggle, merely providing students with such problems does not guarantee that they will struggle productively. After assigning a challenging problem, teachers must keenly observe students as they work in order to determine if their struggles are productive or unproductive. Specifically, they must "notice" struggle, attending to evidence of students' struggles then interpreting that evidence in assessing the magnitude of students' struggles. Only then can they respond as needed, standing back when students' struggles are productive or stepping in when they are not. Little is known, however, about teachers' noticing of student struggle or those aspects of this practice with which teachers might most benefit from support. Moreover, few tools are currently available to support teachers with the complex practice of noticing struggle and few studies have examined the relative proportions of the various types of struggle students encounter and that teachers need to notice. This dissertation contributes to addressing these research needs. The dissertation consists of three separate, but related studies rooted in a collection of classroom videos portraying student struggle during collaborative problem solving. In the first study, four mathematics education researchers, myself included, sought to develop an understanding of struggle, what it looks like and sounds like, and how one can tell if students' struggles are productive or unproductive. We did this by viewing and discussing a collection of eight 10-minute video-clips portraying different groups of students struggling to varying degrees, and in varying ways, while solving challenging problems together. Initially, we sought to identify examples of "struggle," yet found this very challenging to do, as essentially everything in the videos seemed like struggle to us (e.g., student questions, comments, gestures). Over time, we decided to instead look for instances of students becoming stuck with "roadblocks," which we defined as an obstacle or impediment that slowed students' progress. In looking for roadblocks, we found it much easier to spot examples and only considered a question, comment, or gesture as evidence of struggle if it indicated that students had encountered a roadblock. This notion of roadblocks, as well as several other insights we had in our work together, were incorporated into a framework describing different levels and types of struggle students encountered in the videos. In the second study, a second researcher and I conducted a detailed analysis of the different types of struggle, or roadblocks, students in two 45-minute videos encountered in solving challenging problems together. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com.bibliotheek.ehb.be/en-US/products/dissertations/individuals.shtml.]