Education systems are increasingly relying on online and distance education technology as a means of delivering instruction. The issues that are faced in online education settings include how to address the distance between participants and the instructor, and the best way to deliver instruction. Although new online technologies provide the opportunity for many types of synchronous and asynchronous communication, most education settings depend primarily on asynchronous communication, due to reduced cost and increased flexibility for participants. However, another concern in education settings is to provide a setting in which communication and discourse patterns can mirror a classroom setting and encourage critical thinking on the part of participants. This is particularly important in mathematics education, in which communication and discourse within classroom settings are included in the National Council of Teachers of Mathematics (NCTM) standards. There is a need for discussions based on reasoning and evidence to be extended to online mathematics settings. One method which has been attempted to improve online discourse and argumentation is to request that students make use of formal argument models such as Toulmin (1958), and to compose their posts and responses to fit particular categories of argument structure. An example of such a study is Jeong and Joung (2007), in which participants discussing topics in educational technology were asked to use argument constraints for their posts, and sometimes to label their posts in terms of which argument category was used. Jeong and Joung found that the use of labels in addition to constraints reduced the number of times that participants challenged another student's post, and reduced the number of responses to challenges. Mathematics education may differ from other fields, due to the emphasis on argumentation and proof in classroom settings. Thus the current study attempted to replicate Jeong and Joung in the field of mathematics. Participants were 25 mathematics teachers involved in professional development who discussed five mathematics topics in an online setting. They were assigned to either a Constraints Only or a Constraints with Label condition. There were no differences between the two constraint conditions in terms of number of initial posts, challenges and challenge rebuttals. In terms of specific argument categories used, there were more Argument posts in the Constraints with Label condition, and more Critique and Explanation posts in the Constraints Only condition. Exploration of two-post sequences showed more complex patterns in the Constraints Only condition. Response quality did not differ across the two conditions. The results only partially replicate Jeong and Joung (2007). Specifically, the small sample and small discussion groups make direct comparison difficult. However, participants in mathematics education were not reluctant to use labels in their argument structure. Future research could explore other methods of use of argument structure in online discussion. [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/en-US/products/dissertations/individuals.shtml.]