The three dimensions of achievement are, to my mind as a teacher:
1. Understanding
2. Fulfillment of personal goals
3. Creating new goals
Understanding is first and foremost in my conception of achievement because I do not believe that anything can really be accomplished without understanding. Whether it is as simple as completing a task or as complex as creating a new program for your school, if you do not have a sound understanding of what is being asked of you and the concepts you are working with, you will never truly succeed. I think it is important to foster comprehension before a finished product can be put together - I don't want students turning in work if they don't have a full grasp on what is being asked of them, both mechanically and conceptually.
The fulfillment of personal goals is important when considering achievement, namely because that is often what gives one the greatest sense of satisfaction IN achievement. To really feel as though you have been successful at something, it is crucial to have clear in your mind what you consider success to be. As we talked about in class, having students set their own goals is an integral part of the learning process; it is also advisable, however, to conference with students about what those goals are and how they can be made realistic and yet still challenging.
The third dimension of achievement has to do with making sure you don't stagnate. Both in an academic setting and out of it, setting goals is important - but once those goals are achieved (or not), you have to always set new ones. To take a popular, "stereotypical" goal - becoming a millionaire: well, once you become a millionaire, what then? You will have accomplished your goal, good for you - but hopefully you will still have a fair amount of life left to live, and it seems silly to have worked so hard for so long at achieving one thing, and then never striving for anything again. I think this example, though blown out of proportion, translates directly to real-world goals and accomplishments: it is necessary to always be creating new goals, new places to set your sights, or you will stagnate and achievement will cease.
I appreciate you including "understanding" in a definition of achievement. Students will often say, "I didn't understand the assignment", so they struggle to achieve. Clarity as a teacher is critical in giving students access to success. In regard to personal goals, I agree with you that students need to be invested and feel connected to those goals. Can teachers set goals for students then or do students have to set goals for themselves? Maybe that last dimension is a drive to continually achieve, or as you say to continue to set goals, perhaps of increasing challenge as well.
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