2013 Conference Proceedings - University of Nevada, Las Vegas

level structure of the expression in step 1 must be preserved in step 2 (and in subsequent steps).The correct computation of this problem should be as follows.Valid solution:Part of the reasons that cause this type of mistake is the way in which mathematicalexpressions are written traditionally — all symbols, numbers, parentheses, operators, notations,etc. are put in one single line in a linear order. As such, the structure of a mathematicalexpression which is critical for the (understanding of the) meaning of the expression is actuallyembedded in this linear form, and thus may not be easily seen.Our ProposalWe now propose our solutions to the issues raised in this paper.“111” on MMLFor the problems described in section “‘Answers Only’ Needs to be Changed”, we suggestthat MML requires, for most exercise problems, the submission of not only the answer but thesolution process as well. Although letting computers grade solution processes for mathematicalproblems is a challenging task, once the scope of the problem is restricted to certain types, thetask should be manageable. Specifically, for problems of finding limits using limit properties,we suggest that MML Requires students write out both computation steps (including the final answer ofcourse) and the names of the appropriate properties used in the computation. Uses the common “two-column” format in this matter. That is, computation stepswill be written in the left column and names of properties will be written in the rightcolumn. This “two-column” setting is a standard format in the teaching and learningof calculus and general mathematics, and has been practiced using “pencil-and-paper”all the time. Now, it is time to see this activity on MML.Proceedings of the 40 th Annual Meeting of the Research Council on Mathematics Learning 2013 137