2013 Conference Proceedings - University of Nevada, Las Vegas

course titled Calculus with Business and Economic Applications. (This course was used becauseit is taught by both authors and the use of MML was mandated by their University department.)“Answers Only” Needs to be ChangedFor most lower-level mathematics textbooks/courses (e.g., Sullivan (2010), Lial, Hungerford,and Holcomb (2011), and Pirnot (2009)), Pearson offers a matching MML component whichcontains, among other things, the exercises at the end of textbook chapters/sections allowingstudents to complete their homework and tests on line. Unfortunately, for the majority of theseexercises, MML only requires the submission of answers. That is, as long as the final answersubmitted by a student to a problem is correct, then the student will get full credit for thatproblem regardless of the solution process, and even if the solution process is seriously flawed.We give two examples here to show this point. (Throughout the paper, limit properties refer toConstant Property, Identity Function Property, Sum Property, Difference Property, ProductProperty, Quotient Property, Power Property, and Polynomial Property which can be found inany standard calculus-related textbooks.)Example 1. Use limit properties to find(√ )Student solution:(√ )√Here, although the answer (integer 3) is correct, the solution process is fundamentally wrong:√ is not a polynomial and thus the polynomial property cannot be applied to (√) in the first step. Students who make this kind of mistake clearly do not have conceptualunderstanding of polynomials; MML cannot identify this conceptual misunderstanding in that allMML expects from the student is the integer 3. While there may be more than one way to solvethis problem, the following is an example of a valid solution.Proceedings of the 40 th Annual Meeting of the Research Council on Mathematics Learning 2013 134