Massachusetts Tests for Educator Licensure (MTEL ) www.mtel.nesinc.com

Mathematics (09) Practice TestANALYSIS FOR SECOND WEAK RESPONSE TO OPEN-RESPONSEITEM ASSIGNMENT #2This is an example of a weak response because it is characterized by the following:Purpose: The purpose is partially achieved. The candidate finds the volume of a single ball and the volume of asingle piece of stock. In this way, the candidate meets the basic geometry and measurement aspects of theproblem. The candidate is not able to make the transition from the concept of static volumes to a volumefunction. The candidate does not understand the role of speed and related rates in the problem. Finally, thecandidate shows rudimentary skills in the graphing of a function although there is some confusion between themeaning of function notation and multiplication.Subject Matter Knowledge: The candidate demonstrates the ability to determine when and how to apply thetwo different volume formulas. The candidate is able to adapt the formulas in terms of diameter even though theyare given in terms of radius. The candidate shows little, if any, knowledge of functions and function notation.The candidate does not demonstrate the ability to show the relationship between the rate of rubber stock fed intothe machine and the rate of rubber ball production. The candidate demonstrates the basic skill of plotting points.The method of generating the data points, however, is limited and does not provide evidence of understanding offunctions and function notation. The fact that only the discrete points are plotted demonstrates a lack ofunderstanding of the distinction between continuous and discrete functions.Support: The candidate lays out the steps of the solution in a clear and organized manner. The additional verbaldescriptions of the solution process do not add meaning to the response, as the solution process is evident basedon the equations shown. The work is missing labels for the axes of the graph, suggesting lack of attention todetail and possible confusion as to what is actually being graphed.Rationale: The candidate is able to demonstrate only the most basic skills involved in the problem. Besides theuse of two standard volume formulas and the plotting of points, the candidate shows little conceptualunderstanding of the problem. The candidate misses the very important concepts of functions, related rates, andcomparative volumes, the central concepts of the problem.92