Reflect 3.10 Using the 0-1-2-3 rubric presented in this section, what score would you assign to each of the students' responses in figure 3.2 to the problem presented in Reflect 3.3? Explain why you assigned the scores that you did. Which big idea(s) do you think that the problem best assesses? What follow-up questions might you ask students to access their thinking?Assessing Outcomes Unless a question is of the yes-no or true-false type, there is always room for interpretation of students' responses to it. We will not address the construction of rubrics and their applications here, but we do want to emphasize the importance of attending to and assessing a range of students' understanding in other than dichotomous (all right vs, all wrong) terms. Common sense suggests that students' responses to a non- dichotomous question will fall into the following general categories: virtually nothing is correct, some but not many things are correct, most but not all things are correct (including explanations), the explanations are clea and correct. In light of these common-sense notions, we offer the following four-point rubric (see Cooney et al. [2002]): O: Response indicates no appropriate mathematical reasoning. 1: Response indicates some mathematical reasoning but fails to address the item's main mathematical ideas. 2: Response indicates substantial and appropriate mathematical reasoning but is lacking in some minor way(s). 3: Response is correct, and the underlying reasoning process is appropriate and clearly communicated. Consider the actual student responses shown in figure 3.6 to the following problem on function composition (see Cooney et al. [2002]): Identify 2 distinct functions f and g such that f (s (x)) = s (f (x)). Explain why your functions satisfy the condition.Reflect 3.3 Suppose that you gave your students the following problem: If you were to zoom out on the graph below, you would see that it has exactly two x-intercepts. Write an equation of a function that would fit the criterion. Explain why your equation fits the criterion. 3 X What various responses might you expect from your students?Student 1 y = ( *+ 4)(x+9) the graph is a parabola with x-int x- -4 and - 9. Student 2 y= 3 The line passes through point 3 on the yaris Student 3 X2 + 3 3 would be the y- intercept 1? means it crosses the X-axis twice. ig. 3.2. Three students' responses to the problem in Reflect 3.3