Reflect 3.9 Using the 0-1-2-3 rubric presented in this section, what score would you assign to each of the students' responses in figure 3.6? Explain why you assigned the scores that you did. Which big idea(s) do you think the problem best assesses? What follow-up ques- tions might you ask students to gain a better understanding of 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.\fFig. 3.6. Students' work in identifying two functions f and 9 such that ftsl) = good] What aspects of the oroh|em do these four students seem to understand or not understand? Student A has some idea about function composition but falls to compose the functions correctly. Student B provides functions that satisfy the condition but offers no explanation. Student C demonstrates some understanding of function composition but is confused between 1' [ad and six]. Student D seems to think that function composition is a matter of generating a number. a common misunderstanding that we pointed out earlier in students' conceptions oi function. How would you evaluate these responses according to our suggested 4- point rubric? This is the question that Reect 3.9 investigates