The chapter starts with a discussion of the two types of assessment - formative and summative. Then it discusses the purpose of assessment, which is to gather information about how the students are performing, and it can come in many different forms (tests, asking questions in class, journal entries, etc.) - only some of which would affect a grade. Other types of assessment help teachers plan instruction by showing holes in the students' learning. Assessment can also be used to gauge the effectiveness of a program or class (proficieny tests).
The chapter talks about criterion referenced tests (based on a standard), competency tests (criterion tests based on a course of study), and norm referenced tests (comparison to a group - like SAT tests). NCTM talks about the following four purposes of assessment:
Under test construction, the chapter talks about writing tests where the answer can't be guessed. It also talks about the following aspects of assessment:
Next the chapter talks about how to score tests (partial credit, etc.), and the value of including review items. It also talks about the limitiations of tests (the arbitrary meaning of scores, test anxiety, etc.).
The remainder of the chapter includes a discussion of alternate assessment strategies:
I would like to see standardized proficiency tests used as a criteria for graduating particular courses of study. I believe if a particular student passes algebra (for instance), that they should prove themselves against the same criteria as everyone else who passes that class, and that implies standardized assessment being at least part of the passing requirements.
However, I am against using standardized proficiency tests as a criteria for graduating high school. Different people have different strengths, and I believe a student should be able to pass high school by performing well within their areas of strengths. In particular, I don't believe that every student ultimately needs to know algebra to succeed in life, so I hardly see why they need to pass an algebra test to get out of high school.
Conceptual Map for Quadratic Equations Unit
Traditional Test:
Write in standard form: 6x2 = 3x + 4
Solve: 4a2 + 4a = 0
Complete the square: x2 + 8x
Solve using quadratic formula: 3x2 - 7x + 1 = 0
etc.......
Benefits and Drawbacks: The nice thing about a standard test is it is fairly easy to objectively grade them and you don't have to depend on observing each student during class time (which is fairly near impossible in a class of 37). The drawback would be that students don't learn much by taking a test, and some students don't really perform well on tests even though they have at least some understanding of the material.
Performance Task:I did a performance task with my class last week where I had them divide into groups, go to an area of whiteboard, and derive the quadratic formula. I tried to scaffold this task by having them do a "complete the square" exercise beforehand using a problem with regular numerical coefficients.
Benefits and Drawbacks: I thought it worked okay as a "change of pace" exercise, but as a way of assessing the students it was a bit of a flop, because I couldn't really tell how well each student was performing in the group. I think I would have needed to structure it quite a bit more for it to be easy to assess the result. On the other hand, I did at least have a chance to see how many groups could successfully complete the exercise (about half), and I did have a chance to assess teaching strategies for having them do group work.